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I understand that number can have multiple representations, and I can conceive that the positional notation system was better adapted for arithmetics than say the Roman numerals system which led to its wide adoption (or at least I'm willing to believe the Wikipedia article that claims so).

My question is about the common adoption of the radix 10. It's commonly believed that the number was motivated by the natural count of our human fingers, but was this ever demonstrated?

As a programmer, I sometimes have to explain to newcomers the difference between binary, octal, decimal and hexadecimal systems. I start with the general case (before moving to computer specific cases) and usually enjoy pointing out that the base-10 system is more common because of the number of our fingers.

I repeated this enough to start doubting it, and now wonder if anyone has ever tried to know for sure if this claim is true.

In short: Are there proofs or studies that show that the wide adoption of base-10 notations were widely adopted because of the number of our fingers?

rahmu
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    Also the number of members of the Jackson five times two. –  Sep 28 '12 at 15:49
  • In some story by Robert Heinlein a jealous woman wanting to insult a rival questioned whether she could count to $11$ with her shoes on. (But I don't think that's counts as weighty historical evidence.) – Michael Hardy Sep 28 '12 at 16:01
  • 60 minutes per hour and 60 seconds per minute are surviving vestiges of an ancient Babylonian base-60 system, that had sub-base 10. Ptolemy, the ancient mathematical astronomer, measured angles in degrees, minutes, and seconds, as we do now, but he used base 60 only for fractional parts of a number, and base 10 for integer parts. – Michael Hardy Sep 28 '12 at 16:35

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I suggest a very old book I once proofread for project Gutenberg. You will see that some non-decimal structures (binery, ternary, vigesimal, ...) lure in several languages. And you will also see that in many langugaes numerals are in fact partially derived from names of body parts.

Hagen von Eitzen
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    French has base-20 spoken numerals. – Michael Hardy Sep 28 '12 at 16:02
  • @MichaelHardy: Yes, so have in some form or other Basque, Irish and more. And there is also the funny Danish way of saying 55 essentially as "five and half the third twenty". Note that my reference mostly inspects spoken numerals (sometimes gestures) as the lingua franca of indo-arabic digits would ov course cover everything in decimal ... – Hagen von Eitzen Sep 28 '12 at 16:08
  • Another good reference is Karl Menninger's book, which has similar observations. – Per Erik Manne Sep 28 '12 at 17:07
  • @MichaelHardy: I'm pretty sure modern-day French uses "dix-sept" (ten-seven) "dix-huit" (ten-eight) and "dix-neuf" (ten-nine) as spoken numerals (I live in France). Could it be that some spoken numerals got lost with History? – rahmu Oct 03 '12 at 20:17
  • @rahmu : So French doesn't use only base-20 spoken numerals. – Michael Hardy Oct 04 '12 at 02:08