Kolmogorov complexity "is the length of the shortest computer program...that produces [an] object as output" [1]. Being financial inclined, I often wonder about its analogy in economics. Usually I measure weight or energy. The least massive, or smallest amount of energy needed, to make one dollar of value.
More interesting is the shortest program that reproducibly produces one dollar of value. By this measure, Bitcoin is one of the "denser" pieces of fungible information humans have invented.
"Heavy" networked bits must defend against everyone, everywhere, all the time. This enables lots of new turf. It also increases security risk.
>deterministically (and reproducibly) produces one U.S. dollar of value.
Can that really be said of anything, with the nature of markets, and supply and demand?
If I invest in solar panels, or oil wells, then the expected value per unit sold of the product I produce will be dependent on a massive number of predictable and unpredictable inter-playing forces in a global complex system.
While I can make forecasts of an average expected unit price by studying historical prices, factors affecting them, probabilities of various events, etc. there is also the case that my very selling of the product has an effect on the price I can expect.
As a supplier at a certain scale I can expect revenues to follow a downward curve, with each unit supplied a certain amount of demand is satisfied and thus lowering the overall market price and my expected revenue.
It's not exactly a one-way curve, at higher supplies and lower prices, new avenues of demand can be opened and prices can follow a curve upward.
I like the idea and thinking you've proposed here, but it seems like the complexity of markets is more complicated than Kolmogorov complexity.
It seems the like what produces value in terms of the most optimal ratio between input and output is always in flux. And when a maxima of optimal value is found all the mechanisms of market forces work against it being deterministic and precisely reproducible.
I think to deduce a measure like you proposed in an economic context you would have to have a product that is absolutely finite in potential supply and all potential uses for the product strictly defined, enumerable, and un-extendable. And therefore lowering JumpCrisscross complexity would simply be a matter of optimizing production costs.
But I'm not sure any such scenario exists, it would require a deterministic understanding of the universe and it's constituent parts that we don't have and it would have to preclude the ingenuity and creativity that seem to be key human qualities that drive the flux and change we see in the world.
Kolmogorov complexity is useful to talk about because Kolmogorov complexity is easy to bound. It is always less than or equal to the length of the string.
Economics is really a study of organisms. Biologists often make the mistake of trying to define adaptiveness, but there probably is no such thing. In a universe of rock and scissors, it's clear which organism is best, but when paper comes along, suddenly they're equal.
Attempts at formalism come with the caveat that equilibrium strategies, (strategies such that, if all organisms use them, no organism can improve) generally require the zero cost generation of random numbers.
What does this mean for our function which assigns economic value to programs? Non-trivial (not zero everywhere) solutions are not guaranteed to exist, and indeed the case for their existence doesn't look hopeful.
More interesting is the shortest program that reproducibly produces one dollar of value. By this measure, Bitcoin is one of the "denser" pieces of fungible information humans have invented.
"Heavy" networked bits must defend against everyone, everywhere, all the time. This enables lots of new turf. It also increases security risk.
[1] https://en.wikipedia.org/wiki/Kolmogorov_complexity