Even information density

Claim: a text says no more than the reader needs, and spreads what it says: no sentence packs several new ideas, and a dense term arrives after its context.

• Grade: supported with caveat for judged quality; not supported as a way to read faster.
• Evidence: psycholinguistics (sections 1 and 2), against.
• Check: long-sentences (heuristic): a sentence past 35 words; word probabilities from a language model would measure density itself, and are not in checks/.
• Reader styles: none override it.

What it asks

• Cut first: what the reader does not need costs reading time whatever its shape.
• Then spread: one new idea per sentence, the context of a surprising word before the word.

Why

Surprisal is how unexpected a word is, $s = -\log_2 P(\text{word} \mid \text{context})$. A text of $n$ words with surprisals $s_i$, summing to $S$, costs the reader $C = \sum_i f(s_i)$.

• If $f$ is convex, Jensen's inequality makes the uniform spread the cheapest.
• If $f$ is linear, $C = an + bS$, and only $n$ and $S$ matter.
• Reading time is linear in surprisal, across 6 datasets and 11 languages (Shain et al. 2024; Wilcox et al. 2023).
• Uneven surprisal lowers how acceptable a sentence is judged (Meister et al. 2021, who also find reading times consistent with a weakly super-linear effect).

So evenness buys judged quality; cutting buys time.

Limits

The shape of $f$ is still contested, by measure and by the language model used to estimate surprisal (Brothers & Kuperberg 2021; Xu et al. 2023). Speakers spreading information (Jaeger 2010) is evidence about writers, not readers.

The two public guides read set sentence lengths and cite no test. The European Commission's average sentence length of 20 words comes as "hints, not rules" (EC 2011); the Australian Style Manual asks for an average of 15 and a cap of 25 (AU 2024). The US plain-language page read sets no sentence length (GSA 2026). All are convention.