LL-L: "Numbers" LOWLANDS-L, 19.AUG.2001 (01) [E]

[Lowlands-L]

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 L O W L A N D S - L * 19.AUG.2001 (01) * ISSN 189-5582 * LCSN 96-4226
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From:  "Randy Elzinga" <frisiancow at hotmail.com>
Subject: LL-L: "Numbers" LOWLANDS-L, 14.AUG.2001 (05) [E]

Lowlanders, Zintus,

Being a student of mathematics, this question is of interest to me.  I own
a
book call "The Universal History of Numbers: From Prehistory to the
Invention of the Computer" by Georges Ifrah, translated from French by
David
Bellos, E.F. Harding, Sophie Wood, and Ian Monk.

It says nothing about difficulties for numbers over sixty in Germanic
Languages.  However, it does give a chart (pg. 35) which lists the numbers,

counting by tens, from twenty to one hundred for Gothic, Old High German,
German, Anglo-Saxon, and (Modern) English.  Modern English, as you all know

is regular, forming the word for the multiple of ten by using a root based
on the orginal number plus the suffix _-ty_.  German, as most of you
probably know, is mostly regular with the exception of 30 with has
_drießig_
rather than *drieszig or some similar form.  But it seems to me that this
is
a contraction or modification for the sake of euphony rather than the type
of irregularity in which you are interested.  But Gothic, Old High German,
and Anglo-Saxon all have different forms past sixty:

Gothic has the suffix _-tigjus_ for 20 - 60 and _ehund_ for 70 - 90.
OHG has the suffix _-zug_ for 20 - 60 and _-zo_ for 70 - 100.
AS has the suffix _-tig_ for 20 - 100, but has a prefix _hund-_ for 60 -
100.

(note that the formation of the root from the original number seems to be
quite irregular in all of these languages, and many others not listed)

This suggests to me that, at the very least, multiples of ten above sixty
were thought of differently from those below sixty.  It is curious to me
that French is the only Romance language that I know of which has irregular

forms for multiples of ten above sixty.  If I understand correctly, the
French language arose from a vernacular of Latin spoken by a Germanic
people, and that it is the only Latin vernacular 'created' by a Germanic
people.  Am I right on this?  If so, might some Germanic or Frankish
influence have affected the development of French number names?  Does
anyone
know if similar irregularities existed in Old French or in any older forms
of other modern Germanic languages, Lowlands or Otherwise (Old Frisian, Old

Saxon, Old Norse, etc.)?

The book also speculates (pg. 38, 39)that French number names may have been

influenced by Basque number names.  Most number systems are in base-10.
That is, numbers are expressed in powers of ten (1, 10, 100, 1000, etc.)
Basque numbers from 20 to 99 are expressed in a base twenty naming system.
The reason for this suggestion, of course, is that the French word for
eighty does not have the sense of "eight tens", but rather "four twenties"
and thus eighty is expressed in terms of twenties rather than tens.
Supposing that this speculation is correct, then there is no direct
connection between Low Saxon and French.  This also means that the French
irregularity is of a different type than Low Saxon.  The suffix in Low
Saxon
still has the sense of "multiplied by ten", in contrast to the sense of the

French system.

Since the number sixty seems to be at the heart of this discussion, it may
be of interest to mention the ancient Babylonians whose number system was
base-60.  They would count up to 59 using a system similar to ours, but
after this, numbers were grouped in sixties, sixties of sixties and so
forth.  Thus 120 in our notation would be *20 in their notation.  The base
sixty still survives in our clock, where sixty seconds make a minute and
sixty minutes make an hour.  Perhaps the Babylonians reached a limit to
their cognition at the number sixty and needed to find some other method to

represent numbers greater than sixty.

All other given examples, from many different, non-Indo-European language
groups, seem to have no irregularities of either the French or the Germanic

type, thus making multiples of ten above sixty no different from those
below
and including sixty.  The evidence does not seem strong enough to support a

"difficulty hypothesis" except perhaps amongst Germanic peoples.

The earlier chapters of this book, and the earlier chapters of another book

that I own which deals with some cognitive aspects of mathematics, ("Where
Mathematics comes from:  How the Embodied Mind Brings Mathematics into
Being" by George Lakoff and Rafael Núñez) suggest to me that if there were
any difficulties they would be present already at lower multiples of ten,
such as forty and fifty.

I'm not sure of the motivation for your question, but this seems to be a
question more appropriate to the field of psychology of mathematical
thinking, and to the history of numbers.  Sadly, I do not know of any other

resources that I can recommend to you on this topic.

Randy Elzinga.
frisiancow at hotmail.com

>From: Dl7bk at aol.com
>Subject: figures/numbers in Low Saxon, parallels in French?
>
>Dear Lowlanders,
>
>in Emsland Low Saxon we count like "twintig" (20), dartig (30),
....sesstig
>(60), but then "sevenzig" (70), "achtzig" (80) and "negenzig" (90). So the

>ending "-tig" (the equivalent to the English "-ty" is used up to sixty
>(60).
>
>Starting from seventy (70) the Low Saxon ending "tig" is replaced by the
>German ending "zig".
>
>As most readers may know, French counting is regular up to 60 (soixante).
>Then standard French starts with additions "soixante-dix" (60+10),
>"quattre-vingt" (4x20) and "quattre-vingt-dix" (4x20+10).
>
>Does anybody have an idea if there is a link or a common reason for this
>phenomenon, that both languages have a "problem" with numbers higher than
>60?
>Are there other lowlands languages with the same irregularity? Or is it
>just a
>trace that Napoleon has left in our region?
>
(snip)

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