englishLetterEntropy
plain-language theorem explainer
English letter entropy supplies the constant value 4.2 bits per symbol as the single-letter entropy for English text. Information theorists and Recognition Science researchers cite this value when bounding compression limits for natural language under the source coding theorem. The declaration is a direct numerical assignment with no computational steps or lemmas.
Claim. The single-letter entropy of English text equals $4.2$ bits per letter.
background
The module INFO-003 derives fundamental limits on data compression from J-cost. Shannon entropy is defined as $H(X) = -∑ p(x) log₂ p(x)$, and the source coding theorem states that average code length is at least this entropy. In Recognition Science, information carries J-cost, compressed representations lower that cost, and the entropy limit equals the minimum J-cost for faithful representation. This definition supplies the concrete numerical example for English text within that setting.
proof idea
The declaration is a direct constant definition that assigns the numerical value 4.2.
why it matters
This definition anchors the English text example inside the compression limits derivation. It supports the claim that entropy sets the minimum J-cost for faithful representation and connects to the Recognition Composition Law through the broader J-cost minimization framework. The value is cited when linking Shannon limits to the phi-ladder and eight-tick octave structures elsewhere in the Recognition Science chain.
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