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### 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
-----------------

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."

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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