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Equation 19 · Part 2 · How Fast Can a Horizon Learn Which Path You Took?

Symbol delta

Tdec(δ)=inf⁡{T:Idec(T)≥1−δ}.T_{\rm dec}(\delta)= \inf\{T:I_{\rm dec}(T)\geq1-\delta\}.
δ\delta

What this part means

the define a confidence deficit.

Its job in the formula

delta is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Where the article explains it

Define a confidence deficit δ\delta .

The passage around this formula

and a minimum-error decision time is Tdec(δ)=inf⁡{T:Idec(T)≥1−δ}T_{\rm dec}(\delta)= \inf\{T:I_{\rm dec}(T)\geq1-\delta\}. Both are deterministic transformations of the assumed overlap law. Neither is a new field-theory result. Numerically inverting the two binary-entropy equations gives:

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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