Occam's Razor
The simplest explanation is usually the right one. Not because the universe prefers simplicity -- because simpler models have fewer ways to be wrong.
Theory as dopamine. A late-night reward for understanding.
Every message carries a measurable amount of surprise. Shannon's insight: information is uncertainty reduction. The less likely a message, the more information it carries -- the "no way!" moment is high entropy clicking into place.
H(X) = -∑ p(x) log&sub2; p(x)
Every interaction is a game. The Nash equilibrium is the strategy lock where no one benefits from changing course alone. It explains why rational individuals don't always cooperate -- the Prisoner's Dilemma isn't a thought experiment, it's your morning commute.
ui(s*i, s*-i) ≥ ui(si, s*-i)
Tiny differences in initial conditions yield wildly diverging outcomes. That's deterministic chaos, not randomness. The butterfly effect isn't a metaphor -- it's a mathematical property of nonlinear systems. The universe is predictable in theory, impossible in practice.
xn+1 = r · xn (1 - xn)
Every belief is a probability waiting for evidence. Bayes' rule is the update mechanic -- posterior beliefs proportional to prior times likelihood. Rationality isn't refusing to be wrong; it's updating smoothly when the data shifts.
P(H|E) = P(E|H) · P(H) / P(E)
theory bites
Compact theoretical morsels -- the kind you replay in your head on the walk home.
The simplest explanation is usually the right one. Not because the universe prefers simplicity -- because simpler models have fewer ways to be wrong.
Any system powerful enough for arithmetic contains true but unprovable statements. Math has blind spots. Always will.
Wealth, words, earthquakes: most outcomes are tiny, a few are enormous. Averages lie when distributions are heavy-tailed.
No general algorithm can predict whether any other algorithm halts. Some questions are undecidable -- and that limit is mathematically permanent.
The future depends only on the present, not the path. Most of physics -- and a lot of life -- is memoryless.
Across all possible problems, every learner performs equally on average. Specialization is the price of skill.