← Mathematical compendium

Published equation contexts

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)

Why this formula appears here

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.

Read the full article-specific guide →

Read the representative guide

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.

Read this term in its guide →
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.

Read this term in its guide →
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.

Read this term in its guide →
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.

Read this term in its guide →
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.

Read this term in its guide →

How to interpret it

Read it with the definitions, units, and assumptions supplied by the article.

Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

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).

Equation 6 · Evolutionary AI

AI Feeds on the Distance Between an Intention and an Outcome

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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.

Equation guide → · Article →