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Equation 43 · Part 8 · How Fast Can a Horizon Learn Which Path You Took?

Numerator: 1-D_rm irr(t_c)

Iirr(tc)=1−h2 ⁣(1−Dirr(tc)2).I_{\rm irr}(t_c)= 1-h_2\!\left(\frac{1-D_{\rm irr}(t_c)}{2}\right).
1−Dirr(tc)1-D_{\rm irr}(t_c)

What this part means

The complete quantity above the fraction bar.

Its job in the formula

1-DrD_rm irr(tct_c) occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

The infimum asks how little path distinguishability remains after the best allowed attempt to erase it. For equal priors, an associated unavoidable decision information is Iirr(tc)=1−h2 ⁣(1−Dirr(tc)2)I_{\rm irr}(t_c)= 1-h_2\!\left(\frac{1-D_{\rm irr}(t_c)}{2}\right). Finally, the proposed horizon receipt time is

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the article section

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