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Equation 1 · Reactor Phylogenetics: The Family Tree of Fission Power

What does this equation mean?

P(next adopter=A∣nA,nB)=nA+anA+nB+a+bP(\text{next adopter} = A \mid n_A, n_B) = \frac{n_A + a}{n_A + n_B + a + 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.

Start withn_A + a
Divide byn_A + n_B + a + b
This relates toP(next adopter
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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PP

Symbol P

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

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AA

Symbol A

the objectively superior technology, and it can lock in permanently long before the alternative gets a fair trial.

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nAn_A

Symbol n_A

cumulative past adoptions and a.

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nBn_B

Symbol n_B

cumulative past adoptions and a.

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aa

Symbol a

a is one of the signed contributions combined to compute the quantity on the left.

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bb

Symbol b

b occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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=

=

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

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fraction

fraction

Divide the expression above the line by the one below it.

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addition

addition

Add the term after the plus sign to the term or group before it.

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subscript

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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nA+an_A + a

Numerator: n_A + a

The complete quantity above the fraction bar.

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nA+nB+a+bn_A + n_B + a + b

Denominator: n_A + n_B + a + b

The complete quantity below the fraction bar; it must be nonzero for this division.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

Graded against biological evolution, several parts of this history are exact rather than merely suggestive. Descent is literal: design documents, safety-case arguments, and component specifications pass from Nautilus to Shippingport to the commercial PWR fleet as physical inheritance, not metaphorical resemblance. Variation across national programs — American, French, Soviet, British, Canadian, Chinese — produced genuinely distinct lineages under geographic and institutional isolation, exactly as allopatric speciation produces distinct populations under geographic separation. Selection by markets, regulators, and accidents is observably real and, in the case of TMI, Chernobyl, and Fukushima,…
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Graded against biological evolution, several parts of this history are exact rather than merely suggestive. Descent is literal: design documents, safety-case arguments, and component specifications pass from Nautilus to Shippingport to the commercial PWR fleet as physical inheritance, not metaphorical resemblance. Variation across national programs — American, French, Soviet, British, Canadian, Chinese — produced genuinely distinct lineages under geographic and institutional isolation, exactly as allopatric speciation produces distinct populations under geographic separation. Selection by markets, regulators, and accidents is observably real and, in the case of TMI, Chernobyl, and Fukushima, dated and measurable. And the founder-effect and lock-in mechanism Cowan documents is not just analogous to a general economic idea — it is the same model. W. Brian Arthur’s 1989 formalization of competing technologies under increasing returns describes exactly this dynamic as a generalized Pólya urn: two technologies accumulate adopters, and the probability the next adopter chooses technology A over B is proportional to how many adopters A already has, so that P(next adopter=A∣nA,nB)=nA+anA+nB+a+bP(\text{next adopter} = A \mid n_A, n_B) = \frac{n_A + a}{n_A + n_B + a + b}. where nAn_A and nBn_B are cumulative past adoptions and a, b are small initial weights representing early, largely arbitrary advantages [ 2 ] . Once nAn_A pulls ahead by chance or by an unrelated advantage — a submarine program’s development budget, say — the process is self-reinforcing regardless of whether A is the objectively superior technology, and it can lock in permanently long before the alternative gets a fair trial. That is Cowan’s finding about light water stated in the exact mathematical language Arthur built for the general phenomenon, not a loose parallel drawn after the fact [ 1 ] [ 2 ] .

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