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Equation 3 · Part 13 · Humanity Has Always Been a Human–Technology System

Starting index or lower bound: j

x˙i=xi(fi−fˉ)+∑jMjixj−∑jMijxi,\dot{x}_i = x_i(f_i-\bar f) + \sum_j M_{ji}x_j - \sum_j M_{ij}x_i,
jj

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

j 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

A minimal cultural-selection model can represent the frequency xix_i of a variant i as x˙i=xi(fi−fˉ)+∑jMjixj−∑jMijxi\dot{x}_i = x_i(f_i-\bar f) + \sum_j M_{ji}x_j - \sum_j M_{ij}x_i. where fif_i is context-dependent cultural fitness and MijM_{ij} represents transformation or transmission from variant i to j . The equation is illustrative, not a claim that beliefs have fixed genes or that cultural change is reducible to one replicator law. Unlike alleles, cultural variants can be intentionally modified, horizontally transmitted, blended, externally stored, and adopted because of prestige, conformity, coercion, or institutional mandate.

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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.

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Sources cited in the article section

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