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Equation 47 · Part 7 · A Reference Frame Becomes Classical by Publishing Its Orientation

subscript

pblind(ϵ)=ϵ−sin⁡ϵπ.p_{\mathrm{blind}}(\epsilon)=\frac{\epsilon-\sin\epsilon}{\pi}.
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

There is a trap. Even an orientation-blind fragment can sometimes satisfy a loose threshold by guessing from the prior. For uniform SO(3) , the probability that a blind estimate lies within geodesic angle ϵ\epsilon of the true rotation is pblind(ϵ)=ϵ−sin⁡ϵπp_{\mathrm{blind}}(\epsilon)=\frac{\epsilon-\sin\epsilon}{\pi}. This expression follows from the Haar distribution of rotation angle, whose density on [0,π\pi] is 2sin⁡2(θ/2)\sin^2(\theta/2)/π\pi . It passes the limiting checks: at ϵ\epsilon=0 , blind success is zero; at ϵ\epsilon=π\pi , it is one. The redundancy definition is informative only when 1-δ\delta>pblind(ϵ)p_{\mathrm{blind}}(\epsilon) . Otherwise an empty box can qualify as a witness.

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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