Question
How can Kolmogorov complexity be described in layman's terms?
Answer
Read Gregory Chaitin's "Meta Math" for a detailed and interesting popular treatment.
The best way to understand it is as the most elegant, in the sense of shortest, computer program, that produces a certain behavior.
Another way to understand it is in terms of Ockam's razor: the simplest explanation of a set of facts is probably the correct one. This principle is often used to justify picking one scientific theory over another, when they have equal predictive power.
So Copernicus' heliocentric theory had lower Kolmogorov complexity than Ptolemy's geocentric theory (not by much though; it contained epicycles etc. too). Tycho Brahe made things actually worse by producing a monstrous combination helio-geo-centric theory. Finally Kepler produced the familiar elliptical orbit heliocentric theory that did away with epicycles. The most efficient of all.
The two are related if you believe scientific "truth" is merely the most elegant model of a set of facts; i.e. a minimalist aesthetic judgment.
Viewed that way, something like the solar system is nothing more than a blackbox computer program. Inputs are the positions of all planets at [math]t=t_0[/math], outputs are future positions.
The shortest program that produces the correct string of all future planetary position numbers is the "truth."
I find this to be a much more satisfying view of science than thinking in terms of falsifiability. Elegance/beauty tends to be a better thing to look for than looking for "truth" in bureaucratic ways.
The best way to understand it is as the most elegant, in the sense of shortest, computer program, that produces a certain behavior.
Another way to understand it is in terms of Ockam's razor: the simplest explanation of a set of facts is probably the correct one. This principle is often used to justify picking one scientific theory over another, when they have equal predictive power.
So Copernicus' heliocentric theory had lower Kolmogorov complexity than Ptolemy's geocentric theory (not by much though; it contained epicycles etc. too). Tycho Brahe made things actually worse by producing a monstrous combination helio-geo-centric theory. Finally Kepler produced the familiar elliptical orbit heliocentric theory that did away with epicycles. The most efficient of all.
The two are related if you believe scientific "truth" is merely the most elegant model of a set of facts; i.e. a minimalist aesthetic judgment.
Viewed that way, something like the solar system is nothing more than a blackbox computer program. Inputs are the positions of all planets at [math]t=t_0[/math], outputs are future positions.
The shortest program that produces the correct string of all future planetary position numbers is the "truth."
I find this to be a much more satisfying view of science than thinking in terms of falsifiability. Elegance/beauty tends to be a better thing to look for than looking for "truth" in bureaucratic ways.