Equation 33 · AI Feeds on the Distance Between an Intention and an Outcome

What does this equation mean?

W_m(B)=\sum_{(g,h)\in\mathcal{G}}w_{gh}\,\mathbf{1}\{(g,h)\in\mathcal{N}_m(B)\}.

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 operationssum_(g,h)inGw_gh1(g,h)inN_m(B)

Result or conditionW_m(B)

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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W_m

Symbol W_m

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

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B

Symbol B

B is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

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g

Symbol g

in bit-transitions and h in active human minutes.

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h

Symbol h

h 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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\mathcal{G}

Symbol G

G 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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w_{gh}

Symbol w_gh

$w_g$ h is an input to the expression that computes the quantity on the left.

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\mathcal{N}_m

Symbol N_m

$N_m$ is an input to the expression that computes the quantity on the left.

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=

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

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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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(g,h)\in\mathcal{G}

Starting index or lower bound: (g,h)inG

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

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

What the article says around this equation

To compare systems without pretending that this irregular region is a Euclidean animal range, bin the preregistered plane into cells and define width as $W_m(B)=\sum_{(g,h)\in\mathcal{G}}w_{gh}\,\mathbf{1}\{(g,h)\in\mathcal{N}_m(B)\}$ . The unit is weighted grid cells, stated with the binning rule. Report its depth too: the greatest gap or horizon cell satisfying the reliability rule. A broad, shallow system has a large $W_m$ but low maximum depth; a narrow, deep specialist may have small width yet persist at large g or h . Neither is “more intelligent” by definition. The map makes a tradeoff inspectable.

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