Notes

What is Russell’s paradox?

Russell’s paradox is based on examples like this: Consider a group of barbers who shave only those men who do not shave themselves. Suppose there is a barber in this collection who does not shave himself; then by the definition of the collection, he must shave himself. But no barber in the collection can shave himself. (If so, he would be a man who does shave men who shave themselves.)

https://www.scientificamerican.com/article/what-is-russells-paradox/

Price equation

In the theory of evolution and natural selection, the Price equation (also known as Price’s equation or Price’s theorem) describes how a trait or allele changes in frequency over time. The equation uses a covariance between a trait and fitness, to give a mathematical description of evolution and natural selection. It provides a way to understand the effects that gene transmission and natural selection have on the frequency of alleles within each new generation of a population. The Price equation was derived by George R. Price, working in London to re-derive W.D. Hamilton‘s work on kin selectionExamples of the Price equation have been constructed for various evolutionary cases. The Price equation also has applications in economics.

It is important to note that the Price equation is not a physical or biological law. It is not a concise or general expression of experimentally validated results. It is rather a purely mathematical relationship between various statistical descriptors of population dynamics. It is mathematically valid, and therefore not subject to experimental verification. In simple terms, it is a mathematical restatement of the expression “survival of the fittest” which is actually self-evident, given the mathematical definitions of “survival” and “fittest”.

https://en.wikipedia.org/wiki/Price_equation

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