Equation 65 · Part 6 · The Bit Comes Back Before the Bearing

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S = A/4\ell_P^2

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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

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The passage around this formula

where the second equality for a Schwarzschild hole follows directly from Hawking’s temperature formula [ 7 ] and S = A/4 $\ell_P^2$ is the Bekenstein-Hawking entropy [ 6 ] . For a solar-mass hole, $\beta$ $\approx$ 1.24 $\times$ 10^{-4}\, $\mathrm s$ and $\ln$ S $\approx$ 177 , giving $t_*$ $\approx$ 3.5\, $\mathrm{ms}$ — an exact evaluation of the stated formulas, illustrative of the scrambling scale and not a claim about any particular measured hole.

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An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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