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Equation 33 · Part 10 · AI Feeds on the Distance Between an Intention and an Outcome

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

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

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

(g,h)inG 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

To compare systems without pretending that this irregular region is a Euclidean animal range, bin the preregistered plane into cells and define width as Wm(B)=∑(g,h)∈Gwgh 1{(g,h)∈Nm(B)}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 WmW_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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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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