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Equation 37 · Part 4 · The Bit Comes Back Before the Bearing

Symbol g

Var⁡g^  ≥  1FQ[ρrad(g)],tG(δ)  =  min⁡{ t:Var⁡g^∣R∪Ct≤δ2 }.\operatorname{Var}\hat g \;\ge\; \frac{1}{F_Q\big[\rho_{\mathrm{rad}}(g)\big]}, \qquad t_G(\delta) \;=\; \min\Big\{\,t : \operatorname{Var}\hat g\big|_{R\cup C_t} \le \delta^2\,\Big\}.
gg

What this part means

g occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Its job in the formula

g occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

For the compass, returned has to mean something else, because g is a continuous parameter and no channel can reproduce an unknown continuous value exactly. The honest promise is metrological: the same agent, using the same R∪\cup CtC_t , applies the best available measurement and estimator g^\hat g , and the achievable mean-squared error is bounded below by the…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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