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Published equation contexts

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

Why this formula appears here

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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x˙i\dot{x}_i

Symbol ẋ_i

ẋ_i has a dot, marking the rate of change of the underlying indexed quantity with respect to the article’s time variable.

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jj

Symbol j

j 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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jj

Starting index or lower bound: j

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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jj

Starting index or lower bound: j

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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Published contexts (1)

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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,

Equation 3 · Humanity & Technology

Humanity Has Always Been a Human–Technology System

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

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.

Meanings in this article

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