Will your name become extinct? - Numberphile

Numberphile・2 minutes read

Victorians studied the probability of family name extinction based on offspring numbers, with averages less than one ensuring extinction. Different dice with probabilities of offspring were used to show how population growth or decline impacts extinction rates.

Insights

  • Victorians were concerned about the extinction of family names and calculated the probability of a family name dying out based on the average number of children per generation.
  • Different dice with varying probabilities of offspring were used to demonstrate how population growth or decline is influenced, with averages less than one ensuring extinction, except for the case where all sides of the die show 1, preventing extinction despite an average outcome of 1.

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Recent questions

  • How did Victorians calculate family name extinction?

    By using a die to determine offspring.

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Summary

00:00

"Calculating Family Name Extinction Probability"

  • Victorians were concerned about the extinction of family names and wanted to calculate the probability of a family name dying out.
  • A die was used to determine the number of sons a person in the family tree would have, passing on the family name.
  • The family tree was traced through generations, with some branches ending due to no children or limited offspring.
  • The probability of extinction was linked to the average number of children per generation, with averages less than or equal to one guaranteeing extinction.
  • Different dice with varying probabilities of offspring were used to illustrate how population growth or decline is affected.
  • A formula, G(x), was created using probabilities of offspring to calculate the probability of ultimate extinction by generation n.
  • By letting n tend to infinity, the probability of ultimate extinction was determined by solving the equation x=G(x).
  • The probability of ultimate extinction was found to be around 30% for one example, while averages less than one guaranteed extinction.
  • Graphs of G(x) were plotted to visually represent how the probability of extinction is determined by the average number of children per generation.

13:41

"Extinction Prevention: Dice with All 1s"

  • The only exception to guaranteed extinction is a dice with a 1 on every side.
  • Rolling the dice with all sides showing 1 would prevent extinction, although the average outcome is still 1.
  • The probability of extinction by generation n is a key factor to consider.
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