By Likes
- Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev
- The rocket alignment problem
If people talked about the problem of space travel the way they talked about AI...
- Eliezer Yudkowsky
- Bayes' rule: Log-odds form
A simple transformation of Bayes' rule reveals tools for measuring degree of belief, and strength of evidence.
- Eliezer Yudkowsky
- Arbital features
Overview of all Arbital features.
- Alexei Andreev
wiki
- Combining vectors
One of the most useful things we can do with vectors is to combine them!
- Adele Lopez - Elementary Algebra
How do we describe relations between different things? How can we figure out new true things from tr…
- Adele Lopez - Geometric algebra
A geometric algebra is a Clifford algebra over the reals which represents Euclidean geometry and man…
- Adele Lopez - Geometric product
#Motivation
want to incorporate rotors like $e^{\text{I}\theta}$ and scalars $n$ in the same system
…
- Adele Lopez - Geometric product: summary
Product for [multivectors multivectors].
Associative, left and right distributive. Non-commutative. …
- Adele Lopez - Geometry of vectors: direction
What rotation would it take to line up this vector to this one?
- Adele Lopez - Group orbit
When we have a group acting on a set, we are often interested in how the group acts on a particular …
- Adele Lopez - Locale
Topology - but right
- Adele Lopez - Quotient group
Given a group $G$ with operation $\bullet$ and a special kind of subgroup $N \leq G$ called the "no…
- Adele Lopez - Vector arithmetic
Vectors: what they are, and how to add and scale them.
- Adele Lopez
- Welcome to Arbital
Front page explaining what Arbital is all about.
- Alexei Andreev
- Extraordinary claims require extraordinary evidence
The people who adamantly claim they were abducted by aliens do provide some evidence for aliens. They just don't provide quantitatively enough evidence.
- Eliezer Yudkowsky
- Practicing Brevity
Wanna save the world? Write better TLDRs. And spend more time respecting your reader's time.
- Raymond Arnold
- Bayes' rule: Probability form
The original formulation of Bayes' rule.
- Nate Soares
- Solomonoff induction: Intro Dialogue (Math 2)
An introduction to Solomonoff induction for the unfamiliar reader who isn't bad at math
- Eliezer Yudkowsky
- Frequency diagrams: A first look at Bayes
The most straightforward visualization of Bayes' rule.
- Nate Soares
wiki
- Arbital features
Overview of all Arbital features.
- Alexei Andreev - Bayes' rule: Functional form
Bayes' rule for to continuous variables.
- Eliezer Yudkowsky - Bayes' rule: Vector form
For when you want to apply Bayes' rule to lots of evidence and lots of variables, all in one go. (This is more or less how spam filters work.)
- Eliezer Yudkowsky - Free group
The free group is "the purest way to make a group containing a given set".
- Patrick Stevens - Ontology identification problem
How do we link an agent's utility function to its model of the world, when we don't know what that model will look like?
- Eliezer Yudkowsky - Ontology identification problem: Technical tutorial
Technical tutorial for ontology identification problem.
- Eliezer Yudkowsky - Open subproblems in aligning a Task-based AGI
Open research problems, especially ones we can model today, in building an AGI that can "paint all cars pink" without turning its future light cone into pink-painted cars.
- Eliezer Yudkowsky - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- Bayes' rule
Bayes' rule is the core theorem of probability theory saying how to revise our beliefs when we make a new observation.
- Eliezer Yudkowsky - Introductory Bayesian problems
Bayesian problems to try to solve yourself, before beginning to learn about Bayes' rule.
- Eliezer Yudkowsky
- Eigenvalues and eigenvectors
We applied this linear transformation to one of its eigenvectors; you won't believe what happened next!
- Zack M. Davis
wiki
- Complexity theory
Study of the computational resources needed to compute something
- Jaime Sevilla Molina
wiki
- The current message of effective altruism heavily discourages creativity.
Alyssa Vance expands on this point in her [FB post](https://www.facebook.com/alyssamvance/posts/1021…
- Alexei Andreev
- Conditional probability
The notation for writing "The probability that someone has green eyes, if we know that they have red hair."
- Eliezer Yudkowsky
- Eliezer's vision for Arbital
Why are we building this? What's the goal?
- Eric Bruylant
- Waterfall diagram
Visualizing Bayes' rule as the mixing of probability streams.
- Eliezer Yudkowsky
- Arithmetical hierarchy: If you don't read logic
The arithmetical hierarchy is a way of stratifying statements by how many "for every number" and "th…
- Eliezer Yudkowsky
- Introductory Bayesian problems
Bayesian problems to try to solve yourself, before beginning to learn about Bayes' rule.
- Eliezer Yudkowsky
- Vector arithmetic
Vectors: what they are, and how to add and scale them.
- Adele Lopez
- Diamond maximizer
How would you build an agent that made as much diamond material as possible, given vast computing power but an otherwise rich and complicated environment?
- Eliezer Yudkowsky
- Mid Term
Such great mid-term
- Alex Foster - Welcome to Arbital
Front page explaining what Arbital is all about.
- Alexei Andreev
wiki
- A permanent, self-sustaining off-Earth colony would be a much more effective mitigation of x-risk than even an equally well funded system of disaster shelters on Earth.
See also the less precise claim: Establishing a permanent off-Earth colony would be a useful way to …
- Eric Rogstad - For mitigating AI x-risk, an off-Earth colony would be about as useful as a warm scarf
H/T to Eliezer Yudkowsky for ["warm scarf"](https://www.facebook.com/robert.wiblin/posts/75711126783…
- Eric Rogstad - Why waiting to donate harms charities
A blog post explaining the potential reasons why someone would choose to wait to donate and how that leads to suboptimal outcomes for the charity.
- Alexei Andreev
wiki
- AI alignment
The great civilizational problem of creating artificially intelligent computer systems such that running them is a good idea.
- Eliezer Yudkowsky - Advanced agent properties
How smart does a machine intelligence need to be, for its niceness to become an issue? "Advanced" is a broad term to cover cognitive abilities such that we'd need to start considering AI alignment.
- Eliezer Yudkowsky - Arbital path
Arbital path is a linear sequence of pages tailored specifically to teach a given concept to a user.
- Alexei Andreev - Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky - Extraordinary claims
What makes something an 'extraordinary claim' that requires extraordinary evidence?
- Eliezer Yudkowsky - Handling errors with arguments
My [recent proposal](https://arbital.com/p/1v7?title=steps-towards-safe-ai-from-online-learning) f…
- Paul Christiano - Introductory Bayesian problems
Bayesian problems to try to solve yourself, before beginning to learn about Bayes' rule.
- Eliezer Yudkowsky - Modeling AI control with humans
I’ve been trying to build an aligned AI out of reward-maximizing modules. A successful scheme could …
- Paul Christiano - Nick Bostrom
Nick Bostrom, secretly the inventor of Friendly AI
- Eliezer Yudkowsky - Optimization and goals
If we want to write a program that _doesn’t_ pursue a goal, we can have two kinds of trouble:
1. We…
- Paul Christiano - Strength of Bayesian evidence
From a Bayesian standpoint, the strength of evidence can be identified with its likelihood ratio.
- Eliezer Yudkowsky - Vingean reflection
The problem of thinking about your future self when it's smarter than you.
- Eliezer Yudkowsky - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
group
- Duncan Sabien
- Eliezer Yudkowsky
Cofounder, with Nick Bostrom, of the field of value alignment theory.
- Marcello Herreshoff
- Nate Soares
- Rescuing the utility function
If your utility function values 'heat', and then you discover to your horror that there's no ontologically basic heat, switch to valuing disordered kinetic energy. Likewise 'free will' or 'people'.
- Eliezer Yudkowsky
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky - Sparking widgets
10% of widgets are bad and 90% are good. 4% of good widgets emit sparks, and 12% of bad widgets emit…
- Nate Soares - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- Arbital Blog
Stay up to date on all things Arbital
- Alexei Andreev
wiki
- CFAR should explicitly focus on AI safety
The Center for Applied Rationality has historically had a "cause-neutral" mission but has recently r…
- Stephanie Zolayvar - A Return to Discussion - Eric Bruylant
- A whirlwind tour
A rapid tour of Eric's thoughts on the accelerator project.
- Eric Bruylant - AI alignment
The great civilizational problem of creating artificially intelligent computer systems such that running them is a good idea.
- Eliezer Yudkowsky - Advanced agent properties
How smart does a machine intelligence need to be, for its niceness to become an issue? "Advanced" is a broad term to cover cognitive abilities such that we'd need to start considering AI alignment.
- Eliezer Yudkowsky - Against Compromise, or, Deciding as a Team without Succombing to Entropy - Andrea Gallagher
- Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev - Arbital "parent" relationship
Parent-child relationship between pages implies a strong, inseparable connection.
- Alexei Andreev - Arbital "tag" relationship
Tags are a way to connect pages that share a common topic.
- Alexei Andreev - Arbital Blog
Stay up to date on all things Arbital
- Alexei Andreev - Arbital Labs
Landing page for the Arbital Labs domain.
- Alexei Andreev - Arbital Markdown
All about Arbital's extended Markdown syntax.
- Alexei Andreev - Arbital comment
A comment is a way for you to express your thoughts and opinions within the context of a page.
- Alexei Andreev - Arbital community input
Do you have ideas about how to improve Arbital which you think the community should discuss?
- Alexei Andreev - Arbital editor: Basics
The basics of how to use the Arbital editor.
- Alexei Andreev - Arbital features
Overview of all Arbital features.
- Alexei Andreev - Arbital groups
What are groups? How can I create a new group?
- Alexei Andreev - Arbital lens
A lens is a page that presents another page's content from a different angle.
- Alexei Andreev - Arbital likes
What are likes? When should I use them? What happens when I like something?
- Alexei Andreev - Arbital mark
What is a mark on Arbital? When is it created? Why is it important?
- Alexei Andreev - Arbital page summaries
Because only one summary is not enough!
- Alexei Andreev - Arbital page: Basics
Explaining the basic features of an Arbital page.
- Alexei Andreev - Arbital playpen
Want to test a feature? Feel free to edit this page! asdfasfdasfda
- Eliezer Yudkowsky - Arbital quality
Arbital's system for tracking page quality.
- Eric Bruylant - Arbital query
What is a query? How to create it? How to resolve it?
- Alexei Andreev - Arbital should hide probability/approval votes until the user votes
This is to avoid a potential [-anchoring\_effect]. Also, presumably the user would be still be able …
- Alexei Andreev - Arbital subscriptions
What's a subscription? How do you change it? What to expect?
- Alexei Andreev - Arbital: Google Maps for knowledge
Take your understanding from where it is to where it wants to be.
- Alexei Andreev - Arbital: Solving online explanations
An explanation of Arbital's mid-term goals
- Eliezer Yudkowsky - Arbital: better blogging
What makes Arbital the choice blogging platform?
- Alexei Andreev - Arbital: fixing online discussion
How can Arbital do better than existing discussion platforms?
- Alexei Andreev - Arbital: information hub
How will Arbital help you keep up to date on any given subject?
- Alexei Andreev - Arbital: learning from Wikipedia
How is Arbital different from Wikipedia?
- Alexei Andreev - Author's guide to Arbital
How to write intuitive, flexible content on Arbital.
- Alexei Andreev - B-Class
This page is mostly complete and without major problems, but has not had detailed feedback from the target audience and reviewers.
- Eric Bruylant - Bayes' rule
Bayes' rule is the core theorem of probability theory saying how to revise our beliefs when we make a new observation.
- Eliezer Yudkowsky - Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky - Bayesian reasoning
A probability-theory-based view of the world; a coherent way of changing probabilistic beliefs based on evidence.
- Eliezer Yudkowsky - Bayesian view of scientific virtues
Why is it that science relies on bold, precise, and falsifiable predictions? Because of Bayes' rule, of course.
- Eliezer Yudkowsky - Building an intellectual edifice requires ongoing conversation - Eric Bruylant
- Calories-In-Calories-Out
CICO is a proposed conceptual decomposition of the causes of changes in human body mass, particularl…
- Eliezer Yudkowsky - Cauchy's theorem on subgroup existence: intuitive version
Cauchy's Theorem states that if $G$ is a finite [-group], and $p$ is a prime dividing the order of $…
- Patrick Stevens - Circles of discussion - Alexei Andreev
- Claim explainer: donor lotteries and returns to scale
Sometimes, new technical developments in the discourse around effective altruism can be difficult to…
- Benjamin Hoffman - Coherent extrapolated volition (alignment target)
A proposed direction for an extremely well-aligned autonomous superintelligence - do what humans would want, if we knew what the AI knew, thought that fast, and understood ourselves.
- Eliezer Yudkowsky - Contributing to Arbital
Want to help Arbital become awesome?
- Eric Bruylant - Convex function
A function that only curves upward
- Jessica Taylor - Crony belief
**Crony belief** is a concept originally introduced in Kevin Simler's post, "Crony Beliefs". It's us…
- Alexei Andreev - Crony beliefs (from Melting Asphalt)
The original article that introduced and explained "merit beliefs" vs "crony beliefs" dichotomy.
- Alexei Andreev - Cycle notation in symmetric groups
Cycle notation is a convenient way to represent the elements of a symmetric group.
- Patrick Stevens - Derivative
How things change
- Michael Cohen - Double Crux — A Strategy for Resolving Disagreement - Eric Rogstad
- Easier, better, faster, brighter
In which Arbital gets a makeover, shortcuts, quick feedback, and more!
- Alexei Andreev - Edge instantiation
When you ask the AI to make people happy, and it tiles the universe with the smallest objects that can be happy.
- Eliezer Yudkowsky - Establishing a permanent off-Earth colony would be a useful way to mitigate x-risk
- Posed by [purplepeople](http://effective-altruism.com/user/purplepeople/) on the [EA Forum](http:/…
- Eric Rogstad - Exchange rates between digits
In terms of data storage, if a coin is worth $1, a digit wheel is worth more than $3.32, but less than $3.33. Why?
- Nate Soares - Executable philosophy
Philosophical discourse aimed at producing a trustworthy answer or meta-answer, in limited time, which can used in constructing an Artificial Intelligence.
- Eliezer Yudkowsky - Extrapolated volition (normative moral theory)
If someone asks you for orange juice, and you know that the refrigerator contains no orange juice, should you bring them lemonade?
- Eliezer Yudkowsky - Fractional digits
When $b$ and $x$ are integers, $\log_b(x)$ has a few good interpretations. It's roughly the length o…
- Nate Soares - Geometry of vectors: direction
What rotation would it take to line up this vector to this one?
- Adele Lopez - GiveWell: a case study in effective altruism, part 1
> GiveWell has recently [written about](http://blog.givewell.org/2015/11/25/good-ventures-and-giving…
- Alexei Andreev - Group
The algebraic structure that captures symmetry, relationships between transformations, and part of what multiplication and addition have in common.
- Nate Soares - Group: Exercises
Test your understanding of the definition of a group with these exercises.
- Qiaochu Yuan - Guarded definition
A guarded definition is one where at least one position suspects there will be pressure to stretch a…
- Eliezer Yudkowsky - How to author on Arbital!
Want to contribute pages to Arbital? Here's our current version of the ad-hoc guide to being an author!
- Eliezer Yudkowsky - If EA leaders with similar values disagree about how the EA movement should be branded, then they should discuss in detail the subquestions that would cause them to change their minds if they have not already done so. - Ryan Carey
- Improve comments by tagging claims
Comment sections are more important for discourse than I thought. They can be improved by explicitly tagging an article's main claims as anchors for discussion.
- Benjamin Hoffman - Isomorphism: Intro (Math 0)
Things which are basically the same, except for some stuff you don't care about.
- Mark Chimes - Just a requisite
A tag for nodes that just act as part of Arbital's requisite system
- Eliezer Yudkowsky - Log as the change in the cost of communicating
When interpreting logarithms as a generalization of the notion of "length" and as digit exchange rat…
- Nate Soares - Logarithm
The logarithm base $b$ of a number $n,$ written $\log_b(n),$ is the answer to the question "how man…
- Nate Soares - Math 3 example statements
If you can read these formulas, you're in Math 3!
- Joe Zeng - Mathematics
Mathematics is the study of numbers and other ideal objects that can be described by axioms.
- Eliezer Yudkowsky - Meta tags
What are meta tags and when to use them?
- Eliezer Yudkowsky - Methodology of unbounded analysis
What we do and don't understand how to do, using unlimited computing power, is a critical distinction and important frontier.
- Eliezer Yudkowsky - Mic-Ra-finance and the illusion of control
This post discusses the following claims:
* [claim([6th])]
* [claim([6tk])]
* [claim([6tl])]
- Alexei Andreev - Mindcrime
Might a machine intelligence contain vast numbers of unhappy conscious subprocesses?
- Eliezer Yudkowsky - Mindcrime: Introduction
The more predictive accuracy we want from a model, the more detailed the model becomes. A very roug…
- Eliezer Yudkowsky - Missing the weird alternative
People might systematically overlook "make tiny molecular smileyfaces" as a way of "producing smiles", because our brains automatically search for high-utility-to-us ways of "producing smiles".
- Eliezer Yudkowsky - More about Arbital
Lots more information about Arbital vision.
- Alexei Andreev - Nate's ruminations
These posts are a mirror of posts on the blog [MindingOurWay.com](mindingourway.com) which pertain t…
- Nate Soares - Nearest unblocked strategy
If you patch an agent's preference framework to avoid an undesirable solution, what can you expect to happen?
- Eliezer Yudkowsky - No-Free-Lunch theorems are often irrelevant
There's often a theorem proving that some problem has no optimal answer across every possible world. But this may not matter, since the real world is a special case. (E.g., a low-entropy universe.)
- Eliezer Yudkowsky - Nonperson predicate
If we knew which computations were definitely not people, we could tell AIs which programs they were definitely allowed to compute.
- Eliezer Yudkowsky - Now I am become Life, the protector of worlds
In which Arbital is brought forth into the world.
- Alexei Andreev - Odds
Odds express a relative probability.
- Eliezer Yudkowsky - Odds: Introduction
What's the difference between probabilities and odds? Why is a 20% probability of success equivalent to 1 : 4 odds favoring success?
- Nate Soares - On the importance of Less Wrong, or another single conversational locus
In this post, Anna Salamon talks about how Less Wrong used to a locus of discussion, and that it is…
- Alexei Andreev - Ontology identification problem
How do we link an agent's utility function to its model of the world, when we don't know what that model will look like?
- Eliezer Yudkowsky - Ontology identification problem: Technical tutorial
Technical tutorial for ontology identification problem.
- Eliezer Yudkowsky - Open subproblems in aligning a Task-based AGI
Open research problems, especially ones we can model today, in building an AGI that can "paint all cars pink" without turning its future light cone into pink-painted cars.
- Eliezer Yudkowsky - Order theory
The study of binary relations that are reflexive, transitive, and antisymmetic.
- Kevin Clancy - Oropharyngeal cancer is a significant risk of HPV
HPV can cause oral and pharyngeal cancer. The incidence of HPV-associated oropharyngeal cancer is ab…
- Sarah Constantin - Orthogonality Thesis
Will smart AIs automatically become benevolent, or automatically become hostile? Or do different AI designs imply different goals?
- Eliezer Yudkowsky - Our community should relocate to a country other than the US
Claims with specific country proposals:
* [claim([6v8])]
* [claim([6v9])]
Relevant claims:
* [cla…
- Alexei Andreev - Page's title should always be capitalized
Vote "agree" if you think Arbital should enforce the first letter of a page title to always be capit…
- Alexei Andreev - Partially ordered set
A set endowed with a relation that is reflexive, transitive, and antisymmetric.
- Kevin Clancy - Path: Multiple angles on Bayes's Rule
A learning-path placeholder page for learning multiple angles on Bayes's Rule.
- Eliezer Yudkowsky - Paul Christiano's AI control blog
Speculations on the design of safe, efficient AI systems.
- Paul Christiano - Pivotal event
Which types of AIs, if they work, can do things that drastically change the nature of the further game?
- Eliezer Yudkowsky - Possible math pages
A list of things which we may want math pages on
- Eric Bruylant - Practicing Brevity
Wanna save the world? Write better TLDRs. And spend more time respecting your reader's time.
- Raymond Arnold - Primer on Infinite Series
What does it mean to add things together forever?
- Chris Holden - Properties of the logarithm
- $\log_b(x \cdot y) = \log_b(x) + \log_b(y)$ for any $b$, this is the defining characteristic of …
- Nate Soares - Rational arithmetic all works together
The various operations of arithmetic all play nicely together in a certain specific way.
- Patrick Stevens - Relevant powerful agent
An agent is relevant if it completely changes the course of history.
- Eliezer Yudkowsky - Replacing Guilt
In my experience, many people are motivated primarily by either guilt, shame, or some combination of…
- Nate Soares - Rescuing the utility function
If your utility function values 'heat', and then you discover to your horror that there's no ontologically basic heat, switch to valuing disordered kinetic energy. Likewise 'free will' or 'people'.
- Eliezer Yudkowsky - Scalable ways to associate evidence (pro or con) with claims will be more valuable in elevating accuracy than complex voting and reputation systems
Discussions on Less Wrong have delved into [complex systems of voting and moderation](http://lesswro…
- Andrea Gallagher - Separation from hyperexistential risk
The AI should be widely separated in the design space from any AI that would constitute a "hyperexistential risk" (anything worse than death).
- Eliezer Yudkowsky - Solomonoff induction: Intro Dialogue (Math 2)
An introduction to Solomonoff induction for the unfamiliar reader who isn't bad at math
- Eliezer Yudkowsky - Some computations are people
It's possible to have a conscious person being simulated inside a computer or other substrate.
- Eliezer Yudkowsky - Some men just want to watch the world learn
In which Arbital gets paths.
- Alexei Andreev - Square visualization of probabilities on two events: (example) Diseasitis
But it *seems* like the patient with the black tongue depressor has diseasitis...
- Tsvi BT - Style guidelines
Various stylistic conventions people should follow on Arbital
- Alexei Andreev - Submitting a page to a domain
How and why to submit a page to a domain
- Alexei Andreev - Sufficiently optimized agents appear coherent
If you could think as well as a superintelligence, you'd be at least that smart yourself.
- Eliezer Yudkowsky - Team Arbital
The people behind Arbital
- Alexei Andreev - The Robots, AI, and Unemployment Anti-FAQ
Q. Are the current high levels of unemployment being caused by advances in Artificial Intelligence …
- Eliezer Yudkowsky - The Value of Coordination
>When you’re part of a community, the counterfactuals become more complex, and doing the most good b…
- Alexei Andreev - The rocket alignment problem
If people talked about the problem of space travel the way they talked about AI...
- Eliezer Yudkowsky - To math explanations and beyond!
In which Arbital doubles down on math explanations.
- Alexei Andreev - Uncountability: Intuitive Intro
Are all sizes of infinity the same? What does "the same" even mean here?
- Jason Gross - Useless variable decomposition
A variable decomposition can be true but useless if it is a poor guide to intervention due to automa…
- Alexei Andreev - Value alignment problem
You want to build an advanced AI with the right values... but how?
- Eliezer Yudkowsky - Vinge's Principle
An agent building another agent must usually approve its design without knowing the agent's exact policy choices.
- Eliezer Yudkowsky - Vitamin D
Vitamin D refers to a group of fat-soluble secosteroids responsible for enhancing intestinal absorpt…
- Alexei Andreev - Vitamin D helps prevent cancer
There have been a lot of studies performed that show that vitamin D helps prevent cancer, but overal…
- Alexei Andreev - Vitamin D helps prevent cardiovascular disease
This question is a bit vague. There are two ways to make it more specific.
1. Does vitamin D deffic…
- Alexei Andreev - Vitamin D is good for you
We'll consider two categories of vitamin D supplementation: below and above the recommended levels.
…
- Alexei Andreev - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky - Why argument structure is important
How might we make collaborative truth-seeking both fun and easy?
- Andrea Gallagher - Will Narrow AI Seriously Affect Long-Term Employment?
###Definitions:
**Narrow AI** - artificial intelligence capable of doing a narrow task at a level …
- Alexei Andreev - Work in progress
This page is being actively worked on by an editor. Check with them before making major changes.
- Eliezer Yudkowsky - Working out, weightlifting, and nutrition
Just a collection of links / resources I'll be using to seed some content.
# Working out
### How t…
- Alexei Andreev - You're allowed to fight for something
The first sort of guilt I want to address is the listless guilt, that vague feeling one gets after p…
- Nate Soares
group
"$ax2+bx+c=0$ will be displayed as: $ax2+bx+c=0$"
Displays instead of
"S ax^2 + bx + c = 0 S wil…
- Regex Rationalist"Humans Need Not Apply" is a good youtube video on this: https://www.youtube.com/watch?v=7Pq-S557XQU…
- Curtis SerVaas(My first comment on Arbital. Hopefully it contributes.)
As someone who has traded on prediction ma…
- Ted Sanders**Allow (slightly) more HTML**
This engine does allow a subset of HTML, but it's [extremely limited…
- Eric Bruylant**Citations**
Making citations easy to create and maintain will cause more people to use them. Arbi…
- Eric Bruylant**Navigation for the tree of information**
Implementing something like [MediaWiki's CategoryTree](h…
- Eric Bruylant**Posted date on blog pages**
It's often important to know when a blog post was made. The originall…
- Eric Bruylant**Recent Changes / Edit Review system**
On traditional wikis the [recent changes page](https://wiki…
- Eric Bruylant**Transclusion / Template system**
[Templates](https://www.mediawiki.org/wiki/Help:Templates) and […
- Eric Bruylant> The obvious patch is for a sufficiently sophisticated system to have preferences over its own beha…
- Eliezer YudkowskyA summary of the relevant cardinal arithmetic, by the way (in the presence of choice): $$\aleph_{\al…
- Patrick StevensAfter another session of using Arbital, I have a few questions and comments.
1.) Is there any mecha…
- Kevin ClancyAgree this is a problem, but also part of a broader coordination problem in the community and which …
- Peter McIntyreApproved, but the summary could do with a bit of improvement, make it something that a non-mathemati…
- Eric BruylantAre UnforeseenMaximums distinct from EdgeInstantiation problems? Seems like they are EdgeInstantiat…
- Stephanie ZolayvarBollard's more conservative estimate is 38 hen-years per dollar, if you include other expenditures o…
- Benjamin HoffmanCool, show me the designs/plans when that moves near the top of your list for feedback?
- Eric BruylantDoes arbital markdown use any of the markdown table formats? Can latex be included within? Is there …
- Chris HoldenDoses too low (they spend some text on this in the discussion section-- even the 800 IU they say som…
- Daniel SmithFeature proposal: if the greenlink is to a stub (ie the summary = the full content) then the hover-s…
- Malcolm OceanFor what it's worth, I have a bit of experience with Kickstarter campaigns, where a similar pattern …
- Davis KingsleyHaving this as policy rather than something enforced by software seems better. I think Wikipedia did…
- Eric BruylantI agree that For mitigating AI x-risk, an off-Earth colony would be about as useful as a warm scarf.…
- Eric RogstadI am pretty surprised by how confident the voters are!
Is "arbitrarily powerful" intended to includ…
- Paul ChristianoI believe these headings are nonsense. It should instead say something like "Claims that some peopl…
- Anna SalamonI don't think people are properly grasping what it would mean to have a set of shelters on Earth tha…
- Kyle BogosianI don't understand the graph, can someone explain it to me?
- Stephanie ZolayvarI feel it's basically good to be straightforward, and also good to be in motion rather than waiting …
- Anna SalamonI notice that the shade of the bar indicating how many users gave a probability estimate is visible …
- Jeff LadishI think Wikipedia does it pretty well. Defaulting to capitalizing with the option to disable it look…
- Olivia SchaeferI think a good litmus test is "could two people both strongly agree (or strongly disagree) while act…
- Satvik BeriI think it's good to have our high standards of evidence, but once in a while I see someone with a g…
- Kyle BogosianI think one will often still need 'introductory' or 'tutorial' type pages that walk through the hier…
- Eliezer YudkowskyI think that in practice these norms will be hard to enforce just by culture. I would recommend a fe…
- Malcolm OceanI think this claim's title is too long to be used a handle for the concept.
- Stephanie ZolayvarI think this is a factor in whether I feel motivated to donate, but because of unconscious associati…
- Rob BensingerI think this is a good idea for specific 'kickstarter' projects by organizations. I don't think nonp…
- Rob BensingerI think this should be a claim.
- Eric RogstadI was trying to say "append 1 to previous sequence". I guess it needs explanation.
- Eliezer YudkowskyI was under the impression that R+ doesn't include 0. If that's the case, then it is not the same.
- Bryce WoodworthI'd agree more strongly if it had a couple of fixes for obvious problems, so I proposed some.
Probl…
- Patrick LaVictoireI'd be interested to know if you find yourself having that feeling a lot, while interacting with cla…
- Eric RogstadI'd really want to tell this not as a whole new vision, but as moving onto a different part of an ex…
- Eric BruylantI'd tell this story fairly differently. This is not really how I saw math, and presenting it as not-…
- Eric BruylantI'll try to cover probabilistic Turing machines in other article once I have time. Thanks for your i…
- Jaime Sevilla MolinaI've come across a number of argument-structuring tools in the past. I think doing this right is muc…
- Jim BabcockIf there aren't side effects, it seems like the answer is probably yes, since vitamin D deficiency s…
- Paul ChristianoIs "coment" (below) a typo?
"[comment: there has got to be a better metaphor for this]
%%**coment:*…
- Maelle AndreIt depends on the ipsum.
- Anna SalamonJoke stolen shamelessly from the latest post on slatestarcodex.com
- Mark ChimesMisleading conclusion. Their 400 IU dose of Vit D was pathetically low and therefore totally ineffec…
- Daniel SmithNeeds some cushioning, to avoid setting expectations of not just powerful dictator-staff and arrogan…
- Eric BruylantNote that PredictIt [currently thinks](https://www.predictit.org/Contract/4264/Will-the-next-US-pres…
- Eric RogstadOh, the ipsum.
[Edit: this was meant to be an inline comment attached to "the ipsum" in Anna's comm…
- Anton GeraschenkoOkay. I'm happy to be a sounding board/give input when you feel like this is one of the next steps.
…
- Eric BruylantPossibly have it hidden for logged-in users, but shown to logged out users? It'd be good for casual …
- Eric BruylantReddit's reputation system gives new arrivals equal weight to long-standing highly trusted members o…
- Eric BruylantSomething analogous to an "original research" disclaimer would be helpful here. If I read a Wikipedi…
- Qiaochu YuanStrongLifts is also a really good program.
It also details how to do the lifts (e.g. squatti…
- Curtis SerVaasThanks for picking apart my claim, folks! Rather than modify this claim, I think I'll work on a Pos…
- Andrea GallagherThanks!
A^B is the set of functions from B to A. So 2^N is powerset of N (a function f from N to {…
- Jason GrossThat's another approach, but gets into annoying subjective judgements really easily. I'm confident i…
- Eric BruylantThe best discussion platform I know of currently is http://www.discourse.org by some of the people b…
- Eric BruylantThe question of tradeoffs between X and Y and winners' curses reminds me of Bostrom's paper, [The Un…
- Eric RogstadThe urls are displaying as:
https://arbital.com/learn/?path=$bayes_rule_details,$bayes_update_detail…
- Mark ChimesThere appears to be an inconsistency in the rendering of this page and its rendering in the preview …
- Eric LeeseThis doesn't seem like a controversial of a claim (be specific and not vague is one of the most time…
- Timothy ChuThis gives a few clear examples, but does not help much with slightly less clear judgements (e.g. sh…
- Eric BruylantThis is a more general pattern in theoretical research. When you first start to attack a hard proble…
- Paul ChristianoThis is redacted in a very confusing way.
- Jaime Sevilla MolinaThis seems like it specifically addresses the "lumpy" case where a program only makes sense above a …
- Benjamin HoffmanThis seems to be highly sensitive to the amount of time EAs currently spend on deciding. I think tha…
- Adele LopezTo clarify my view, I think EA moderately discourages creativity but this is a big mistake: it shoul…
- Ryan CareyTo make sure we're on the same page, Orthogonality is true if it's possible for a paperclip maximize…
- Eliezer YudkowskyUh, well, it's hard to reply-to, or something? Like, it wants to jam the conversation into question…
- Anna SalamonWhat if it was tagged with claims? Would that give you what you're wanting from a summary? I feel …
- Stephanie ZolayvarWorking out how to handle karma on wikis is something I spent a bunch of brain cycles on a while ago…
- Eric BruylantYes.
As far as I can tell, the current message of effective altruism sort of focuses in too strongly…
- Timothy ChuYes. In particular, the first milestone or two should probably be small (assuming there are no assoc…
- Rob BensingerAlexei Andreev This page includes a conditional example that only shows up for people who know real …
- Kevin Clancyawkwardish, probably best drop functional, and maybe use network of knowledge rather than database?
- Eric Bruylant{{lowercase title}} is for things like eBay and iPod, IIRC -- which arbital should support eventuall…
- Nate Soares
wiki
- Distant superintelligences can coerce the most probable environment of your AI
Distant superintelligences may be able to hack your local AI, if your AI's preference framework depends on its most probable environment.
- Eliezer Yudkowsky - Don't try to solve the entire alignment problem
New to AI alignment theory? Want to work in this area? Already been working in it for years? Don't try to solve the entire alignment problem with your next good idea!
- Eliezer Yudkowsky - Goodhart's Curse
The Optimizer's Curse meets Goodhart's Law. For example, if our values are V, and an AI's utility function U is a proxy for V, optimizing for high U seeks out 'errors'--that is, high values of U - V.
- Eliezer Yudkowsky
- Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev - Arbital: learning from Wikipedia
How is Arbital different from Wikipedia?
- Alexei Andreev
- Frequency diagram
Visualizing Bayes' rule by manipulating frequencies in large populations
- Nate Soares - Interpretations of "probability"
What does it *mean* to say that a fair coin has a 50% probability of coming up heads?
- Nate Soares - Odds
Odds express a relative probability.
- Eliezer Yudkowsky - Probability
The degree to which someone believes something, measured on a scale from 0 to 1, allowing us to do math to it.
- Eliezer Yudkowsky - Waterfall diagram
Visualizing Bayes' rule as the mixing of probability streams.
- Eliezer Yudkowsky
- Predictions For 2017
Scott Alexander made 105 predictions for 2017. Most of them are not personal and are listed below. …
- Alexei Andreev - Why argument structure is important
How might we make collaborative truth-seeking both fun and easy?
- Andrea Gallagher - Zero-Shot Translation with Google’s Multilingual Neural Machine Translation System
Sorry, old news. But I'll leave it up.
- Andrea Gallagher
wiki
- Some computations are people
It's possible to have a conscious person being simulated inside a computer or other substrate.
- Eliezer Yudkowsky
wiki
- Arbital claims are significantly more useful* when they are fairly well-specified and unambiguous**
\* At least 30% more valuable to people sharing models.
** Not lojban level, but with some thoug…
- Eric Bruylant - Improve comments by tagging claims
Comment sections are more important for discourse than I thought. They can be improved by explicitly tagging an article's main claims as anchors for discussion.
- Benjamin Hoffman - Practicing Brevity
Wanna save the world? Write better TLDRs. And spend more time respecting your reader's time.
- Raymond Arnold
- Bayes' rule: Definition
Bayes' rule is the mathematics of probability theory governing how to update your beliefs in the lig…
- Nate Soares - Bayes' rule: Log-odds form
A simple transformation of Bayes' rule reveals tools for measuring degree of belief, and strength of evidence.
- Eliezer Yudkowsky
- Frequency diagram
Visualizing Bayes' rule by manipulating frequencies in large populations
- Nate Soares
- Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- Identifying ambiguous inductions
What do a "red strawberry", a "red apple", and a "red cherry" have in common that a "yellow carrot" doesn't? Are they "red fruits" or "red objects"?
- Eliezer Yudkowsky - Machine Intelligence Research Institute
Where to work if you're doing more formal or technical work on AI safety, of a kind not easily milked for publications.
- Alexei Andreev
- Fractional digits
When $b$ and $x$ are integers, $\log_b(x)$ has a few good interpretations. It's roughly the length o…
- Nate Soares
wiki
- A $1 donation to a top animal charity alleviates more suffering than is caused by a day of eating meat.
For the purposes of this claim, top animal welfare charities include:
- [Animal Charity Evaluators…
- Eric Rogstad - AI alignment
The great civilizational problem of creating artificially intelligent computer systems such that running them is a good idea.
- Eliezer Yudkowsky - Arbital features
Overview of all Arbital features.
- Alexei Andreev - Arbital: Solving online explanations
An explanation of Arbital's mid-term goals
- Eliezer Yudkowsky - Arbital: better blogging
What makes Arbital the choice blogging platform?
- Alexei Andreev - Arbital: learning from Wikipedia
How is Arbital different from Wikipedia?
- Alexei Andreev - Bayes' rule: Odds form
The simplest and most easily understandable form of Bayes' rule uses relative odds.
- Eliezer Yudkowsky - Bayes' rule: Vector form
For when you want to apply Bayes' rule to lots of evidence and lots of variables, all in one go. (This is more or less how spam filters work.)
- Eliezer Yudkowsky - Bayesian view of scientific virtues
Why is it that science relies on bold, precise, and falsifiable predictions? Because of Bayes' rule, of course.
- Eliezer Yudkowsky - Belief revision as probability elimination
Update your beliefs by throwing away large chunks of probability mass.
- Eliezer Yudkowsky - Coordinative AI development hypothetical
What would safe AI development look like if we didn't have to worry about anything else?
- Eliezer Yudkowsky - Corrigibility
"I can't let you do that, Dave."
- Nate Soares - Diamond maximizer
How would you build an agent that made as much diamond material as possible, given vast computing power but an otherwise rich and complicated environment?
- Eliezer Yudkowsky - Fundraisers should have a threshold amount which, if not hit, results in a refund.
When starting a fundraiser, a nonprofit should declare a threshold amount. If the nonprofit doesn't …
- Alexei Andreev - It's good for GiveWell and Good Ventures to crowd out donors by their donations. - Alexei Andreev
- Known-algorithm non-self-improving agent
Possible advanced AIs that aren't self-modifying, aren't self-improving, and where we know and understand all the component algorithms.
- Eliezer Yudkowsky - Methodology of unbounded analysis
What we do and don't understand how to do, using unlimited computing power, is a critical distinction and important frontier.
- Eliezer Yudkowsky - Non-adversarial principle
At no point in constructing an Artificial General Intelligence should we construct a computation that tries to hurt us, and then try to stop it from hurting us.
- Eliezer Yudkowsky - Ontology identification problem
How do we link an agent's utility function to its model of the world, when we don't know what that model will look like?
- Eliezer Yudkowsky - Open subproblems in aligning a Task-based AGI
Open research problems, especially ones we can model today, in building an AGI that can "paint all cars pink" without turning its future light cone into pink-painted cars.
- Eliezer Yudkowsky - Optimization daemons
When you optimize something so hard that it crystalizes into an optimizer, like the way natural selection optimized apes so hard they turned into human-level intelligences
- Eliezer Yudkowsky - Orthogonality Thesis
Will smart AIs automatically become benevolent, or automatically become hostile? Or do different AI designs imply different goals?
- Eliezer Yudkowsky - Patch resistance
One does not simply solve the value alignment problem.
- Eliezer Yudkowsky - Pivotal event
Which types of AIs, if they work, can do things that drastically change the nature of the further game?
- Eliezer Yudkowsky - Report likelihoods, not p-values
If scientists reported likelihood functions instead of p-values, this could help science avoid p-ha…
- Nate Soares - Rescuing the utility function
If your utility function values 'heat', and then you discover to your horror that there's no ontologically basic heat, switch to valuing disordered kinetic energy. Likewise 'free will' or 'people'.
- Eliezer Yudkowsky - Scalable AI control
By AI control, I mean the problem of getting AI systems to do what we want them to do, to the best…
- Paul Christiano - Separation from hyperexistential risk
The AI should be widely separated in the design space from any AI that would constitute a "hyperexistential risk" (anything worse than death).
- Eliezer Yudkowsky - The rocket alignment problem
If people talked about the problem of space travel the way they talked about AI...
- Eliezer Yudkowsky - Universal property of the product
The product can be defined in a very general way, applicable to the natural numbers, to sets, to algebraic structures, and so on.
- Patrick Stevens - Value achievement dilemma
How can Earth-originating intelligent life achieve most of its potential value, whether by AI or otherwise?
- Eliezer Yudkowsky - Why waiting to donate harms charities
A blog post explaining the potential reasons why someone would choose to wait to donate and how that leads to suboptimal outcomes for the charity.
- Alexei Andreev
- Finishing your Bayesian path on Arbital
The page that comes at the end of reading the Arbital Guide to Bayes' rule
- Eliezer Yudkowsky
- Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- Arbital: Google Maps for knowledge
Take your understanding from where it is to where it wants to be.
- Alexei Andreev - Bayes' rule examples
Interesting problems solvable by Bayes' rule
- Eliezer Yudkowsky - Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky - Realistic (Math 1)
Real-life examples of Bayesian reasoning
- Eliezer Yudkowsky
wiki
- Introduction to Bayes' rule: Odds form
Bayes' rule is simple, if you think in terms of relative odds.
- Eliezer Yudkowsky
- Arbital playpen
Want to test a feature? Feel free to edit this page! asdfasfdasfda
- Eliezer Yudkowsky - Identifying ambiguous inductions
What do a "red strawberry", a "red apple", and a "red cherry" have in common that a "yellow carrot" doesn't? Are they "red fruits" or "red objects"?
- Eliezer Yudkowsky - List: value-alignment subjects
Bullet point list of core VAT subjects.
- Eliezer Yudkowsky - Nearest unblocked strategy
If you patch an agent's preference framework to avoid an undesirable solution, what can you expect to happen?
- Eliezer Yudkowsky - Patch resistance
One does not simply solve the value alignment problem.
- Eliezer Yudkowsky
- Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- Bayes' rule
Bayes' rule is the core theorem of probability theory saying how to revise our beliefs when we make a new observation.
- Eliezer Yudkowsky
- Introductory Bayesian problems
Bayesian problems to try to solve yourself, before beginning to learn about Bayes' rule.
- Eliezer Yudkowsky - Math 2
Do you work with math on a fairly routine basis? Do you have little trouble grasping abstract structures and ideas?
- Eliezer Yudkowsky
- Odds
Odds express a relative probability.
- Eliezer Yudkowsky
- Welcome to Arbital
Front page explaining what Arbital is all about.
- Alexei Andreev
- Coherent decisions imply consistent utilities
Why do we all use the 'expected utility' formalism? Because any behavior that can't be viewed from that perspective, must be qualitatively self-defeating (in various mathy ways).
- Eliezer Yudkowsky - Coherent extrapolated volition (alignment target)
A proposed direction for an extremely well-aligned autonomous superintelligence - do what humans would want, if we knew what the AI knew, thought that fast, and understood ourselves.
- Eliezer Yudkowsky - Extrapolated volition (normative moral theory)
If someone asks you for orange juice, and you know that the refrigerator contains no orange juice, should you bring them lemonade?
- Eliezer Yudkowsky
- Why waiting to donate harms charities
A blog post explaining the potential reasons why someone would choose to wait to donate and how that leads to suboptimal outcomes for the charity.
- Alexei Andreev
- Conditional probability
The notation for writing "The probability that someone has green eyes, if we know that they have red hair."
- Eliezer Yudkowsky
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky
- Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
wiki
- Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev - Arbital features
Overview of all Arbital features.
- Alexei Andreev - Improve comments by tagging claims
Comment sections are more important for discourse than I thought. They can be improved by explicitly tagging an article's main claims as anchors for discussion.
- Benjamin Hoffman - Practicing Brevity
Wanna save the world? Write better TLDRs. And spend more time respecting your reader's time.
- Raymond Arnold - Solomonoff induction: Intro Dialogue (Math 2)
An introduction to Solomonoff induction for the unfamiliar reader who isn't bad at math
- Eliezer Yudkowsky - Why argument structure is important
How might we make collaborative truth-seeking both fun and easy?
- Andrea Gallagher
group
- Eliezer Yudkowsky
Cofounder, with Nick Bostrom, of the field of value alignment theory.
wiki
- Introduction to Bayes' rule: Odds form
Bayes' rule is simple, if you think in terms of relative odds.
- Eliezer Yudkowsky
- Accelerator Project
The Accelerator Project aims to create a low-cost environment which facilitates rapid personal growt…
- Eric Bruylant - The missing step between Zero and Hero
Creating a space for high potential people grow and improve the world at scale.
- Eric Bruylant
- Now I am become Life, the protector of worlds
In which Arbital is brought forth into the world.
- Alexei Andreev - Value alignment problem
You want to build an advanced AI with the right values... but how?
- Eliezer Yudkowsky
wiki
- A typical donor with a $5,000 charity budget, on the margin, has increasing returns to scale - Benjamin Hoffman
- Crowdsourcing moderation without sacrificing quality - Eric Rogstad
- Donor lotteries: demonstration and FAQ - Ryan Carey
- GiveWell: a case study in effective altruism, part 1
> GiveWell has recently [written about](http://blog.givewell.org/2015/11/25/good-ventures-and-giving…
- Alexei Andreev - Rescuing the utility function
If your utility function values 'heat', and then you discover to your horror that there's no ontologically basic heat, switch to valuing disordered kinetic energy. Likewise 'free will' or 'people'.
- Eliezer Yudkowsky - Why waiting to donate harms charities
A blog post explaining the potential reasons why someone would choose to wait to donate and how that leads to suboptimal outcomes for the charity.
- Alexei Andreev
- Predictions For 2017
Scott Alexander made 105 predictions for 2017. Most of them are not personal and are listed below. …
- Alexei Andreev
- Executable philosophy
Philosophical discourse aimed at producing a trustworthy answer or meta-answer, in limited time, which can used in constructing an Artificial Intelligence.
- Eliezer Yudkowsky
- Reliable prediction
How can we train predictors that reliably predict observable phenomena such as human behavior?
- Jessica Taylor
wiki
- An Introduction to Logical Decision Theory for Everyone Else
So like what the heck is 'logical decision theory' in terms a normal person can understand?
- Eliezer Yudkowsky - Why waiting to donate harms charities
A blog post explaining the potential reasons why someone would choose to wait to donate and how that leads to suboptimal outcomes for the charity.
- Alexei Andreev
- Submitting a page to a domain
How and why to submit a page to a domain
- Alexei Andreev
- AI alignment
The great civilizational problem of creating artificially intelligent computer systems such that running them is a good idea.
- Eliezer Yudkowsky - Arbital lens
A lens is a page that presents another page's content from a different angle.
- Alexei Andreev - Executable philosophy
Philosophical discourse aimed at producing a trustworthy answer or meta-answer, in limited time, which can used in constructing an Artificial Intelligence.
- Eliezer Yudkowsky - Some computations are people
It's possible to have a conscious person being simulated inside a computer or other substrate.
- Eliezer Yudkowsky
- Introduction to Bayes' rule: Odds form
Bayes' rule is simple, if you think in terms of relative odds.
- Eliezer Yudkowsky
- Relation
A **relation** is a set of [tuple\_mathematics tuples], all of which have the same [tuple\_arity ar…
- Kevin Clancy
- A whirlwind tour
A rapid tour of Eric's thoughts on the accelerator project.
- Eric Bruylant - AIXI
How to build an (evil) superintelligent AI using unlimited computing power and one page of Python code.
- Eliezer Yudkowsky - Big-picture strategic awareness
We start encountering new AI alignment issues at the point where a machine intelligence recognizes the existence of a real world, the existence of programmers, and how these relate to its goals.
- Eliezer Yudkowsky - Nearest unblocked strategy
If you patch an agent's preference framework to avoid an undesirable solution, what can you expect to happen?
- Eliezer Yudkowsky - Rescuing the utility function
If your utility function values 'heat', and then you discover to your horror that there's no ontologically basic heat, switch to valuing disordered kinetic energy. Likewise 'free will' or 'people'.
- Eliezer Yudkowsky - The missing step between Zero and Hero
Creating a space for high potential people grow and improve the world at scale.
- Eric Bruylant - Unforeseen maximum
When you tell AI to produce world peace and it kills everyone. (Okay, some SF writers saw that one coming.)
- Eliezer Yudkowsky
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky - Introductory Bayesian problems
Bayesian problems to try to solve yourself, before beginning to learn about Bayes' rule.
- Eliezer Yudkowsky
- Bayesian update
Bayesian updating: the ideal way to change probabilistic beliefs based on evidence.
- Eliezer Yudkowsky
- Goodhart's Curse
The Optimizer's Curse meets Goodhart's Law. For example, if our values are V, and an AI's utility function U is a proxy for V, optimizing for high U seeks out 'errors'--that is, high values of U - V.
- Eliezer Yudkowsky
- How to build your own Lumenator
Treating Seasonal Affective Disorder using MOAR LIGHT can sometimes solve what dinky little lightboxes can't.
- Eliezer Yudkowsky - Practicing Brevity
Wanna save the world? Write better TLDRs. And spend more time respecting your reader's time.
- Raymond Arnold
wiki
- Ontology identification problem
How do we link an agent's utility function to its model of the world, when we don't know what that model will look like?
- Eliezer Yudkowsky
- Bayes' rule
Bayes' rule is the core theorem of probability theory saying how to revise our beliefs when we make a new observation.
- Eliezer Yudkowsky - Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky
wiki
- Bayes' rule: Odds form
The simplest and most easily understandable form of Bayes' rule uses relative odds.
- Eliezer Yudkowsky - Conditional probability
The notation for writing "The probability that someone has green eyes, if we know that they have red hair."
- Eliezer Yudkowsky - Extraordinary claims require extraordinary evidence
The people who adamantly claim they were abducted by aliens do provide some evidence for aliens. They just don't provide quantitatively enough evidence.
- Eliezer Yudkowsky
wiki
- Frequency diagrams: A first look at Bayes
The most straightforward visualization of Bayes' rule.
- Nate Soares
wiki
- Alexei Andreev: Personal
Fun things Alexei Andreev likes to do.
- Alexei Andreev
group
- Alexei Andreev
There is no spoon
- Introduction to Bayes' rule: Odds form
Bayes' rule is simple, if you think in terms of relative odds.
- Eliezer Yudkowsky
- Relative likelihood
How relatively likely an observation is, given two or more hypotheses, determines the strength and direction of evidence.
- Eliezer Yudkowsky
- Empirical probabilities are not exactly 0 or 1
"Cromwell's Rule" says that probabilities of exactly 0 or 1 should never be applied to empirical propositions - there's always some probability, however tiny, of being mistaken.
- Eliezer Yudkowsky - Isomorphism
A morphism between two objects which describes how they are "essentially equivalent" for the purposes of the theory under consideration.
- Mark Chimes - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
wiki
- AI alignment
The great civilizational problem of creating artificially intelligent computer systems such that running them is a good idea.
- Eliezer Yudkowsky - Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev - Building an intellectual edifice requires ongoing conversation - Eric Bruylant
- Claim explainer: donor lotteries and returns to scale
Sometimes, new technical developments in the discourse around effective altruism can be difficult to…
- Benjamin Hoffman - Executable philosophy
Philosophical discourse aimed at producing a trustworthy answer or meta-answer, in limited time, which can used in constructing an Artificial Intelligence.
- Eliezer Yudkowsky - Goodhart's Curse
The Optimizer's Curse meets Goodhart's Law. For example, if our values are V, and an AI's utility function U is a proxy for V, optimizing for high U seeks out 'errors'--that is, high values of U - V.
- Eliezer Yudkowsky - Improve comments by tagging claims
Comment sections are more important for discourse than I thought. They can be improved by explicitly tagging an article's main claims as anchors for discussion.
- Benjamin Hoffman - On the importance of Less Wrong, or another single conversational locus
In this post, Anna Salamon talks about how Less Wrong used to a locus of discussion, and that it is…
- Alexei Andreev - Predictions For 2017
Scott Alexander made 105 predictions for 2017. Most of them are not personal and are listed below. …
- Alexei Andreev - Scalable ways to associate evidence (pro or con) with claims will be more valuable in elevating accuracy than complex voting and reputation systems
Discussions on Less Wrong have delved into [complex systems of voting and moderation](http://lesswro…
- Andrea Gallagher - The current message of effective altruism heavily discourages creativity.
Alyssa Vance expands on this point in her [FB post](https://www.facebook.com/alyssamvance/posts/1021…
- Alexei Andreev - Why argument structure is important
How might we make collaborative truth-seeking both fun and easy?
- Andrea Gallagher - Why waiting to donate harms charities
A blog post explaining the potential reasons why someone would choose to wait to donate and how that leads to suboptimal outcomes for the charity.
- Alexei Andreev
group
- Eliezer Yudkowsky
Cofounder, with Nick Bostrom, of the field of value alignment theory.
- Conditional probability
The notation for writing "The probability that someone has green eyes, if we know that they have red hair."
- Eliezer Yudkowsky
- Odds: Introduction
What's the difference between probabilities and odds? Why is a 20% probability of success equivalent to 1 : 4 odds favoring success?
- Nate Soares
- Arbital features
Overview of all Arbital features.
- Alexei Andreev - Bayesian update
Bayesian updating: the ideal way to change probabilistic beliefs based on evidence.
- Eliezer Yudkowsky - Edge instantiation
When you ask the AI to make people happy, and it tiles the universe with the smallest objects that can be happy.
- Eliezer Yudkowsky - Executable philosophy
Philosophical discourse aimed at producing a trustworthy answer or meta-answer, in limited time, which can used in constructing an Artificial Intelligence.
- Eliezer Yudkowsky
- Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- AI alignment
The great civilizational problem of creating artificially intelligent computer systems such that running them is a good idea.
- Eliezer Yudkowsky
- The rocket alignment problem
If people talked about the problem of space travel the way they talked about AI...
- Eliezer Yudkowsky
wiki
- Optimization daemons
When you optimize something so hard that it crystalizes into an optimizer, like the way natural selection optimized apes so hard they turned into human-level intelligences
- Eliezer Yudkowsky
- Church-Turing thesis: Evidence for the Church-Turing thesis
Why do we believe in CT thesis?
- Jaime Sevilla Molina - Guarded definition
A guarded definition is one where at least one position suspects there will be pressure to stretch a…
- Eliezer Yudkowsky - High-speed intro to Bayes's rule
A high-speed introduction to Bayes's Rule on one page, for the impatient and mathematically adept.
- Eliezer Yudkowsky - Pivotal event
Which types of AIs, if they work, can do things that drastically change the nature of the further game?
- Eliezer Yudkowsky - Requisites for personal growth
A mashup of models
- Toon Alfrink - Why is the decimal expansion of log2(3) infinite?
Because 2 and 3 are relatively prime.
- Nate Soares
- Orthogonality Thesis
Will smart AIs automatically become benevolent, or automatically become hostile? Or do different AI designs imply different goals?
- Eliezer Yudkowsky
- Isomorphism: Intro (Math 0)
Things which are basically the same, except for some stuff you don't care about.
- Mark Chimes
wiki
- Curtis's Blog
I'm testing the blogging functionality.
- Curtis SerVaas - Ontology identification problem
How do we link an agent's utility function to its model of the world, when we don't know what that model will look like?
- Eliezer Yudkowsky - Vitamin D helps prevent cancer
There have been a lot of studies performed that show that vitamin D helps prevent cancer, but overal…
- Alexei Andreev
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky
- Optimization daemons
When you optimize something so hard that it crystalizes into an optimizer, like the way natural selection optimized apes so hard they turned into human-level intelligences
- Eliezer Yudkowsky
- Distant superintelligences can coerce the most probable environment of your AI
Distant superintelligences may be able to hack your local AI, if your AI's preference framework depends on its most probable environment.
- Eliezer Yudkowsky - Separation from hyperexistential risk
The AI should be widely separated in the design space from any AI that would constitute a "hyperexistential risk" (anything worse than death).
- Eliezer Yudkowsky
- Predictions For 2017
Scott Alexander made 105 predictions for 2017. Most of them are not personal and are listed below. …
- Alexei Andreev
- Odds
Odds express a relative probability.
- Eliezer Yudkowsky
- Log as the change in the cost of communicating
When interpreting logarithms as a generalization of the notion of "length" and as digit exchange rat…
- Nate Soares
- Introduction to Bayes' rule: Odds form
Bayes' rule is simple, if you think in terms of relative odds.
- Eliezer Yudkowsky - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky
- Why argument structure is important
How might we make collaborative truth-seeking both fun and easy?
- Andrea Gallagher
- Problem of fully updated deference
Why moral uncertainty doesn't stop an AI from defending its off-switch.
- Eliezer Yudkowsky
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky
- High-speed intro to Bayes's rule
A high-speed introduction to Bayes's Rule on one page, for the impatient and mathematically adept.
- Eliezer Yudkowsky
- Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- Arbital Blog
Stay up to date on all things Arbital
- Alexei Andreev
- Arbital page
The Arbital is a series of pages.
- Alexei Andreev - Welcome to Arbital
Front page explaining what Arbital is all about.
- Alexei Andreev
- Comprehensive guide to Bayes' Rule
This is an arc that includes all Bayes content.
- Alexei Andreev
wiki
- A quick econ FAQ for AI/ML folks concerned about technological unemployment
Yudkowsky's attempted description of standard economic concepts that he thinks are vital for talking about technological unemployment and related issues.
- Eliezer Yudkowsky - A whirlwind tour
A rapid tour of Eric's thoughts on the accelerator project.
- Eric Bruylant - Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev - Arbital claims are significantly more useful* when they are fairly well-specified and unambiguous**
\* At least 30% more valuable to people sharing models.
** Not lojban level, but with some thoug…
- Eric Bruylant - Arbital should hide probability/approval votes until the user votes
This is to avoid a potential [-anchoring\_effect]. Also, presumably the user would be still be able …
- Alexei Andreev - Arbital: Solving online explanations
An explanation of Arbital's mid-term goals
- Eliezer Yudkowsky - Author's guide to Arbital
How to write intuitive, flexible content on Arbital.
- Alexei Andreev - Bayesian view of scientific virtues
Why is it that science relies on bold, precise, and falsifiable predictions? Because of Bayes' rule, of course.
- Eliezer Yudkowsky - Hexayurt
External resource: http://hexayurt.com/]
- [claim([6x4])]
- [claim([6xf])]
- Eric Rogstad - Requisites for personal growth
A mashup of models
- Toon Alfrink - Rescuing the utility function
If your utility function values 'heat', and then you discover to your horror that there's no ontologically basic heat, switch to valuing disordered kinetic energy. Likewise 'free will' or 'people'.
- Eliezer Yudkowsky - The current message of effective altruism heavily discourages creativity.
Alyssa Vance expands on this point in her [FB post](https://www.facebook.com/alyssamvance/posts/1021…
- Alexei Andreev - The missing step between Zero and Hero
Creating a space for high potential people grow and improve the world at scale.
- Eric Bruylant - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky - Who needs civilization?
The most common difference between my model and that of people I've discussed this with is that many…
- Eric Bruylant
- Why waiting to donate harms charities
A blog post explaining the potential reasons why someone would choose to wait to donate and how that leads to suboptimal outcomes for the charity.
- Alexei Andreev
- Lambda calculus
A minimal, inefficient, and hard-to-read, but still interesting and useful, programming language.
- Dylan Hendrickson - Rice's Theorem: Intro (Math 1)
You can't write a program that looks at another programs source code, and tells you whether it computes the Fibonacci sequence.
- Dylan Hendrickson
- Arbital: learning from Wikipedia
How is Arbital different from Wikipedia?
- Alexei Andreev - Goodhart's Curse
The Optimizer's Curse meets Goodhart's Law. For example, if our values are V, and an AI's utility function U is a proxy for V, optimizing for high U seeks out 'errors'--that is, high values of U - V.
- Eliezer Yudkowsky - Introductory Bayesian problems
Bayesian problems to try to solve yourself, before beginning to learn about Bayes' rule.
- Eliezer Yudkowsky - Practicing Brevity
Wanna save the world? Write better TLDRs. And spend more time respecting your reader's time.
- Raymond Arnold - Why waiting to donate harms charities
A blog post explaining the potential reasons why someone would choose to wait to donate and how that leads to suboptimal outcomes for the charity.
- Alexei Andreev
- Solomonoff induction: Intro Dialogue (Math 2)
An introduction to Solomonoff induction for the unfamiliar reader who isn't bad at math
- Eliezer Yudkowsky
- Frequency diagrams: A first look at Bayes
The most straightforward visualization of Bayes' rule.
- Nate Soares - Mathematical induction
Proving a statement about all positive integers by knocking them down like dominoes.
- Douglas Weathers
- Bayes' rule: Log-odds form
A simple transformation of Bayes' rule reveals tools for measuring degree of belief, and strength of evidence.
- Eliezer Yudkowsky
wiki
- Aligning an AGI adds significant development time
Aligning an advanced AI foreseeably involves extra code and extra testing and not being able to do everything the fastest way, so it takes longer.
- Eliezer Yudkowsky - Bayes' rule: Proportional form
The fastest way to say something both convincing and true about belief-updating.
- Eliezer Yudkowsky - Belief revision as probability elimination
Update your beliefs by throwing away large chunks of probability mass.
- Eliezer Yudkowsky - Function
Intuitively, a function $f$ is a procedure (or machine) that takes an input and performs some opera…
- Nate Soares - Psychologizing
It's sometimes important to consider how other people might be led into error. But psychoanalyzing them is also dangerous! Arbital discussion norms say to explicitly note this as "psychologizing".
- Eliezer Yudkowsky - The ideal Arbital math page
Think of the best math textbook you've ever read -- why was it good?
- Eric Rogstad
- Eigenvalues and eigenvectors
We applied this linear transformation to one of its eigenvectors; you won't believe what happened next!
- Zack M. Davis
- AI alignment
The great civilizational problem of creating artificially intelligent computer systems such that running them is a good idea.
- Eliezer Yudkowsky - List: value-alignment subjects
Bullet point list of core VAT subjects.
- Eliezer Yudkowsky
wiki
- AI safety mindset
Asking how AI designs could go wrong, instead of imagining them going right.
- Eliezer Yudkowsky - AIXI
How to build an (evil) superintelligent AI using unlimited computing power and one page of Python code.
- Eliezer Yudkowsky - Advanced agent properties
How smart does a machine intelligence need to be, for its niceness to become an issue? "Advanced" is a broad term to cover cognitive abilities such that we'd need to start considering AI alignment.
- Eliezer Yudkowsky - Almost all real-world domains are rich
Anything you're trying to accomplish in the real world can potentially be accomplished in a *lot* of different ways.
- Eliezer Yudkowsky - Ambitious vs. narrow value learning
Suppose I’m trying to build an AI system that “learns what I want” and helps me get it. I think tha…
- Paul Christiano - Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev - Arbital playpen
Want to test a feature? Feel free to edit this page! asdfasfdasfda
- Eliezer Yudkowsky - Arbital practices
Guidelines and rules for interacting on Arbital.
- Eliezer Yudkowsky - Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky - Behaviorist genie
An advanced agent that's forbidden to model minds in too much detail.
- Eliezer Yudkowsky - Boxed AI
Idea: what if we limit how AI can interact with the world. That'll make it safe, right??
- Eliezer Yudkowsky - Central examples
The "central examples" for a subject are examples that are referred to over and over again in the co…
- Eliezer Yudkowsky - Central examples
List of central examples in Value Alignment Theory domain.
- Eliezer Yudkowsky - Cognitive uncontainability
'Cognitive uncontainability' is when we can't hold all of an agent's possibilities inside our own minds.
- Eliezer Yudkowsky - Conceivability
A hypothetical scenario is 'conceivable' or 'imaginable' when it is not *immediately* incoherent, al…
- Eliezer Yudkowsky - Consequentialist cognition
The cognitive ability to foresee the consequences of actions, prefer some outcomes to others, and output actions leading to the preferred outcomes.
- Eliezer Yudkowsky - Context disaster
Some possible designs cause your AI to behave nicely while developing, and behave a lot less nicely when it's smarter.
- Eliezer Yudkowsky - Epistemic and instrumental efficiency
An efficient agent never makes a mistake you can predict. You can never successfully predict a directional bias in its estimates.
- Eliezer Yudkowsky - Epistemology
What is truth?
- Eliezer Yudkowsky - Executable philosophy
Philosophical discourse aimed at producing a trustworthy answer or meta-answer, in limited time, which can used in constructing an Artificial Intelligence.
- Eliezer Yudkowsky - Glossary (Value Alignment Theory)
Words that have a special meaning in the context of creating nice AIs.
- Eliezer Yudkowsky - Guarded definition
A guarded definition is one where at least one position suspects there will be pressure to stretch a…
- Eliezer Yudkowsky - Happiness maximizer
It is sometimes proposed that we build an AI intended to maximize human happiness. (One early propo…
- Eliezer Yudkowsky - High-speed intro to Bayes's rule
A high-speed introduction to Bayes's Rule on one page, for the impatient and mathematically adept.
- Eliezer Yudkowsky - Instrumental
What is "instrumental" in the context of Value Alignment Theory?
- Eliezer Yudkowsky - Instrumental convergence
Some strategies can help achieve most possible simple goals. E.g., acquiring more computing power or more material resources. By default, unless averted, we can expect advanced AIs to do that.
- Eliezer Yudkowsky - Instrumental pressure
A consequentialist agent will want to bring about certain instrumental events that will help to fulfill its goals.
- Eliezer Yudkowsky - Intended goal
Definition. An "intended goal" refers to the intuitive intention in the mind of a human programmer …
- Eliezer Yudkowsky - Intension vs. extension
"Red is a light with a wavelength of 700 nm" vs. "Look at this red apple, red car, and red cup."
- Eliezer Yudkowsky - Likelihood functions, p-values, and the replication crisis
What's the whole Bayesian-vs.-frequentist debate about?
- Eliezer Yudkowsky - Link glossary pages for overloaded words
If your subject is using what sound like ordinary-language words in a special sense, create a glossa…
- Eliezer Yudkowsky - List: value-alignment subjects
Bullet point list of core VAT subjects.
- Eliezer Yudkowsky - Logical game
Game's mathematical structure at its purest form.
- Eliezer Yudkowsky - Look where I'm pointing, not at my finger
When trying to communicate the concept "glove", getting the AGI to focus on "gloves" rather than "my user's decision to label something a glove" or "anything that depresses the glove-labeling button".
- Eliezer Yudkowsky - Low impact
The open problem of having an AI carry out tasks in ways that cause minimum side effects and change as little of the rest of the universe as possible.
- Eliezer Yudkowsky - Mathematical induction
Proving a statement about all positive integers by knocking them down like dominoes.
- Douglas Weathers - Methodology of foreseeable difficulties
Building a nice AI is likely to be hard enough, and contain enough gotchas that won't show up in the AI's early days, that we need to foresee problems coming in advance.
- Eliezer Yudkowsky - Methodology of unbounded analysis
What we do and don't understand how to do, using unlimited computing power, is a critical distinction and important frontier.
- Eliezer Yudkowsky - Mindcrime
Might a machine intelligence contain vast numbers of unhappy conscious subprocesses?
- Eliezer Yudkowsky - Omnipotence test for AI safety
Would your AI produce disastrous outcomes if it suddenly gained omnipotence and omniscience? If so, why did you program something that *wants* to hurt you and is held back only by lacking the power?
- Eliezer Yudkowsky - Ontology identification problem: Technical tutorial
Technical tutorial for ontology identification problem.
- Eliezer Yudkowsky - Open subproblems in aligning a Task-based AGI
Open research problems, especially ones we can model today, in building an AGI that can "paint all cars pink" without turning its future light cone into pink-painted cars.
- Eliezer Yudkowsky - Oracle
System designed to safely answer questions.
- Eliezer Yudkowsky - Paperclip maximizer
This agent will not stop until the entire universe is filled with paperclips.
- Eliezer Yudkowsky - Perfect rolling sphere
If you don't understand something, start by assuming it's a perfect rolling sphere.
- Eliezer Yudkowsky - Pivotal event
Which types of AIs, if they work, can do things that drastically change the nature of the further game?
- Eliezer Yudkowsky - Programmer
Who is building these advanced agents?
- Eliezer Yudkowsky - Programmer deception
Programmer deception is when the AI's decision process leads it to optimize for an instrumental goal…
- Eliezer Yudkowsky - Rationality
The subject domain for [ epistemic] and [ instrumental] rationality.
- Eliezer Yudkowsky - Rescuing the utility function
If your utility function values 'heat', and then you discover to your horror that there's no ontologically basic heat, switch to valuing disordered kinetic energy. Likewise 'free will' or 'people'.
- Eliezer Yudkowsky - Rich domain
A domain is 'rich', relative to our own intelligence, to the extent that (1) its [ search space] is …
- Eliezer Yudkowsky - Solomonoff induction
A simple way to superintelligently predict sequences of data, given unlimited computing power.
- Eliezer Yudkowsky - Standard agent properties
What's a Standard Agent, and what can it do?
- Eliezer Yudkowsky - Strained argument
A phenomenological feeling associated with a step of reasoning going from X to Y where it feels like…
- Eliezer Yudkowsky - Sufficiently optimized agents appear coherent
If you could think as well as a superintelligence, you'd be at least that smart yourself.
- Eliezer Yudkowsky - Task-directed AGI
An advanced AI that's meant to pursue a series of limited-scope goals given it by the user. In Bostrom's terminology, a Genie.
- Eliezer Yudkowsky - The empiricist-theorist false dichotomy
No discussion here yet: See https://www.facebook.com/groups/674486385982694/permalink/7846641016315…
- Eliezer Yudkowsky - Utility
What is "utility" in the context of Value Alignment Theory?
- Eliezer Yudkowsky - Vingean uncertainty
You can't predict the exact actions of an agent smarter than you - so is there anything you _can_ say about them?
- Eliezer Yudkowsky - Zermelo-Fraenkel provability oracle
We might be able to build a system that can safely inform us that a theorem has a proof in set theory, but we can't see how to use that capability to save the world.
- Eliezer Yudkowsky
- Comprehensive guide to Bayes' Rule
This is an arc that includes all Bayes content.
- Alexei Andreev - Frequency diagram
Visualizing Bayes' rule by manipulating frequencies in large populations
- Nate Soares
- Arbital features
Overview of all Arbital features.
- Alexei Andreev - Arbital lens
A lens is a page that presents another page's content from a different angle.
- Alexei Andreev - Some men just want to watch the world learn
In which Arbital gets paths.
- Alexei Andreev
wiki
- Arbital scope
What kind of content is Arbital looking for?
- Eric Bruylant - Arbital: learning from Wikipedia
How is Arbital different from Wikipedia?
- Alexei Andreev - Epistemic and instrumental efficiency
An efficient agent never makes a mistake you can predict. You can never successfully predict a directional bias in its estimates.
- Eliezer Yudkowsky - Factorial
The number of ways you can order things. (Alternately subtitled: Is that exclamation point a factorial, or are you just excited to see me?)
- Michael Cohen - Mindcrime: Introduction
The more predictive accuracy we want from a model, the more detailed the model becomes. A very roug…
- Eliezer Yudkowsky - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- Odds
Odds express a relative probability.
- Eliezer Yudkowsky
wiki
- Algebraic structure tree
When is a monoid a semilattice? What's the difference between a semigroup and a groupoid? Find out here!
- Ryan Hendrickson - Category theory
How mathematical objects are related to others in the same category.
- Mark Chimes
- Bayes' rule: Odds form
The simplest and most easily understandable form of Bayes' rule uses relative odds.
- Eliezer Yudkowsky - Introductory Bayesian problems
Bayesian problems to try to solve yourself, before beginning to learn about Bayes' rule.
- Eliezer Yudkowsky
wiki
- 0.999...=1
No, it's not "infinitesimally far" from 1 or anything like that. 0.999... and 1 are literally the same number.
- Dylan Hendrickson - A googolplex
A moderately large number, as large numbers go.
- Nate Soares - A-Class
This page is well-written, high-quality, and essentially complete.
- Eric Bruylant - Accelerator Project
The Accelerator Project aims to create a low-cost environment which facilitates rapid personal growt…
- Eric Bruylant - Ackermann function
The slowest-growing fast-growing function.
- Alex Appel - Algebraic structure
Roughly speaking, an algebraic structure is a set $X$, known as the underlying set, paired with a co…
- Nate Soares - Algebraic structure tree
When is a monoid a semilattice? What's the difference between a semigroup and a groupoid? Find out here!
- Ryan Hendrickson - Algorithmic complexity
When you compress the information, what you are left with determines the complexity.
- Eliezer Yudkowsky - Aligning an AGI adds significant development time
Aligning an advanced AI foreseeably involves extra code and extra testing and not being able to do everything the fastest way, so it takes longer.
- Eliezer Yudkowsky - Alternating group
The alternating group is the only normal subgroup of the symmetric group (on five or more generators).
- Patrick Stevens - An introductory guide to modern logic
Logic, provability, Löb, Gödel and more!
- Jaime Sevilla Molina - Approaches to strategic disagreement
Organizations self-select staff to agree with their strategies. By default, this causes them to sacrifice the fulfillment of others' plans. How can we resolve these strategic disagreements?
- Ryan Carey - Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev - Arbital "parent" relationship
Parent-child relationship between pages implies a strong, inseparable connection.
- Alexei Andreev - Arbital "requires" relationship
A page can require a requisite if the reader needs to have it before they are able to understand the page.
- Alexei Andreev - Arbital "tag" relationship
Tags are a way to connect pages that share a common topic.
- Alexei Andreev - Arbital "teaches" relationship
A page can teach a requisite when the user can acquire it by reading the page.
- Alexei Andreev - Arbital Labs
Landing page for the Arbital Labs domain.
- Alexei Andreev - Arbital Markdown
All about Arbital's extended Markdown syntax.
- Alexei Andreev - Arbital Slack
Where the cool kids hang out.
- Eric Bruylant - Arbital as single conversational locus
Proposal and outline of Arbital's steps to create a single conversational locus.
- Alexei Andreev - Arbital comment
A comment is a way for you to express your thoughts and opinions within the context of a page.
- Alexei Andreev - Arbital community input
Do you have ideas about how to improve Arbital which you think the community should discuss?
- Alexei Andreev - Arbital content license
What license does Arbital use for its content?
- Alexei Andreev - Arbital domain
What is a domain? Why is it important?
- Alexei Andreev - Arbital features
Overview of all Arbital features.
- Alexei Andreev - Arbital greenlink
What happens when you hover over an Arbital link?
- Alexei Andreev - Arbital groups
What are groups? How can I create a new group?
- Alexei Andreev - Arbital lens
A lens is a page that presents another page's content from a different angle.
- Alexei Andreev - Arbital likes
What are likes? When should I use them? What happens when I like something?
- Alexei Andreev - Arbital page
The Arbital is a series of pages.
- Alexei Andreev - Arbital page clickbait
The text you are reading right now is clickbait.
- Eric Rogstad - Arbital page summaries
Because only one summary is not enough!
- Alexei Andreev - Arbital playpen
Want to test a feature? Feel free to edit this page! asdfasfdasfda
- Eliezer Yudkowsky - Arbital practices
Guidelines and rules for interacting on Arbital.
- Eliezer Yudkowsky - Arbital projects
Arbital projects are small-scale drives to fill in areas of content.
- Eric Bruylant - Arbital requisites
To understand a thing you often need to understand some other things.
- Alexei Andreev - Arbital reviewer
Reviewers help writers improve their pages, check over all changes to Arbital's content, and assess page quality.
- Eric Bruylant - Arbital scope
What kind of content is Arbital looking for?
- Eric Bruylant - Arbital trusted user
Trusted users can edit most pages directly, and don't need approval to add pages to a domain.
- Eric Bruylant - Arbital unlisted page
What do you call a page that's not part of any domain?
- Alexei Andreev - Arbital user groups
Users can attain different powers and responsibilities on Arbital.
- Eric Bruylant - Arbital: Google Maps for knowledge
Take your understanding from where it is to where it wants to be.
- Alexei Andreev - Arbital: Solving online explanations
An explanation of Arbital's mid-term goals
- Eliezer Yudkowsky - Arbital: better blogging
What makes Arbital the choice blogging platform?
- Alexei Andreev - Arbital: fixing online discussion
How can Arbital do better than existing discussion platforms?
- Alexei Andreev - Arbital: information hub
How will Arbital help you keep up to date on any given subject?
- Alexei Andreev - Arbital: learning from Wikipedia
How is Arbital different from Wikipedia?
- Alexei Andreev - Arithmetic of rational numbers (Math 0)
How do we combine rational numbers together?
- Patrick Stevens - Arithmetical hierarchy
The arithmetical hierarchy is a way of classifying logical statements by the number of clauses saying "for every object" and "there exists an object".
- Eliezer Yudkowsky - Arithmetical hierarchy: If you don't read logic
The arithmetical hierarchy is a way of stratifying statements by how many "for every number" and "th…
- Eliezer Yudkowsky - Arity (of a function)
The arity of a function is the number of parameters that it takes. For example, the function $f(a, b…
- Nate Soares - Associative operation
An **associative operation** $\bullet : X \times X \to X$ is a binary operation such that for all $x…
- Nate Soares - Associativity vs commutativity
Associativity and commutativity are often confused, because they are both constraints on how a funct…
- Nate Soares - Associativity: Examples
Yes: [Addition], [multiplication], string concatenation. No: [subtraction], [division], a Function …
- Nate Soares - Associativity: Intuition
Associative functions can be interpreted as families of functions that reduce lists down to a singl…
- Nate Soares - Author's guide to Arbital
How to write intuitive, flexible content on Arbital.
- Alexei Andreev - Averting the convergent instrumental strategy of self-improvement
We probably want the first AGI to *not* improve as fast as possible, but improving as fast as possible is a convergent strategy for accomplishing most things.
- Eliezer Yudkowsky - Axiom
An **axiom** of a [theory\_mathematics theory] $T$ is a [well\_formed well-formed] [sentence\_mathem…
- Eric Bruylant - Axiom of Choice
The most controversial axiom of the 20th century.
- Mark Chimes - Axiom of Choice: History and Controversy
Really? The *most* controversial axiom of the 20th century? Yes.
- Mark Chimes - B-Class
This page is mostly complete and without major problems, but has not had detailed feedback from the target audience and reviewers.
- Eric Bruylant - Bag
In mathematics, a "bag" is an unordered list. A bag differs from a set in that it can contain the sa…
- Nate Soares - Bayes' rule
Bayes' rule is the core theorem of probability theory saying how to revise our beliefs when we make a new observation.
- Eliezer Yudkowsky - Bayes' rule: Definition
Bayes' rule is the mathematics of probability theory governing how to update your beliefs in the lig…
- Nate Soares - Bayes' rule: Functional form
Bayes' rule for to continuous variables.
- Eliezer Yudkowsky - Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky - Bayes' rule: Log-odds form
A simple transformation of Bayes' rule reveals tools for measuring degree of belief, and strength of evidence.
- Eliezer Yudkowsky - Bayes' rule: Probability form
The original formulation of Bayes' rule.
- Nate Soares - Bayes' rule: Proportional form
The fastest way to say something both convincing and true about belief-updating.
- Eliezer Yudkowsky - Bayes' rule: Vector form
For when you want to apply Bayes' rule to lots of evidence and lots of variables, all in one go. (This is more or less how spam filters work.)
- Eliezer Yudkowsky - Bayesian reasoning
A probability-theory-based view of the world; a coherent way of changing probabilistic beliefs based on evidence.
- Eliezer Yudkowsky - Bayesian update
Bayesian updating: the ideal way to change probabilistic beliefs based on evidence.
- Eliezer Yudkowsky - Bayesian view of scientific virtues
Why is it that science relies on bold, precise, and falsifiable predictions? Because of Bayes' rule, of course.
- Eliezer Yudkowsky - Belief revision as probability elimination
Update your beliefs by throwing away large chunks of probability mass.
- Eliezer Yudkowsky - Bijective Function: Intro (Math 0)
Two boxes are bijective if they contain the same number of items.
- Mark Chimes - Bijective function
A bijective function is a function with an inverse.
- Patrick Stevens - Binary notation
A way to write down numbers using powers of two.
- Malcolm McCrimmon - Bit
The term "bit" refers to different concepts in different fields. The common theme across all the us…
- Nate Soares - Bit (abstract)
An abstract bit is an element of the set $\mathbb B$, which has two elements. An abstract bit is to …
- Nate Soares - Bit (of data)
A bit of data is the amount of data required to single out one message from a set of two. Equivalen…
- Nate Soares - Boolean
A value in logic that evaluates to either "true" or "false".
- Malcolm McCrimmon - Bézout's theorem
Bézout's theorem is an important link between highest common factors and the integer solutions of a certain equation.
- Patrick Stevens - C-Class
This page has substantial content, but may not thoroughly cover the topic, may not meet style and prose standards, or may not explain the concept in a way the target audience will reliably understand.
- Eric Bruylant - Cardinality
The "size" of a set, or the "number of elements" that it has.
- Joe Zeng - Category (mathematics)
A description of how a collection of mathematical objects are related to one another.
- Mark Chimes - Category theory
How mathematical objects are related to others in the same category.
- Mark Chimes - Cauchy's theorem on subgroup existence: intuitive version
Cauchy's Theorem states that if $G$ is a finite [-group], and $p$ is a prime dividing the order of $…
- Patrick Stevens - Church-Turing thesis
A thesis about computational models
- Jaime Sevilla Molina - Church-Turing thesis: Evidence for the Church-Turing thesis
Why do we believe in CT thesis?
- Jaime Sevilla Molina - Codomain vs image
It is useful to distinguish codomain from image both (a) when the type of thing that the function pr…
- Nate Soares - Coherent extrapolated volition (alignment target)
A proposed direction for an extremely well-aligned autonomous superintelligence - do what humans would want, if we knew what the AI knew, thought that fast, and understood ourselves.
- Eliezer Yudkowsky - Commutativity: Examples
Yes: addition, multiplication, maximum, minimum, rock-paper-scissors. No: subtraction, division, st…
- Nate Soares - Commutativity: Intuition
We can think of commutativity either as an artifact of notation, or as a symmetry in the output of a…
- Nate Soares - Complete lattice
A poset that is closed under arbitrary joins and meets.
- Kevin Clancy - Complex number
A complex number is a number of the form $z = a + b\textrm{i}$, where $\textrm{i}$ is the imaginary …
- Eliana Ruby - Complexity theory
Study of the computational resources needed to compute something
- Jaime Sevilla Molina - Conceivability
A hypothetical scenario is 'conceivable' or 'imaginable' when it is not *immediately* incoherent, al…
- Eliezer Yudkowsky - Concept
Add this meta tag to pages which are concepts.
- Alexei Andreev - Consequentialist preferences are reflectively stable by default
Gandhi wouldn't take a pill that made him want to kill people, because he knows in that case more people will be murdered. A paperclip maximizer doesn't want to stop maximizing paperclips.
- Eliezer Yudkowsky - Contributing to Arbital
Want to help Arbital become awesome?
- Eric Bruylant - Convex function
A function that only curves upward
- Jessica Taylor - Convex set
A set that contains all line segments between points in the set
- Jessica Taylor - Countability
Some infinities are bigger than others. Countable infinities are the smallest infinities.
- Alexei Andreev - Creating a /learn/ link
What options are available when creating a /learn/ link?
- Alexei Andreev - Crony beliefs (from Melting Asphalt)
The original article that introduced and explained "merit beliefs" vs "crony beliefs" dichotomy.
- Alexei Andreev - Currying
Transforms a function of many arguments into a function into a function of a single argument
- M Yass - Cycle notation in symmetric groups
Cycle notation is a convenient way to represent the elements of a symmetric group.
- Patrick Stevens - Cycle type of a permutation
The cycle type is an invariant of a permutation in the symmetric group.
- Patrick Stevens - Cyclic Group Intro (Math 0)
A finite cyclic group is a little bit like a clock.
- Mark Chimes - Death in Damascus
Death tells you that It is coming for you tomorrow. You can stay in Damascus or flee to Aleppo. Whichever decision you actually make is the wrong one. This gives some decision theories trouble.
- Eliezer Yudkowsky - Decimal notation
The winning architecture for numerals
- Michael Cohen - Decision problem
Formalization of general problems
- Jaime Sevilla Molina - Decit
Decimal digit
- Nate Soares - Definition
Meta tag used to mark pages that strictly define a particular term or phrase.
- Eliezer Yudkowsky - Dependent messages can be encoded cheaply
Say you want to transmit a 2-message, a 4-message, and a 256-message to somebody. For example, you m…
- Nate Soares - Derivative
How things change
- Michael Cohen - Dihedral group
The dihedral groups are natural examples of groups, arising from the symmetries of regular polygons.
- Patrick Stevens - Discussion norms
What makes conversation productive?
- Eric Rogstad - Do-What-I-Mean hierarchy
Successive levels of "Do What I Mean" or AGIs that understand their users increasingly well
- Eliezer Yudkowsky - Easier, better, faster, brighter
In which Arbital gets a makeover, shortcuts, quick feedback, and more!
- Alexei Andreev - Edge instantiation
When you ask the AI to make people happy, and it tiles the universe with the smallest objects that can be happy.
- Eliezer Yudkowsky - Elementary Algebra
How do we describe relations between different things? How can we figure out new true things from tr…
- Adele Lopez - Eliezer's vision for Arbital
Why are we building this? What's the goal?
- Eric Bruylant - Empirical probabilities are not exactly 0 or 1
"Cromwell's Rule" says that probabilities of exactly 0 or 1 should never be applied to empirical propositions - there's always some probability, however tiny, of being mistaken.
- Eliezer Yudkowsky - Empty set
The empty set, $\emptyset$, is the set with no elements. For every object $x$, $x$ is not in $\empt…
- Patrick Stevens - Epistemic and instrumental efficiency
An efficient agent never makes a mistake you can predict. You can never successfully predict a directional bias in its estimates.
- Eliezer Yudkowsky - Equaliser (category theory)
In Category theory, an *equaliser* of a pair of arrows $f, g: A \to B$ is an object $E$ and a univer…
- Patrick Stevens - Equivalence relation
A relation that allows you to partition a set into equivalence classes.
- Dylan Hendrickson - Euclidean domains are principal ideal domains
A Euclidean domain is one where we may somehow perform the division algorithm; this gives us access to some of the nicest properties of the integers.
- Patrick Stevens - Every group is a quotient of a free group
Given a group $G$, there is a Free group $F(X)$ on some set $X$, such that $G$ is isomorphic to some…
- Patrick Stevens - Every member of a symmetric group on finitely many elements is a product of transpositions
This fact can often simplify arguments about permutations: if we can show that something holds for transpositions, and that it holds for products, then it holds for everything.
- Patrick Stevens - Exchange rates between digits
In terms of data storage, if a coin is worth $1, a digit wheel is worth more than $3.32, but less than $3.33. Why?
- Nate Soares - Expected value
Trying to assign value to an uncertain state? The weighted average of outcomes is probably the tool you need.
- Michael Cohen - Explicit Bayes as a counter for 'worrying'
Explicitly walking through Bayes's Rule can summarize your knowledge and thereby stop you from bouncing around pieces of it.
- Eliezer Yudkowsky - Exponential
Any function that constantly gets larger as a proportion of itself.
- Joe Zeng - Exponential notation for function spaces
Why $Y^X$ is good notation for the space of maps from $X$ to $Y$
- Izaak Meckler - Externality
Positive and negative affects on third parties, and the considerations they introduce
- Silas Barta - Extraordinary claims
What makes something an 'extraordinary claim' that requires extraordinary evidence?
- Eliezer Yudkowsky - Extraordinary claims require extraordinary evidence
The people who adamantly claim they were abducted by aliens do provide some evidence for aliens. They just don't provide quantitatively enough evidence.
- Eliezer Yudkowsky - Factorial
The number of ways you can order things. (Alternately subtitled: Is that exclamation point a factorial, or are you just excited to see me?)
- Michael Cohen - Factorial
The *factorial* of a number $n$ is how we describe "how many different ways we can arrange $n$ obje…
- Patrick Stevens - Featured math content
Some Arbital pages we think are great!
- Eric Bruylant - Fixed point theorem of provability logic
Deal with those pesky self-referential sentences!
- Jaime Sevilla Molina - For mitigating AI x-risk, an off-Earth colony would be about as useful as a warm scarf
H/T to Eliezer Yudkowsky for ["warm scarf"](https://www.facebook.com/robert.wiblin/posts/75711126783…
- Eric Rogstad - Formal definition
This page gives a purely formal definition of a topic, rather than motivating, explaining, and giving examples.
- Eric Bruylant - Formal definition of the free group
Van der Waerden's trick lets us define the free groups in a slick but mostly incomprehensible way.
- Patrick Stevens - Formatting issues
This page has formatting or mathjax issues.
- Eric Bruylant - Fractional bits: Expected cost interpretation
In the GalCom thought experiment, you regularly have to send large volumes of information through de…
- Nate Soares - Fractional digits
When $b$ and $x$ are integers, $\log_b(x)$ has a few good interpretations. It's roughly the length o…
- Nate Soares - Free group
The free group is "the purest way to make a group containing a given set".
- Patrick Stevens - Free group universal property
The Free group may be defined by a Universal property, allowing Category theory to talk about free …
- Patrick Stevens - Freely reduced word
"Freely reduced" captures the idea of "no cancellation" in a free group.
- Patrick Stevens - Function
Intuitively, a function $f$ is a procedure (or machine) that takes an input and performs some opera…
- Nate Soares - Function: Physical metaphor
Many functions can be visualized as physical mechanisms of wheels and gears, that take their inputs …
- Nate Soares - Fundamental Theorem of Arithmetic
The FTA tells us that natural numbers can be decomposed uniquely into prime factors; it is the basis of almost all number theory.
- Patrick Stevens - GalCom
In the GalCom thought experiment, you live in the future, and make your money by living in the Dene…
- Nate Soares - Generalized element
A category-theoretic generalization of the notion of element of a set.
- Luke Sciarappa - Geometric product
#Motivation
want to incorporate rotors like $e^{\text{I}\theta}$ and scalars $n$ in the same system
…
- Adele Lopez - Geometry of vectors: direction
What rotation would it take to line up this vector to this one?
- Adele Lopez - Goodness estimate biaser
Some of the main problems in AI alignment can be seen as scenarios where actual goodness is likely to be systematically lower than a broken way of estimating goodness.
- Eliezer Yudkowsky - Greatest lower bound in a poset
The greatest lower bound is an abstraction of the idea of the greatest common divisor to a general poset.
- Patrick Stevens - Group
The algebraic structure that captures symmetry, relationships between transformations, and part of what multiplication and addition have in common.
- Nate Soares - Group conjugate
Conjugation lets us perform permutations "from the point of view of" another permutation.
- Patrick Stevens - Group coset
Given a subgroup $H$ of Group $G$, the *left cosets* of $H$ in $G$ are sets of the form $\{ gh : h \…
- Patrick Stevens - Group homomorphism
A group homomorphism is a "function between groups" that "respects the group structure".
- Patrick Stevens - Group isomorphism
"Isomorphism" is the proper notion of "sameness" or "equality" among groups.
- Patrick Stevens - Group orbit
When we have a group acting on a set, we are often interested in how the group acts on a particular …
- Adele Lopez - Group orbits partition
When a group acts on a set, the set falls naturally into distinct pieces, where the group action only permutes elements within any given piece, not between them.
- Patrick Stevens - Group presentation
Presentations are a fairly compact way of expressing groups.
- Patrick Stevens - Groups as symmetires
A group is an abstraction of a collection of symmetries of an object. Examples of groups include th…
- Daniel Satanove - Guarded definition
A guarded definition is one where at least one position suspects there will be pressure to stretch a…
- Eliezer Yudkowsky - Gödel encoding and self-reference
The formalism that mathematicians use to talk about arithmetic turns out to be able to talk about itself.
- Patrick LaVictoire - Hard problem of corrigibility
Can you build an agent that reasons as if it knows itself to be incomplete and sympathizes with your wanting to rebuild or correct it?
- Eliezer Yudkowsky - High-speed intro to Bayes's rule
A high-speed introduction to Bayes's Rule on one page, for the impatient and mathematically adept.
- Eliezer Yudkowsky - How to author on Arbital!
Want to contribute pages to Arbital? Here's our current version of the ad-hoc guide to being an author!
- Eliezer Yudkowsky - Hub page
This tag is applied to pages which server the role of a "hub": the user starts there, goes off to learn more about the topic, and then comes back. This meta tag modifies the page's UI.
- Alexei Andreev - Humans doing Bayes
The human use of Bayesian reasoning in everyday life
- Eliezer Yudkowsky - Identity element
An element in a set with a binary operation that leaves every element unchanged when used as the other operand.
- Joe Zeng - Iff
If and only if...
- Alexei Andreev - Information
Information is a measure of how much a message grants an observer the ability to predict the world.…
- Nate Soares - Injective function
A Function $f: X \to Y$ is *injective* if it has the property that whenever $f(x) = f(y)$, it is the…
- Patrick Stevens - Instrumental convergence
Some strategies can help achieve most possible simple goals. E.g., acquiring more computing power or more material resources. By default, unless averted, we can expect advanced AIs to do that.
- Eliezer Yudkowsky - Integer
An **integer** is a Number that can be represented as either a Natural number or its [-additive\_inv…
- Michael Cohen - Integers: Intro (Math 0)
The integers are the whole numbers extended into the negatives.
- Joe Zeng - Intentional Communities wiki pages
A categorized, handpicked list of articles relevant to the Accelerator project
- Toon Alfrink - Intersection
The intersection of two sets is the set of elements they have in common
- M Yass - Intradependent encoding
An encoding $E(m)$ of a message $m$ is intradependent if the fact that $E(m)$ encodes $m$ can be de…
- Nate Soares - Intradependent encodings can be compressed
Given an encoding scheme $E$ which gives an Intradependent encoding of a message $m,$ we can in prin…
- Nate Soares - Intro to Number Sets
An introduction to number sets for people who have no idea what a number set is.
- Joe Zeng - Introduction to Bayes' rule: Odds form
Bayes' rule is simple, if you think in terms of relative odds.
- Eliezer Yudkowsky - Introduction to Logical Decision Theory for Computer Scientists
'Logical decision theory' from a math/programming standpoint, including how two agents with mutual knowledge of each other's code can cooperate on the Prisoner's Dilemma.
- Eliezer Yudkowsky - Introductory guide to logarithms
Welcome to the Arbital introduction to logarithms! In modern education, logarithms are often mention…
- Nate Soares - Inverse function
The inverse of a function returns an input of the original function when fed the original's corresponding output.
- Michael Cohen - Irrational number
Real numbers that are not rational numbers
- Joe Zeng - Irreducible element (ring theory)
This is the appropriate abstraction of the concept of "prime number" to general rings.
- Patrick Stevens - Isomorphism
A morphism between two objects which describes how they are "essentially equivalent" for the purposes of the theory under consideration.
- Mark Chimes - Isomorphism: Intro (Math 0)
Things which are basically the same, except for some stuff you don't care about.
- Mark Chimes - Join and meet
Let $\langle P, \leq \rangle$ be a poset, and let $S \subseteq P$. The **join** of $S$ in $P$, deno…
- Kevin Clancy - Join and meet: Examples
A union of sets and the least common multiple of a set of natural numbers can both be viewed as join…
- Kevin Clancy - Kernel of group homomorphism
The kernel of a Group homomorphism $f: G \to H$ is the collection of all elements $g$ in $G$ such th…
- Patrick Stevens - Kernel of ring homomorphism
The kernel of a ring homomorphism is the collection of things which that homomorphism sends to 0.
- Patrick Stevens - Kripke model
The semantics of modal logic
- Jaime Sevilla Molina - Lagrange theorem on subgroup size
Lagrange's Theorem is an important restriction on the sizes of subgroups of a finite group.
- Patrick Stevens - Lagrange theorem on subgroup size: Intuitive version
Lagrange's theorem strongly restricts the size a subgroup of a group can be.
- Patrick Stevens - Lattice (Order Theory)
A poset that is closed under binary joins and meets.
- Kevin Clancy - Left cosets partition the parent group
In a group, every element has a unique coset in which it lies, allowing us to compress some of the information about the group.
- Patrick Stevens - Life in logspace
The log lattice hints at the reason that engineers, scientists, and AI researchers find logarithms s…
- Nate Soares - Likelihood
"Likelihood", when speaking of Bayesian reasoning, denotes *the probability of an observation, sup…
- Nate Soares - Likelihood function
Let's say you have a piece of evidence $e$ and a set of hypotheses $\mathcal H.$ Each $H_i \in \math…
- Nate Soares - Likelihood ratio
Given a piece of evidence $e$ and two hypothsese $H_i$ and $H_j,$ the likelihood ratio between them…
- Nate Soares - List
A list is an ordered collection of objects, such as `[0, 1, 2, 3]` or `["red", "blue", 0, "shoe"]`. …
- Nate Soares - List of Eliezer's current most desired fixes and features
A place for Eliezer to note down his current list of personally-wanted features for editing and writing.
- Eliezer Yudkowsky - Log as generalized length
To estimate the log (base 10) of a number, count how many digits it has.
- Nate Soares - Log as the change in the cost of communicating
When interpreting logarithms as a generalization of the notion of "length" and as digit exchange rat…
- Nate Soares - Log base infinity
There is no log base infinity, but if there were, it would send everything to zero
- Nate Soares - Logarithm
The logarithm base $b$ of a number $n,$ written $\log_b(n),$ is the answer to the question "how man…
- Nate Soares - Logarithm base 1
There is no log base 1.
- Nate Soares - Logarithm tutorial overview
The logarithm tutorial covers the following six subjects:
1. What are logarithms?
2. Logarithms as…
- Nate Soares - Logarithmic identities
- [ Inversion of exponentials]: $b^{\log_b(n)} = \log_b(b^n) = n.$
- [ Log of 1 is 0]: $\log_b(1) …
- Nate Soares - Logarithms invert exponentials
The function $\log_b(\cdot)$ inverts the function $b^{(\cdot)}.$ In other words, $\log_b(n) = x$ imp…
- Nate Soares - Logical decision theories
Root page for topics on logical decision theory, with multiple intros for different audiences.
- Eliezer Yudkowsky - Logical system
Logical systems (a.k.a. formal systems) are mathematical abstractions that aim to capture the notion…
- Jaime Sevilla Molina - Logistic function
A monotonic function from the real numbers to the open unit interval.
- Joe Zeng - Löb's theorem
Löb's theorem
- Jaime Sevilla Molina - Math 0
Are you not actively bad at math, nor traumatized about math?
- Eliezer Yudkowsky - Math 2
Do you work with math on a fairly routine basis? Do you have little trouble grasping abstract structures and ideas?
- Eliezer Yudkowsky - Math style guidelines
Stylistic conventions specific to pages about math.
- Dylan Hendrickson - Mathematical induction
Proving a statement about all positive integers by knocking them down like dominoes.
- Douglas Weathers - Mathematics
Mathematics is the study of numbers and other ideal objects that can be described by axioms.
- Eliezer Yudkowsky - Meta tags
What are meta tags and when to use them?
- Eliezer Yudkowsky - Metaethics
Metaethics asks "What kind of stuff is goodness made of?" (or "How would we compute goodness?") rather than "Which particular policies or outcomes are good or not-good?"
- Eliezer Yudkowsky - Metric
A metric is a function that defines a distance between elements in a set and follows some basic rules.
- Bryce Woodworth - Modal combat
Modal combat
- Jaime Sevilla Molina - Modal logic
The logic of boxes and bots.
- Jaime Sevilla Molina - Modular arithmetic
Addition as traveling around a circle, instead of along a line.
- Malcolm McCrimmon - Monotone function
An order-preserving map between posets.
- Kevin Clancy - More about Arbital
Lots more information about Arbital vision.
- Alexei Andreev - Morphism
A morphism is the abstract representation of a relation between mathematical objects.
Usually, it i…
- Jaime Sevilla Molina - Most complex things are not very compressible
We can't *prove* it's impossible, but it would be *extremely surprising* to discover a 500-state Turing machine that output the exact text of "Romeo and Juliet".
- Eliezer Yudkowsky - Multiplication of rational numbers (Math 0)
"Multiplication" is the idea of "now do the same as you just did, but instead of doing it to one apple, do it to some other number".
- Patrick Stevens - Mutually exclusive and exhaustive
The condition needed for probabilities to sum to 1
- Eliezer Yudkowsky - Natural numbers: Intro to Number Sets
Natural numbers are the numbers we use to count in everyday life.
- Joe Zeng - Nearest unblocked strategy
If you patch an agent's preference framework to avoid an undesirable solution, what can you expect to happen?
- Eliezer Yudkowsky - Needs exercises
Add this tag to a page which doesn't have enough exercises.
- Alexei Andreev - Needs links
This page could do with more greenlinks.
- Eric Bruylant - Needs parent
This page is not attached to an appropriate parent page. If you know where it should go, please help categorize it!
- Eric Bruylant - Needs requisites
This page has important requisites which are not listed. If you know what they are, you could help add them!
- Eric Bruylant - Needs summary
This page does not have a summary which provides an informative overview of the page's primary topic.
- Alexei Andreev - Newcomb's Problem
There are two boxes in front of you, Box A and Box B. You can take both boxes, or only Box B. Box A contains $1000. Box B contains $1,000,000 if and only if Omega predicted you'd take only Box B.
- Eliezer Yudkowsky - Newcomblike decision problems
Decision problems in which your choice correlates with something other than its physical consequences (say, because somebody has predicted you very well) can do weird things to some decision theories.
- Eliezer Yudkowsky - Nonperson predicate
If we knew which computations were definitely not people, we could tell AIs which programs they were definitely allowed to compute.
- Eliezer Yudkowsky - Normal subgroup
Normal subgroups are subgroups which are in some sense "the same from all points of view".
- Patrick Stevens - Now I am become Life, the protector of worlds
In which Arbital is brought forth into the world.
- Alexei Andreev - Odds
Odds express a relative probability.
- Eliezer Yudkowsky - Odds form to probability form
The odds form of Bayes' rule works for any two hypotheses $H_i$ and $H_j,$ and looks like this:
$$\…
- Nate Soares - On the importance of Less Wrong, or another single conversational locus
In this post, Anna Salamon talks about how Less Wrong used to a locus of discussion, and that it is…
- Alexei Andreev - Operations in Set theory
An operation in set theory is a Function of two sets, that returns a set.
Common set operations inc…
- M Yass - Operator
An operation $f$ on a set $S$ is a function that takes some values from $S$ and produces a new value…
- Nate Soares - Optimization daemons
When you optimize something so hard that it crystalizes into an optimizer, like the way natural selection optimized apes so hard they turned into human-level intelligences
- Eliezer Yudkowsky - Orbit-Stabiliser theorem: External Resources
External resources on the Orbit-Stabiliser theorem.
- Mark Chimes - Orbit-stabiliser theorem
The Orbit-Stabiliser theorem tells us a lot about how a group acts on a given element.
- Patrick Stevens - Order of a group element
Given an element $g$ of group $(G, +)$ (which henceforth we abbreviate simply as $G$), the order of …
- Patrick Stevens - Order of operations
Conventions used for disambiguating infix notation.
- Joe Zeng - Order relation
A way of determining which elements of a set come "before" or "after" other elements.
- Joe Zeng - Ordered ring
A ring with a total ordering compatible with its ring structure.
- Dylan Hendrickson - Ordinary claims require ordinary evidence
Extraordinary claims require extraordinary evidence, but ordinary claims *don't*.
- Nate Soares - Out of date
Meta tag used when the page has a lot of information that's obsolete
- Alexei Andreev - P (Polynomial Time Complexity Class)
P is the class of problems which can be solved by algorithms whose run time is bounded by a polynomial.
- Eric Leese - Paperclip maximizer
This agent will not stop until the entire universe is filled with paperclips.
- Eliezer Yudkowsky - Parfit's Hitchhiker
You are dying in the desert. A truck-driver who is very good at reading faces finds you, and offers to drive you into the city if you promise to pay $1,000 on arrival. You are a selfish rationalist.
- Eliezer Yudkowsky - Partial function
A partial function is one which "might not be defined everywhere one might expect it to be".
- Patrick Stevens - Partially ordered set
A set endowed with a relation that is reflexive, transitive, and antisymmetric.
- Kevin Clancy - Perfect rolling sphere
If you don't understand something, start by assuming it's a perfect rolling sphere.
- Eliezer Yudkowsky - Pi is irrational
The number pi is famously not rational, in spite of joking attempts at legislation to fix its value at 3 or 22/7.
- Patrick Stevens - Pivotal event
Which types of AIs, if they work, can do things that drastically change the nature of the further game?
- Eliezer Yudkowsky - Poset: Examples
The standard $\leq$ relation on integers, the $\subseteq$ relation on sets, and the $|$ (divisibilit…
- Kevin Clancy - Poset: Exercises
Try these exercises to test your poset knowledge.
# Corporate Ladder
Imagine a company with five …
- Kevin Clancy - Posterior probability
What we believe, after seeing the evidence and doing a Bayesian update.
- Eliezer Yudkowsky - Predictions For 2017
Scott Alexander made 105 predictions for 2017. Most of them are not personal and are listed below. …
- Alexei Andreev - Prime number
The prime numbers are the "building blocks" of the counting numbers.
- Patrick Stevens - Prime order groups are cyclic
This is the first step on the road to classifying the finite groups.
- Patrick Stevens - Principal ideal domain
A principal ideal domain is a kind of ring, in which all ideals have a certain nice form.
- Patrick Stevens - Prior
A state of prior knowledge, before seeing information on a new problem. Potentially complicated.
- Eliezer Yudkowsky - Prior probability
What we believed before seeing the evidence.
- Eliezer Yudkowsky - Probability
The degree to which someone believes something, measured on a scale from 0 to 1, allowing us to do math to it.
- Eliezer Yudkowsky - Probability distribution: Motivated definition
People keep writing things like P(sick)=0.3. What does this mean, on a technical level?
- Nate Soares - Probability notation for Bayes' rule: Intro (Math 1)
How to read, and identify, the probabilities in Bayesian problems.
- Eliezer Yudkowsky - Product (Category Theory)
How a product is characterized rather than how it's constructed
- Mark Chimes - Project outline: Intro to the Universal Property
Outline detailing all the work required for a proposed Arbital Project
- Eric Rogstad - Project proposal: Intro to the Universal Property
Proposal for one of the first Arbital Projects.
- Patrick Stevens - Proof by contradiction
Discover what 'reductio ad absurdum' means!
- Jaime Sevilla Molina - Proof of Bayes' rule
Proofs of Bayes' rule, with graphics
- Eliezer Yudkowsky - Proof of Bayes' rule: Probability form
Let $\mathbf H$ be a [random\_variable variable] in $\mathbb P$ for the true hypothesis, and let $H_…
- Nate Soares - Proof of Löb's theorem
Proving that I am Santa Claus
- Jaime Sevilla Molina - Proof of Rice's theorem
A standalone proof of Rice's theorem, including one surprising lemma.
- Patrick Stevens - Proof that there are infinitely many primes
Suppose there were finitely many primes. Then consider the product of all the primes plus 1...
- Joe Zeng - Properties of the logarithm
- $\log_b(x \cdot y) = \log_b(x) + \log_b(y)$ for any $b$, this is the defining characteristic of …
- Nate Soares - Proportion
A representation of a value as a fraction or multiple of another value.
- Joe Zeng - Provability logic
Learn how to reason about provability!
- Jaime Sevilla Molina - Provability predicate
A provability predicate of a theory $T$ is a formula $P(x)$ with one free variable $x$ such that:
…
- Jaime Sevilla Molina - Quine
A computer program that prints (or does other computations to) its own source code, using indirect self-reference.
- Patrick LaVictoire - Quotient group
Given a group $G$ with operation $\bullet$ and a special kind of subgroup $N \leq G$ called the "no…
- Adele Lopez - Rational number
The rational numbers are "fractions".
- Patrick Stevens - Rational numbers: Intro (Math 0)
The rational numbers are "fractions". While the natural numbers measure the answer to the question …
- Patrick Stevens - Real number (as Cauchy sequence)
There are several ways to construct real numbers; this is the most natural way to use them in computations.
- Patrick Stevens - Real number (as Dedekind cut)
A way to construct the real numbers that follows the intuition of filling in the gaps.
- Joe Zeng - Real numbers are uncountable
The real numbers are uncountable.
- Eric Bruylant - Reflexive relation
A binary relation over some set is **reflexive** when every element of that set is related to itself…
- Ryan Hendrickson - Regex's feedback on site design Feb 15th 2017
Wherein Regex is confused about the current state of things
- Regex Rationalist - Relation
A **relation** is a set of [tuple\_mathematics tuples], all of which have the same [tuple\_arity ar…
- Kevin Clancy - Report likelihoods not p-values: FAQ
This page answers frequently asked questions about the Report likelihoods, not p-values proposal for…
- Nate Soares - Requisites for personal growth
A mashup of models
- Toon Alfrink - Rescuing the utility function
If your utility function values 'heat', and then you discover to your horror that there's no ontologically basic heat, switch to valuing disordered kinetic energy. Likewise 'free will' or 'people'.
- Eliezer Yudkowsky - Rice's Theorem
Rice's Theorem tells us that if we want to determine pretty much anything about the behaviour of an arbitrary computer program, we can't in general do better than just running it.
- Patrick Stevens - Rice's Theorem: Intro (Math 1)
You can't write a program that looks at another programs source code, and tells you whether it computes the Fibonacci sequence.
- Dylan Hendrickson - Rice's theorem and the Halting problem
We will show that Rice's theorem and the the halting problem are equivalent.
#The Halting theorem i…
- Jaime Sevilla Molina - Ring
A ring is a kind of Algebraic structure which we obtain by considering groups as being "things with…
- Nate Soares - Seed
Seeds are outlines of pages. They're not much use for readers, but can help authors.
- Eric Bruylant - Set
An unordered collection of distinct objects.
- Nate Soares - Shannon
The shannon (Sh) is a unit of Information. One shannon is the difference in [info\_entropy entropy] …
- Nate Soares - Shift towards the hypothesis of least surprise
When you see new evidence, ask: which hypothesis is *least surprised?*
- Nate Soares - Solomonoff induction
A simple way to superintelligently predict sequences of data, given unlimited computing power.
- Eliezer Yudkowsky - Solovay's theorems of arithmetical adequacy for GL
Using GL to reason about PA, and viceversa
- Jaime Sevilla Molina - Some men just want to watch the world learn
In which Arbital gets paths.
- Alexei Andreev - Square visualization of probabilities on two events
$$
\newcommand{\true}{\text{True}}
\newcommand{\false}{\text{False}}
\newcommand{\bP}{\mathbb{P}}
…
- Tsvi BT - Square visualization of probabilities on two events: (example) Diseasitis
But it *seems* like the patient with the black tongue depressor has diseasitis...
- Tsvi BT - Standard provability predicate
Encoding provability as a statement of arithmetic
- Jaime Sevilla Molina - Strictly confused
A hypothesis is strictly confused by the raw data, if the hypothesis did much worse in predicting it than the hypothesis itself expected.
- Eliezer Yudkowsky - Strong Church Turing thesis
A strengthening of the Church Turing thesis
- Jaime Sevilla Molina - Style guidelines
Various stylistic conventions people should follow on Arbital
- Alexei Andreev - Subgroup
A group that lives inside a bigger group.
- Dylan Hendrickson - Subgroup is normal if and only if it is a union of conjugacy classes
A useful way to think about normal subgroups, which meshes with their "closed under conjugation" interpretation.
- Patrick Stevens - Subjective probability
Probability is in the mind, not in the environment. If you don't know whether a coin came up heads or tails, that's a fact about you, not a fact about the coin.
- Eliezer Yudkowsky - Surjective function
A surjective function is one which "hits everything in the codomain".
- Patrick Stevens - Symmetric group
The symmetric groups form the fundamental link between group theory and the notion of symmetry.
- Patrick Stevens - Terminal versus instrumental goals / values / preferences
Distinguish events wanted for their consequences, from events wanted locally.
- Eliezer Yudkowsky - The End (of the basic log tutorial)
That concludes our introductory tutorial on logarithms! You have made it to the end.
Throughout thi…
- Nate Soares - The absentee billionaire
Once each day, Hugh wakes for 10 minutes. During these 10 minutes, he spends 10 million dollars. The…
- Paul Christiano - The alternating group on five elements is simple
The smallest (nontrivial) simple group is the alternating group on five elements.
- Patrick Stevens - The alternating groups on more than four letters are simple
The alternating groups are the most accessible examples of simple groups, and this fact also tells us that the symmetric groups are "complicated" in some sense.
- Patrick Stevens - The characteristic of the logarithm
Any time you find an output that adds whenever the input multiplies, you're probably looking at a (…
- Nate Soares - The current message of effective altruism heavily discourages creativity.
Alyssa Vance expands on this point in her [FB post](https://www.facebook.com/alyssamvance/posts/1021…
- Alexei Andreev - The empty set is the only set which satisfies the universal property of the empty set
This theorem tells us that the universal property provides a sensible way to define the empty set uniquely.
- Patrick Stevens - The ideal Arbital math page
Think of the best math textbook you've ever read -- why was it good?
- Eric Rogstad - The log lattice
Log as the change in the cost of communicating and other pages give physical interpretations of what…
- Nate Soares - The reals (constructed as classes of Cauchy sequences of rationals) form a field
The reals are an archetypal example of a field, but if we are to construct them from simpler objects, we need to show that our construction does indeed have the right properties.
- Patrick Stevens - The set of rational numbers is countable
Although there are "lots and lots" of rational numbers, there are still only countably many of them.
- Patrick Stevens - The sign of a permutation is well-defined
This result is what allows the alternating group to exist.
- Patrick Stevens - The square root of 2 is irrational
The number whose square is 2 can't be written is a quotient of natural numbers
- Dylan Hendrickson - There is only one logarithm
All logarithm functions are the same, up to a multiplicative constant.
- Nate Soares - To math explanations and beyond!
In which Arbital doubles down on math explanations.
- Alexei Andreev - Transcendental number
A transcendental number is one which is not the root of any integer-coefficient polynomial.
- Patrick Stevens - Transparent Newcomb's Problem
Omega has left behind a transparent Box A containing $1000, and a transparent Box B containing $1,000,000 or nothing. Box B is full iff Omega thinks you one-box on seeing a full Box B.
- Eliezer Yudkowsky - Transposition (as an element of a symmetric group)
A transposition is the simplest kind of permutation: it swaps two elements.
- Patrick Stevens - Turing machine
A Turing Machine is a simple mathematical model of computation that is powerful enough to describe any computation a computer can do.
- Eric Leese - Two independent events
What do [a pair of dice], [a pair of coins], and [a pair of people on opposite sides of the planet] all have in common?
- Tsvi BT - Two independent events: Square visualization
$$
\newcommand{\true}{\text{True}}
\newcommand{\false}{\text{False}}
\newcommand{\bP}{\mathbb{P}}
…
- Tsvi BT - Uncomputability
The diagonal function and the halting problem
- Jaime Sevilla Molina - Uncountability
Some infinities are bigger than others. Uncountable infinities are larger than countable infinities.
- Jason Gross - Uncountability (Math 3)
Formal definition of uncountability, and foundational considerations.
- Patrick Stevens - Uncountability: Intro (Math 1)
Not all infinities are created equal. The infinity of real numbers is infinitely larger than the infinity of counting numbers.
- Jason Gross - Uncountability: Intuitive Intro
Are all sizes of infinity the same? What does "the same" even mean here?
- Jason Gross - Underlying set
What do a Group, a Partially ordered set, and a [ topological space] have in common? Each is a Set …
- Nate Soares - Unique factorisation domain
This is the correct way to abstract from the integers the fact that every integer can be written uniquely as a product of prime numbers.
- Patrick Stevens - Universal prior
A "universal prior" is a probability distribution containing *all* the hypotheses, for some reasonable meaning of "all". E.g., "every possible computer program that computes probabilities".
- Eliezer Yudkowsky - Universal property of the disjoint union
Just as the empty set may be described by a universal property, so too may the disjoint union of sets.
- Patrick Stevens - Universal property of the empty set
The empty set can be characterised by how it interacts with other sets, rather than by any explicit property of the empty set itself.
- Patrick Stevens - Universal property of the product
The product can be defined in a very general way, applicable to the natural numbers, to sets, to algebraic structures, and so on.
- Patrick Stevens - Up to isomorphism
A phrase mathematicians use when saying "we only care about the structure of an object, not about specific implementation details of the object".
- Patrick Stevens - Utility indifference
How can we make an AI indifferent to whether we press a button that changes its goals?
- Eliezer Yudkowsky - Vector arithmetic
Vectors: what they are, and how to add and scale them.
- Adele Lopez - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky - Welcome to Arbital
Front page explaining what Arbital is all about.
- Alexei Andreev - Well-defined
A mathematical object is "well-defined" if we have given it a completely unambiguous definition.
- Patrick Stevens - What is a logarithm?
Logarithms are a group of functions that take a number as input and produce another number. There i…
- Nate Soares - Whole number
A term that can refer to three different sets of "numbers that are not fractions".
- Joe Zeng - Why is log like length?
If a number $x$ is $n$ digits long (in Decimal notation), then its logarithm (base 10) is between $n…
- Nate Soares - Why is the decimal expansion of log2(3) infinite?
Because 2 and 3 are relatively prime.
- Nate Soares
group
- Alexei Andreev
There is no spoon
- Eliezer Yudkowsky
Cofounder, with Nick Bostrom, of the field of value alignment theory.
- Eric Rogstad
- Jaime Sevilla Molina
- Joe Zeng
- Kevin Clancy
- Malcolm Ocean
- Mark Chimes
- Mars (person)
The planet's nice too, but harder to cuddle with.
- Michael Cohen
- Patrick LaVictoire
Patrick is a Research Fellow at the Machine Intelligence Research Institute. He mainly works on deci…
- Patrick Stevens
- Stephanie Zolayvar
> The notification showed me my post rather than the comment.
Fixed
- Alexei Andreev"has some resistance to Eternal September" -> "is resistant to Eternal September" ?
- Eric Rogstad"identity" is probably not a sufficiently specific link; I'd go for math_identity, probably.
- Patrick StevensAgreed. Blogging will be one of the major areas we focus on after the announcement. (He keeps saying…
- Alexei AndreevAre the *other* tags part of the quality scale?
When a page has the message, "This page's quality i…
- Eric RogstadAre there existing pages that need this tag?
I'm wondering if adding a second, brief summary is the…
- Eric RogstadAre there going to be visual explanations put here for the examples? I found that quite helpful in t…
- Emmanuel SmithCan the image below be cropped? The excessive whitespace is distracting.
- Malcolm McCrimmonCan you expand on what you mean here? They're a higher priority in what sense?
Improving them is a …
- Eric RogstadChild, because "Nick Bostrom is a person" and "Nick is a part of the 'people' object" and without "N…
- Alexei AndreevCould be nice to add a concrete "real-life" (non-math) example, say like the following:
You are a d…
- Mark ChimesCurrent thinking is that we should allow claims to be edited, but that past users' votes appear gray…
- Eric RogstadDo user pages need quality tags? That seems unnecessary to me...
- Malcolm McCrimmonFor 3, I imagine clarifications in parentheses are okay, maybe good enough, for the math domain. A m…
- Ryan HendricksonFor what it's worth, I have a bit of experience with Kickstarter campaigns, where a similar pattern …
- Davis KingsleyFrom [this paper's](http://marginalrevolution.com/marginalrevolution/2015/12/the-rise-and-decline-of…
- Alexei AndreevFunny enough we had something like that in an older version. We'll definitely bring it back. One way…
- Alexei AndreevHere are some things I'd love to be able to add to this page to make it more explanatory (some of th…
- Ryan HendricksonI feel like symmetric_group should be a requisite for this page. However, this page is linked in the…
- Patrick StevensI have a question about general Arbital practice here. A mathematician will probably already know wh…
- Patrick StevensI imagine Ashley [Watson](http://tvtropes.org/pmwiki/pmwiki.php/Main/TheWatson) [leaning against the…
- Zack M. DavisI love the effect, but I would drop one of the 'as much's for increased lyricism.
- Jaime Sevilla MolinaI think I'm happy to have TCS concepts on relatively equal footing with other math pages. Are there …
- Eric RogstadI think it is important. I now want to refine the claim.
- Stephanie ZolayvarI think it's important for claims to be very clear, and that this one isn't clear enough.
- Stephanie ZolayvarI think it's inevitable that we'll need to build our own editor. I'm not at all sure what that will …
- Alexei AndreevI think that in practice these norms will be hard to enforce just by culture. I would recommend a fe…
- Malcolm OceanI think this bit is slightly confusing. Is it a new lens per resource?
And what do you mean by stan…
- Eric RogstadI think this section conflates two things: 1) the role LW used to play, and 2) the role ultimate-Arb…
- Eric RogstadI think we need a more appropriate definition of Math 0 that doesn't rely on the negation of some pr…
- Joe ZengI took the plunge and put it on its own page.
- Patrick StevensI would very much encourage the norm here to be, "If you feel the need to veto something, explicitly…
- Mars (person)I'd like to add some pictures to this page at some point, but due to current circumstances I can't f…
- Mark ChimesI, for one, am fine with the current, simple comment system. It's close to what's on Stack Overflow …
- Emile KroegerIn the body: you as a personal pronoun, y/n?
- Joe ZengIs there a way to link to a section within a page? (E.g. for tables of contents.)
- Tsvi BTJust to make this super concrete, could we give some examples of topics we'd like to include later b…
- Eric RogstadLet me experiment with using a Page for this purpose, and see what seems like it's missing.
I think…
- Andrea GallagherMy fault, it should be \ulcorner.
- Jaime Sevilla MolinaMy main intuition against: I think that the value that an arbitrary researcher gives to a field is h…
- Ben PaceRequest for comment: is the definition of "cycle" something that should be on its own page? They're …
- Patrick StevensSo I suppose I should attempt a real reply.
I think:
- information hazards should be avoided
- peo…
- Eric RogstadSometimes ambiguous claims can be good too. Just to get a quick sense of where people are at. And fo…
- Alexei AndreevSounds right, but this "page" you speak of is new to me. I assume it's the base structure of the ma…
- Andrea GallagherThe non-existence of a total order on $\mathbb{C}$ is fun and interesting, I think, and also not ver…
- Patrick StevensThe section sounds slightly too passive to me. What would you think of the following re-write?
Exte…
- Eric RogstadThis is awkward phrasing.
- Alexei AndreevThis is definitely a page which admits two lenses: the "easy" proof and the "theory-heavy" proof. Wh…
- Patrick StevensThis is helpful! I don't think I've seen a clearer description of the assumptions behind CEV or what…
- Eric RogstadThis is the explanation of derivative I was looking for. I would like to read that good explanation …
- Szymon SlawinskiThis page doesn't disambiguate between "left inverse" and "inverse". Strictly an "inverse" is a two-…
- Patrick StevensThis should probably be re-titled to "Needs splitting by mastery" or something. "Needs splitting by …
- Alexei AndreevWhen should we apply this tag?
Let's add some guidelines for when this tag is appropriate.
Eric Br…
- Eric RogstadYeah, I think More comments and claims should be driven by cruxes..
- Alexei AndreevYeah, that's a bug.
Yes, hard delete will be a thing too.
- Alexei AndreevYes! That's going to be the major priority in the upcoming months.
- Alexei AndreevYes.
As far as I can tell, the current message of effective altruism sort of focuses in too strongly…
- Timothy ChuAlexei Andreev This page includes a conditional example that only shows up for people who know real …
- Kevin ClancyEric Bruylant That would be great, thanks! I've sent you an email.
- Mark Chimeswould add "by highlighting text and using the menu that appears on the margin" (or other text that b…
- Nate Soares
wiki
- There will be a week during which it is more common to buy food with gold than any other form of money (e.g., USD) in some US settlement with at least 1000 people in 2017.
The wording might not be perfect, but I’m trying to get at the idea that gold should be purchased an…
- Adam Seyfarth - 0.999...=1
No, it's not "infinitesimally far" from 1 or anything like that. 0.999... and 1 are literally the same number.
- Dylan Hendrickson - A googol
A pretty small large number.
- Nate Soares - A googolplex
A moderately large number, as large numbers go.
- Nate Soares - AI arms races
AI arms races are bad
- Eliezer Yudkowsky - AI safety mindset
Asking how AI designs could go wrong, instead of imagining them going right.
- Eliezer Yudkowsky - Abelian group
A group where the operation commutes. Named after Niels Henrik Abel.
- Nate Soares - Absent-Minded Driver dilemma
A road contains two identical intersections. An absent-minded driver wants to turn right at the second intersection. "With what probability should the driver turn right?" argue decision theorists.
- Eliezer Yudkowsky - Abstract algebra
The study of groups, fields, vector spaces, arithmetics, algebras, and more.
- Nate Soares - Ackermann function
The slowest-growing fast-growing function.
- Alex Appel - Alexei Andreev: Personal
Fun things Alexei Andreev likes to do.
- Alexei Andreev - Algebraic structure
Roughly speaking, an algebraic structure is a set $X$, known as the underlying set, paired with a co…
- Nate Soares - Algebraic structure tree
When is a monoid a semilattice? What's the difference between a semigroup and a groupoid? Find out here!
- Ryan Hendrickson - Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev - Arbital Slack
Where the cool kids hang out.
- Eric Bruylant - Arbital biographies
As a very strong default (presently an absolute rule), Joe Smith's page only says nice things about Joe. Even if a negative fact is true, it doesn't go on Joe's page.
- Eliezer Yudkowsky - Arbital needs a mechanism for defining terms
Much of the discussion in claims seems to be about defining terms, which is a foundational part of r…
- Andrea Gallagher - Arbital projects
Arbital projects are small-scale drives to fill in areas of content.
- Eric Bruylant - Arbital scope
What kind of content is Arbital looking for?
- Eric Bruylant - Arbital unlisted page
What do you call a page that's not part of any domain?
- Alexei Andreev - Arbital: Solving online explanations
An explanation of Arbital's mid-term goals
- Eliezer Yudkowsky - Arity (of a function)
The arity of a function is the number of parameters that it takes. For example, the function $f(a, b…
- Nate Soares - Artificial General Intelligence
An AI which has the same kind of "significantly more general" intelligence that humans have compared to chimpanzees; it can learn new domains, like we can.
- Eliezer Yudkowsky - Associative operation
An **associative operation** $\bullet : X \times X \to X$ is a binary operation such that for all $x…
- Nate Soares - Bag
In mathematics, a "bag" is an unordered list. A bag differs from a set in that it can contain the sa…
- Nate Soares - Bayes' rule
Bayes' rule is the core theorem of probability theory saying how to revise our beliefs when we make a new observation.
- Eliezer Yudkowsky - Bayesian view of scientific virtues
Why is it that science relies on bold, precise, and falsifiable predictions? Because of Bayes' rule, of course.
- Eliezer Yudkowsky - Big-picture strategic awareness
We start encountering new AI alignment issues at the point where a machine intelligence recognizes the existence of a real world, the existence of programmers, and how these relate to its goals.
- Eliezer Yudkowsky - Binary function
A binary function $f$ is a function of two inputs (i.e., a function with arity 2). For example, $+,$…
- Nate Soares - Bit (abstract)
An abstract bit is an element of the set $\mathbb B$, which has two elements. An abstract bit is to …
- Nate Soares - Bit (of data)
A bit of data is the amount of data required to single out one message from a set of two. Equivalen…
- Nate Soares - Bit (of data): Examples
In the game "20 questions", one player (the "leader") thinks of a concept, and the other players ask…
- Nate Soares - Cardinality
The "size" of a set, or the "number of elements" that it has.
- Joe Zeng - Cartesian product
The Cartesian product of two sets $A$ and $B,$ denoted $A \times B,$ is the set of all [ordered\_pai…
- Nate Soares - Ceiling
The ceiling of a real number $x,$ denoted $\lceil x \rceil$ or sometimes $\operatorname{ceil}(x),$ i…
- Nate Soares - Closure
A set $S$ is _closed_ under an operation $f$ if, whenever $f$ is fed elements of $S$, it produces an…
- Nate Soares - Codomain (of a function)
The codomain $\operatorname{cod}(f)$ of a function $f : X \to Y$ is $Y$, the set of possible outputs…
- Nate Soares - Codomain vs image
It is useful to distinguish codomain from image both (a) when the type of thing that the function pr…
- Nate Soares - Cognitive steganography
Disaligned AIs that are modeling human psychology and trying to deceive their programmers will want to hide their internal thought processes from their programmers.
- Eliezer Yudkowsky - Coherent extrapolated volition (alignment target)
A proposed direction for an extremely well-aligned autonomous superintelligence - do what humans would want, if we knew what the AI knew, thought that fast, and understood ourselves.
- Eliezer Yudkowsky - Colon-to notation
Find out what the notation "f : X -> Y" means that everyone keeps using.
- Qiaochu Yuan - Combining vectors
One of the most useful things we can do with vectors is to combine them!
- Adele Lopez - Communication: magician example
Imagine that you and I are both magicians, performing a trick where I think of a card from a deck of…
- Nate Soares - Commutative operation
A commutative function $f$ is a function that takes multiple inputs from a set $X$ and produces an o…
- Nate Soares - Commutativity: Intuition
We can think of commutativity either as an artifact of notation, or as a symmetry in the output of a…
- Nate Soares - Compressing multiple messages
How many bits of data does it take to encode an $n$-message? Naively, the answer is $\lceil \log_2(n…
- Nate Soares - Conservative concept boundary
Given N example burritos, draw a boundary around what is a 'burrito' that is relatively simple and allows as few positive instances as possible. Helps make sure the next thing generated is a burrito.
- Eliezer Yudkowsky - Contributing to Arbital
Want to help Arbital become awesome?
- Eric Bruylant - Convergent instrumental strategies
Paperclip maximizers can make more paperclips by improving their cognitive abilities or controlling more resources. What other strategies would almost-any AI try to use?
- Eliezer Yudkowsky - Convex function
A function that only curves upward
- Jessica Taylor - Convex set
A set that contains all line segments between points in the set
- Jessica Taylor - Correct credit-tracking is very important if we want our community to generate new good ideas.
Correct credit-tracking is very important if we want our community to generate new good ideas.
- Anna Salamon - Crowdsourcing moderation without sacrificing quality - Eric Rogstad
- Data capacity
The data capacity of an object is defined to be the Logarithm of the number of different distinguish…
- Nate Soares - Decit
Decimal digit
- Nate Soares - Dependent messages can be encoded cheaply
Say you want to transmit a 2-message, a 4-message, and a 256-message to somebody. For example, you m…
- Nate Soares - Derivative
How things change
- Michael Cohen - Digit wheel
A mechanical device for storing a number from 0 to 9.
![](http://www.cl.cam.ac.uk/~djg11/howcompu…
- Nate Soares - Displaying the list of fundraiser donors sorted by the donation date would help with the "wait and see" problem. - Alexei Andreev
- Division of rational numbers (Math 0)
"Division" is the idea of "dividing something up among some people so that we can give equal amounts to each person".
- Patrick Stevens - Do-What-I-Mean hierarchy
Successive levels of "Do What I Mean" or AGIs that understand their users increasingly well
- Eliezer Yudkowsky - Domain (of a function)
The domain $\operatorname{dom}(f)$ of a function $f : X \to Y$ is $X$, the set of valid inputs for t…
- Nate Soares - Don't try to solve the entire alignment problem
New to AI alignment theory? Want to work in this area? Already been working in it for years? Don't try to solve the entire alignment problem with your next good idea!
- Eliezer Yudkowsky - Effective altruism
What's the most good you can do?
- Eric Rogstad - Eigenvalues and eigenvectors
We applied this linear transformation to one of its eigenvectors; you won't believe what happened next!
- Zack M. Davis - Emulating digits
In general, given enough $n$-digits, you can emulate an $m$-digit, for any $m, n \in$ $\mathbb N$. I…
- Nate Soares - Encoding trits with GalCom bits
There are $\log_2(3) \approx 1.585$ bits to a Trit. Why is it that particular value? Consider the Ga…
- Nate Soares - Epistemic and instrumental efficiency
An efficient agent never makes a mistake you can predict. You can never successfully predict a directional bias in its estimates.
- Eliezer Yudkowsky - Establishing a permanent off-Earth colony would be a useful way to mitigate x-risk
- Posed by [purplepeople](http://effective-altruism.com/user/purplepeople/) on the [EA Forum](http:/…
- Eric Rogstad - Exchange rates between digits
In terms of data storage, if a coin is worth $1, a digit wheel is worth more than $3.32, but less than $3.33. Why?
- Nate Soares - Executable philosophy
Philosophical discourse aimed at producing a trustworthy answer or meta-answer, in limited time, which can used in constructing an Artificial Intelligence.
- Eliezer Yudkowsky - Exponential
Any function that constantly gets larger as a proportion of itself.
- Joe Zeng - Extensionality Axiom
If two sets have exactly the same members, then they are equal
- Ilia Zaichuk - Extraordinary claims
What makes something an 'extraordinary claim' that requires extraordinary evidence?
- Eliezer Yudkowsky - Extrapolated volition (normative moral theory)
If someone asks you for orange juice, and you know that the refrigerator contains no orange juice, should you bring them lemonade?
- Eliezer Yudkowsky - Faithful simulation
How would you identify, to a Task AGI (aka Genie), the problem of scanning a human brain, and then running a sufficiently accurate simulation of it for the simulation to not be crazy or psychotic?
- Eliezer Yudkowsky - For most EA-Blank projects, we would expect more good to be done if they would: i) disband or ii) remove EA from the name and aim to outgrow the EA movement.
The claim refers to projects like:
* Effective Altruism Forum
* Effective Altruism Handbook
* Effec…
- Ryan Carey - Fractional bits
It takes $\log_2(8) = 3$ bits of data to carry one message from a set of 8 possible messages. Simila…
- Nate Soares - Fractional digits
When $b$ and $x$ are integers, $\log_b(x)$ has a few good interpretations. It's roughly the length o…
- Nate Soares - Freely reduced word
"Freely reduced" captures the idea of "no cancellation" in a free group.
- Patrick Stevens - Function
Intuitively, a function $f$ is a procedure (or machine) that takes an input and performs some opera…
- Nate Soares - Function: Physical metaphor
Many functions can be visualized as physical mechanisms of wheels and gears, that take their inputs …
- Nate Soares - GalCom
In the GalCom thought experiment, you live in the future, and make your money by living in the Dene…
- Nate Soares - GalCom: Rules
1. It costs 1 galcoin per bit to reserve on-peak bits in advance. (Galcoins are very expensive.)
2. …
- Nate Soares - Generalized associative law
Given an associative operator $\cdot$ and a list $[a, b, c, \ldots]$ of parameters, all ways of red…
- Nate Soares - GiveWell and the problem of partial funding
A foundation that plans to move around ten billion dollars and is relying on advice from GiveWell isn’t enough to get the top charities fully funded. That’s weird and surprising.
- Benjamin Hoffman - Graham's number
A fairly large number, as numbers go.
- Nate Soares - Group
The algebraic structure that captures symmetry, relationships between transformations, and part of what multiplication and addition have in common.
- Nate Soares - Group theory: Examples
What does thinking in terms of group theory actually look like? And what does it buy you?
- Qiaochu Yuan - Guide
Meta tag for the start page of a multi-page guide.
- Eric Bruylant - How many bits to a trit?
$\log_2(3) \approx 1.585.$ This can be interpreted a few different ways:
1. If you multiply the nu…
- Nate Soares - How much of the discussion around AI safety should be public? - Alexei Andreev
- How to author on Arbital!
Want to contribute pages to Arbital? Here's our current version of the ad-hoc guide to being an author!
- Eliezer Yudkowsky - Iff
If and only if...
- Alexei Andreev - Image (of a function)
The image $\operatorname{im}(f)$ of a function $f : X \to Y$ is the set of all possible outputs of $…
- Nate Soares - Improve comments by tagging claims
Comment sections are more important for discourse than I thought. They can be improved by explicitly tagging an article's main claims as anchors for discussion.
- Benjamin Hoffman - Information
Information is a measure of how much a message grants an observer the ability to predict the world.…
- Nate Soares - Information theory
The study (and quantificaiton) of information, and its communication and storage.
- Nate Soares - Infrahuman, par-human, superhuman, efficient, optimal
A categorization of AI ability levels relative to human, with some gotchas in the ordering. E.g., in simple domains where humans can play optimally, optimal play is not superhuman.
- Eliezer Yudkowsky - Instrumental goals are almost-equally as tractable as terminal goals
Getting the milk from the refrigerator because you want to drink it, is not vastly harder than getting the milk from the refrigerator because you inherently desire it.
- Eliezer Yudkowsky - Integer
An **integer** is a Number that can be represented as either a Natural number or its [-additive\_inv…
- Michael Cohen - Intelligence explosion
What happens if a self-improving AI gets to the point where each amount x of self-improvement triggers >x further self-improvement, and it stays that way for a while.
- Eliezer Yudkowsky - Intradependent encoding
An encoding $E(m)$ of a message $m$ is intradependent if the fact that $E(m)$ encodes $m$ can be de…
- Nate Soares - Intradependent encodings can be compressed
Given an encoding scheme $E$ which gives an Intradependent encoding of a message $m,$ we can in prin…
- Nate Soares - Intro to Number Sets
An introduction to number sets for people who have no idea what a number set is.
- Joe Zeng - Introduction to Logical Decision Theory for Analytic Philosophers
Why "choose as if controlling the logical output of your decision algorithm" is the most appealing candidate for the principle of rational choice.
- Eliezer Yudkowsky - Introduction to Logical Decision Theory for Economists
An introduction to 'logical decision theory' and its implications for the Ultimatum Game, voting in elections, bargaining problems, and more.
- Eliezer Yudkowsky - Introductory guide to logarithms
Welcome to the Arbital introduction to logarithms! In modern education, logarithms are often mention…
- Nate Soares - Inverse function
The inverse of a function returns an input of the original function when fed the original's corresponding output.
- Michael Cohen - Invisible background fallacies
Universal laws also apply to objects and ideas that may fade into the invisible background. Reasoning as if these laws didn't apply to less obtrusive concepts is a type of fallacy.
- Eliezer Yudkowsky - Irrelevant nitpicks are an important problem in comment sections on sites such as LessWrong.
Source of claim: Improve comments by tagging claims by Benjamin Hoffman
- Stephanie Zolayvar - Lattice (Order Theory)
A poset that is closed under binary joins and meets.
- Kevin Clancy - Life in logspace
The log lattice hints at the reason that engineers, scientists, and AI researchers find logarithms s…
- Nate Soares - Limited AGI
Task-based AGIs don't need unlimited cognitive and material powers to carry out their Tasks; which means their powers can potentially be limited.
- Eliezer Yudkowsky - List
A list is an ordered collection of objects, such as `[0, 1, 2, 3]` or `["red", "blue", 0, "shoe"]`. …
- Nate Soares - Log as the change in the cost of communicating
When interpreting logarithms as a generalization of the notion of "length" and as digit exchange rat…
- Nate Soares - Log base infinity
There is no log base infinity, but if there were, it would send everything to zero
- Nate Soares - Logarithm base 1
There is no log base 1.
- Nate Soares - Logarithm tutorial overview
The logarithm tutorial covers the following six subjects:
1. What are logarithms?
2. Logarithms as…
- Nate Soares - Logarithm: Examples
$\log_{10}(100)=2.$ $\log_2(4)=2.$ $\log_2(3)\approx 1.58.$ (TODO)
- Nate Soares - Logarithm: Exercises
Without using a calculator: What is $\log_{10}(4321)$? What integer is it larger than, what integer …
- Nate Soares - Logarithmic identities
- [ Inversion of exponentials]: $b^{\log_b(n)} = \log_b(b^n) = n.$
- [ Log of 1 is 0]: $\log_b(1) …
- Nate Soares - Logarithms invert exponentials
The function $\log_b(\cdot)$ inverts the function $b^{(\cdot)}.$ In other words, $\log_b(n) = x$ imp…
- Nate Soares - Math 3 example statements
If you can read these formulas, you're in Math 3!
- Joe Zeng - Mathematical induction
Proving a statement about all positive integers by knocking them down like dominoes.
- Douglas Weathers - Mechanical Turk (example)
The 19th-century chess-playing automaton known as the Mechanical Turk actually had a human operator inside. People at the time had interesting thoughts about the possibility of mechanical chess.
- Eliezer Yudkowsky - Meta tags which request an edit to the page
Tags that mean your page should be edited.
- Stephanie Zolayvar - Metric
A metric is a function that defines a distance between elements in a set and follows some basic rules.
- Bryce Woodworth - Missing the weird alternative
People might systematically overlook "make tiny molecular smileyfaces" as a way of "producing smiles", because our brains automatically search for high-utility-to-us ways of "producing smiles".
- Eliezer Yudkowsky - Monotone function
An order-preserving map between posets.
- Kevin Clancy - Most complex things are not very compressible
We can't *prove* it's impossible, but it would be *extremely surprising* to discover a 500-state Turing machine that output the exact text of "Romeo and Juliet".
- Eliezer Yudkowsky - NGDP level targeting
Central banks ought to regularize the total flow of money to increase at a predictable 5% rate per year, and doing this would solve a surprising number of other problems.
- Eliezer Yudkowsky - Natural number
The numbers we use to count: 0, 1, 2, 3, ...
- Jaime Sevilla Molina - Needs exercises
Add this tag to a page which doesn't have enough exercises.
- Alexei Andreev - Needs motivation
A tag for text that could benefit from some motivating statements. Why is the reader interested in w…
- Eric Rogstad - Needs summary
This page does not have a summary which provides an informative overview of the page's primary topic.
- Alexei Andreev - Needs technical summary
Meta tag for pages which need a technical summary.
- Eric Bruylant - No-Free-Lunch theorems are often irrelevant
There's often a theorem proving that some problem has no optimal answer across every possible world. But this may not matter, since the real world is a special case. (E.g., a low-entropy universe.)
- Eliezer Yudkowsky - Non-standard terminology
A tag for terminology that is Arbital-specific, Arbital-originated, or just not very common outside …
- Nate Soares - On the importance of Less Wrong, or another single conversational locus
In this post, Anna Salamon talks about how Less Wrong used to a locus of discussion, and that it is…
- Alexei Andreev - Order of a group
The order $|G|$ of a group $G$ is the size of its underlying set. For example, if $G=(X,\bullet)$ an…
- Nate Soares - Order of a group element
Given an element $g$ of group $(G, +)$ (which henceforth we abbreviate simply as $G$), the order of …
- Patrick Stevens - P vs NP
Is creativity purely mechanical?
- Jaime Sevilla Molina - P vs NP: Arguments against P=NP
Why we believe P and NP are different
- Jaime Sevilla Molina - Partially ordered set
A set endowed with a relation that is reflexive, transitive, and antisymmetric.
- Kevin Clancy - Patch resistance
One does not simply solve the value alignment problem.
- Eliezer Yudkowsky - Path targeting
Don't say "We want this price to go up at 2%/year", say "We want this to be $1 in year 1, $1.02 in year 2, $1.04 in year 3" and don't change the rest of the path if you miss one year's target.
- Eliezer Yudkowsky - People
A category for human beings!
- Eliezer Yudkowsky - Pi
Pi, usually written $π$, is a number equal to the ratio of a circle's [-circumference] to its [-diam…
- Michael Cohen - Poset: Examples
The standard $\leq$ relation on integers, the $\subseteq$ relation on sets, and the $|$ (divisibilit…
- Kevin Clancy - Potential new users are confused by the goal of Arbital and how they can best contribute - Ted Sanders
- Practicing Brevity
Wanna save the world? Write better TLDRs. And spend more time respecting your reader's time.
- Raymond Arnold - Predictions For 2017
Scott Alexander made 105 predictions for 2017. Most of them are not personal and are listed below. …
- Alexei Andreev - Probability distribution (countable sample space)
A function assigning a probability to each point in the sample space.
- Tsvi BT - Programming in Dependent Type Theory
Working with simple types in Lean
- Jack Gallagher - Proof by contradiction
Discover what 'reductio ad absurdum' means!
- Jaime Sevilla Molina - Quine
A computer program that prints (or does other computations to) its own source code, using indirect self-reference.
- Patrick LaVictoire - Quotient group
Given a group $G$ with operation $\bullet$ and a special kind of subgroup $N \leq G$ called the "no…
- Adele Lopez - Range (of a function)
The "range" of a function is an ambiguous term that is generally used to refer to either the functio…
- Nate Soares - Real analysis
The study of real numbers and real-valued functions.
- Kevin Clancy - Reflexive relation
A binary relation over some set is **reflexive** when every element of that set is related to itself…
- Ryan Hendrickson - Rescuing the utility function
If your utility function values 'heat', and then you discover to your horror that there's no ontologically basic heat, switch to valuing disordered kinetic energy. Likewise 'free will' or 'people'.
- Eliezer Yudkowsky - Safe but useless
Sometimes, at the end of locking down your AI so that it seems extremely safe, you'll end up with an AI that can't be used to do anything interesting.
- Eliezer Yudkowsky - Sample space
The set of possible things that could happen in a part of the world that you are uncertain about.
- Tsvi BT - Sample spaces are too large
Sample spaces are often large, so it is hard to do probabilistic computations using a raw distribution over the sample space.
- Tsvi BT - Scalable ways to associate evidence (pro or con) with claims will be more valuable in elevating accuracy than complex voting and reputation systems
Discussions on Less Wrong have delved into [complex systems of voting and moderation](http://lesswro…
- Andrea Gallagher - Separation from hyperexistential risk
The AI should be widely separated in the design space from any AI that would constitute a "hyperexistential risk" (anything worse than death).
- Eliezer Yudkowsky - Set
An unordered collection of distinct objects.
- Nate Soares - Set builder notation
$\{ 2n \mid n \in \mathbb N \}$ denotes the set of all even numbers, using set builder notation. Set…
- Nate Soares - Shannon
The shannon (Sh) is a unit of Information. One shannon is the difference in [info\_entropy entropy] …
- Nate Soares - Small donors are more likely to do other good if crowded out - Alexei Andreev
- Start
This page gives a basic overview of the topic, but may be missing important information or have stylistic issues. If you're able to, please help expand or improve it!
- Eliezer Yudkowsky - String (of text)
A string (of text) is a series of letters (often denoted by quote marks), such as `"abcd"` or `"hell…
- Nate Soares - Style guidelines
Various stylistic conventions people should follow on Arbital
- Alexei Andreev - Superintelligent
A "superintelligence" is strongly superhuman (strictly higher-performing than any and all humans) on every cognitive problem.
- Eliezer Yudkowsky - Task (AI goal)
When building the first AGIs, it may be wiser to assign them only goals that are bounded in space and time, and can be satisfied by bounded efforts.
- Eliezer Yudkowsky - The End (of the basic log tutorial)
That concludes our introductory tutorial on logarithms! You have made it to the end.
Throughout thi…
- Nate Soares - The Necessity of Credibility - Eric Rogstad
- The characteristic of the logarithm
Any time you find an output that adds whenever the input multiplies, you're probably looking at a (…
- Nate Soares - The current message of effective altruism heavily discourages creativity.
Alyssa Vance expands on this point in her [FB post](https://www.facebook.com/alyssamvance/posts/1021…
- Alexei Andreev - The ideal Arbital math page
Think of the best math textbook you've ever read -- why was it good?
- Eric Rogstad - The log lattice
Log as the change in the cost of communicating and other pages give physical interpretations of what…
- Nate Soares - There is only one logarithm
All logarithm functions are the same, up to a multiplicative constant.
- Nate Soares - To math explanations and beyond!
In which Arbital doubles down on math explanations.
- Alexei Andreev - Trit
Trinary digit
- Nate Soares - Uncomputability
The diagonal function and the halting problem
- Jaime Sevilla Molina - Uncountable sample spaces are way too large
We can't define probability distributions over uncountable sample spaces by just assigning numbers to each point in the sample space.
- Tsvi BT - Underestimating complexity of value because goodness feels like a simple property
When you just want to yell at the AI, "Just do normal high-value X, dammit, not weird low-value X!" and that 'high versus low value' boundary is way more complicated than your brain wants to think.
- Eliezer Yudkowsky - Underlying set
What do a Group, a Partially ordered set, and a [ topological space] have in common? Each is a Set …
- Nate Soares - Utility
What is "utility" in the context of Value Alignment Theory?
- Eliezer Yudkowsky - Valley of Dangerous Complacency
When the AGI works often enough that you let down your guard, but it still has bugs. Imagine a robotic car that almost always steers perfectly, but sometimes heads off a cliff.
- Eliezer Yudkowsky - Vector space
A vector space is a field $F$ paired with a Group $V$ and a function $\cdot : F \times V \to V$ (cal…
- Nate Soares - What is a logarithm?
Logarithms are a group of functions that take a number as input and produce another number. There i…
- Nate Soares - Why argument structure is important
How might we make collaborative truth-seeking both fun and easy?
- Andrea Gallagher - Why is log like length?
If a number $x$ is $n$ digits long (in Decimal notation), then its logarithm (base 10) is between $n…
- Nate Soares - Why is the decimal expansion of log2(3) infinite?
Because 2 and 3 are relatively prime.
- Nate Soares - Why waiting to donate harms charities
A blog post explaining the potential reasons why someone would choose to wait to donate and how that leads to suboptimal outcomes for the charity.
- Alexei Andreev - William Frankena's list of terminal values
Life, consciousness, and activity; health and strength; pleasures and satisfactions of all or certain kinds; happiness, beatitude, contentment, etc.; truth; knowledge and true opinions...
- Eliezer Yudkowsky - concat (function)
The string concatenation function `concat` puts two strings together, i.e., `concat("one","two")="on…
- Nate Soares - n-digit
An $n$-digit is a physical object that can be stably placed into any of $n$ distinguishable states. …
- Nate Soares - n-message
A message singling out one thing from a set of $n$ is sometimes called an $n$-message. For example,…
- Nate Soares
group
**Feedback system / incentivising valuable criticism and productive response**
Partly inspired by […
- Eric Bruylant**Recent Changes / Edit Review system**
On traditional wikis the [recent changes page](https://wiki…
- Eric Bruylant> Are you asking for safety even if one of these systems or subsystems becomes omniscient while othe…
- Eliezer Yudkowsky> Even so, while the outputs are still abstract and not-yet-computed, Alice doesn't have much of a p…
- Paul Christiano> I feel it's basically good to be straightforward, and also good to be in motion rather than waitin…
- Alexei Andreev> What is "be more useful"?
The question is what would happen if the people actually running the pr…
- Ryan Carey>Does this actually work for any proportions of A and B? Is there a simple proof?
Yes, but I'm not …
- Tsvi BTAfter reading the Doc(tm), I think there is still design space to explore. For most readers, and ma…
- Andrea GallagherAll good points. I've updated my vote.
- Alexei AndreevAnother solution to the problem is that heat *as heat* is ontologically basic, *because* it is part …
- Daniel SatanoveApparently it's "which conscious states feel good, which ones feel bad?"
- Alexei AndreevBollard's more conservative estimate is 38 hen-years per dollar, if you include other expenditures o…
- Benjamin HoffmanConsider an AI system composed of many interacting subsystems, or a world containing many AI systems…
- Paul ChristianoCould be nice to add a concrete "real-life" (non-math) example, say like the following:
You are a d…
- Mark ChimesEliezer [objects](https://arbital.com/p/2fr/?l=2fr#subpage-2h4) to this post's optimism about robust…
- Paul ChristianoFixed. (Would be nice to have a way to resolve these comments.)
- Nate SoaresHmm. I find it difficult to form an opinion on a claim as fuzzy as this. I am sensitive of appearing…
- Ted SandersHow's this?
- Nate SoaresI agree that For mitigating AI x-risk, an off-Earth colony would be about as useful as a warm scarf.…
- Eric RogstadI cannot evaluate this claim in full generality, but I entered my estimate based on my current estim…
- lahwran -I disagree mostly on priors, since it's quite unlikely that we discovered, understood, and pinpointe…
- Alexei AndreevI don't think the existence of such a colony would directly mitigate AI risk, but it could help in t…
- Paul ChristianoI feel it's basically good to be straightforward, and also good to be in motion rather than waiting …
- Anna SalamonI suggest we can assume that almost everyone in Math 3 is familiar with either calculus concepts or …
- Patrick LaVictoireI think if one was to attempt it, it would be important to get the messaging right. If you just did …
- Alexei AndreevI think nitpicks are a problem on LW, not because they clog the comments, but because the expectatio…
- Patrick LaVictoireI think offsets are an excellent way to keep some cause-promoters honest. For instance, if people wh…
- Benjamin HoffmanI think this is a factor in whether I feel motivated to donate, but because of unconscious associati…
- Rob BensingerI think this is a good idea for specific 'kickstarter' projects by organizations. I don't think nonp…
- Rob BensingerI think we need a more appropriate definition of Math 0 that doesn't rely on the negation of some pr…
- Joe ZengI want a wrong question button!! :/
- Anna SalamonI would rather a claim is always in a clarification period. If a claim can't be modified or varied,…
- Andrea GallagherI'll add a link when the archive exists, Alexei said to write the page first.
- Eric BruylantI'm surprised you want to use the word "advanced" to for this concept; implies to me this is the *ma…
- Kenzi AmodeiI've come across a number of argument-structuring tools in the past. I think doing this right is muc…
- Jim BabcockI've updated down to slightly weaker agreement because of the example given by Aceso Under Glass in …
- Benjamin HoffmanIt seems unlikely we'll ever build systems that "maximize X, but rule out some bad solutions with th…
- Paul ChristianoLikes work as substitutes. More granular likes and more variety of expressions (ala FB reactions) wo…
- Alexei AndreevLooks good to me!
- Patrick StevensMight one of the following examples work?
The Riemann hypothesis asserts that the real part of ever…
- Jason GrossMore believable, but risks discouraging people from writing the other types of content? I think ambi…
- Eric BruylantMost technical version goes onto the primary page (this one). Easier versions get their own lenses. …
- Alexei AndreevMy main intuition against: I think that the value that an arbitrary researcher gives to a field is h…
- Ben PaceNeat, I'm a contrarian. I guess I should explain why my credence is about 80% different from everyon…
- Eric BruylantOkay now I'm also confused. (Eric Rogstad)
Why don't we just say its codomain is {1}?
- Alexei AndreevOn the other hand, I think we should be skeptical of these estimates. ACE has a [history](https://ac…
- Benjamin HoffmanOn the pro side: The whole "farmed animal welfare" field in the US gets less than $100MM per year, a…
- Benjamin HoffmanOne natural standard: it should be hard to distinguish an adequate model from the system-to-be-model…
- Paul ChristianoPaul, I'm having trouble isolating a background proposition on which we could more sharply disagree.…
- Eliezer YudkowskyPlease clarify this claim, since there's an enormous difference between recruitment and outreach, be…
- Patrick LaVictoirePotential issues (the results of my 5 minutes of thought)
1) Opportunity cost. Should people practi…
- Raymond ArnoldRegarding corporations:
I have seen very few arguments about superintelligence that rest on epistem…
- Paul ChristianoSay we value article views and user signups. If I'm taking actions that achieve n views for each los…
- Ryan CareyShould be "two tile wide", right?
- Gustavo BicalhoShould be fixed. Try now.
- Alexei AndreevSounds right, but this "page" you speak of is new to me. I assume it's the base structure of the ma…
- Andrea GallagherSuperficially, there are two quite different concerns:
1. You optimize a system for X. You are unha…
- Paul ChristianoThanks for the critique, Ted. We are currently figuring out the life-cycle of a claim, and will find…
- Alexei AndreevThanks for the feedback! I'd prefer to have the explanations underneath the requirement they refer t…
- Bryce WoodworthThe novel [David's Sling](https://www.amazon.com/Davids-Sling-Marc-Stiegler/dp/0671653695/) by Marc …
- Malcolm OceanThe point of 'efficiency' is that:
- It's an extremely plausible thing to expect given enough raw c…
- Eliezer YudkowskyThey are smooth relative to my state of knowledge. I don't know exactly how things are in the charit…
- Paul CrowleyThis (and many of your concerns) seem basically sensible to me. But I tend to read them more broadly…
- Paul ChristianoThis is a more general pattern in theoretical research. When you first start to attack a hard proble…
- Paul ChristianoThis is a rough jumble of thoughts explaining some of the reasoning behind the proposed policy.
**D…
- Eric BruylantThis is awkward phrasing.
- Alexei AndreevThis is definitely a page which admits two lenses: the "easy" proof and the "theory-heavy" proof. Wh…
- Patrick StevensThis makes me think that perhaps more, smaller milestones would be good.
- Alexei AndreevThis page asks me if I learnt the concept of "Odds ratio" - but nowhere in the page does it actually…
- Emile KroegerThis raises a new issue of how e.g. Steph is supposed to feel when the claim's wording has changed, …
- Ryan CareyThis statement is just wrong. I will fix it. (The correct statement is that there's a group acting o…
- Qiaochu YuanTo clarify my view, I think EA moderately discourages creativity but this is a big mistake: it shoul…
- Ryan CareyUh, well, it's hard to reply-to, or something? Like, it wants to jam the conversation into question…
- Anna SalamonYes.
As far as I can tell, the current message of effective altruism sort of focuses in too strongly…
- Timothy ChuYes. In particular, the first milestone or two should probably be small (assuming there are no assoc…
- Rob BensingerYou named two charities, and I ended up deciding that the case for *one* of them was plausible (CiWF…
- Benjamin HoffmanYou're quite right to flag this up; I was being sloppy. There are three main ways to construct the f…
- Patrick StevensEric Rogstad But... but... poset office was a *pun*, not a typo.
- Mark ChimesEric Rogstad Elmo comes to visit. Does that seem fine you think?
- Mark ChimesEric Rogstad The post has been updated with an isomorphic version of what you suggested. Thanks!
- Mark Chimesright, fixed!
- Adele Lopezwould add "by highlighting text and using the menu that appears on the margin" (or other text that b…
- Nate Soares
- Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- Waterfall diagram
Visualizing Bayes' rule as the mixing of probability streams.
- Eliezer Yudkowsky
wiki
- Factorial
The *factorial* of a number $n$ is how we describe "how many different ways we can arrange $n$ obje…
- Patrick Stevens
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky - Introductory Bayesian problems
Bayesian problems to try to solve yourself, before beginning to learn about Bayes' rule.
- Eliezer Yudkowsky
wiki
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky - Bayesian view of scientific virtues
Why is it that science relies on bold, precise, and falsifiable predictions? Because of Bayes' rule, of course.
- Eliezer Yudkowsky - Interpretations of "probability"
What does it *mean* to say that a fair coin has a 50% probability of coming up heads?
- Nate Soares - Likelihood functions, p-values, and the replication crisis
What's the whole Bayesian-vs.-frequentist debate about?
- Eliezer Yudkowsky
- First order linear equations
A **first order lineal equation** has the form
$$
u'=a(t)u+b(t)
$$
where $a$ and $b$ are continuous …
- Jaime Sevilla Molina
- AI alignment
The great civilizational problem of creating artificially intelligent computer systems such that running them is a good idea.
- Eliezer Yudkowsky
- Diamond maximizer
How would you build an agent that made as much diamond material as possible, given vast computing power but an otherwise rich and complicated environment?
- Eliezer Yudkowsky
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky - Introductory Bayesian problems
Bayesian problems to try to solve yourself, before beginning to learn about Bayes' rule.
- Eliezer Yudkowsky
- Orthogonality Thesis
Will smart AIs automatically become benevolent, or automatically become hostile? Or do different AI designs imply different goals?
- Eliezer Yudkowsky
- Alexei Andreev
There is no spoon
- Introduction to Bayes' rule: Odds form
Bayes' rule is simple, if you think in terms of relative odds.
- Eliezer Yudkowsky
- An Effective Altruist's Guide to the Future
The future is unknown, but not unknowable. What evidence do we have about what will happen, and what considerations are most important for doing good in a rapidly changing world?
- Eric Bruylant - Requisites for personal growth
A mashup of models
- Toon Alfrink
wiki
- Solutions Paper - Solving Employment in the Light of Automation
GeM Labs solution space to tackle labour market challenges that arise from the rise of automation and artificial intelligence.
- Geneva Macro Labs
group
- Geneva Macro Labs
Leveraging the collective intelligence of Geneva and surroundings to solve the world's biggest problems.
- Odds: Introduction
What's the difference between probabilities and odds? Why is a 20% probability of success equivalent to 1 : 4 odds favoring success?
- Nate Soares
- Arbital page summaries
Because only one summary is not enough!
- Alexei Andreev
- Frequency diagrams: A first look at Bayes
The most straightforward visualization of Bayes' rule.
- Nate Soares
- Bayes' rule: Probability form
The original formulation of Bayes' rule.
- Nate Soares - Frequency diagrams: A first look at Bayes
The most straightforward visualization of Bayes' rule.
- Nate Soares
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky
- High-speed intro to Bayes's rule
A high-speed introduction to Bayes's Rule on one page, for the impatient and mathematically adept.
- Eliezer Yudkowsky
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky
- Predictions For 2017
Scott Alexander made 105 predictions for 2017. Most of them are not personal and are listed below. …
- Alexei Andreev
wiki
- Bayes' rule
Bayes' rule is the core theorem of probability theory saying how to revise our beliefs when we make a new observation.
- Eliezer Yudkowsky - Bayes' rule: Log-odds form
A simple transformation of Bayes' rule reveals tools for measuring degree of belief, and strength of evidence.
- Eliezer Yudkowsky - Extraordinary claims require extraordinary evidence
The people who adamantly claim they were abducted by aliens do provide some evidence for aliens. They just don't provide quantitatively enough evidence.
- Eliezer Yudkowsky - Frequency diagrams: A first look at Bayes
The most straightforward visualization of Bayes' rule.
- Nate Soares - Introduction to Bayes' rule: Odds form
Bayes' rule is simple, if you think in terms of relative odds.
- Eliezer Yudkowsky - Log as generalized length
To estimate the log (base 10) of a number, count how many digits it has.
- Nate Soares - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
wiki
- Arbital: Solving online explanations
An explanation of Arbital's mid-term goals
- Eliezer Yudkowsky - Decision problem
Formalization of general problems
- Jaime Sevilla Molina - Diagonal lemma
Constructing self-referential sentences
- Jaime Sevilla Molina - Equaliser (category theory)
In Category theory, an *equaliser* of a pair of arrows $f, g: A \to B$ is an object $E$ and a univer…
- Patrick Stevens - Likelihood functions, p-values, and the replication crisis
What's the whole Bayesian-vs.-frequentist debate about?
- Eliezer Yudkowsky - Mathematics
Mathematics is the study of numbers and other ideal objects that can be described by axioms.
- Eliezer Yudkowsky
wiki
- Factorial
The number of ways you can order things. (Alternately subtitled: Is that exclamation point a factorial, or are you just excited to see me?)
- Michael Cohen
wiki
- Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev - To math explanations and beyond!
In which Arbital doubles down on math explanations.
- Alexei Andreev - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- Why argument structure is important
How might we make collaborative truth-seeking both fun and easy?
- Andrea Gallagher
- Frequency diagrams: A first look at Bayes
The most straightforward visualization of Bayes' rule.
- Nate Soares - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky
- Frequency diagrams: A first look at Bayes
The most straightforward visualization of Bayes' rule.
- Nate Soares
- Introduction to Bayes' rule: Odds form
Bayes' rule is simple, if you think in terms of relative odds.
- Eliezer Yudkowsky
- Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev - Welcome to Arbital
Front page explaining what Arbital is all about.
- Alexei Andreev
- Answer to sparking widgets problem
Odds of 1 : 3, probability of 1/4.
- Eliezer Yudkowsky - Arbital Blog
Stay up to date on all things Arbital
- Alexei Andreev - Arbital features
Overview of all Arbital features.
- Alexei Andreev - Arithmetical hierarchy
The arithmetical hierarchy is a way of classifying logical statements by the number of clauses saying "for every object" and "there exists an object".
- Eliezer Yudkowsky - Bayes' rule: Odds form
The simplest and most easily understandable form of Bayes' rule uses relative odds.
- Eliezer Yudkowsky - Bayes' rule: Vector form
For when you want to apply Bayes' rule to lots of evidence and lots of variables, all in one go. (This is more or less how spam filters work.)
- Eliezer Yudkowsky - Bayesian view of scientific virtues
Why is it that science relies on bold, precise, and falsifiable predictions? Because of Bayes' rule, of course.
- Eliezer Yudkowsky - Waterfall diagram
Visualizing Bayes' rule as the mixing of probability streams.
- Eliezer Yudkowsky - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky
- Frequency diagrams: A first look at Bayes
The most straightforward visualization of Bayes' rule.
- Nate Soares
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky
- Welcome to Arbital
Front page explaining what Arbital is all about.
- Alexei Andreev
- Answer to sparking widgets problem
Odds of 1 : 3, probability of 1/4.
- Eliezer Yudkowsky - Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky - Prime number
The prime numbers are the "building blocks" of the counting numbers.
- Patrick Stevens - Probability notation for Bayes' rule: Intro (Math 1)
How to read, and identify, the probabilities in Bayesian problems.
- Eliezer Yudkowsky
- Bayes' rule: Log-odds form
A simple transformation of Bayes' rule reveals tools for measuring degree of belief, and strength of evidence.
- Eliezer Yudkowsky
- Waterfall diagram
Visualizing Bayes' rule as the mixing of probability streams.
- Eliezer Yudkowsky
- Exponential notation for function spaces
Why $Y^X$ is good notation for the space of maps from $X$ to $Y$
- Izaak Meckler
- Bayes' rule: Definition
Bayes' rule is the mathematics of probability theory governing how to update your beliefs in the lig…
- Nate Soares
- Introduction to Bayes' rule: Odds form
Bayes' rule is simple, if you think in terms of relative odds.
- Eliezer Yudkowsky
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky - Guarded definition
A guarded definition is one where at least one position suspects there will be pressure to stretch a…
- Eliezer Yudkowsky - High-speed intro to Bayes's rule
A high-speed introduction to Bayes's Rule on one page, for the impatient and mathematically adept.
- Eliezer Yudkowsky - Mathematics
Mathematics is the study of numbers and other ideal objects that can be described by axioms.
- Eliezer Yudkowsky - Proof of Bayes' rule
Proofs of Bayes' rule, with graphics
- Eliezer Yudkowsky - Vingean uncertainty
You can't predict the exact actions of an agent smarter than you - so is there anything you _can_ say about them?
- Eliezer Yudkowsky
wiki
- 0.999...=1
No, it's not "infinitesimally far" from 1 or anything like that. 0.999... and 1 are literally the same number.
- Dylan Hendrickson - 99LDT x 1CDT oneshot PD tournament as arguable counterexample to LDT doing better than CDT
Arguendo, if 99 LDT agents and 1 CDT agent are facing off in a one-shot Prisoner's Dilemma tournament, the CDT agent does better on a problem that CDT considers 'fair'.
- Eliezer Yudkowsky - A beginner's guide to explaining things
Good explanations can be very different, but most of them have a few things in common.
- Duncan Sabien - A whirlwind tour
A rapid tour of Eric's thoughts on the accelerator project.
- Eric Bruylant - Accelerator Project
The Accelerator Project aims to create a low-cost environment which facilitates rapid personal growt…
- Eric Bruylant - Ackermann function
The slowest-growing fast-growing function.
- Alex Appel - An Introduction to Logical Decision Theory for Everyone Else
So like what the heck is 'logical decision theory' in terms a normal person can understand?
- Eliezer Yudkowsky - An introductory guide to modern logic
Logic, provability, Löb, Gödel and more!
- Jaime Sevilla Molina - Arbital Markdown
All about Arbital's extended Markdown syntax.
- Alexei Andreev - Arbital reviewer
Reviewers help writers improve their pages, check over all changes to Arbital's content, and assess page quality.
- Eric Bruylant - Arithmetical hierarchy
The arithmetical hierarchy is a way of classifying logical statements by the number of clauses saying "for every object" and "there exists an object".
- Eliezer Yudkowsky - Axiom of Choice
The most controversial axiom of the 20th century.
- Mark Chimes - Bayesian view of scientific virtues
Why is it that science relies on bold, precise, and falsifiable predictions? Because of Bayes' rule, of course.
- Eliezer Yudkowsky - Belief revision as probability elimination
Update your beliefs by throwing away large chunks of probability mass.
- Eliezer Yudkowsky - Bit
The term "bit" refers to different concepts in different fields. The common theme across all the us…
- Nate Soares - Cantor-Schröder-Bernstein theorem
This theorem tells us that comparing sizes of sets makes sense: if one set is smaller than another, and the other is smaller than the one, then they are the same size.
- Patrick Stevens - Category theory
How mathematical objects are related to others in the same category.
- Mark Chimes - Claim explainer: donor lotteries and returns to scale
Sometimes, new technical developments in the discourse around effective altruism can be difficult to…
- Benjamin Hoffman - Codomain vs image
It is useful to distinguish codomain from image both (a) when the type of thing that the function pr…
- Nate Soares - Complexity theory
Study of the computational resources needed to compute something
- Jaime Sevilla Molina - Cyclic Group Intro (Math 0)
A finite cyclic group is a little bit like a clock.
- Mark Chimes - Cyclic group
Cyclic groups form one of the most simple classes of groups.
- Patrick Stevens - Data capacity
The data capacity of an object is defined to be the Logarithm of the number of different distinguish…
- Nate Soares - Elementary Algebra
How do we describe relations between different things? How can we figure out new true things from tr…
- Adele Lopez - Empirical probabilities are not exactly 0 or 1
"Cromwell's Rule" says that probabilities of exactly 0 or 1 should never be applied to empirical propositions - there's always some probability, however tiny, of being mistaken.
- Eliezer Yudkowsky - Encoding trits with GalCom bits
There are $\log_2(3) \approx 1.585$ bits to a Trit. Why is it that particular value? Consider the Ga…
- Nate Soares - Euclid's Lemma on prime numbers
A very basic but vitally important property of the prime numbers is that they "can't be split between factors": if a prime divides a product then it must divide one of the individual factors.
- Patrick Stevens - Factorial
The number of ways you can order things. (Alternately subtitled: Is that exclamation point a factorial, or are you just excited to see me?)
- Michael Cohen - Factorial
The *factorial* of a number $n$ is how we describe "how many different ways we can arrange $n$ obje…
- Patrick Stevens - Fixed point theorem of provability logic
Deal with those pesky self-referential sentences!
- Jaime Sevilla Molina - Fractional bits: Expected cost interpretation
In the GalCom thought experiment, you regularly have to send large volumes of information through de…
- Nate Soares - Free group
The free group is "the purest way to make a group containing a given set".
- Patrick Stevens - GalCom
In the GalCom thought experiment, you live in the future, and make your money by living in the Dene…
- Nate Soares - Group homomorphism
A group homomorphism is a "function between groups" that "respects the group structure".
- Patrick Stevens - Group presentation
Presentations are a fairly compact way of expressing groups.
- Patrick Stevens - Gödel encoding and self-reference
The formalism that mathematicians use to talk about arithmetic turns out to be able to talk about itself.
- Patrick LaVictoire - High-speed intro to Bayes's rule
A high-speed introduction to Bayes's Rule on one page, for the impatient and mathematically adept.
- Eliezer Yudkowsky - Introductory guide to logarithms
Welcome to the Arbital introduction to logarithms! In modern education, logarithms are often mention…
- Nate Soares - Isomorphism
A morphism between two objects which describes how they are "essentially equivalent" for the purposes of the theory under consideration.
- Mark Chimes - Least common multiple
The **least common multiple (LCM)** of two positive natural numbers a, b is the smallest natural …
- Johannes Schmitt - Left cosets are all in bijection
The left cosets of a subgroup in a parent group are all the same size.
- Patrick Stevens - Likelihood functions, p-values, and the replication crisis
What's the whole Bayesian-vs.-frequentist debate about?
- Eliezer Yudkowsky - Logarithm
The logarithm base $b$ of a number $n,$ written $\log_b(n),$ is the answer to the question "how man…
- Nate Soares - Logarithm base 1
There is no log base 1.
- Nate Soares - Logarithm tutorial overview
The logarithm tutorial covers the following six subjects:
1. What are logarithms?
2. Logarithms as…
- Nate Soares - Math 3 example statements
If you can read these formulas, you're in Math 3!
- Joe Zeng - Metric
A metric is a function that defines a distance between elements in a set and follows some basic rules.
- Bryce Woodworth - Monoid
A monoid $M$ is a pair $(X, \diamond)$ where $X$ is a [set\_theory\_set set] and $\diamond$ is an [a…
- Nate Soares - Monotone function
An order-preserving map between posets.
- Kevin Clancy - More about Arbital
Lots more information about Arbital vision.
- Alexei Andreev - Morphism
A morphism is the abstract representation of a relation between mathematical objects.
Usually, it i…
- Jaime Sevilla Molina - Nearest unblocked strategy
If you patch an agent's preference framework to avoid an undesirable solution, what can you expect to happen?
- Eliezer Yudkowsky - No-Free-Lunch theorems are often irrelevant
There's often a theorem proving that some problem has no optimal answer across every possible world. But this may not matter, since the real world is a special case. (E.g., a low-entropy universe.)
- Eliezer Yudkowsky - Odds
Odds express a relative probability.
- Eliezer Yudkowsky - On the margin, effective altruist researchers and leaders should carry out more empirical investigation of strategic questions.
Strategic question might include:
* How can we shape the development of brain-computer interfaces?
…
- Ryan Carey - Order relation
A way of determining which elements of a set come "before" or "after" other elements.
- Joe Zeng - P vs NP: Arguments against P=NP
Why we believe P and NP are different
- Jaime Sevilla Molina - Parfit's Hitchhiker
You are dying in the desert. A truck-driver who is very good at reading faces finds you, and offers to drive you into the city if you promise to pay $1,000 on arrival. You are a selfish rationalist.
- Eliezer Yudkowsky - Pi is irrational
The number pi is famously not rational, in spite of joking attempts at legislation to fix its value at 3 or 22/7.
- Patrick Stevens - Predictions For 2017
Scott Alexander made 105 predictions for 2017. Most of them are not personal and are listed below. …
- Alexei Andreev - Prime order groups are cyclic
This is the first step on the road to classifying the finite groups.
- Patrick Stevens - Proof of Löb's theorem
Proving that I am Santa Claus
- Jaime Sevilla Molina - Proof of Rice's theorem
A standalone proof of Rice's theorem, including one surprising lemma.
- Patrick Stevens - Real number (as Dedekind cut)
A way to construct the real numbers that follows the intuition of filling in the gaps.
- Joe Zeng - Report likelihoods, not p-values
If scientists reported likelihood functions instead of p-values, this could help science avoid p-ha…
- Nate Soares - Rice's Theorem
Rice's Theorem tells us that if we want to determine pretty much anything about the behaviour of an arbitrary computer program, we can't in general do better than just running it.
- Patrick Stevens - Rice's Theorem: Intro (Math 1)
You can't write a program that looks at another programs source code, and tells you whether it computes the Fibonacci sequence.
- Dylan Hendrickson - Solomonoff induction: Intro Dialogue (Math 2)
An introduction to Solomonoff induction for the unfamiliar reader who isn't bad at math
- Eliezer Yudkowsky - Square visualization of probabilities on two events
$$
\newcommand{\true}{\text{True}}
\newcommand{\false}{\text{False}}
\newcommand{\bP}{\mathbb{P}}
…
- Tsvi BT - Symmetric group
The symmetric groups form the fundamental link between group theory and the notion of symmetry.
- Patrick Stevens - The characteristic of the logarithm
Any time you find an output that adds whenever the input multiplies, you're probably looking at a (…
- Nate Soares - The empty set is the only set which satisfies the universal property of the empty set
This theorem tells us that the universal property provides a sensible way to define the empty set uniquely.
- Patrick Stevens - The missing step between Zero and Hero
Creating a space for high potential people grow and improve the world at scale.
- Eric Bruylant - Uncomputability
The diagonal function and the halting problem
- Jaime Sevilla Molina - Uncountability
Some infinities are bigger than others. Uncountable infinities are larger than countable infinities.
- Jason Gross - Uncountability: Intuitive Intro
Are all sizes of infinity the same? What does "the same" even mean here?
- Jason Gross - Unique factorisation domain
This is the correct way to abstract from the integers the fact that every integer can be written uniquely as a product of prime numbers.
- Patrick Stevens - Universal property of the disjoint union
Just as the empty set may be described by a universal property, so too may the disjoint union of sets.
- Patrick Stevens - Universal property of the empty set
The empty set can be characterised by how it interacts with other sets, rather than by any explicit property of the empty set itself.
- Patrick Stevens - Waterfall diagram
Visualizing Bayes' rule as the mixing of probability streams.
- Eliezer Yudkowsky - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky - Well-defined
A mathematical object is "well-defined" if we have given it a completely unambiguous definition.
- Patrick Stevens - What is a logarithm?
Logarithms are a group of functions that take a number as input and produce another number. There i…
- Nate Soares - n-digit
An $n$-digit is a physical object that can be stably placed into any of $n$ distinguishable states. …
- Nate Soares
group
At this point, I think the evidence points away from there being any deeply useful form of optimalit…
- Patrick LaVictoireCould be nice to add a concrete "real-life" (non-math) example, say like the following:
You are a d…
- Mark ChimesDoes x correspond to a *statement* (as used in the previous sentence about expressiveness), or does …
- Eric RogstadGlad to see this! Second order soon?
- Faisal AlZabenHow can I get permission to edit this page, please?
- Mark ChimesHuh... Not sure I understand this. I have BS in CS, but don't remember running across this. Would lo…
- Alexei AndreevI have a question about general Arbital practice here. A mathematician will probably already know wh…
- Patrick StevensI think the halting problem probably should have its own page, rather than being linked to the umbre…
- Patrick StevensI'll edit to be more precise: A CDT agent thinks "me and an LDT agent facing off against 99 other LD…
- Eliezer YudkowskyMakes sense (though the versus you quote wasn't being advocated as a fair example by either agent). …
- Eliezer YudkowskyNice! I've never seen an example like this before, and it's actually kind of surprising. It seems to…
- Alexei AndreevOh no! That's a bug, we are looking into it...
- Eric RogstadOh, not at all. Probably a bug; I'm going to look into it right now.
- Alexei AndreevShould be fixed. Try now.
- Alexei AndreevSimply that I didn't know the name :) I'll edit it in.
- Patrick StevensThis is a great page! I think the intro/summary could be made a little more accessible though? The u…
- Eric BruylantThis is one of two ways I know of proving Löb's theorem, and I find them both illuminating. (The oth…
- Patrick LaVictoireWhy is it called a *decision problem*? As a reader looking for an intuitive understanding, that's on…
- Eric RogstadJaime Sevilla Molina
I've submitted an edit to the page on morphisms and wrote an intuitive guide t…
- Mark Chimesraises?
- Eric Rogstad
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky
- Instrumental convergence
Some strategies can help achieve most possible simple goals. E.g., acquiring more computing power or more material resources. By default, unless averted, we can expect advanced AIs to do that.
- Eliezer Yudkowsky
- The rocket alignment problem
If people talked about the problem of space travel the way they talked about AI...
- Eliezer Yudkowsky
- Odds: Introduction
What's the difference between probabilities and odds? Why is a 20% probability of success equivalent to 1 : 4 odds favoring success?
- Nate Soares
- Path: Insights from Bayesian updating
A learning-path placeholder page for insights derived from the Bayesian rule for updating beliefs.
- Eliezer Yudkowsky
- Prior probability
What we believed before seeing the evidence.
- Eliezer Yudkowsky - Waterfall diagram
Visualizing Bayes' rule as the mixing of probability streams.
- Eliezer Yudkowsky
wiki
- AI safety mindset
Asking how AI designs could go wrong, instead of imagining them going right.
- Eliezer Yudkowsky
wiki
- GalCom
In the GalCom thought experiment, you live in the future, and make your money by living in the Dene…
- Nate Soares
- Minimality principle
The first AGI ever built should save the world in a way that requires the least amount of the least dangerous cognition.
- Eliezer Yudkowsky - Psychologizing
It's sometimes important to consider how other people might be led into error. But psychoanalyzing them is also dangerous! Arbital discussion norms say to explicitly note this as "psychologizing".
- Eliezer Yudkowsky
wiki
- AI safety mindset
Asking how AI designs could go wrong, instead of imagining them going right.
- Eliezer Yudkowsky - Arbital Blog
Stay up to date on all things Arbital
- Alexei Andreev - Arbital Markdown
All about Arbital's extended Markdown syntax.
- Alexei Andreev - Arbital features
Overview of all Arbital features.
- Alexei Andreev - Arbital requisites
To understand a thing you often need to understand some other things.
- Alexei Andreev - Arbital: Solving online explanations
An explanation of Arbital's mid-term goals
- Eliezer Yudkowsky - Now I am become Life, the protector of worlds
In which Arbital is brought forth into the world.
- Alexei Andreev - Orthogonality Thesis
Will smart AIs automatically become benevolent, or automatically become hostile? Or do different AI designs imply different goals?
- Eliezer Yudkowsky - Predictions For 2017
Scott Alexander made 105 predictions for 2017. Most of them are not personal and are listed below. …
- Alexei Andreev - To math explanations and beyond!
In which Arbital doubles down on math explanations.
- Alexei Andreev - Value alignment problem
You want to build an advanced AI with the right values... but how?
- Eliezer Yudkowsky
- Arbital greenlink
What happens when you hover over an Arbital link?
- Alexei Andreev
- Don't try to solve the entire alignment problem
New to AI alignment theory? Want to work in this area? Already been working in it for years? Don't try to solve the entire alignment problem with your next good idea!
- Eliezer Yudkowsky
- A Return to Discussion - Eric Bruylant
- Epistemic and instrumental efficiency
An efficient agent never makes a mistake you can predict. You can never successfully predict a directional bias in its estimates.
- Eliezer Yudkowsky - The current message of effective altruism heavily discourages creativity.
Alyssa Vance expands on this point in her [FB post](https://www.facebook.com/alyssamvance/posts/1021…
- Alexei Andreev
- Introductory guide to logarithms
Welcome to the Arbital introduction to logarithms! In modern education, logarithms are often mention…
- Nate Soares - The End (of the basic log tutorial)
That concludes our introductory tutorial on logarithms! You have made it to the end.
Throughout thi…
- Nate Soares
- AI alignment
The great civilizational problem of creating artificially intelligent computer systems such that running them is a good idea.
- Eliezer Yudkowsky - Programmer
Who is building these advanced agents?
- Eliezer Yudkowsky - Welcome to Arbital
Front page explaining what Arbital is all about.
- Alexei Andreev
wiki
- Addition of rational numbers (Math 0)
The simplest operation on rational numbers is addition.
- Patrick Stevens - Bayesian view of scientific virtues
Why is it that science relies on bold, precise, and falsifiable predictions? Because of Bayes' rule, of course.
- Eliezer Yudkowsky - Cyclic Group Intro (Math 0)
A finite cyclic group is a little bit like a clock.
- Mark Chimes - Definition
Meta tag used to mark pages that strictly define a particular term or phrase.
- Eliezer Yudkowsky - Guarded definition
A guarded definition is one where at least one position suspects there will be pressure to stretch a…
- Eliezer Yudkowsky - Introductory Bayesian problems
Bayesian problems to try to solve yourself, before beginning to learn about Bayes' rule.
- Eliezer Yudkowsky - Introductory guide to logarithms
Welcome to the Arbital introduction to logarithms! In modern education, logarithms are often mention…
- Nate Soares - Likelihood functions, p-values, and the replication crisis
What's the whole Bayesian-vs.-frequentist debate about?
- Eliezer Yudkowsky - Most complex things are not very compressible
We can't *prove* it's impossible, but it would be *extremely surprising* to discover a 500-state Turing machine that output the exact text of "Romeo and Juliet".
- Eliezer Yudkowsky - Ordinary claims require ordinary evidence
Extraordinary claims require extraordinary evidence, but ordinary claims *don't*.
- Nate Soares - Psychologizing
It's sometimes important to consider how other people might be led into error. But psychoanalyzing them is also dangerous! Arbital discussion norms say to explicitly note this as "psychologizing".
- Eliezer Yudkowsky - Real number (as Cauchy sequence)
There are several ways to construct real numbers; this is the most natural way to use them in computations.
- Patrick Stevens - Report likelihoods, not p-values
If scientists reported likelihood functions instead of p-values, this could help science avoid p-ha…
- Nate Soares - Subtraction of rational numbers (Math 0)
In which we meet anti-apples.
- Patrick Stevens - The reals (constructed as Dedekind cuts) form a field
The reals are an archetypal example of a field, but if we are to construct them from simpler objects, we need to show that our construction does indeed have the right properties.
- Patrick Stevens - The reals (constructed as classes of Cauchy sequences of rationals) form a field
The reals are an archetypal example of a field, but if we are to construct them from simpler objects, we need to show that our construction does indeed have the right properties.
- Patrick Stevens
- Bayesian view of scientific virtues
Why is it that science relies on bold, precise, and falsifiable predictions? Because of Bayes' rule, of course.
- Eliezer Yudkowsky
- Introductory guide to logarithms
Welcome to the Arbital introduction to logarithms! In modern education, logarithms are often mention…
- Nate Soares
- Least common multiple
The **least common multiple (LCM)** of two positive natural numbers a, b is the smallest natural …
- Johannes Schmitt
- Bayes' rule
Bayes' rule is the core theorem of probability theory saying how to revise our beliefs when we make a new observation.
- Eliezer Yudkowsky
- Diamond maximizer
How would you build an agent that made as much diamond material as possible, given vast computing power but an otherwise rich and complicated environment?
- Eliezer Yudkowsky
- Frequency diagrams: A first look at Bayes
The most straightforward visualization of Bayes' rule.
- Nate Soares
- Introductory Bayesian problems
Bayesian problems to try to solve yourself, before beginning to learn about Bayes' rule.
- Eliezer Yudkowsky
- Math 2
Do you work with math on a fairly routine basis? Do you have little trouble grasping abstract structures and ideas?
- Eliezer Yudkowsky
- Predictions For 2017
Scott Alexander made 105 predictions for 2017. Most of them are not personal and are listed below. …
- Alexei Andreev
- Vitamin D helps prevent cancer
There have been a lot of studies performed that show that vitamin D helps prevent cancer, but overal…
- Alexei Andreev
- Welcome to Arbital
Front page explaining what Arbital is all about.
- Alexei Andreev
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky - Known-algorithm non-self-improving agent
Possible advanced AIs that aren't self-modifying, aren't self-improving, and where we know and understand all the component algorithms.
- Eliezer Yudkowsky
wiki
- Corrigibility
"I can't let you do that, Dave."
- Nate Soares
- High-speed intro to Bayes's rule
A high-speed introduction to Bayes's Rule on one page, for the impatient and mathematically adept.
- Eliezer Yudkowsky
- Bayes' rule: Probability form
The original formulation of Bayes' rule.
- Nate Soares
- Introduction to Bayes' rule: Odds form
Bayes' rule is simple, if you think in terms of relative odds.
- Eliezer Yudkowsky - Waterfall diagram
Visualizing Bayes' rule as the mixing of probability streams.
- Eliezer Yudkowsky - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- Odds
Odds express a relative probability.
- Eliezer Yudkowsky
- Introduction to Logical Decision Theory for Analytic Philosophers
Why "choose as if controlling the logical output of your decision algorithm" is the most appealing candidate for the principle of rational choice.
- Eliezer Yudkowsky
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky
- Ideological Turing test
Can you explain the opposing position well enough that people can't tell whether you or a real advocate of that position created the explanation?
- Eliezer Yudkowsky
- Introductory Bayesian problems
Bayesian problems to try to solve yourself, before beginning to learn about Bayes' rule.
- Eliezer Yudkowsky
- Extraordinary claims require extraordinary evidence
The people who adamantly claim they were abducted by aliens do provide some evidence for aliens. They just don't provide quantitatively enough evidence.
- Eliezer Yudkowsky - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- Bayes' rule: Probability form
The original formulation of Bayes' rule.
- Nate Soares - Bayesian view of scientific virtues
Why is it that science relies on bold, precise, and falsifiable predictions? Because of Bayes' rule, of course.
- Eliezer Yudkowsky - Report likelihoods, not p-values
If scientists reported likelihood functions instead of p-values, this could help science avoid p-ha…
- Nate Soares
- Odds: Introduction
What's the difference between probabilities and odds? Why is a 20% probability of success equivalent to 1 : 4 odds favoring success?
- Nate Soares
wiki
wiki
- Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev - Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky - Bit (of data)
A bit of data is the amount of data required to single out one message from a set of two. Equivalen…
- Nate Soares - Cartesian product
The Cartesian product of two sets $A$ and $B,$ denoted $A \times B,$ is the set of all [ordered\_pai…
- Nate Soares - Category theory
How mathematical objects are related to others in the same category.
- Mark Chimes - Combining vectors
One of the most useful things we can do with vectors is to combine them!
- Adele Lopez - Division of rational numbers (Math 0)
"Division" is the idea of "dividing something up among some people so that we can give equal amounts to each person".
- Patrick Stevens - Elementary Algebra
How do we describe relations between different things? How can we figure out new true things from tr…
- Adele Lopez - Exponential notation for function spaces
Why $Y^X$ is good notation for the space of maps from $X$ to $Y$
- Izaak Meckler - Factorial
The number of ways you can order things. (Alternately subtitled: Is that exclamation point a factorial, or are you just excited to see me?)
- Michael Cohen - Generalized element
A category-theoretic generalization of the notion of element of a set.
- Luke Sciarappa - Geometry of vectors: direction
What rotation would it take to line up this vector to this one?
- Adele Lopez - Locale
Topology - but right
- Adele Lopez - Mathematical induction
Proving a statement about all positive integers by knocking them down like dominoes.
- Douglas Weathers - Ordered ring
A ring with a total ordering compatible with its ring structure.
- Dylan Hendrickson - Pi
Pi, usually written $π$, is a number equal to the ratio of a circle's [-circumference] to its [-diam…
- Michael Cohen - Primer on Infinite Series
What does it mean to add things together forever?
- Chris Holden - Reflexive relation
A binary relation over some set is **reflexive** when every element of that set is related to itself…
- Ryan Hendrickson - Vector arithmetic
Vectors: what they are, and how to add and scale them.
- Adele Lopez - Welcome to Arbital
Front page explaining what Arbital is all about.
- Alexei Andreev - Well-ordered set
An ordered set with an order that always has a "next element".
- Dylan Hendrickson
- A whirlwind tour
A rapid tour of Eric's thoughts on the accelerator project.
- Eric Bruylant - The missing step between Zero and Hero
Creating a space for high potential people grow and improve the world at scale.
- Eric Bruylant - Who needs civilization?
The most common difference between my model and that of people I've discussed this with is that many…
- Eric Bruylant
- Children in a sidebar
I always forget to scroll all the way down. I shouldn't have to. Putting children in a sidebar allow…
- Olivia Schaefer
wiki
- Arbital Markdown
All about Arbital's extended Markdown syntax.
- Alexei Andreev - Requisites for personal growth
A mashup of models
- Toon Alfrink - The current message of effective altruism heavily discourages creativity.
Alyssa Vance expands on this point in her [FB post](https://www.facebook.com/alyssamvance/posts/1021…
- Alexei Andreev
Ah, interesting. Do you mean: "Once you found a working business / movement model, it's time to redu…
- Alexei AndreevAlyssa defines Creativity as "having new ideas rather than evaluating existing ones," but I would ar…
- Glenn DavisBollard's more conservative estimate is 38 hen-years per dollar, if you include other expenditures o…
- Benjamin HoffmanDoes this track history of predictions so that an update after new information can lead to a new agg…
- Brandon ReinhartEA discourages creativity, and I think that's valuable for the movement at this stage. The most visi…
- Robert CordwellEA discourages creativity, but that's true for most movements and institutions. A more interesting …
- John MaxwellI think it's good to have our high standards of evidence, but once in a while I see someone with a g…
- Kyle BogosianIs there a way to link to a section within a page? (E.g. for tables of contents.)
- Tsvi BTNote that PredictIt [currently thinks](https://www.predictit.org/Contract/4264/Will-the-next-US-pres…
- Eric RogstadSee also: http://www.metaculus.com/questions/377/will-donald-trump-be-the-president-of-the-united-st…
- Eric RogstadThere have been 3 US presidents where impeachment procedures have taken place against a president. T…
- Travis RiveraThere is now! This page even has a TOC.
- Eric BruylantTo clarify my view, I think EA moderately discourages creativity but this is a big mistake: it shoul…
- Ryan CareyTwo ways impeachment could happen:
- Trump becomes an albatross on the GOP, to the degree that the…
- Patrick LaVictoireYes.
As far as I can tell, the current message of effective altruism sort of focuses in too strongly…
- Timothy Chu
- Eliezer Yudkowsky
Cofounder, with Nick Bostrom, of the field of value alignment theory.
- Bayes' rule
Bayes' rule is the core theorem of probability theory saying how to revise our beliefs when we make a new observation.
- Eliezer Yudkowsky - Conditional probability
The notation for writing "The probability that someone has green eyes, if we know that they have red hair."
- Eliezer Yudkowsky
wiki
- Complexity of value
There's no simple way to describe the goals we want Artificial Intelligences to want.
- Eliezer Yudkowsky - Probability theory
The logic of science; coherence relations on quantitative degrees of belief.
- Eliezer Yudkowsky
group
- Lancelot Verinia
Formalise everything.
wiki
- Object-level vs. indirect goals
Difference between "give Alice the apple" and "give Alice what she wants".
- Eliezer Yudkowsky - Strictly confused
A hypothesis is strictly confused by the raw data, if the hypothesis did much worse in predicting it than the hypothesis itself expected.
- Eliezer Yudkowsky
- Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- Relative likelihood
How relatively likely an observation is, given two or more hypotheses, determines the strength and direction of evidence.
- Eliezer Yudkowsky
- Arbital requisites
To understand a thing you often need to understand some other things.
- Alexei Andreev - Arithmetical hierarchy
The arithmetical hierarchy is a way of classifying logical statements by the number of clauses saying "for every object" and "there exists an object".
- Eliezer Yudkowsky
- Welcome to Arbital
Front page explaining what Arbital is all about.
- Alexei Andreev
- Introduction to Bayes' rule: Odds form
Bayes' rule is simple, if you think in terms of relative odds.
- Eliezer Yudkowsky
- Separation from hyperexistential risk
The AI should be widely separated in the design space from any AI that would constitute a "hyperexistential risk" (anything worse than death).
- Eliezer Yudkowsky
- Corrigibility
"I can't let you do that, Dave."
- Nate Soares
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky - Extraordinary claims require extraordinary evidence
The people who adamantly claim they were abducted by aliens do provide some evidence for aliens. They just don't provide quantitatively enough evidence.
- Eliezer Yudkowsky
- Introduction to Bayes' rule: Odds form
Bayes' rule is simple, if you think in terms of relative odds.
- Eliezer Yudkowsky
wiki
- An Introduction to Logical Decision Theory for Everyone Else
So like what the heck is 'logical decision theory' in terms a normal person can understand?
- Eliezer Yudkowsky - Arbital lens: TL;DR
Much shorter version of Arbital Lens page
- Alexei Andreev - Arbital: Solving online explanations
An explanation of Arbital's mid-term goals
- Eliezer Yudkowsky - Function
Intuitively, a function $f$ is a procedure (or machine) that takes an input and performs some opera…
- Nate Soares - Group
The algebraic structure that captures symmetry, relationships between transformations, and part of what multiplication and addition have in common.
- Nate Soares - Group theory
What kinds of symmetry can an object have?
- Nate Soares - Introductory guide to logarithms
Welcome to the Arbital introduction to logarithms! In modern education, logarithms are often mention…
- Nate Soares - Mindcrime: Introduction
The more predictive accuracy we want from a model, the more detailed the model becomes. A very roug…
- Eliezer Yudkowsky - Morphism
A morphism is the abstract representation of a relation between mathematical objects.
Usually, it i…
- Jaime Sevilla Molina - Reflective stability
Wanting to think the way you currently think, building other agents and self-modifications that think the same way.
- Eliezer Yudkowsky - Rescuing the utility function
If your utility function values 'heat', and then you discover to your horror that there's no ontologically basic heat, switch to valuing disordered kinetic energy. Likewise 'free will' or 'people'.
- Eliezer Yudkowsky - Set
An unordered collection of distinct objects.
- Nate Soares - Some men just want to watch the world learn
In which Arbital gets paths.
- Alexei Andreev - Underlying set
What do a Group, a Partially ordered set, and a [ topological space] have in common? Each is a Set …
- Nate Soares
- AI alignment
The great civilizational problem of creating artificially intelligent computer systems such that running them is a good idea.
- Eliezer Yudkowsky
- Shift towards the hypothesis of least surprise
When you see new evidence, ask: which hypothesis is *least surprised?*
- Nate Soares
wiki
- Bayes' rule: Log-odds form
A simple transformation of Bayes' rule reveals tools for measuring degree of belief, and strength of evidence.
- Eliezer Yudkowsky - Digit wheel
A mechanical device for storing a number from 0 to 9.
![](http://www.cl.cam.ac.uk/~djg11/howcompu…
- Nate Soares - Empirical probabilities are not exactly 0 or 1
"Cromwell's Rule" says that probabilities of exactly 0 or 1 should never be applied to empirical propositions - there's always some probability, however tiny, of being mistaken.
- Eliezer Yudkowsky - Fractional digits
When $b$ and $x$ are integers, $\log_b(x)$ has a few good interpretations. It's roughly the length o…
- Nate Soares - Function
Intuitively, a function $f$ is a procedure (or machine) that takes an input and performs some opera…
- Nate Soares - Log as the change in the cost of communicating
When interpreting logarithms as a generalization of the notion of "length" and as digit exchange rat…
- Nate Soares - Lt. Gilbert S. Daniels and the myth of averages
There is no such thing as an average pilot
- Duncan Sabien - Mathematical induction
Proving a statement about all positive integers by knocking them down like dominoes.
- Douglas Weathers - Odds: Introduction
What's the difference between probabilities and odds? Why is a 20% probability of success equivalent to 1 : 4 odds favoring success?
- Nate Soares - Proof by contradiction
Discover what 'reductio ad absurdum' means!
- Jaime Sevilla Molina - Proof of Löb's theorem
Proving that I am Santa Claus
- Jaime Sevilla Molina - Shift towards the hypothesis of least surprise
When you see new evidence, ask: which hypothesis is *least surprised?*
- Nate Soares - Strictly confused
A hypothesis is strictly confused by the raw data, if the hypothesis did much worse in predicting it than the hypothesis itself expected.
- Eliezer Yudkowsky - The log lattice
Log as the change in the cost of communicating and other pages give physical interpretations of what…
- Nate Soares - The rocket alignment problem
If people talked about the problem of space travel the way they talked about AI...
- Eliezer Yudkowsky - To math explanations and beyond!
In which Arbital doubles down on math explanations.
- Alexei Andreev - Uncountability: Intuitive Intro
Are all sizes of infinity the same? What does "the same" even mean here?
- Jason Gross
wiki
- A whirlwind tour
A rapid tour of Eric's thoughts on the accelerator project.
- Eric Bruylant - Accelerator Project
The Accelerator Project aims to create a low-cost environment which facilitates rapid personal growt…
- Eric Bruylant - Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev - Arbital Blog
Stay up to date on all things Arbital
- Alexei Andreev - Arbital greenlink
What happens when you hover over an Arbital link?
- Alexei Andreev - Arbital: Solving online explanations
An explanation of Arbital's mid-term goals
- Eliezer Yudkowsky - Artificial General Intelligence
An AI which has the same kind of "significantly more general" intelligence that humans have compared to chimpanzees; it can learn new domains, like we can.
- Eliezer Yudkowsky - Bit
The term "bit" refers to different concepts in different fields. The common theme across all the us…
- Nate Soares - Finishing your Bayesian path on Arbital
The page that comes at the end of reading the Arbital Guide to Bayes' rule
- Eliezer Yudkowsky - Practicing Brevity
Wanna save the world? Write better TLDRs. And spend more time respecting your reader's time.
- Raymond Arnold - Requisites for personal growth
A mashup of models
- Toon Alfrink - The missing step between Zero and Hero
Creating a space for high potential people grow and improve the world at scale.
- Eric Bruylant - Vitamin D is good for you
We'll consider two categories of vitamin D supplementation: below and above the recommended levels.
…
- Alexei Andreev - Why waiting to donate harms charities
A blog post explaining the potential reasons why someone would choose to wait to donate and how that leads to suboptimal outcomes for the charity.
- Alexei Andreev
- Answer to sparking widgets problem
Odds of 1 : 3, probability of 1/4.
- Eliezer Yudkowsky - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- Arbital: Solving online explanations
An explanation of Arbital's mid-term goals
- Eliezer Yudkowsky - Executable philosophy
Philosophical discourse aimed at producing a trustworthy answer or meta-answer, in limited time, which can used in constructing an Artificial Intelligence.
- Eliezer Yudkowsky - Mindcrime
Might a machine intelligence contain vast numbers of unhappy conscious subprocesses?
- Eliezer Yudkowsky - Path: Insights from Bayesian updating
A learning-path placeholder page for insights derived from the Bayesian rule for updating beliefs.
- Eliezer Yudkowsky - Waterfall diagram
Visualizing Bayes' rule as the mixing of probability streams.
- Eliezer Yudkowsky
wiki
- Frequency diagrams: A first look at Bayes
The most straightforward visualization of Bayes' rule.
- Nate Soares
wiki
- AI safety mindset
Asking how AI designs could go wrong, instead of imagining them going right.
- Eliezer Yudkowsky - Contributing to Arbital
Want to help Arbital become awesome?
- Eric Bruylant - Group theory
What kinds of symmetry can an object have?
- Nate Soares - Intersection
The intersection of two sets is the set of elements they have in common
- M Yass - Isomorphism
A morphism between two objects which describes how they are "essentially equivalent" for the purposes of the theory under consideration.
- Mark Chimes - Likelihood functions, p-values, and the replication crisis
What's the whole Bayesian-vs.-frequentist debate about?
- Eliezer Yudkowsky - Logarithm
The logarithm base $b$ of a number $n,$ written $\log_b(n),$ is the answer to the question "how man…
- Nate Soares - Math 3 example statements
If you can read these formulas, you're in Math 3!
- Joe Zeng - Proof by contradiction
Discover what 'reductio ad absurdum' means!
- Jaime Sevilla Molina - Reflexive relation
A binary relation over some set is **reflexive** when every element of that set is related to itself…
- Ryan Hendrickson - Set
An unordered collection of distinct objects.
- Nate Soares - Square visualization of probabilities on two events
$$
\newcommand{\true}{\text{True}}
\newcommand{\false}{\text{False}}
\newcommand{\bP}{\mathbb{P}}
…
- Tsvi BT - Two independent events: Square visualization
$$
\newcommand{\true}{\text{True}}
\newcommand{\false}{\text{False}}
\newcommand{\bP}{\mathbb{P}}
…
- Tsvi BT - Universal property of the empty set
The empty set can be characterised by how it interacts with other sets, rather than by any explicit property of the empty set itself.
- Patrick Stevens
- Bayes' rule: Log-odds form
A simple transformation of Bayes' rule reveals tools for measuring degree of belief, and strength of evidence.
- Eliezer Yudkowsky - Introduction to Bayes' rule: Odds form
Bayes' rule is simple, if you think in terms of relative odds.
- Eliezer Yudkowsky
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky
- Logarithm
The logarithm base $b$ of a number $n,$ written $\log_b(n),$ is the answer to the question "how man…
- Nate Soares
- Ring
A ring is a kind of Algebraic structure which we obtain by considering groups as being "things with…
- Nate Soares
- Conditional probability
The notation for writing "The probability that someone has green eyes, if we know that they have red hair."
- Eliezer Yudkowsky
- Welcome to Arbital
Front page explaining what Arbital is all about.
- Alexei Andreev
- Bayes' rule: Proportional form
The fastest way to say something both convincing and true about belief-updating.
- Eliezer Yudkowsky
wiki
- Guarded definition
A guarded definition is one where at least one position suspects there will be pressure to stretch a…
- Eliezer Yudkowsky - Pivotal event
Which types of AIs, if they work, can do things that drastically change the nature of the further game?
- Eliezer Yudkowsky - Report likelihoods, not p-values
If scientists reported likelihood functions instead of p-values, this could help science avoid p-ha…
- Nate Soares
- Predictions For 2017
Scott Alexander made 105 predictions for 2017. Most of them are not personal and are listed below. …
- Alexei Andreev
wiki
- Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev - Arbital: Solving online explanations
An explanation of Arbital's mid-term goals
- Eliezer Yudkowsky - Bayesian view of scientific virtues
Why is it that science relies on bold, precise, and falsifiable predictions? Because of Bayes' rule, of course.
- Eliezer Yudkowsky
group
- Eliezer Yudkowsky
Cofounder, with Nick Bostrom, of the field of value alignment theory.
- AI alignment
The great civilizational problem of creating artificially intelligent computer systems such that running them is a good idea.
- Eliezer Yudkowsky
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky
- Welcome to Arbital
Front page explaining what Arbital is all about.
- Alexei Andreev
- An early stage prioritisation model
How do you choose which projects to work on, early on in life?
- Ben Pace
wiki
- Bayes' rule: Proportional form
The fastest way to say something both convincing and true about belief-updating.
- Eliezer Yudkowsky
- Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
wiki
- Arbital: Solving online explanations
An explanation of Arbital's mid-term goals
- Eliezer Yudkowsky - Complexity theory
Study of the computational resources needed to compute something
- Jaime Sevilla Molina
group
- Eliezer Yudkowsky
Cofounder, with Nick Bostrom, of the field of value alignment theory.
- Decimal notation
The winning architecture for numerals
- Michael Cohen - Problem of fully updated deference
Why moral uncertainty doesn't stop an AI from defending its off-switch.
- Eliezer Yudkowsky
wiki
- Join and meet: Exercises
Try these exercises to test your knowledge of joins and meets.
Tangled up
--------------------
!…
- Kevin Clancy - Practicing Brevity
Wanna save the world? Write better TLDRs. And spend more time respecting your reader's time.
- Raymond Arnold - Why argument structure is important
How might we make collaborative truth-seeking both fun and easy?
- Andrea Gallagher
- Introductory Bayesian problems
Bayesian problems to try to solve yourself, before beginning to learn about Bayes' rule.
- Eliezer Yudkowsky
- Bayes' rule: Definition
Bayes' rule is the mathematics of probability theory governing how to update your beliefs in the lig…
- Nate Soares
- Eliezer Yudkowsky
Cofounder, with Nick Bostrom, of the field of value alignment theory.
group
- Eliezer Yudkowsky
Cofounder, with Nick Bostrom, of the field of value alignment theory.
wiki
- AI safety mindset
Asking how AI designs could go wrong, instead of imagining them going right.
- Eliezer Yudkowsky - Advanced agent properties
How smart does a machine intelligence need to be, for its niceness to become an issue? "Advanced" is a broad term to cover cognitive abilities such that we'd need to start considering AI alignment.
- Eliezer Yudkowsky - Almost all real-world domains are rich
Anything you're trying to accomplish in the real world can potentially be accomplished in a *lot* of different ways.
- Eliezer Yudkowsky - Consequentialist preferences are reflectively stable by default
Gandhi wouldn't take a pill that made him want to kill people, because he knows in that case more people will be murdered. A paperclip maximizer doesn't want to stop maximizing paperclips.
- Eliezer Yudkowsky - Executable philosophy
Philosophical discourse aimed at producing a trustworthy answer or meta-answer, in limited time, which can used in constructing an Artificial Intelligence.
- Eliezer Yudkowsky - For mitigating AI x-risk, an off-Earth colony would be about as useful as a warm scarf
H/T to Eliezer Yudkowsky for ["warm scarf"](https://www.facebook.com/robert.wiblin/posts/75711126783…
- Eric Rogstad - Introductory guide to logarithms
Welcome to the Arbital introduction to logarithms! In modern education, logarithms are often mention…
- Nate Soares - Rich domain
A domain is 'rich', relative to our own intelligence, to the extent that (1) its [ search space] is …
- Eliezer Yudkowsky - Superintelligent
A "superintelligence" is strongly superhuman (strictly higher-performing than any and all humans) on every cognitive problem.
- Eliezer Yudkowsky - Vinge's Principle
An agent building another agent must usually approve its design without knowing the agent's exact policy choices.
- Eliezer Yudkowsky - Why waiting to donate harms charities
A blog post explaining the potential reasons why someone would choose to wait to donate and how that leads to suboptimal outcomes for the charity.
- Alexei Andreev
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky
- Practicing Brevity
Wanna save the world? Write better TLDRs. And spend more time respecting your reader's time.
- Raymond Arnold
- Frequency diagram
Visualizing Bayes' rule by manipulating frequencies in large populations
- Nate Soares
- Bayes' rule: Log-odds form
A simple transformation of Bayes' rule reveals tools for measuring degree of belief, and strength of evidence.
- Eliezer Yudkowsky - Bayes' rule: Odds form
The simplest and most easily understandable form of Bayes' rule uses relative odds.
- Eliezer Yudkowsky - Extraordinary claims require extraordinary evidence
The people who adamantly claim they were abducted by aliens do provide some evidence for aliens. They just don't provide quantitatively enough evidence.
- Eliezer Yudkowsky - Frequency diagrams: A first look at Bayes
The most straightforward visualization of Bayes' rule.
- Nate Soares - Introduction to Bayes' rule: Odds form
Bayes' rule is simple, if you think in terms of relative odds.
- Eliezer Yudkowsky
- Arbital: learning from Wikipedia
How is Arbital different from Wikipedia?
- Alexei Andreev - Some computations are people
It's possible to have a conscious person being simulated inside a computer or other substrate.
- Eliezer Yudkowsky
- Frequency diagrams: A first look at Bayes
The most straightforward visualization of Bayes' rule.
- Nate Soares - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
wiki
- AI alignment
The great civilizational problem of creating artificially intelligent computer systems such that running them is a good idea.
- Eliezer Yudkowsky - Advanced agent properties
How smart does a machine intelligence need to be, for its niceness to become an issue? "Advanced" is a broad term to cover cognitive abilities such that we'd need to start considering AI alignment.
- Eliezer Yudkowsky - Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev - Arbital Blog
Stay up to date on all things Arbital
- Alexei Andreev - Associative operation
An **associative operation** $\bullet : X \times X \to X$ is a binary operation such that for all $x…
- Nate Soares - Associativity vs commutativity
Associativity and commutativity are often confused, because they are both constraints on how a funct…
- Nate Soares - Associativity: Examples
Yes: [Addition], [multiplication], string concatenation. No: [subtraction], [division], a Function …
- Nate Soares - Associativity: Intuition
Associative functions can be interpreted as families of functions that reduce lists down to a singl…
- Nate Soares - Bayes' rule
Bayes' rule is the core theorem of probability theory saying how to revise our beliefs when we make a new observation.
- Eliezer Yudkowsky - Bayes' rule: Definition
Bayes' rule is the mathematics of probability theory governing how to update your beliefs in the lig…
- Nate Soares - Bayes' rule: Functional form
Bayes' rule for to continuous variables.
- Eliezer Yudkowsky - Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky - Bayes' rule: Log-odds form
A simple transformation of Bayes' rule reveals tools for measuring degree of belief, and strength of evidence.
- Eliezer Yudkowsky - Bayes' rule: Odds form
The simplest and most easily understandable form of Bayes' rule uses relative odds.
- Eliezer Yudkowsky - Bayes' rule: Probability form
The original formulation of Bayes' rule.
- Nate Soares - Bayes' rule: Proportional form
The fastest way to say something both convincing and true about belief-updating.
- Eliezer Yudkowsky - Bayes' rule: Vector form
For when you want to apply Bayes' rule to lots of evidence and lots of variables, all in one go. (This is more or less how spam filters work.)
- Eliezer Yudkowsky - Bayesian reasoning
A probability-theory-based view of the world; a coherent way of changing probabilistic beliefs based on evidence.
- Eliezer Yudkowsky - Bayesian view of scientific virtues
Why is it that science relies on bold, precise, and falsifiable predictions? Because of Bayes' rule, of course.
- Eliezer Yudkowsky - Belief revision as probability elimination
Update your beliefs by throwing away large chunks of probability mass.
- Eliezer Yudkowsky - Bit
The term "bit" refers to different concepts in different fields. The common theme across all the us…
- Nate Soares - Bit (abstract)
An abstract bit is an element of the set $\mathbb B$, which has two elements. An abstract bit is to …
- Nate Soares - Bit (of data)
A bit of data is the amount of data required to single out one message from a set of two. Equivalen…
- Nate Soares - Church-Turing thesis: Evidence for the Church-Turing thesis
Why do we believe in CT thesis?
- Jaime Sevilla Molina - Codomain vs image
It is useful to distinguish codomain from image both (a) when the type of thing that the function pr…
- Nate Soares - Cognitive steganography
Disaligned AIs that are modeling human psychology and trying to deceive their programmers will want to hide their internal thought processes from their programmers.
- Eliezer Yudkowsky - Commutative operation
A commutative function $f$ is a function that takes multiple inputs from a set $X$ and produces an o…
- Nate Soares - Commutativity: Examples
Yes: addition, multiplication, maximum, minimum, rock-paper-scissors. No: subtraction, division, st…
- Nate Soares - Commutativity: Intuition
We can think of commutativity either as an artifact of notation, or as a symmetry in the output of a…
- Nate Soares - Conditional probability: Refresher
Is P(yellow | banana) the probability that a banana is yellow, or the probability that a yellow thing is a banana?
- Nate Soares - Contributing to Arbital
Want to help Arbital become awesome?
- Eric Bruylant - Convex function
A function that only curves upward
- Jessica Taylor - Convex set
A set that contains all line segments between points in the set
- Jessica Taylor - Correspondence visualizations for different interpretations of "probability"
Let's say you have a model which says a particular coin is 70% likely to be heads. How should we as…
- Nate Soares - Data capacity
The data capacity of an object is defined to be the Logarithm of the number of different distinguish…
- Nate Soares - Diamond maximizer
How would you build an agent that made as much diamond material as possible, given vast computing power but an otherwise rich and complicated environment?
- Eliezer Yudkowsky - Edge instantiation
When you ask the AI to make people happy, and it tiles the universe with the smallest objects that can be happy.
- Eliezer Yudkowsky - Empirical probabilities are not exactly 0 or 1
"Cromwell's Rule" says that probabilities of exactly 0 or 1 should never be applied to empirical propositions - there's always some probability, however tiny, of being mistaken.
- Eliezer Yudkowsky - Exchange rates between digits
In terms of data storage, if a coin is worth $1, a digit wheel is worth more than $3.32, but less than $3.33. Why?
- Nate Soares - Extraordinary claims require extraordinary evidence
The people who adamantly claim they were abducted by aliens do provide some evidence for aliens. They just don't provide quantitatively enough evidence.
- Eliezer Yudkowsky - Extrapolated volition (normative moral theory)
If someone asks you for orange juice, and you know that the refrigerator contains no orange juice, should you bring them lemonade?
- Eliezer Yudkowsky - Fractional bits
It takes $\log_2(8) = 3$ bits of data to carry one message from a set of 8 possible messages. Simila…
- Nate Soares - Fractional bits: Expected cost interpretation
In the GalCom thought experiment, you regularly have to send large volumes of information through de…
- Nate Soares - Fractional digits
When $b$ and $x$ are integers, $\log_b(x)$ has a few good interpretations. It's roughly the length o…
- Nate Soares - Frequency diagram
Visualizing Bayes' rule by manipulating frequencies in large populations
- Nate Soares - Frequency diagrams: A first look at Bayes
The most straightforward visualization of Bayes' rule.
- Nate Soares - Generalized associative law
Given an associative operator $\cdot$ and a list $[a, b, c, \ldots]$ of parameters, all ways of red…
- Nate Soares - Group
The algebraic structure that captures symmetry, relationships between transformations, and part of what multiplication and addition have in common.
- Nate Soares - Group action
"Groups, as men, will be known by their actions."
- Qiaochu Yuan - Group theory
What kinds of symmetry can an object have?
- Nate Soares - Hard problem of corrigibility
Can you build an agent that reasons as if it knows itself to be incomplete and sympathizes with your wanting to rebuild or correct it?
- Eliezer Yudkowsky - High-speed intro to Bayes's rule
A high-speed introduction to Bayes's Rule on one page, for the impatient and mathematically adept.
- Eliezer Yudkowsky - Identifying causal goal concepts from sensory data
If the intended goal is "cure cancer" and you show the AI healthy patients, it sees, say, a pattern of pixels on a webcam. How do you get to a goal concept *about* the real patients?
- Eliezer Yudkowsky - Information
Information is a measure of how much a message grants an observer the ability to predict the world.…
- Nate Soares - Interpretations of "probability"
What does it *mean* to say that a fair coin has a 50% probability of coming up heads?
- Nate Soares - Introduction to Bayes' rule: Odds form
Bayes' rule is simple, if you think in terms of relative odds.
- Eliezer Yudkowsky - Introductory guide to logarithms
Welcome to the Arbital introduction to logarithms! In modern education, logarithms are often mention…
- Nate Soares - Lattice: Exercises
Try these exercises to test your knowledge of lattices.
## Distributivity
Does the lattice meet op…
- Kevin Clancy - Life in logspace
The log lattice hints at the reason that engineers, scientists, and AI researchers find logarithms s…
- Nate Soares - Likelihood
"Likelihood", when speaking of Bayesian reasoning, denotes *the probability of an observation, sup…
- Nate Soares - Likelihood function
Let's say you have a piece of evidence $e$ and a set of hypotheses $\mathcal H.$ Each $H_i \in \math…
- Nate Soares - Likelihood functions, p-values, and the replication crisis
What's the whole Bayesian-vs.-frequentist debate about?
- Eliezer Yudkowsky - Likelihood ratio
Given a piece of evidence $e$ and two hypothsese $H_i$ and $H_j,$ the likelihood ratio between them…
- Nate Soares - Log as generalized length
To estimate the log (base 10) of a number, count how many digits it has.
- Nate Soares - Log as the change in the cost of communicating
When interpreting logarithms as a generalization of the notion of "length" and as digit exchange rat…
- Nate Soares - Log base infinity
There is no log base infinity, but if there were, it would send everything to zero
- Nate Soares - Logarithm
The logarithm base $b$ of a number $n,$ written $\log_b(n),$ is the answer to the question "how man…
- Nate Soares - Logarithm base 1
There is no log base 1.
- Nate Soares - Logarithm tutorial overview
The logarithm tutorial covers the following six subjects:
1. What are logarithms?
2. Logarithms as…
- Nate Soares - Logarithmic identities
- [ Inversion of exponentials]: $b^{\log_b(n)} = \log_b(b^n) = n.$
- [ Log of 1 is 0]: $\log_b(1) …
- Nate Soares - Logarithms invert exponentials
The function $\log_b(\cdot)$ inverts the function $b^{(\cdot)}.$ In other words, $\log_b(n) = x$ imp…
- Nate Soares - Methodology of unbounded analysis
What we do and don't understand how to do, using unlimited computing power, is a critical distinction and important frontier.
- Eliezer Yudkowsky - No-Free-Lunch theorems are often irrelevant
There's often a theorem proving that some problem has no optimal answer across every possible world. But this may not matter, since the real world is a special case. (E.g., a low-entropy universe.)
- Eliezer Yudkowsky - Odds: Introduction
What's the difference between probabilities and odds? Why is a 20% probability of success equivalent to 1 : 4 odds favoring success?
- Nate Soares - Odds: Refresher
A quick review of the notations and mathematical behaviors for odds (e.g. odds of 1 : 2 for drawing a red ball vs. green ball from a barrel).
- Nate Soares - Ordinary claims require ordinary evidence
Extraordinary claims require extraordinary evidence, but ordinary claims *don't*.
- Nate Soares - Orthogonality Thesis
Will smart AIs automatically become benevolent, or automatically become hostile? Or do different AI designs imply different goals?
- Eliezer Yudkowsky - Partially ordered set
A set endowed with a relation that is reflexive, transitive, and antisymmetric.
- Kevin Clancy - Probability distribution: Motivated definition
People keep writing things like P(sick)=0.3. What does this mean, on a technical level?
- Nate Soares - Probability interpretations: Examples
Consider evaluating, in June of 2016, the question: "What is the probability of Hillary Clinton wi…
- Nate Soares - Proof of Bayes' rule
Proofs of Bayes' rule, with graphics
- Eliezer Yudkowsky - Proof of Bayes' rule: Probability form
Let $\mathbf H$ be a [random\_variable variable] in $\mathbb P$ for the true hypothesis, and let $H_…
- Nate Soares - Properties of the logarithm
- $\log_b(x \cdot y) = \log_b(x) + \log_b(y)$ for any $b$, this is the defining characteristic of …
- Nate Soares - Quine
A computer program that prints (or does other computations to) its own source code, using indirect self-reference.
- Patrick LaVictoire - Report likelihoods not p-values: FAQ
This page answers frequently asked questions about the Report likelihoods, not p-values proposal for…
- Nate Soares - Report likelihoods, not p-values
If scientists reported likelihood functions instead of p-values, this could help science avoid p-ha…
- Nate Soares - Rescuing the utility function
If your utility function values 'heat', and then you discover to your horror that there's no ontologically basic heat, switch to valuing disordered kinetic energy. Likewise 'free will' or 'people'.
- Eliezer Yudkowsky - Shift towards the hypothesis of least surprise
When you see new evidence, ask: which hypothesis is *least surprised?*
- Nate Soares - Show me what you've broken
To demonstrate competence at computer security, or AI alignment, think in terms of breaking proposals and finding technically demonstrable flaws in them.
- Eliezer Yudkowsky - Shutdown problem
How to build an AGI that lets you shut it down, despite the obvious fact that this will interfere with whatever the AGI's goals are.
- Eliezer Yudkowsky - Solomonoff induction: Intro Dialogue (Math 2)
An introduction to Solomonoff induction for the unfamiliar reader who isn't bad at math
- Eliezer Yudkowsky - Some men just want to watch the world learn
In which Arbital gets paths.
- Alexei Andreev - Subjective probability
Probability is in the mind, not in the environment. If you don't know whether a coin came up heads or tails, that's a fact about you, not a fact about the coin.
- Eliezer Yudkowsky - Superintelligent
A "superintelligence" is strongly superhuman (strictly higher-performing than any and all humans) on every cognitive problem.
- Eliezer Yudkowsky - The End (of the basic log tutorial)
That concludes our introductory tutorial on logarithms! You have made it to the end.
Throughout thi…
- Nate Soares - The characteristic of the logarithm
Any time you find an output that adds whenever the input multiplies, you're probably looking at a (…
- Nate Soares - The log lattice
Log as the change in the cost of communicating and other pages give physical interpretations of what…
- Nate Soares - The rocket alignment problem
If people talked about the problem of space travel the way they talked about AI...
- Eliezer Yudkowsky - There is only one logarithm
All logarithm functions are the same, up to a multiplicative constant.
- Nate Soares - Time-machine metaphor for efficient agents
Don't imagine a paperclip maximizer as a mind. Imagine it as a time machine that always spits out the output leading to the greatest number of future paperclips.
- Eliezer Yudkowsky - Two independent events: Square visualization
$$
\newcommand{\true}{\text{True}}
\newcommand{\false}{\text{False}}
\newcommand{\bP}{\mathbb{P}}
…
- Tsvi BT - Uncountability: Intuitive Intro
Are all sizes of infinity the same? What does "the same" even mean here?
- Jason Gross - Unforeseen maximum
When you tell AI to produce world peace and it kills everyone. (Okay, some SF writers saw that one coming.)
- Eliezer Yudkowsky - User manipulation
If not otherwise averted, many of an AGI's desired outcomes are likely to interact with users and hence imply an incentive to manipulate users.
- Eliezer Yudkowsky - User maximization
A sub-principle of avoiding user manipulation - if you see an argmax over X or 'optimize X' instruction and X includes a user interaction, you've just told the AI to optimize the user.
- Eliezer Yudkowsky - Utility indifference
How can we make an AI indifferent to whether we press a button that changes its goals?
- Eliezer Yudkowsky - Value
The word 'value' in the phrase 'value alignment' is a metasyntactic variable that indicates the speaker's future goals for intelligent life.
- Eliezer Yudkowsky - Vinge's Principle
An agent building another agent must usually approve its design without knowing the agent's exact policy choices.
- Eliezer Yudkowsky - Waterfall diagram
Visualizing Bayes' rule as the mixing of probability streams.
- Eliezer Yudkowsky - What is a logarithm?
Logarithms are a group of functions that take a number as input and produce another number. There i…
- Nate Soares - Why is log like length?
If a number $x$ is $n$ digits long (in Decimal notation), then its logarithm (base 10) is between $n…
- Nate Soares - Why is the decimal expansion of log2(3) infinite?
Because 2 and 3 are relatively prime.
- Nate Soares - You can't get more paperclips that way
Most arguments that "A paperclip maximizer could get more paperclips by (doing nice things)" are flawed.
- Eliezer Yudkowsky
wiki
- Behaviorist genie
An advanced agent that's forbidden to model minds in too much detail.
- Eliezer Yudkowsky - Harmless supernova fallacy
False dichotomies and continuum fallacies which can be used to argue that anything, including a supernova, must be harmless.
- Eliezer Yudkowsky - Likelihood functions, p-values, and the replication crisis
What's the whole Bayesian-vs.-frequentist debate about?
- Eliezer Yudkowsky - Nonperson predicate
If we knew which computations were definitely not people, we could tell AIs which programs they were definitely allowed to compute.
- Eliezer Yudkowsky - Programmer deception
Programmer deception is when the AI's decision process leads it to optimize for an instrumental goal…
- Eliezer Yudkowsky
- Arbital Blog
Stay up to date on all things Arbital
- Alexei Andreev - Conservative concept boundary
Given N example burritos, draw a boundary around what is a 'burrito' that is relatively simple and allows as few positive instances as possible. Helps make sure the next thing generated is a burrito.
- Eliezer Yudkowsky - How to author on Arbital!
Want to contribute pages to Arbital? Here's our current version of the ad-hoc guide to being an author!
- Eliezer Yudkowsky - Some men just want to watch the world learn
In which Arbital gets paths.
- Alexei Andreev
- Descriptive versus normative propositions
A normative proposition talks about what should be; a descriptive proposition talks about what is.
- Eliezer Yudkowsky - Paperclip maximizer
This agent will not stop until the entire universe is filled with paperclips.
- Eliezer Yudkowsky - Rescuing the utility function
If your utility function values 'heat', and then you discover to your horror that there's no ontologically basic heat, switch to valuing disordered kinetic energy. Likewise 'free will' or 'people'.
- Eliezer Yudkowsky
wiki
- Arbital Blog
Stay up to date on all things Arbital
- Alexei Andreev - Axiom of Choice
The most controversial axiom of the 20th century.
- Mark Chimes - Introductory guide to logarithms
Welcome to the Arbital introduction to logarithms! In modern education, logarithms are often mention…
- Nate Soares - Practicing Brevity
Wanna save the world? Write better TLDRs. And spend more time respecting your reader's time.
- Raymond Arnold
- Predictions For 2017
Scott Alexander made 105 predictions for 2017. Most of them are not personal and are listed below. …
- Alexei Andreev
- Corrigibility
"I can't let you do that, Dave."
- Nate Soares - Shutdown problem
How to build an AGI that lets you shut it down, despite the obvious fact that this will interfere with whatever the AGI's goals are.
- Eliezer Yudkowsky
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky
- Shift towards the hypothesis of least surprise
When you see new evidence, ask: which hypothesis is *least surprised?*
- Nate Soares
- Behaviorist genie
An advanced agent that's forbidden to model minds in too much detail.
- Eliezer Yudkowsky - Context disaster
Some possible designs cause your AI to behave nicely while developing, and behave a lot less nicely when it's smarter.
- Eliezer Yudkowsky - Instrumental pressure
A consequentialist agent will want to bring about certain instrumental events that will help to fulfill its goals.
- Eliezer Yudkowsky - Mindcrime: Introduction
The more predictive accuracy we want from a model, the more detailed the model becomes. A very roug…
- Eliezer Yudkowsky - Modeling distant superintelligences
The several large problems that might occur if an AI starts to think about alien superintelligences.
- Eliezer Yudkowsky
- Edge instantiation
When you ask the AI to make people happy, and it tiles the universe with the smallest objects that can be happy.
- Eliezer Yudkowsky - Patch resistance
One does not simply solve the value alignment problem.
- Eliezer Yudkowsky
- Operator
An operation $f$ on a set $S$ is a function that takes some values from $S$ and produces a new value…
- Nate Soares
- Nearest unblocked strategy
If you patch an agent's preference framework to avoid an undesirable solution, what can you expect to happen?
- Eliezer Yudkowsky - Separation from hyperexistential risk
The AI should be widely separated in the design space from any AI that would constitute a "hyperexistential risk" (anything worse than death).
- Eliezer Yudkowsky
wiki
- Replacing Guilt
In my experience, many people are motivated primarily by either guilt, shame, or some combination of…
- Nate Soares
- Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev - Arbital lens
A lens is a page that presents another page's content from a different angle.
- Alexei Andreev - Executable philosophy
Philosophical discourse aimed at producing a trustworthy answer or meta-answer, in limited time, which can used in constructing an Artificial Intelligence.
- Eliezer Yudkowsky - Goodhart's Curse
The Optimizer's Curse meets Goodhart's Law. For example, if our values are V, and an AI's utility function U is a proxy for V, optimizing for high U seeks out 'errors'--that is, high values of U - V.
- Eliezer Yudkowsky
wiki
- Arbital lens
A lens is a page that presents another page's content from a different angle.
- Alexei Andreev - Edge instantiation
When you ask the AI to make people happy, and it tiles the universe with the smallest objects that can be happy.
- Eliezer Yudkowsky - Epistemic and instrumental efficiency
An efficient agent never makes a mistake you can predict. You can never successfully predict a directional bias in its estimates.
- Eliezer Yudkowsky - Guarded definition
A guarded definition is one where at least one position suspects there will be pressure to stretch a…
- Eliezer Yudkowsky - Programmer
Who is building these advanced agents?
- Eliezer Yudkowsky
- An Introduction to Logical Decision Theory for Everyone Else
So like what the heck is 'logical decision theory' in terms a normal person can understand?
- Eliezer Yudkowsky - Goodhart's Curse
The Optimizer's Curse meets Goodhart's Law. For example, if our values are V, and an AI's utility function U is a proxy for V, optimizing for high U seeks out 'errors'--that is, high values of U - V.
- Eliezer Yudkowsky - Introduction to Logical Decision Theory for Computer Scientists
'Logical decision theory' from a math/programming standpoint, including how two agents with mutual knowledge of each other's code can cooperate on the Prisoner's Dilemma.
- Eliezer Yudkowsky
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky
wiki
- AI safety mindset
Asking how AI designs could go wrong, instead of imagining them going right.
- Eliezer Yudkowsky - Conservative concept boundary
Given N example burritos, draw a boundary around what is a 'burrito' that is relatively simple and allows as few positive instances as possible. Helps make sure the next thing generated is a burrito.
- Eliezer Yudkowsky - Context disaster
Some possible designs cause your AI to behave nicely while developing, and behave a lot less nicely when it's smarter.
- Eliezer Yudkowsky - Corrigibility
"I can't let you do that, Dave."
- Nate Soares - Epistemic and instrumental efficiency
An efficient agent never makes a mistake you can predict. You can never successfully predict a directional bias in its estimates.
- Eliezer Yudkowsky - Fixed point theorem of provability logic
Deal with those pesky self-referential sentences!
- Jaime Sevilla Molina - Gödel II and Löb's theorem
[ Gödel's second incompleteness theorem] and [ Löb's theorem] are equivalent to each other. ]
The …
- Jaime Sevilla Molina - How to author on Arbital!
Want to contribute pages to Arbital? Here's our current version of the ad-hoc guide to being an author!
- Eliezer Yudkowsky - Informed oversight
Incentivize a reinforcement learner that's less smart than you to accomplish some task
- Jessica Taylor - Low impact
The open problem of having an AI carry out tasks in ways that cause minimum side effects and change as little of the rest of the universe as possible.
- Eliezer Yudkowsky - Methodology of unbounded analysis
What we do and don't understand how to do, using unlimited computing power, is a critical distinction and important frontier.
- Eliezer Yudkowsky - Mild optimization
An AGI which, if you ask it to paint one car pink, just paints one car pink and doesn't tile the universe with pink-painted cars, because it's not trying *that* hard to max out its car-painting score.
- Eliezer Yudkowsky - Orthogonality Thesis
Will smart AIs automatically become benevolent, or automatically become hostile? Or do different AI designs imply different goals?
- Eliezer Yudkowsky - Proof of Löb's theorem
Proving that I am Santa Claus
- Jaime Sevilla Molina - Selective similarity metrics for imitation
Can we make human-imitators more efficient by scoring them more heavily on imitating the aspects of human behavior we care about more?
- Jessica Taylor - Uncountability: Intuitive Intro
Are all sizes of infinity the same? What does "the same" even mean here?
- Jason Gross - Why waiting to donate harms charities
A blog post explaining the potential reasons why someone would choose to wait to donate and how that leads to suboptimal outcomes for the charity.
- Alexei Andreev
- Partial function
A partial function is one which "might not be defined everywhere one might expect it to be".
- Patrick Stevens - Proof of Löb's theorem
Proving that I am Santa Claus
- Jaime Sevilla Molina - Rice's Theorem
Rice's Theorem tells us that if we want to determine pretty much anything about the behaviour of an arbitrary computer program, we can't in general do better than just running it.
- Patrick Stevens - Transcendental number
A transcendental number is one which is not the root of any integer-coefficient polynomial.
- Patrick Stevens
wiki
- An introductory guide to modern logic
Logic, provability, Löb, Gödel and more!
- Jaime Sevilla Molina - Arbital examplar pages
Exemplar pages on Arbital.
- Eric Bruylant - Bit
The term "bit" refers to different concepts in different fields. The common theme across all the us…
- Nate Soares - Church encoding
How can you represent things like numbers as lambda expressions?
- Dylan Hendrickson - Church-Turing thesis: Evidence for the Church-Turing thesis
Why do we believe in CT thesis?
- Jaime Sevilla Molina - Cyclic Group Intro (Math 0)
A finite cyclic group is a little bit like a clock.
- Mark Chimes - Group orbit
When we have a group acting on a set, we are often interested in how the group acts on a particular …
- Adele Lopez - Isomorphism: Intro (Math 0)
Things which are basically the same, except for some stuff you don't care about.
- Mark Chimes - Lagrange theorem on subgroup size: Intuitive version
Lagrange's theorem strongly restricts the size a subgroup of a group can be.
- Patrick Stevens - Non-standard terminology
A tag for terminology that is Arbital-specific, Arbital-originated, or just not very common outside …
- Nate Soares - Opinion page
Opinion pages represent one position on a topic (often from a single author), and are not necessarily balanced or a reflection of consensus.
- Eric Bruylant - Order of operations
Conventions used for disambiguating infix notation.
- Joe Zeng - Project proposal: Intro to numbers
Should Arbital's first "project" be a guide to numbers?
- Eric Rogstad - Quotient group
Given a group $G$ with operation $\bullet$ and a special kind of subgroup $N \leq G$ called the "no…
- Adele Lopez - Representability theorem for computable functions
A [ logical theory] $T$ is said to satisfy the **representability theorem for computable functions**…
- Jaime Sevilla Molina - Seed
Seeds are outlines of pages. They're not much use for readers, but can help authors.
- Eric Bruylant - Solovay's theorems of arithmetical adequacy for GL
Using GL to reason about PA, and viceversa
- Jaime Sevilla Molina - Standard provability predicate
Encoding provability as a statement of arithmetic
- Jaime Sevilla Molina - Vector arithmetic
Vectors: what they are, and how to add and scale them.
- Adele Lopez
Are all the words in the free group, or just the freely-reduced words?
If the latter, does saying t…
- Eric RogstadDo you think we could have the actual names of the rules as subheadings or as footnotes? Like, at th…
- Joe ZengFor core/definition pages I think we want to have super modular content (easier browsing, lets peopl…
- Eric BruylantI suggest we can assume that almost everyone in Math 3 is familiar with either calculus concepts or …
- Patrick LaVictoireI think having it as a requisite is best? I see the issue, but some people may arrive from other pag…
- Eric BruylantI think we need a more appropriate definition of Math 0 that doesn't rely on the negation of some pr…
- Joe ZengIf those are the only two options, then you've gone mad :-)
L(H|e) is defined to be P(e|H) (which, …
- Nate SoaresMight one of the following examples work?
The Riemann hypothesis asserts that the real part of ever…
- Jason GrossMost technical version goes onto the primary page (this one). Easier versions get their own lenses. …
- Alexei AndreevPedantic remark: Aren't you missing the identity of free groups in your intuitive construction?
We …
- Jaime Sevilla MolinaShould we discourage titles for the top section of a page (e.g. Group homomorphism)? I think the top…
- Eric BruylantThanks, I've corrected it. That was a strange typo.
- Izaak MecklerThat's right. I know very little group theory.
I was just remarking to Stephanie how I was able to …
- Eric RogstadThe title mentions Cauchy sequences, but the body does not. Doesn't this definition consider classes…
- Kevin ClancyThis relies on a principle "other way" introduces but, in my opinion, is not explicit enough about: …
- Kevin ClancyThis wording suggests the group contains only some of the elements from the following list. I think …
- Eric RogstadWould be great to have an example of the kind of formula one might expect to see.
- Eric RogstadYou're welcome to join our slack channel if you'd like to get more real-time feedback, send me your …
- Eric Bruylantso8res: "I would set up the page as follows:
A group homomorphism is X. Key properties of group hom…
- Eric Bruylant
- Arbital features
Overview of all Arbital features.
- Alexei Andreev
- Contributing to Arbital
Want to help Arbital become awesome?
- Eric Bruylant
- Ability to read logic
Can you read sentences symbolically stating "For all x: exists y: phi(x, y) or not theta(y)" without slowing down too much?
- Eliezer Yudkowsky
- Diamond maximizer
How would you build an agent that made as much diamond material as possible, given vast computing power but an otherwise rich and complicated environment?
- Eliezer Yudkowsky - Rescuing the utility function
If your utility function values 'heat', and then you discover to your horror that there's no ontologically basic heat, switch to valuing disordered kinetic energy. Likewise 'free will' or 'people'.
- Eliezer Yudkowsky - The rocket alignment problem
If people talked about the problem of space travel the way they talked about AI...
- Eliezer Yudkowsky
- Frequency diagrams: A first look at Bayes
The most straightforward visualization of Bayes' rule.
- Nate Soares
- Optimization daemons
When you optimize something so hard that it crystalizes into an optimizer, like the way natural selection optimized apes so hard they turned into human-level intelligences
- Eliezer Yudkowsky
- Why waiting to donate harms charities
A blog post explaining the potential reasons why someone would choose to wait to donate and how that leads to suboptimal outcomes for the charity.
- Alexei Andreev
- Arbital Blog
Stay up to date on all things Arbital
- Alexei Andreev - Probability
The degree to which someone believes something, measured on a scale from 0 to 1, allowing us to do math to it.
- Eliezer Yudkowsky
- Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- Arbital path
Arbital path is a linear sequence of pages tailored specifically to teach a given concept to a user.
- Alexei Andreev
wiki
- Frequency diagrams: A first look at Bayes
The most straightforward visualization of Bayes' rule.
- Nate Soares
- Bayes' rule: Probability form
The original formulation of Bayes' rule.
- Nate Soares - Likelihood functions, p-values, and the replication crisis
What's the whole Bayesian-vs.-frequentist debate about?
- Eliezer Yudkowsky - Odds: Introduction
What's the difference between probabilities and odds? Why is a 20% probability of success equivalent to 1 : 4 odds favoring success?
- Nate Soares
wiki
- Frequency diagrams: A first look at Bayes
The most straightforward visualization of Bayes' rule.
- Nate Soares - Introduction to Bayes' rule: Odds form
Bayes' rule is simple, if you think in terms of relative odds.
- Eliezer Yudkowsky - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- High-speed intro to Bayes's rule
A high-speed introduction to Bayes's Rule on one page, for the impatient and mathematically adept.
- Eliezer Yudkowsky
wiki
- Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev - Arbital Blog
Stay up to date on all things Arbital
- Alexei Andreev - Arbital features
Overview of all Arbital features.
- Alexei Andreev - Arbital lens
A lens is a page that presents another page's content from a different angle.
- Alexei Andreev - Arbital: Solving online explanations
An explanation of Arbital's mid-term goals
- Eliezer Yudkowsky - Edge instantiation
When you ask the AI to make people happy, and it tiles the universe with the smallest objects that can be happy.
- Eliezer Yudkowsky - Orthogonality Thesis
Will smart AIs automatically become benevolent, or automatically become hostile? Or do different AI designs imply different goals?
- Eliezer Yudkowsky - Work in progress
This page is being actively worked on by an editor. Check with them before making major changes.
- Eliezer Yudkowsky
group
- Frequency diagrams: A first look at Bayes
The most straightforward visualization of Bayes' rule.
- Nate Soares
- Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev
- Fundraisers should have a threshold amount which, if not hit, results in a refund.
When starting a fundraiser, a nonprofit should declare a threshold amount. If the nonprofit doesn't …
- Alexei Andreev
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky
- Report likelihoods, not p-values
If scientists reported likelihood functions instead of p-values, this could help science avoid p-ha…
- Nate Soares
wiki
- Coherent extrapolated volition (alignment target)
A proposed direction for an extremely well-aligned autonomous superintelligence - do what humans would want, if we knew what the AI knew, thought that fast, and understood ourselves.
- Eliezer Yudkowsky - Goodhart's Curse
The Optimizer's Curse meets Goodhart's Law. For example, if our values are V, and an AI's utility function U is a proxy for V, optimizing for high U seeks out 'errors'--that is, high values of U - V.
- Eliezer Yudkowsky - Problem of fully updated deference
Why moral uncertainty doesn't stop an AI from defending its off-switch.
- Eliezer Yudkowsky - Report likelihoods, not p-values
If scientists reported likelihood functions instead of p-values, this could help science avoid p-ha…
- Nate Soares
wiki
- Aligning an AGI adds significant development time
Aligning an advanced AI foreseeably involves extra code and extra testing and not being able to do everything the fastest way, so it takes longer.
- Eliezer Yudkowsky
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky - Introductory Bayesian problems
Bayesian problems to try to solve yourself, before beginning to learn about Bayes' rule.
- Eliezer Yudkowsky
- Convergent instrumental strategies
Paperclip maximizers can make more paperclips by improving their cognitive abilities or controlling more resources. What other strategies would almost-any AI try to use?
- Eliezer Yudkowsky - Epistemic and instrumental efficiency
An efficient agent never makes a mistake you can predict. You can never successfully predict a directional bias in its estimates.
- Eliezer Yudkowsky - Harmless supernova fallacy
False dichotomies and continuum fallacies which can be used to argue that anything, including a supernova, must be harmless.
- Eliezer Yudkowsky
- Logical Induction (incomplete)
The theoretically ideal algorithm for bounded reasoning with lots of computational resources
- Alex Appel - Rescuing the utility function
If your utility function values 'heat', and then you discover to your horror that there's no ontologically basic heat, switch to valuing disordered kinetic energy. Likewise 'free will' or 'people'.
- Eliezer Yudkowsky
wiki
- Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev
- Frequency diagrams: A first look at Bayes
The most straightforward visualization of Bayes' rule.
- Nate Soares
- Conditional probability
The notation for writing "The probability that someone has green eyes, if we know that they have red hair."
- Eliezer Yudkowsky - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- AIXI
How to build an (evil) superintelligent AI using unlimited computing power and one page of Python code.
- Eliezer Yudkowsky - Edge instantiation
When you ask the AI to make people happy, and it tiles the universe with the smallest objects that can be happy.
- Eliezer Yudkowsky - Linguistic conventions in value alignment
How and why to use precise language and words with special meaning when talking about value alignment.
- Eliezer Yudkowsky - Orthogonality Thesis
Will smart AIs automatically become benevolent, or automatically become hostile? Or do different AI designs imply different goals?
- Eliezer Yudkowsky - Preference framework
What's the thing an agent uses to compare its preferences?
- Eliezer Yudkowsky - Solomonoff induction
A simple way to superintelligently predict sequences of data, given unlimited computing power.
- Eliezer Yudkowsky - Solomonoff induction: Intro Dialogue (Math 2)
An introduction to Solomonoff induction for the unfamiliar reader who isn't bad at math
- Eliezer Yudkowsky
- Behaviorist genie
An advanced agent that's forbidden to model minds in too much detail.
- Eliezer Yudkowsky - Limited AGI
Task-based AGIs don't need unlimited cognitive and material powers to carry out their Tasks; which means their powers can potentially be limited.
- Eliezer Yudkowsky - Low impact
The open problem of having an AI carry out tasks in ways that cause minimum side effects and change as little of the rest of the universe as possible.
- Eliezer Yudkowsky - Mild optimization
An AGI which, if you ask it to paint one car pink, just paints one car pink and doesn't tile the universe with pink-painted cars, because it's not trying *that* hard to max out its car-painting score.
- Eliezer Yudkowsky - Oracle
System designed to safely answer questions.
- Eliezer Yudkowsky - Preference framework
What's the thing an agent uses to compare its preferences?
- Eliezer Yudkowsky - Querying the AGI user
Postulating that an advanced agent will check something with its user, probably comes with some standard issues and gotchas (e.g., prioritizing what to query, not manipulating the user, etc etc).
- Eliezer Yudkowsky - Task-directed AGI
An advanced AI that's meant to pursue a series of limited-scope goals given it by the user. In Bostrom's terminology, a Genie.
- Eliezer Yudkowsky - User maximization
A sub-principle of avoiding user manipulation - if you see an argmax over X or 'optimize X' instruction and X includes a user interaction, you've just told the AI to optimize the user.
- Eliezer Yudkowsky
wiki
- The current message of effective altruism heavily discourages creativity.
Alyssa Vance expands on this point in her [FB post](https://www.facebook.com/alyssamvance/posts/1021…
- Alexei Andreev
- An Introduction to Logical Decision Theory for Everyone Else
So like what the heck is 'logical decision theory' in terms a normal person can understand?
- Eliezer Yudkowsky - Arbital "parent" relationship
Parent-child relationship between pages implies a strong, inseparable connection.
- Alexei Andreev - Arbital needs a mechanism for defining terms
Much of the discussion in claims seems to be about defining terms, which is a foundational part of r…
- Andrea Gallagher - Bayes' rule: Log-odds form
A simple transformation of Bayes' rule reveals tools for measuring degree of belief, and strength of evidence.
- Eliezer Yudkowsky - Bayes' rule: Odds form
The simplest and most easily understandable form of Bayes' rule uses relative odds.
- Eliezer Yudkowsky - How much of the discussion around AI safety should be public? - Alexei Andreev
- Introduction to Logical Decision Theory for Analytic Philosophers
Why "choose as if controlling the logical output of your decision algorithm" is the most appealing candidate for the principle of rational choice.
- Eliezer Yudkowsky - Introduction to Logical Decision Theory for Computer Scientists
'Logical decision theory' from a math/programming standpoint, including how two agents with mutual knowledge of each other's code can cooperate on the Prisoner's Dilemma.
- Eliezer Yudkowsky - Introduction to Logical Decision Theory for Economists
An introduction to 'logical decision theory' and its implications for the Ultimatum Game, voting in elections, bargaining problems, and more.
- Eliezer Yudkowsky - Known-algorithm non-self-improving agent
Possible advanced AIs that aren't self-modifying, aren't self-improving, and where we know and understand all the component algorithms.
- Eliezer Yudkowsky - Logical decision theories
Root page for topics on logical decision theory, with multiple intros for different audiences.
- Eliezer Yudkowsky - Ontology identification problem
How do we link an agent's utility function to its model of the world, when we don't know what that model will look like?
- Eliezer Yudkowsky - The current message of effective altruism heavily discourages creativity.
Alyssa Vance expands on this point in her [FB post](https://www.facebook.com/alyssamvance/posts/1021…
- Alexei Andreev - Updateless decision theories
Decision theories that maximize their policies (mappings from sense inputs to actions), rather than using their sense inputs to update their beliefs and then selecting actions.
- Eliezer Yudkowsky - Value alignment problem
You want to build an advanced AI with the right values... but how?
- Eliezer Yudkowsky
- Report likelihoods, not p-values
If scientists reported likelihood functions instead of p-values, this could help science avoid p-ha…
- Nate Soares
wiki
- Advanced agent properties
How smart does a machine intelligence need to be, for its niceness to become an issue? "Advanced" is a broad term to cover cognitive abilities such that we'd need to start considering AI alignment.
- Eliezer Yudkowsky - Big-picture strategic awareness
We start encountering new AI alignment issues at the point where a machine intelligence recognizes the existence of a real world, the existence of programmers, and how these relate to its goals.
- Eliezer Yudkowsky - Building an intellectual edifice requires ongoing conversation - Eric Bruylant
- Development phase unpredictable
Several proposed problems in advanced safety are alleged to be difficult because they depend on some…
- Eliezer Yudkowsky - Infrahuman, par-human, superhuman, efficient, optimal
A categorization of AI ability levels relative to human, with some gotchas in the ordering. E.g., in simple domains where humans can play optimally, optimal play is not superhuman.
- Eliezer Yudkowsky - Methodology of unbounded analysis
What we do and don't understand how to do, using unlimited computing power, is a critical distinction and important frontier.
- Eliezer Yudkowsky - Nearest unblocked strategy
If you patch an agent's preference framework to avoid an undesirable solution, what can you expect to happen?
- Eliezer Yudkowsky - Orthogonality Thesis
Will smart AIs automatically become benevolent, or automatically become hostile? Or do different AI designs imply different goals?
- Eliezer Yudkowsky - Reliable prediction
How can we train predictors that reliably predict observable phenomena such as human behavior?
- Jessica Taylor - Shutdown utility function
A special case of a low-impact utility function where you just want the AGI to switch itself off harmlessly (and not create subagents to make absolutely sure it stays off, etcetera).
- Eliezer Yudkowsky - Task-directed AGI
An advanced AI that's meant to pursue a series of limited-scope goals given it by the user. In Bostrom's terminology, a Genie.
- Eliezer Yudkowsky - The current message of effective altruism heavily discourages creativity.
Alyssa Vance expands on this point in her [FB post](https://www.facebook.com/alyssamvance/posts/1021…
- Alexei Andreev - Unforeseen maximum
When you tell AI to produce world peace and it kills everyone. (Okay, some SF writers saw that one coming.)
- Eliezer Yudkowsky - Valley of Dangerous Complacency
When the AGI works often enough that you let down your guard, but it still has bugs. Imagine a robotic car that almost always steers perfectly, but sometimes heads off a cliff.
- Eliezer Yudkowsky - Zermelo-Fraenkel provability oracle
We might be able to build a system that can safely inform us that a theorem has a proof in set theory, but we can't see how to use that capability to save the world.
- Eliezer Yudkowsky
> Each leader takes small steps to avoid trading off others' goals too aggressively.
This seems har…
- Alexei Andreev> On the other hand, for a startup-style outreach-focused project, substantial value comes from the …
- Alexei Andreev@Ben Pace: For a brand-new, never-been-tested, fully self-sustaining off-Earth colony, $50B seems su…
- Ted SandersHmm. I find it difficult to form an opinion on a claim as fuzzy as this. I am sensitive of appearing…
- Ted SandersI don't think the existence of such a colony would directly mitigate AI risk, but it could help in t…
- Paul ChristianoI expect you know my answer on this one.
I agree that if there is a *really* fast transition (e.g. …
- Paul ChristianoI have similar qualms about the name. Got something better?
Leaving that aside, if you have an AI …
- Eliezer YudkowskyI think it's going to be hard to talk or think clearly about these problems (even at the level of se…
- Paul ChristianoI think it's important for claims to be very clear, and that this one isn't clear enough.
- Stephanie ZolayvarI wouldn't call this "Christiano's hack." I appreciate the implicit praise that I can think up esote…
- Paul ChristianoI'd be interested to know if you find yourself having that feeling a lot, while interacting with cla…
- Eric RogstadMaking a page and greenlinking to it (with comments / edits / splits available) seems fine to me?
- Eric BruylantSounds right, but this "page" you speak of is new to me. I assume it's the base structure of the ma…
- Andrea GallagherSuggested edit: remove the word 'permanent' from the claim. It seems a little funny in the context o…
- Ted SandersThanks for the critique, Ted. We are currently figuring out the life-cycle of a claim, and will find…
- Alexei AndreevThis topic consistently frustrates me; the proposed typology is obviously incomplete, and I don't th…
- Paul ChristianoWould it be fair to summarize the idea of a conservative concept boundary as a classifier that avoid…
- Eric Rogstad
- Comprehensive guide to Bayes' Rule
This is an arc that includes all Bayes content.
- Alexei Andreev - There is only one logarithm
All logarithm functions are the same, up to a multiplicative constant.
- Nate Soares
- Eliezer Yudkowsky
Cofounder, with Nick Bostrom, of the field of value alignment theory.
- Properties of the logarithm
- $\log_b(x \cdot y) = \log_b(x) + \log_b(y)$ for any $b$, this is the defining characteristic of …
- Nate Soares
- Predictions For 2017
Scott Alexander made 105 predictions for 2017. Most of them are not personal and are listed below. …
- Alexei Andreev
- Welcome to Arbital
Front page explaining what Arbital is all about.
- Alexei Andreev
- Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky - Bayesian view of scientific virtues
Why is it that science relies on bold, precise, and falsifiable predictions? Because of Bayes' rule, of course.
- Eliezer Yudkowsky
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky
- Welcome to Arbital
Front page explaining what Arbital is all about.
- Alexei Andreev
- Predictions For 2017
Scott Alexander made 105 predictions for 2017. Most of them are not personal and are listed below. …
- Alexei Andreev
- A quick econ FAQ for AI/ML folks concerned about technological unemployment
Yudkowsky's attempted description of standard economic concepts that he thinks are vital for talking about technological unemployment and related issues.
- Eliezer Yudkowsky
- Replacing Guilt
In my experience, many people are motivated primarily by either guilt, shame, or some combination of…
- Nate Soares - Will Narrow AI Seriously Affect Long-Term Employment?
###Definitions:
**Narrow AI** - artificial intelligence capable of doing a narrow task at a level …
- Alexei Andreev
wiki
- Octalysis Framework
In the Octalysis Framework %…
- Sarah Wolf
group
- Arbital: learning from Wikipedia
How is Arbital different from Wikipedia?
- Alexei Andreev - More about Arbital
Lots more information about Arbital vision.
- Alexei Andreev
- AI alignment
The great civilizational problem of creating artificially intelligent computer systems such that running them is a good idea.
- Eliezer Yudkowsky
- Frequency diagrams: A first look at Bayes
The most straightforward visualization of Bayes' rule.
- Nate Soares - Introduction to Bayes' rule: Odds form
Bayes' rule is simple, if you think in terms of relative odds.
- Eliezer Yudkowsky - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- Ordinary claims require ordinary evidence
Extraordinary claims require extraordinary evidence, but ordinary claims *don't*.
- Nate Soares
- Algorithmic complexity
When you compress the information, what you are left with determines the complexity.
- Eliezer Yudkowsky - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- The rocket alignment problem
If people talked about the problem of space travel the way they talked about AI...
- Eliezer Yudkowsky
- A whirlwind tour
A rapid tour of Eric's thoughts on the accelerator project.
- Eric Bruylant
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky
- Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev
- Belief revision as probability elimination
Update your beliefs by throwing away large chunks of probability mass.
- Eliezer Yudkowsky - Extraordinary claims require extraordinary evidence
The people who adamantly claim they were abducted by aliens do provide some evidence for aliens. They just don't provide quantitatively enough evidence.
- Eliezer Yudkowsky
wiki
- Bayes' rule: Vector form
For when you want to apply Bayes' rule to lots of evidence and lots of variables, all in one go. (This is more or less how spam filters work.)
- Eliezer Yudkowsky - Introduction to Bayes' rule: Odds form
Bayes' rule is simple, if you think in terms of relative odds.
- Eliezer Yudkowsky - Logarithm
The logarithm base $b$ of a number $n,$ written $\log_b(n),$ is the answer to the question "how man…
- Nate Soares - Normalization (probability)
That thingy we do to make sure our probabilities sum to 1, when they should sum to 1.
- Eliezer Yudkowsky - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
wiki
- AI alignment
The great civilizational problem of creating artificially intelligent computer systems such that running them is a good idea.
- Eliezer Yudkowsky - Ackermann function
The slowest-growing fast-growing function.
- Alex Appel - Advanced agent properties
How smart does a machine intelligence need to be, for its niceness to become an issue? "Advanced" is a broad term to cover cognitive abilities such that we'd need to start considering AI alignment.
- Eliezer Yudkowsky - Approaches to strategic disagreement
Organizations self-select staff to agree with their strategies. By default, this causes them to sacrifice the fulfillment of others' plans. How can we resolve these strategic disagreements?
- Ryan Carey - Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev - Arbital norms should encourage disagreement. - Alexei Andreev
- Arbital unlisted page
What do you call a page that's not part of any domain?
- Alexei Andreev - Arithmetical hierarchy
The arithmetical hierarchy is a way of classifying logical statements by the number of clauses saying "for every object" and "there exists an object".
- Eliezer Yudkowsky - Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky - Bit (of data)
A bit of data is the amount of data required to single out one message from a set of two. Equivalen…
- Nate Soares - Commutativity: Intuition
We can think of commutativity either as an artifact of notation, or as a symmetry in the output of a…
- Nate Soares - Decision problem
Formalization of general problems
- Jaime Sevilla Molina - Derivative
How things change
- Michael Cohen - Diamond maximizer
How would you build an agent that made as much diamond material as possible, given vast computing power but an otherwise rich and complicated environment?
- Eliezer Yudkowsky - Distant superintelligences can coerce the most probable environment of your AI
Distant superintelligences may be able to hack your local AI, if your AI's preference framework depends on its most probable environment.
- Eliezer Yudkowsky - Double Crux — A Strategy for Resolving Disagreement - Eric Rogstad
- Empirical probabilities are not exactly 0 or 1
"Cromwell's Rule" says that probabilities of exactly 0 or 1 should never be applied to empirical propositions - there's always some probability, however tiny, of being mistaken.
- Eliezer Yudkowsky - Equivalence relation
A relation that allows you to partition a set into equivalence classes.
- Dylan Hendrickson - Explicitly tagging the core claims of a post will make people substantially more likely to respond to these claims.
Source of claim: Improve comments by tagging claims by Benjamin Hoffman
- Stephanie Zolayvar - Fractional bits
It takes $\log_2(8) = 3$ bits of data to carry one message from a set of 8 possible messages. Simila…
- Nate Soares - How to author on Arbital!
Want to contribute pages to Arbital? Here's our current version of the ad-hoc guide to being an author!
- Eliezer Yudkowsky - If we can’t lie to others, we will lie to ourselves - Eric Rogstad
- Improve comments by tagging claims
Comment sections are more important for discourse than I thought. They can be improved by explicitly tagging an article's main claims as anchors for discussion.
- Benjamin Hoffman - Information
Information is a measure of how much a message grants an observer the ability to predict the world.…
- Nate Soares - Introductory guide to logarithms
Welcome to the Arbital introduction to logarithms! In modern education, logarithms are often mention…
- Nate Soares - It's good for GiveWell and Good Ventures to crowd out donors by their donations. - Alexei Andreev
- List: value-alignment subjects
Bullet point list of core VAT subjects.
- Eliezer Yudkowsky - Log as generalized length
To estimate the log (base 10) of a number, count how many digits it has.
- Nate Soares - Meta tags
What are meta tags and when to use them?
- Eliezer Yudkowsky - Nearest unblocked strategy
If you patch an agent's preference framework to avoid an undesirable solution, what can you expect to happen?
- Eliezer Yudkowsky - Ontology identification problem
How do we link an agent's utility function to its model of the world, when we don't know what that model will look like?
- Eliezer Yudkowsky - Orthogonality Thesis
Will smart AIs automatically become benevolent, or automatically become hostile? Or do different AI designs imply different goals?
- Eliezer Yudkowsky - Partially ordered set
A set endowed with a relation that is reflexive, transitive, and antisymmetric.
- Kevin Clancy - Predictions For 2017
Scott Alexander made 105 predictions for 2017. Most of them are not personal and are listed below. …
- Alexei Andreev - Project outline: Intro to the Universal Property
Outline detailing all the work required for a proposed Arbital Project
- Eric Rogstad - Proof of Löb's theorem
Proving that I am Santa Claus
- Jaime Sevilla Molina - Scalable ways to associate evidence (pro or con) with claims will be more valuable in elevating accuracy than complex voting and reputation systems
Discussions on Less Wrong have delved into [complex systems of voting and moderation](http://lesswro…
- Andrea Gallagher - Some men just want to watch the world learn
In which Arbital gets paths.
- Alexei Andreev - The current message of effective altruism heavily discourages creativity.
Alyssa Vance expands on this point in her [FB post](https://www.facebook.com/alyssamvance/posts/1021…
- Alexei Andreev - The ideal Arbital math page
Think of the best math textbook you've ever read -- why was it good?
- Eric Rogstad - Uncomputability
The diagonal function and the halting problem
- Jaime Sevilla Molina
group
Agree this is a problem, but also part of a broader coordination problem in the community and which …
- Peter McIntyreApparently it's "which conscious states feel good, which ones feel bad?"
- Alexei AndreevDefinitely have a strong feeling of wanting to read a summary instead of the entire article.
- Alexei AndreevDoes "better" include "more like the in-group"? If yes, this seems very plausible. If no, I'd guess …
- Eric BruylantI agree with this on timescales of around 1,000,000 years or so, but disagree with the colloquial in…
- Adele LopezI disagree mostly on priors, since it's quite unlikely that we discovered, understood, and pinpointe…
- Alexei AndreevI want a clarification on the claim. How should this be handled, should it be attached to the claim?…
- Eric BruylantI want a wrong question button!! :/
- Anna SalamonPossibly have it hidden for logged-in users, but shown to logged out users? It'd be good for casual …
- Eric Bruylanthttps://arbital.com/p/6mt/ => If we can’t lie to others, we will lie to ourselves
- Alexei Andreev
- High-speed intro to Bayes's rule
A high-speed introduction to Bayes's Rule on one page, for the impatient and mathematically adept.
- Eliezer Yudkowsky - Odds
Odds express a relative probability.
- Eliezer Yudkowsky
wiki
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky - Coherent extrapolated volition (alignment target)
A proposed direction for an extremely well-aligned autonomous superintelligence - do what humans would want, if we knew what the AI knew, thought that fast, and understood ourselves.
- Eliezer Yudkowsky - Vingean reflection
The problem of thinking about your future self when it's smarter than you.
- Eliezer Yudkowsky
group
- AI alignment
The great civilizational problem of creating artificially intelligent computer systems such that running them is a good idea.
- Eliezer Yudkowsky - Arbital lens
A lens is a page that presents another page's content from a different angle.
- Alexei Andreev - Arbital lens: TL;DR
Much shorter version of Arbital Lens page
- Alexei Andreev - Fractional bits
It takes $\log_2(8) = 3$ bits of data to carry one message from a set of 8 possible messages. Simila…
- Nate Soares - In notation
There's a weird E-looking symbol called \in in LaTeX. What does it mean?
- Qiaochu Yuan
- Boxed AI
Idea: what if we limit how AI can interact with the world. That'll make it safe, right??
- Eliezer Yudkowsky - Empirical probabilities are not exactly 0 or 1
"Cromwell's Rule" says that probabilities of exactly 0 or 1 should never be applied to empirical propositions - there's always some probability, however tiny, of being mistaken.
- Eliezer Yudkowsky - Harmless supernova fallacy
False dichotomies and continuum fallacies which can be used to argue that anything, including a supernova, must be harmless.
- Eliezer Yudkowsky - Likelihood functions, p-values, and the replication crisis
What's the whole Bayesian-vs.-frequentist debate about?
- Eliezer Yudkowsky - No-Free-Lunch theorems are often irrelevant
There's often a theorem proving that some problem has no optimal answer across every possible world. But this may not matter, since the real world is a special case. (E.g., a low-entropy universe.)
- Eliezer Yudkowsky - Oracle
System designed to safely answer questions.
- Eliezer Yudkowsky - Proving too much
If your argument could just as naturally be used to prove that Bigfoot exists and that Peano arithmetic is inconsistent, maybe it's an untrustworthy kind of argument.
- Eliezer Yudkowsky - Strong cognitive uncontainability
An advanced agent can win in ways humans can't understand in advance.
- Eliezer Yudkowsky
wiki
- Rice's Theorem
Rice's Theorem tells us that if we want to determine pretty much anything about the behaviour of an arbitrary computer program, we can't in general do better than just running it.
- Patrick Stevens
- Bayes' rule: Log-odds form
A simple transformation of Bayes' rule reveals tools for measuring degree of belief, and strength of evidence.
- Eliezer Yudkowsky - Bayes' rule: Proportional form
The fastest way to say something both convincing and true about belief-updating.
- Eliezer Yudkowsky - Bayesian view of scientific virtues
Why is it that science relies on bold, precise, and falsifiable predictions? Because of Bayes' rule, of course.
- Eliezer Yudkowsky - Belief revision as probability elimination
Update your beliefs by throwing away large chunks of probability mass.
- Eliezer Yudkowsky - Binary notation
A way to write down numbers using powers of two.
- Malcolm McCrimmon - Derivative
How things change
- Michael Cohen - Eliezer's vision for Arbital
Why are we building this? What's the goal?
- Eric Bruylant - Exchange rates between digits
In terms of data storage, if a coin is worth $1, a digit wheel is worth more than $3.32, but less than $3.33. Why?
- Nate Soares - Extraordinary claims require extraordinary evidence
The people who adamantly claim they were abducted by aliens do provide some evidence for aliens. They just don't provide quantitatively enough evidence.
- Eliezer Yudkowsky - Fractional digits
When $b$ and $x$ are integers, $\log_b(x)$ has a few good interpretations. It's roughly the length o…
- Nate Soares - Introductory guide to logarithms
Welcome to the Arbital introduction to logarithms! In modern education, logarithms are often mention…
- Nate Soares - Life in logspace
The log lattice hints at the reason that engineers, scientists, and AI researchers find logarithms s…
- Nate Soares - Log as generalized length
To estimate the log (base 10) of a number, count how many digits it has.
- Nate Soares - Log as the change in the cost of communicating
When interpreting logarithms as a generalization of the notion of "length" and as digit exchange rat…
- Nate Soares - Ordinary claims require ordinary evidence
Extraordinary claims require extraordinary evidence, but ordinary claims *don't*.
- Nate Soares - Probability notation for Bayes' rule: Intro (Math 1)
How to read, and identify, the probabilities in Bayesian problems.
- Eliezer Yudkowsky - Properties of the logarithm
- $\log_b(x \cdot y) = \log_b(x) + \log_b(y)$ for any $b$, this is the defining characteristic of …
- Nate Soares - Shift towards the hypothesis of least surprise
When you see new evidence, ask: which hypothesis is *least surprised?*
- Nate Soares - The End (of the basic log tutorial)
That concludes our introductory tutorial on logarithms! You have made it to the end.
Throughout thi…
- Nate Soares - The characteristic of the logarithm
Any time you find an output that adds whenever the input multiplies, you're probably looking at a (…
- Nate Soares - The log lattice
Log as the change in the cost of communicating and other pages give physical interpretations of what…
- Nate Soares - There is only one logarithm
All logarithm functions are the same, up to a multiplicative constant.
- Nate Soares - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky - What is a logarithm?
Logarithms are a group of functions that take a number as input and produce another number. There i…
- Nate Soares
wiki
- Bayes' rule: Functional form
Bayes' rule for to continuous variables.
- Eliezer Yudkowsky - Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky - Bayes' rule: Log-odds form
A simple transformation of Bayes' rule reveals tools for measuring degree of belief, and strength of evidence.
- Eliezer Yudkowsky - Bayes' rule: Odds form
The simplest and most easily understandable form of Bayes' rule uses relative odds.
- Eliezer Yudkowsky - Bayes' rule: Proportional form
The fastest way to say something both convincing and true about belief-updating.
- Eliezer Yudkowsky - Bayes' rule: Vector form
For when you want to apply Bayes' rule to lots of evidence and lots of variables, all in one go. (This is more or less how spam filters work.)
- Eliezer Yudkowsky - Bayesian view of scientific virtues
Why is it that science relies on bold, precise, and falsifiable predictions? Because of Bayes' rule, of course.
- Eliezer Yudkowsky - Belief revision as probability elimination
Update your beliefs by throwing away large chunks of probability mass.
- Eliezer Yudkowsky - Building an intellectual edifice requires ongoing conversation - Eric Bruylant
- Conditional probability
The notation for writing "The probability that someone has green eyes, if we know that they have red hair."
- Eliezer Yudkowsky - Correspondence visualizations for different interpretations of "probability"
Let's say you have a model which says a particular coin is 70% likely to be heads. How should we as…
- Nate Soares - Digit wheel
A mechanical device for storing a number from 0 to 9.
![](http://www.cl.cam.ac.uk/~djg11/howcompu…
- Nate Soares - Empirical probabilities are not exactly 0 or 1
"Cromwell's Rule" says that probabilities of exactly 0 or 1 should never be applied to empirical propositions - there's always some probability, however tiny, of being mistaken.
- Eliezer Yudkowsky - Extraordinary claims
What makes something an 'extraordinary claim' that requires extraordinary evidence?
- Eliezer Yudkowsky - Extraordinary claims require extraordinary evidence
The people who adamantly claim they were abducted by aliens do provide some evidence for aliens. They just don't provide quantitatively enough evidence.
- Eliezer Yudkowsky - Frequency diagrams: A first look at Bayes
The most straightforward visualization of Bayes' rule.
- Nate Soares - Harmless supernova fallacy
False dichotomies and continuum fallacies which can be used to argue that anything, including a supernova, must be harmless.
- Eliezer Yudkowsky - Interpretations of "probability"
What does it *mean* to say that a fair coin has a 50% probability of coming up heads?
- Nate Soares - Introduction to Bayes' rule: Odds form
Bayes' rule is simple, if you think in terms of relative odds.
- Eliezer Yudkowsky - Likelihood
"Likelihood", when speaking of Bayesian reasoning, denotes *the probability of an observation, sup…
- Nate Soares - Likelihood function
Let's say you have a piece of evidence $e$ and a set of hypotheses $\mathcal H.$ Each $H_i \in \math…
- Nate Soares - Likelihood notation
The likelihood of a piece of evidence $e$ according to a hypothesis $H,$ known as "the likelihood of…
- Nate Soares - Likelihood ratio
Given a piece of evidence $e$ and two hypothsese $H_i$ and $H_j,$ the likelihood ratio between them…
- Nate Soares - Normalization (probability)
That thingy we do to make sure our probabilities sum to 1, when they should sum to 1.
- Eliezer Yudkowsky - Odds form to probability form
The odds form of Bayes' rule works for any two hypotheses $H_i$ and $H_j,$ and looks like this:
$$\…
- Nate Soares - Odds: Introduction
What's the difference between probabilities and odds? Why is a 20% probability of success equivalent to 1 : 4 odds favoring success?
- Nate Soares - Ordinary claims require ordinary evidence
Extraordinary claims require extraordinary evidence, but ordinary claims *don't*.
- Nate Soares - Perfect rolling sphere
If you don't understand something, start by assuming it's a perfect rolling sphere.
- Eliezer Yudkowsky - Probability
The degree to which someone believes something, measured on a scale from 0 to 1, allowing us to do math to it.
- Eliezer Yudkowsky - Probability distribution: Motivated definition
People keep writing things like P(sick)=0.3. What does this mean, on a technical level?
- Nate Soares - Probability interpretations: Examples
Consider evaluating, in June of 2016, the question: "What is the probability of Hillary Clinton wi…
- Nate Soares - Probability notation for Bayes' rule: Intro (Math 1)
How to read, and identify, the probabilities in Bayesian problems.
- Eliezer Yudkowsky - Psychologizing
It's sometimes important to consider how other people might be led into error. But psychoanalyzing them is also dangerous! Arbital discussion norms say to explicitly note this as "psychologizing".
- Eliezer Yudkowsky - Relative likelihood
How relatively likely an observation is, given two or more hypotheses, determines the strength and direction of evidence.
- Eliezer Yudkowsky - Strained argument
A phenomenological feeling associated with a step of reasoning going from X to Y where it feels like…
- Eliezer Yudkowsky - Subjective probability
Probability is in the mind, not in the environment. If you don't know whether a coin came up heads or tails, that's a fact about you, not a fact about the coin.
- Eliezer Yudkowsky - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky - Welcome to Arbital
Front page explaining what Arbital is all about.
- Alexei Andreev - What is a logarithm?
Logarithms are a group of functions that take a number as input and produce another number. There i…
- Nate Soares - n-digit
An $n$-digit is a physical object that can be stably placed into any of $n$ distinguishable states. …
- Nate Soares - n-message
A message singling out one thing from a set of $n$ is sometimes called an $n$-message. For example,…
- Nate Soares
- Coherent extrapolated volition (alignment target)
A proposed direction for an extremely well-aligned autonomous superintelligence - do what humans would want, if we knew what the AI knew, thought that fast, and understood ourselves.
- Eliezer Yudkowsky
- Intension vs. extension
"Red is a light with a wavelength of 700 nm" vs. "Look at this red apple, red car, and red cup."
- Eliezer Yudkowsky
- Welcome to Arbital
Front page explaining what Arbital is all about.
- Alexei Andreev
- The Robots, AI, and Unemployment Anti-FAQ
Q. Are the current high levels of unemployment being caused by advances in Artificial Intelligence …
- Eliezer Yudkowsky - Welcome to Arbital
Front page explaining what Arbital is all about.
- Alexei Andreev
- Factorial
The number of ways you can order things. (Alternately subtitled: Is that exclamation point a factorial, or are you just excited to see me?)
- Michael Cohen - What is a logarithm?
Logarithms are a group of functions that take a number as input and produce another number. There i…
- Nate Soares
- Extrapolated volition (normative moral theory)
If someone asks you for orange juice, and you know that the refrigerator contains no orange juice, should you bring them lemonade?
- Eliezer Yudkowsky - Rescuing the utility function
If your utility function values 'heat', and then you discover to your horror that there's no ontologically basic heat, switch to valuing disordered kinetic energy. Likewise 'free will' or 'people'.
- Eliezer Yudkowsky
- Odds
Odds express a relative probability.
- Eliezer Yudkowsky
- Introductory Bayesian problems
Bayesian problems to try to solve yourself, before beginning to learn about Bayes' rule.
- Eliezer Yudkowsky
- Bayes' rule: Vector form
For when you want to apply Bayes' rule to lots of evidence and lots of variables, all in one go. (This is more or less how spam filters work.)
- Eliezer Yudkowsky
wiki
- A clarification period for claims is net positive for Arbital
Example pros: Claims are more carefully defined and less ambiguous, less wrong questions visible
Ex…
- Eric Bruylant - Arbital claims are significantly more useful* when they are fairly well-specified and unambiguous**
\* At least 30% more valuable to people sharing models.
** Not lojban level, but with some thoug…
- Eric Bruylant - The current message of effective altruism heavily discourages creativity.
Alyssa Vance expands on this point in her [FB post](https://www.facebook.com/alyssamvance/posts/1021…
- Alexei Andreev
- Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev
- Problem of fully updated deference
Why moral uncertainty doesn't stop an AI from defending its off-switch.
- Eliezer Yudkowsky
- Vitamin D is good for you
We'll consider two categories of vitamin D supplementation: below and above the recommended levels.
…
- Alexei Andreev
wiki
- Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev - Nate's ruminations
These posts are a mirror of posts on the blog [MindingOurWay.com](mindingourway.com) which pertain t…
- Nate Soares - Replacing Guilt
In my experience, many people are motivated primarily by either guilt, shame, or some combination of…
- Nate Soares - Value alignment problem
You want to build an advanced AI with the right values... but how?
- Eliezer Yudkowsky - Vitamin D helps prevent cardiovascular disease
This question is a bit vague. There are two ways to make it more specific.
1. Does vitamin D deffic…
- Alexei Andreev
group
- Reflective stability
Wanting to think the way you currently think, building other agents and self-modifications that think the same way.
- Eliezer Yudkowsky
- Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky - Introductory guide to logarithms
Welcome to the Arbital introduction to logarithms! In modern education, logarithms are often mention…
- Nate Soares
wiki
- A whirlwind tour
A rapid tour of Eric's thoughts on the accelerator project.
- Eric Bruylant - Requisites for personal growth
A mashup of models
- Toon Alfrink - The missing step between Zero and Hero
Creating a space for high potential people grow and improve the world at scale.
- Eric Bruylant - Who needs civilization?
The most common difference between my model and that of people I've discussed this with is that many…
- Eric Bruylant
wiki
- An introductory guide to modern logic
Logic, provability, Löb, Gödel and more!
- Jaime Sevilla Molina - Arbital Blog
Stay up to date on all things Arbital
- Alexei Andreev - Arbital Markdown
All about Arbital's extended Markdown syntax.
- Alexei Andreev - Arbital claims are significantly more useful* when they are fairly well-specified and unambiguous**
\* At least 30% more valuable to people sharing models.
** Not lojban level, but with some thoug…
- Eric Bruylant - Arbital: Google Maps for knowledge
Take your understanding from where it is to where it wants to be.
- Alexei Andreev - Arbital: Solving online explanations
An explanation of Arbital's mid-term goals
- Eliezer Yudkowsky - Arbital: learning from Wikipedia
How is Arbital different from Wikipedia?
- Alexei Andreev - Bayes' rule: Vector form
For when you want to apply Bayes' rule to lots of evidence and lots of variables, all in one go. (This is more or less how spam filters work.)
- Eliezer Yudkowsky - Building an intellectual edifice requires ongoing conversation - Eric Bruylant
- Cardinality
The "size" of a set, or the "number of elements" that it has.
- Joe Zeng - Coherent decisions imply consistent utilities
Why do we all use the 'expected utility' formalism? Because any behavior that can't be viewed from that perspective, must be qualitatively self-defeating (in various mathy ways).
- Eliezer Yudkowsky - Conceivability
A hypothetical scenario is 'conceivable' or 'imaginable' when it is not *immediately* incoherent, al…
- Eliezer Yudkowsky - Correct credit-tracking is very important if we want our community to generate new good ideas.
Correct credit-tracking is very important if we want our community to generate new good ideas.
- Anna Salamon - Ethics research should proceed in parallel to value alignment research - Eric Rogstad
- Executable philosophy
Philosophical discourse aimed at producing a trustworthy answer or meta-answer, in limited time, which can used in constructing an Artificial Intelligence.
- Eliezer Yudkowsky - Formal Logic
Formal logic studies the form of correct arguments through rigorous and precise mathematical theories.
- Erik Istre - I often wait to see how much other people will donate to a fundraiser before donating myself. - Alexei Andreev
- Introduction to Bayes' rule: Odds form
Bayes' rule is simple, if you think in terms of relative odds.
- Eliezer Yudkowsky - Isomorphism
A morphism between two objects which describes how they are "essentially equivalent" for the purposes of the theory under consideration.
- Mark Chimes - Isomorphism: Intro (Math 0)
Things which are basically the same, except for some stuff you don't care about.
- Mark Chimes - Logistic function
A monotonic function from the real numbers to the open unit interval.
- Joe Zeng - On the importance of Less Wrong, or another single conversational locus
In this post, Anna Salamon talks about how Less Wrong used to a locus of discussion, and that it is…
- Alexei Andreev - Proof by contradiction
Discover what 'reductio ad absurdum' means!
- Jaime Sevilla Molina - Report likelihoods not p-values: FAQ
This page answers frequently asked questions about the Report likelihoods, not p-values proposal for…
- Nate Soares - Report likelihoods, not p-values
If scientists reported likelihood functions instead of p-values, this could help science avoid p-ha…
- Nate Soares - Set
An unordered collection of distinct objects.
- Nate Soares - What is a logarithm?
Logarithms are a group of functions that take a number as input and produce another number. There i…
- Nate Soares - Why waiting to donate harms charities
A blog post explaining the potential reasons why someone would choose to wait to donate and how that leads to suboptimal outcomes for the charity.
- Alexei Andreev - Zero-Shot Translation with Google’s Multilingual Neural Machine Translation System
Sorry, old news. But I'll leave it up.
- Andrea Gallagher
group
- Eliezer Yudkowsky
Cofounder, with Nick Bostrom, of the field of value alignment theory.
- Predictions For 2017
Scott Alexander made 105 predictions for 2017. Most of them are not personal and are listed below. …
- Alexei Andreev
- Indirect decision theory
In which I argue that understanding decision theory can be delegated to AI.
### Indirect normativit…
- Paul Christiano - P vs NP: Arguments against P=NP
Why we believe P and NP are different
- Jaime Sevilla Molina
- Logarithm: Exercises
Without using a calculator: What is $\log_{10}(4321)$? What integer is it larger than, what integer …
- Nate Soares
- Odds: Introduction
What's the difference between probabilities and odds? Why is a 20% probability of success equivalent to 1 : 4 odds favoring success?
- Nate Soares
- Featured math content
Some Arbital pages we think are great!
- Eric Bruylant
- Conditional probability
The notation for writing "The probability that someone has green eyes, if we know that they have red hair."
- Eliezer Yudkowsky - Some men just want to watch the world learn
In which Arbital gets paths.
- Alexei Andreev
- Belief revision as probability elimination
Update your beliefs by throwing away large chunks of probability mass.
- Eliezer Yudkowsky - Frequency diagrams: A first look at Bayes
The most straightforward visualization of Bayes' rule.
- Nate Soares
wiki
- Frequency diagrams: A first look at Bayes
The most straightforward visualization of Bayes' rule.
- Nate Soares
wiki
- Ackermann function
The slowest-growing fast-growing function.
- Alex Appel - Bayesian view of scientific virtues
Why is it that science relies on bold, precise, and falsifiable predictions? Because of Bayes' rule, of course.
- Eliezer Yudkowsky - Convergent instrumental strategies
Paperclip maximizers can make more paperclips by improving their cognitive abilities or controlling more resources. What other strategies would almost-any AI try to use?
- Eliezer Yudkowsky - Decision problem
Formalization of general problems
- Jaime Sevilla Molina - Generalized associative law
Given an associative operator $\cdot$ and a list $[a, b, c, \ldots]$ of parameters, all ways of red…
- Nate Soares - Group: Exercises
Test your understanding of the definition of a group with these exercises.
- Qiaochu Yuan - Guarded definition
A guarded definition is one where at least one position suspects there will be pressure to stretch a…
- Eliezer Yudkowsky - Mathematical induction
Proving a statement about all positive integers by knocking them down like dominoes.
- Douglas Weathers - Needs exercises
Add this tag to a page which doesn't have enough exercises.
- Alexei Andreev - Poset: Examples
The standard $\leq$ relation on integers, the $\subseteq$ relation on sets, and the $|$ (divisibilit…
- Kevin Clancy - Quotient group
Given a group $G$ with operation $\bullet$ and a special kind of subgroup $N \leq G$ called the "no…
- Adele Lopez - Report likelihoods not p-values: FAQ
This page answers frequently asked questions about the Report likelihoods, not p-values proposal for…
- Nate Soares - Rescuing the utility function
If your utility function values 'heat', and then you discover to your horror that there's no ontologically basic heat, switch to valuing disordered kinetic energy. Likewise 'free will' or 'people'.
- Eliezer Yudkowsky - Rice's Theorem
Rice's Theorem tells us that if we want to determine pretty much anything about the behaviour of an arbitrary computer program, we can't in general do better than just running it.
- Patrick Stevens - Rice's theorem and the Halting problem
We will show that Rice's theorem and the the halting problem are equivalent.
#The Halting theorem i…
- Jaime Sevilla Molina - Solomonoff induction: Intro Dialogue (Math 2)
An introduction to Solomonoff induction for the unfamiliar reader who isn't bad at math
- Eliezer Yudkowsky - Uncountability
Some infinities are bigger than others. Uncountable infinities are larger than countable infinities.
- Jason Gross - Unique factorisation domain
This is the correct way to abstract from the integers the fact that every integer can be written uniquely as a product of prime numbers.
- Patrick Stevens - Universal property of the empty set
The empty set can be characterised by how it interacts with other sets, rather than by any explicit property of the empty set itself.
- Patrick Stevens - Well-defined
A mathematical object is "well-defined" if we have given it a completely unambiguous definition.
- Patrick Stevens
- Solomonoff induction: Intro Dialogue (Math 2)
An introduction to Solomonoff induction for the unfamiliar reader who isn't bad at math
- Eliezer Yudkowsky
- Introduction to Bayes' rule: Odds form
Bayes' rule is simple, if you think in terms of relative odds.
- Eliezer Yudkowsky
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky - Eigenvalues and eigenvectors
We applied this linear transformation to one of its eigenvectors; you won't believe what happened next!
- Zack M. Davis
- Why waiting to donate harms charities
A blog post explaining the potential reasons why someone would choose to wait to donate and how that leads to suboptimal outcomes for the charity.
- Alexei Andreev
- Bayesian view of scientific virtues
Why is it that science relies on bold, precise, and falsifiable predictions? Because of Bayes' rule, of course.
- Eliezer Yudkowsky
- Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev
- Associativity vs commutativity
Associativity and commutativity are often confused, because they are both constraints on how a funct…
- Nate Soares - Solomonoff induction: Intro Dialogue (Math 2)
An introduction to Solomonoff induction for the unfamiliar reader who isn't bad at math
- Eliezer Yudkowsky - Uncountable sample spaces are way too large
We can't define probability distributions over uncountable sample spaces by just assigning numbers to each point in the sample space.
- Tsvi BT
- Author's guide to Arbital
How to write intuitive, flexible content on Arbital.
- Alexei Andreev
- Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- High-speed intro to Bayes's rule
A high-speed introduction to Bayes's Rule on one page, for the impatient and mathematically adept.
- Eliezer Yudkowsky - Vector arithmetic
Vectors: what they are, and how to add and scale them.
- Adele Lopez
- Join and meet
Let $\langle P, \leq \rangle$ be a poset, and let $S \subseteq P$. The **join** of $S$ in $P$, deno…
- Kevin Clancy
- Bayesian view of scientific virtues
Why is it that science relies on bold, precise, and falsifiable predictions? Because of Bayes' rule, of course.
- Eliezer Yudkowsky
- Introduction to Bayes' rule: Odds form
Bayes' rule is simple, if you think in terms of relative odds.
- Eliezer Yudkowsky
- Bayes' rule: Guide
The Arbital guide to Bayes' rule
- Eliezer Yudkowsky - Welcome to Arbital
Front page explaining what Arbital is all about.
- Alexei Andreev
- Answer to sparking widgets problem
Odds of 1 : 3, probability of 1/4.
- Eliezer Yudkowsky - Bayes' rule: Log-odds form
A simple transformation of Bayes' rule reveals tools for measuring degree of belief, and strength of evidence.
- Eliezer Yudkowsky
- Math 2
Do you work with math on a fairly routine basis? Do you have little trouble grasping abstract structures and ideas?
- Eliezer Yudkowsky - Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
wiki
- AI alignment
The great civilizational problem of creating artificially intelligent computer systems such that running them is a good idea.
- Eliezer Yudkowsky - Welcome to Arbital
Front page explaining what Arbital is all about.
- Alexei Andreev
group
- Odds: Technical explanation
Formal definitions, alternate representations, and uses of odds and odds ratios (like a 1 : 2 chance of drawing a red ball vs. green ball from a barrel).
- Alexei Andreev
- Probability notation for Bayes' rule: Intro (Math 1)
How to read, and identify, the probabilities in Bayesian problems.
- Eliezer Yudkowsky
- Waterfall diagrams and relative odds
A way to visualize Bayes' rule that yields an easier way to solve some problems
- Eliezer Yudkowsky
- Conditional probability
The notation for writing "The probability that someone has green eyes, if we know that they have red hair."
- Eliezer Yudkowsky - Proof of Bayes' rule: Intro
Proof of Bayes' rule, assuming you know the rule itself, and the notations for the quantities involved.
- Eliezer Yudkowsky
- Introduction to Bayes' rule: Odds form
Bayes' rule is simple, if you think in terms of relative odds.
- Eliezer Yudkowsky
- Arbital
Arbital is the place for crowdsourced, intuitive math explanations.
- Alexei Andreev
- Conditional probability
The notation for writing "The probability that someone has green eyes, if we know that they have red hair."
- Eliezer Yudkowsky
- Bayesian view of scientific virtues
Why is it that science relies on bold, precise, and falsifiable predictions? Because of Bayes' rule, of course.
- Eliezer Yudkowsky
- Frequency diagrams: A first look at Bayes
The most straightforward visualization of Bayes' rule.
- Nate Soares