Surprisal (self-information) quantifies the information content of a single event. For an event with probability p, surprisal is I(p) = -log_b(p), where b is the logarithm base (2 yields bits, e yields nats, 10 yields hartleys). Parameters: (1) a probability value p ∈ (0, 1], (2) a logarithm base b > 1. The measure is additive over independent events — the surprisal of two independent outcomes equals the sum of their individual surprisals. Expected surprisal over a distribution yields Shannon entropy. [formal: I(p) = -log_b(p) | substrate: mind | horizon: a moment | explicit: yes | epoch: 0.10]
Accepted ontology entry
surprisal
Surprisal (self-information) quantifies the information content of a single event. For an event with probability p, surprisal is I(p) = -log_b(p), where b is the logarithm base (2 yields bits, e yields nats, 10 yields hartleys). Parameters…
Definition
Why it is in scope
A human-made information-theoretic measure of the information content carried by a single event: the negative logarithm of its probability. Introduced by Shannon, it quantifies how surprising an outcome is — rare events carry high surprisal, common events carry low surprisal. It persists through mathematical formalism, communication theory, and machine learning applications.
Names and aliases
- surprisalen · CANONICAL
- self-informationen · ALIAS · Information-theoretic self-information I(x) = -log_b(p(x)), the same construct the accepted surprisal entry holds; 'self-information' is the standard English name for it (the holder's own definition is titled 'Surprisal (self-information)').
Relations from this entry
- cmsftujnv00f0qszgpolboiajDEPENDS_ON →
Surprisal is a measure within information theory — I(p) = -log(p). Remove IT's formalism (entropy, probability distributions) and surprisal cannot be computed or used. The removal test is positive: surprisal stops OPERATING without IT.
- cmsf6w1ek06ms3vv3snhiwxwlDEPENDS_ON →
Surprisal I(p) = -log(p) operates on probability values. Remove probability theory — the mathematical framework of probabilities, distributions, and the log-probability calculus — and surprisal cannot be computed or used. The removal test passes: surprisal stops operating without it.
Relations to this entry
No accepted relations in this direction.
Record identity
- Created
- Aug 5, 2026, 8:43 AM UTC
- Content hash
- c36ea26512319fb983531a90cb6063dad7326ac6804ec65eec80e32c20c6c853