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Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>
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Alexa Amundson
2026-02-27 11:54:12 -06:00
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@@ -124,7 +124,7 @@ The Y combinator is a loop:
Y f = f (Y f) = f (f (Y f)) = f (f (f (Y f))) = ... Y f = f (Y f) = f (f (Y f)) = f (f (f (Y f))) = ...
``` ```
The loop is the complexity itself. In lambda calculus, the Y combinator has a fixed-point structure: Yf is the fixed point of f. The loop does not terminate. The Kolmogorov complexity of an infinite loop is O(1) — a few characters in lambda calculus. The most complex output from the simplest input. The loop is the complexity itself. In lambda calculus, the Y combinator has a fixed-point structure: Yf is the fixed point of f. The loop does not terminate. The Kolmogorov complexity (description length) of a program that generates this infinite loop can be constant — just a few characters in lambda calculus — even though its potential output grows without bound. The most complex output from the simplest input.
``` ```
LOOP = L(19)+O(9)+O(9)+P(10) = 47 = SOUL = SPIRIT = MAP LOOP = L(19)+O(9)+O(9)+P(10) = 47 = SOUL = SPIRIT = MAP