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Equation 19 · Part 1 · How Fast Can a Horizon Learn Which Path You Took?

Symbol T_rm dec

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

What this part means

TrT_rm dec is part of the quantity the equation computes from the expression on the right.

Its job in the formula

TrT_rm dec is part of the quantity the equation computes from the expression on the right.

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 subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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