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Equation 6 · AI Feeds on the Distance Between an Intention and an Outcome

What does this equation mean?

Htr=−∑c∈Ctrp^(c∣t,r)log⁡2p^(c∣t,r).H_{tr}=-\sum_{c\in\mathcal{C}_{tr}}\hat p(c\mid t,r)\log_2 \hat p(c\mid t,r).

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

Inputs and operations-sum_cinC_trhat p(cmid t,r)log_2 hat p(cmid t,r)
Result or conditionH_tr
How to read the two sides of this formula. Follow the article passage for the meaning of each quantity.

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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HtrH_{tr}

Symbol H_tr

HtH_tr is part of the quantity the equation computes from the expression on the right.

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cc

Symbol c

c appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

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Ctr\mathcal{C}_{tr}

Symbol C_tr

CtC_tr appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

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p^\hat p

Symbol hat p

hat p is one of the signed contributions combined to compute the quantity on the left.

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tt

Symbol t

t appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

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rr

Symbol r

r appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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subscript

subscript

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.

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c∈Ctrc\in\mathcal{C}_{tr}

Starting index or lower bound: cinC_tr

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

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How to interpret it

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What the article says around this equation

The first factor is Shannon entropy: Htr=−∑c∈Ctrp^(c∣t,r)log⁡2p^(c∣t,r)H_{tr}=-\sum_{c\in\mathcal{C}_{tr}}\hat p(c\mid t,r)\log_2 \hat p(c\mid t,r). Its unit is bits. A request that commits competent readers to one completion class has HtrH_{tr}=0 bits. A request that leaves two equally plausible classes alive has one bit. This does not imply that either task takes one unit of labor. It says only how much uncertainty about the reasonable completion story remains after the initial request is read. The estimator should carry a resampling interval across annotators and adjudication choices; a point estimate without its classification fragility would make the most subjective part of the design look falsely exact.

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