The Welsh Vigesimal Number System
Date: 02/17/2003 at 11:47:33 From: Andy Spitzley Subject: The Welsh Vigesimal Number System What can you tell me about the Welsh version of the Vigesimal Number System?
Date: 02/17/2003 at 15:52:27 From: Doctor Jodi Subject: Re: The Welsh Vigesimal Number System Hi Andy, Thanks for your question! I didn't know that the Welsh had such an interesting number system. It turns out that they have two sets of counting words: decimal and vigesimal. I searched for "Vigesimal Welsh" and "Vigesimal Wales" at Google. There's not much out there. The best hope I have for you is two books I found recommendations of (at the end). Welsh uses vigesimal and decimal numbers. I didn't find any evidence of a vigesimal number system per se, just the continued use of counting numbers From Michael Morgan at <http://lists.village.virginia.edu/lists_archive/Humanist/v05/ 0265.html> "In Welsh, for example, 30 is ten-on-twenty, 31 is eleven-on-twenty, 40 is two-twenties, 60 is three-twenties, 80 is four-twenties (pedwar ugain, cf. French quatre-vingts). "... Welsh teens are fairly complicated: 11 is one-on-ten, 12 is two-ten, 13 is three-on-ten, 14 is four-on-ten, 15 is five-ten, 16 is one-on-five-ten, 17 is two-on-five-ten, 18 is two-nines, 19 is four-on-five-ten. These numbers combine with the units of twenties mentioned above, so that a number like 97 for example, is: dau ar bymtheg ar bedwar ugain (two-on-five-ten-on-four-twenties). Simple really, and I can't understand why this system hasn't been more widely adopted." ----------------- You can find a list of all the numbers at clwb malu cachu - numerals http://www.clwbmalucachu.co.uk/cheat/cheat_numerals.htm According to this postscript paper, http://www.telenor.no/fou/prosjekter/taletek/ttkvkn/Papers/Euro97.ps the use of base twenty is not uncommon: "Languages that at least partly use this vigesimal system are: Albanian, Basque, Breton, Danish, Faroese, French, Irish, Scottish Gaelic and Welsh." Someone on the linguistlist.org archives recommended Menninger, Karl. 1970 Number Words and Number Symbols. Cambridge, Mass.: MIT Press. A bookseller includes this in its description: "All cultures have evolved or inherited number systems of some sort and the comparison yields significant clues as to the universals of language and culture and a measure of their actual divergence." http://www.rpi.edu/~sofkam/reading.html recommends Jan Gullberg. Mathematics: From the Birth of Numbers, W.W. Norton & Company, New York, 1997. "A history of mathematics. Not mathematicians, mathematics. Early chapters are on the etymology of counting systems, including systems of enumeration in about 20 or 30 languages (Icelandic, Irish, Old English, Old Norse,....) There is quite a variety in counting systems. The most unusual was Welsh, which is vigesimal (20 based). Thirty is literally "second half times twenty" where 1/2 is the first half, 1 1/2 is the second half, 2 1/2 is the third half, etc. "Later chapters include number theory, logic, topology, calculus, and differential equations. An excellent overview of many fields of mathematics, and a good starting point for exploring more. " I hope this helps. Please let us know what you find out. - Doctor Jodi, The Math Forum http://mathforum.org/dr.math/
Date: 02/17/2003 at 18:59:42 From: Andy Spitzley Subject: Thank you (The Welsh Vigesimal Number System) Thank you very much for your response. I will use your tips to further my research. Andy
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