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Note that I didn't say anything about France. You seem very doubtful that any society would use something besides base 10; why? > Is there a society that actua

Note that I didn't say anything about France. You seem very doubtful that any society would use something besides base 10; why? > Is there a society that actually used base 20 numbers? From Struik, the book mentioned above, here is what I could find quickly: Of 307 number systems of primitive American peoples investigated by W.C. Eels, 146 were decimal, 106 quinary [base 5] and quinary decimal, vigesimal [base 20] and quinary vigesimal. The vigesimal system in its most characteristic form occurred among the Mayans of Mexico and the Celts in Europe. Give the book a try if you are interested in these things; he writes clearly and engagingly, with a personality and sophistication; the short factual passage above isn't representative. With due respect, I'm going to rely on the highly-regarded writing of arguably the leading historian in the field over Wikipedia. None of these number systems map directly to ours; I've omitted plenty of complexity (and Struik probably omitted more).

thaumasiotes 10y ago
> Note that I didn't say anything about France. You seem very doubtful that any society would use something besides base 10; why? That's all you. I'm not doubtful that a society would use something besides base 10, but when you make the same claim that a lot of other people make, you risk being perceived as similar to those other people. The form of my comment is "I hear this same claim a lot from people who clearly don't know what they're talking about. Do you have something better than they have?" I bought the book. Struik doesn't bother to expand on the selection you quoted at all. His citation, however, does have a bit more ( https://archive.org/stream/jstor-2972526/2972526_djvu.txt https://archive.org/stream/jstor-2972526/2972526_djvu.txt ): > The vigesimal system usually occurs in connection with some other system. > Quinary-vigesimal. This is most frequent. The Greenland Eskimo says "other hand two" for 7, "first foot two" for 12, "other foot two" for 17 and similar combinations to 20, "man ended." The Unalit is also quinary to twenty which is "man completed." But 40 is "two sets of animals' paws," 60 "three sets of animals' paws" and so on regularly to 400 where there is an interesting change in the formation of this primary base (20 X 20) from animals back to man, for 400 is "20 sets of man's paws." A list of nahuatl numbers can be found here ( http://www.omniglot.com/language/numbers/nahuatl.htm http://www.omniglot.com/language/numbers/nahuatl.htm ), and it is quinary-vigesimal. Maya numerals, in their symbolic written form, are also quinary-vigesimal (in the same sense that written Sumerian numerals are decimal-sexagesimal -- that is to say, they are purely quinary, but the forms 20 to 24 aren't used), and Celtic numerals (the words) seem to be a weird quinary-decimal-vigesimal hybrid. This doesn't fill me with confidence in Struik. But Celtic aside, I am satisfied that several American number systems were vigesimal and not decimal. >> I also note, in https://en.wikipedia.org/wiki/Sexagesimal#Usage https://en.wikipedia.org/wiki/Sexagesimal#Usage , that the Sumerians didn't have symbols for 0..59 . They represent large numbers as a series of coefficients of powers of 60, but their "digits" have a base-10 internal structure > With due respect, I'm going to rely on the highly-regarded writing of arguably the leading historian in the field over Wikipedia If you looked at the link, you might notice that all I was relying on was pictures of the cuneiform glyphs. But hey, why read when you can just generally slam wikipedia?
- hackuser 10y ago
  I'm not sure what inspired these somewhat angry responses. I'm just discussing ancient mathematics, which is not a hot button issue. Sorry if I offended you somehow.

thaumasiotes 10y ago

> Note that I didn't say anything about France. You seem very doubtful that any society would use something besides base 10; why? That's all you. I'm not doubtful that a society would use something besides base 10, but when you make the same claim that a lot of other people make, you risk being perceived as similar to those other people. The form of my comment is "I hear this same claim a lot from people who clearly don't know what they're talking about. Do you have something better than they have?" I bought the book. Struik doesn't bother to expand on the selection you quoted at all. His citation, however, does have a bit more ( https://archive.org/stream/jstor-2972526/2972526_djvu.txt https://archive.org/stream/jstor-2972526/2972526_djvu.txt ): > The vigesimal system usually occurs in connection with some other system. > Quinary-vigesimal. This is most frequent. The Greenland Eskimo says "other hand two" for 7, "first foot two" for 12, "other foot two" for 17 and similar combinations to 20, "man ended." The Unalit is also quinary to twenty which is "man completed." But 40 is "two sets of animals' paws," 60 "three sets of animals' paws" and so on regularly to 400 where there is an interesting change in the formation of this primary base (20 X 20) from animals back to man, for 400 is "20 sets of man's paws." A list of nahuatl numbers can be found here ( http://www.omniglot.com/language/numbers/nahuatl.htm http://www.omniglot.com/language/numbers/nahuatl.htm ), and it is quinary-vigesimal. Maya numerals, in their symbolic written form, are also quinary-vigesimal (in the same sense that written Sumerian numerals are decimal-sexagesimal -- that is to say, they are purely quinary, but the forms 20 to 24 aren't used), and Celtic numerals (the words) seem to be a weird quinary-decimal-vigesimal hybrid. This doesn't fill me with confidence in Struik. But Celtic aside, I am satisfied that several American number systems were vigesimal and not decimal. >> I also note, in https://en.wikipedia.org/wiki/Sexagesimal#Usage https://en.wikipedia.org/wiki/Sexagesimal#Usage , that the Sumerians didn't have symbols for 0..59 . They represent large numbers as a series of coefficients of powers of 60, but their "digits" have a base-10 internal structure > With due respect, I'm going to rely on the highly-regarded writing of arguably the leading historian in the field over Wikipedia If you looked at the link, you might notice that all I was relying on was pictures of the cuneiform glyphs. But hey, why read when you can just generally slam wikipedia?

hackuser 10y ago
I'm not sure what inspired these somewhat angry responses. I'm just discussing ancient mathematics, which is not a hot button issue. Sorry if I offended you somehow.