KAKURITSU — THE CALCULUS OF LIKELIHOOD
The posterior probability of a hypothesis given observed evidence — the fundamental act of updating belief in the face of new data, as organisms update their luminescence in response to pressure changes in the abyss.
A mathematical object defined as a collection of random variables indexed by time or space — the formal language for describing systems whose evolution contains inherent uncertainty.
"Probability is not about the odds, but about the belief in the existence of information that, once known, would make the outcome certain."
— E.T. Jaynes
As a sample size grows, its mean converges to the expected value. The drowned archive reveals its patterns only to those patient enough to observe at scale.
The sum of many independent random variables tends toward a normal distribution, regardless of the underlying distribution — order emerging from the depths of chaos.
The measure of uncertainty inherent in a random variable's possible outcomes. Maximum entropy corresponds to maximum ignorance — the deepest, most lightless trenches of the probability ocean where all outcomes are equally unknown.
A stochastic model describing a sequence of possible events where the probability of each depends only on the state attained in the previous event. Memory-less, like deep currents that know only their present direction.