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Equation 8 · Part 4 · What a Rule Can Bind When the System Changes Weekly

Symbol τ

Ceq(t)=C∗⋅2 t/τ,τ≈8 months.C_{\mathrm{eq}}(t) = C^{*} \cdot 2^{\,t/\tau}, \qquad \tau \approx 8\ \mathrm{months}.
τ\tau

What this part means

the halving time.

Its job in the formula

τ is one factor in the product that computes the quantity on the left.

Where the article explains it

If a threshold is fixed at C∗C^{*} and efficiency improves with a halving time τ\tau , the capability reachable below the threshold grows as though the budget were expanding: Ceq(t)=C∗⋅2 t/τ,τ≈8 monthsC_{\mathrm{eq}}(t) = C^{*} \cdot 2^{\,t/\tau}, \qquad \tau \approx 8\ \mathrm{months}.

The passage around this formula

…a set performance threshold has halved roughly every eight months, with a 95% confidence interval of about five to fourteen months [ 19 ] . If a threshold is fixed at C∗C^{*} and efficiency improves with a halving time τ\tau , the capability reachable below the threshold grows as though the budget were expanding: Ceq(t)=C∗⋅2 t/τ,τ≈8 monthsC_{\mathrm{eq}}(t) = C^{*} \cdot 2^{\,t/\tau}, \qquad \tau \approx 8\ \mathrm{months}. The analysis that follows is mine rather than the authors’. Taking the central estimate at face value, a threshold left unamended for two years admits models with roughly the…

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Sources cited in the surrounding passage

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