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.