The law of anomalous numbers

Or, Benford’s law, is a fascinating natural occurrence in the frequency distribution of leading digits – which makes sense once you think about it.

Briefly, the law states that the leading digit is likely to be small; 1 occurs most often, then 2 etc. This holds true for any bases, not just for base 10 numbers, as above. It also follows that it holds true irrespective of scale. Though I find it intuitive, mathematicians have of course worked on why for some time.

I was reminded of Benford’s law by Jen Golbeck refutal “Benford’s Law Does Not Prove Fraud in the 2020 US Presidential Election“, which explains that election results are not a set of numbers where Benford’s law applies. So I’ll take this as a reminder that Benford’s law, though general is not universal.

Benford’s law is also an example of things not being named after the first person describing them, as Simon Newcomb beat Frank Benford to it by more than half a century.

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