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Equation 6 · Part 9 · AI Feeds on the Distance Between an Intention and an Outcome

Starting index or lower bound: cinC_tr

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).
c∈Ctrc\in\mathcal{C}_{tr}

What this part means

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.

Its job in the formula

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

The passage around this formula

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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Learn the underlying idea

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

Open the illustrated sums and products: repeat an operation over an index guide →

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