GalCom

[summary: In the GalCom thought experiment, you live in the future, and make your money by living in the Deneb star system and sending information to an automated stock trader you own in the Vega star system. Sending interstellar information is possible, but very expensive — and you have a lot of data to send. If you're clever, you can reprogram the computer on Vega in the low-cost off-hours, but to send the key market data (at the critical moment) you have to reserve high-cost precisely-timed bits far in advance. When reserving those bits you have to pick a fixed set of messages and buy enough bits to cover the longest message that you might want to send. If you end up sending a shorter message you can sell some of the bits back. You send a very high volume of data, so small decreases in the average cost of sending a bit are worth a lot of effort.]

[summary(Rules):

1. It costs 1 galcoin per bit to reserve on-peak bits in advance. Galcoins are very expensive.
2. You can reprogram your machine on Vega in advance, using cheap, off-peak bits. Don't worry about the cost of those.
3. You can resell reserved bits that you don't use (including fractional bits).
4. Any decrease in the expected cost of transmitting a message, no matter how small, is worthwhile.]

The GalCom hypothetical is a thought experiment where sending a bit of information is a clearly defined and very expensive action, which makes it useful for understanding various concepts in Information theory and Probability theory.

The year is 21026. Humanity has become a flourishing inter-stellar civilization. Capitalism never died, and stock markets are thriving in various star systems. Due to the light-speed limitations, the markets are out of sync, and there's a lot of money to be made by setting up an automated trader in one star system, moving to another star system, and sending information about the stock market to your automated trader the instant that that information becomes available.

You set up your own automated trader in the Vega star system, and you currently make a living by transmitting market data from the Deneb star system. To transmit that data, you use the deep-space Galactic Communications network known as "GalCom."

You have a lot of data to transmit, and sending information on GalCom isn't cheap. Fortunately, it is efficient: GalCom is a highly optimized network used by trillions of citizens to send and receive pulses of light across the cosmos. To send information via GalCom, you purchase bits. For each bit you purchase, you are allowed to control a single pulse in the GalCom signal, making it either be present (representing a 1) or absent (representing a 0).

It's relatively cheap to buy bits on non-peak hours (to, e.g., reprogram your machine on Vega), but it's very expensive to reserve bits during peak hours (i.e., just after a juicy earnings report is published). You make your money by being among the very first people to send information about the stock market, so you have to reserve those very expensive precisely-timed bits in advance. This means that you have to know what messages you might want to send in advance, and reserve enough bits for the longest possible message that you might send. Fortunately, there's a secondary market on peak-hour bits, so if you end up reserving 5 bits and then only using 3 of them, you can resell the last two bits.

For example, say you know that you're going to send one of the following messages: "buy", "sell", or "hold". GalCom would require you to purchase 4 bytes of information (enough to transmit four letters), and then if you actually end up transmitting "buy" you can sell the last byte back (because you only used 3 of the 4).

Of course, you can send that message using much less than 4 bytes, if you're clever, both by developing efficient [ encoding schemes] and by [ accounting for the fact that some outcomes are more likely than others]. Your profit margins depend on you finding ways to transmit information as efficiently as possible. To do that, you can use Information theory.