# [FOM] Why Voevodsky was concerned about the foundations of the natural numbers?

José Manuel Rodriguez Caballero josephcmac at gmail.com
Thu Aug 9 12:53:06 EDT 2018

>
> Sam Sanders said:
> I believe we are not giving VERY, and other qualitative statements, enough
> scientific credit, when we say:
> In Jean Benabou's language, the word VERY is a sort of fossil from a time
> when the Western civilization didn't have natural numbers

It can be scientifically proved or disproved that VERY comes from a time
when the Western civilization didn't have natural numbers. Of course, at
that time the ancestors of people from what now we call Western
civilization, they called themselves in a different way (this was an abuse
of terminology to make the text shorter). The scientific proof could be
based in the study of ancient languages, using archeological data and
computer simulations to fill the gaps.

Now, I will talk from a mathematical point of view. Let freq(W, n) be the
number of occurrences of word W during the year n. We have that freq(VERY,
n) is larger than freq(1, n), for b between 1910 and 2008. I guess that
this tendency continues for n = 2018. On the other hand, freq(1, n) is
larger than freq(VERY, n) for 1750 < n < 1900. So, VERY was more common in
the past than the numbers (this is evidence for my claim, although it is
not concluding evidence).

By the way, you can verify that freq(1, n) > freq(2, n) > freq(3, n) > ...
> freq(9, n). The theory behind this regularity, known as  Benford's Law,
was developped by Ted Hill:
https://en.wikipedia.org/wiki/Ted_Hill_(mathematician)

You can find the data here: https://books.google.com/ngrams/

Jose M.
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