kakuritsu.com

P(A|B) = P(B|A) · P(A) / P(B) σ² = E[(X - μ)²] P(X = k) = C(n,k) · p^k · (1-p)^(n-k) E[X] = Σ x·P(x) f(x) = (1/σ√2π) e^(-½((x-μ)/σ)²) P(A∪B) = P(A) + P(B) - P(A∩B) P(A|B) = P(B|A) · P(A) / P(B) σ² = E[(X - μ)²]

P = 0.95

The Certainty of Uncertainty

Probability is not about predicting the future. It is about measuring ignorance -- quantifying what we do not know with mathematical precision. Every coin flip, every weather forecast, every medical diagnosis lives within the framework of kakuritsu (確率, probability).

The beauty of probability theory lies in its paradox: by accepting that nothing is certain, we gain a powerful tool for navigating uncertainty. The bell curve is not a bell at all -- it is a map of where things are most likely to land.

normal distribution

Var(X+Y) = Var(X) + Var(Y) + 2Cov(X,Y) H(X) = -Σ P(x) log P(x) λ^k · e^(-λ) / k! P(A'|B) = 1 - P(A|B) Var(X+Y) = Var(X) + Var(Y) + 2Cov(X,Y) H(X) = -Σ P(x) log P(x)

P = 0.68

Bayesian Thinking

Thomas Bayes changed everything with a single insight: prior knowledge matters. Your estimate of probability is not fixed -- it updates as new evidence arrives. The posterior probability is the bridge between what you believed before and what the data tells you now.

In a world drowning in data, Bayesian reasoning is the life raft. It provides a formal framework for changing your mind -- for updating beliefs rationally in the face of new evidence.

posterior distribution

P = 0.50

The Illusion of Randomness

Humans are terrible at generating random sequences. We see patterns in noise, find faces in clouds, and assign meaning to coincidence. True randomness is inhuman in its indifference -- it does not care about patterns, narratives, or our desperate need for order.

kakuritsu.com exists to make probability visible. When you see 200 dots arranged by chance, you begin to understand that randomness has its own architecture -- not designed, but emergent. The bell curve is the shape of democracy among random events.

random scatter