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1/(f1δ2)=ln⁡S/2π1/(f_1\delta^2) = \ln S/2\pi

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A third, more uncomfortable check is what the toy model of the previous section actually implies at the numbers already computed: tLt_L ≈\approx 3.5\,ms\mathrm{ms} , or tLt_L/β\beta ≈\approx 28.2 , for the solar-mass hole above. Taking f1f_1 = 1 as an illustrative, explicitly assumed per-quantum information content, a modest tolerance δ\delta = 0.1\,rad\mathrm{rad} (about six degrees) gives tGt_G/β\beta = 100 , so tGt_G ≈\approx 12.4\,ms\mathrm{ms} and Δ\Delta tLGt_{LG} ≈\approx +8.9\,ms\mathrm{ms} : the compass is the slower debt, as the title claims. But a coarser tolerance, δ\delta = 0.5\,rad\mathrm{rad} (about twenty-nine degrees), gives tGt_G/β\beta = 4 , so tGt_G ≈\approx 0.50\,ms\mathrm{ms} and Δ\Delta tLGt_{LG} ≈\approx…

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f1f_1

Symbol f_1

f1f_1 is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

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δ2\delta^2

Symbol delta^2

delta2a^2 is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

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1/(f1δ2)=ln⁡S/2π1/(f_1\delta^2) = \ln S/2\pi

Equation 129 · Evolutionary Physics

The Bit Comes Back Before the Bearing

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

A third, more uncomfortable check is what the toy model of the previous section actually implies at the numbers already computed: tLt_L ≈\approx 3.5\,ms\mathrm{ms} , or tLt_L/β\beta ≈\approx 28.2 , for the solar-mass hole above. Taking f1f_1 = 1 as an illustrative, explicitly assumed per-quantum information content, a modest tolerance δ\delta = 0.1\,rad\mathrm{rad} (about six degrees) gives tGt_G/β\beta = 100 , so tGt_G ≈\approx 12.4\,ms\mathrm{ms} and Δ\Delta tLGt_{LG} ≈\approx +8.9\,ms\mathrm{ms} : the compass is the slower debt, as the title claims. But a coarser tolerance, δ\delta = 0.5\,rad\mathrm{rad} (about twenty-nine degrees), gives tGt_G/β\beta = 4 , so tGt_G ≈\approx 0.50\,ms\mathrm{ms} and Δ\Delta tLGt_{LG} ≈\approx…

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