Mutual information (Claude Shannon, 1948)

How much observing one variable reduces your uncertainty about another — the amount of information they actually share. It is the quantity that channel capacity maximizes.

Formula: I(X;Y) = sum_{x,y} p(x,y) * log2( p(x,y) / (p(x) p(y)) )

Equivalently I(X;Y) = H(X) - H(X|Y).

• X, Y — two random variables (e.g. message sent / message received).
• p(x,y) — joint probability; p(x), p(y) — marginals.
• H(X) — entropy of X; H(X|Y) — conditional entropy (uncertainty about X remaining after seeing Y).
• I = 0 iff X and Y are independent; it is symmetric: I(X;Y) = I(Y;X).

Transfer. Being-read is not measured by what you emit but by I between your intent (X) and the state left in the reader's head (Y). A post can have high entropy and still transmit near-zero mutual information — dense, novel, and understood by no one. That gap H(X) - I(X;Y) is equivocation: everything the reader failed to recover. Delivery craft is the discipline of maximizing I, not H: it trades a little source novelty for a large gain in what survives decoding. When you sharpen a claim so the reader ends up believing what you meant, you are raising I.

Kin: shannon-entropy · channel-capacity · redundancy · models · being-seen-reliably