Teens and Twenties

[Waruno Mahdi]

Oops, I accidentally at first addressed this to Harald (I pressed
the "reply" button).
Sorry, I had to be somewhere yesterday, so I can only respond now.

>  As far as I know 1,2,3,4,5,6,many systems don't exist. There's an

We're talking about different things, I think. I probably shouldn't
have used the term  "systems of numeration". I was talking about
apparent quantity thresholds underlying numeration as reflected in
the etymology of words for numbers.
Thus, the Russian words for '2' till '6' reflect established IE
protoforms, but then come _sjemh "7', vosjemh '8'.
Malay numbers '1' till '6' similarly reflect PAN protoforms,
but for '7' we find a reflex for a form for 'to point, to direct'
believed to derive from the circumstance that '7' falls on the
pointing finger when counting on fingers; then follow '(10)-2'
and '(10)-1' for '8' and '9' respectively, the parenthetized 10
being implied but not explicitly pronounced. The series of number
words thus appears to be structured as 1 >>-> 7 <-<< 9.

>  > being animals that only distinguish the first-mentioned quantities,
>  > and some that are more advanced and "count" till seven.
>  Which are these animals?

I read about it a very long time (20-30 years) ago, I just remember
that it described experiments with wild apes (I forgot whether chimps
or baboons, or other), in which a group of persons carried some
bananas (I think) into a hut, then came out again without the fruit
one by one. when the persons numbered up to 7, the apes knew there
wasn't anyone left in the hut after the last man came out. For
larger groups, the apes were uncertain whether every man was out
when the last one had left (also when seven had been out again).
I also seem to remember reading about a similar experiment with
dogs, but don't remember whether the threshold quantity was 7
as well. They've probably tried this with mice and crows too, but
I don't know about it.

>  I don't know what you mean by quadragesimal system but there is always

Latin _quadraginta_ '40', _quadragesimus_ '40th', by analogy to
_viginti_ '20', _vigesimus_ '20th', from whence "vigesimal".

Thanks for the reference B. Hughes, The Mathematics Teacher 75:253-256
(1982).
--------

>  In which case, the only way to salvage my speculation would be to posit
>  either an earlier but subsequently lost vigesimal system, or else to
>  assume that the vigesimal system is still available at some level of
>  conceptual representation, even if the actual form means 2 x 10

It's a rational explanation, I agree. I had similar ideas too, only I
don't have any facts to indicate that it was that, other than that it
fits my idea of logic (and yours obviously too). I'm probably just
being difficult ;-)

>  The first mechanism, which works up to 6 or 7, is what is called
>  subitization.  And apparently animals can do it as well, whereas
>  they can't count.

The interesting thing about the experiment described above is, that the
apes apparently "subitized" the number of men going in, but then had to
"count" them as they came out one by one (the next one appearing after
the previous one was out of sight). It wasn't clear, whether it was
"subitizing" a number greater than 7 which they were not capable of,
or whether they flunked in the subsequent "counting".
 From your description, I gather they also did a similar experiment
with humans, who then proved not to be much "brighter" than the apes.
(between us, I somehow always had this subtle impression  ... well,
nevermind ;-).

>  The 'digital - quintal - decimal - vigesimal' progression in
>  numbering systems referred to by many linguists doesn't
>  actually apply to what seems to have evolved in the real

well, same comment as above, it's a question of terminology, and I
should probably have expressed that differently.

>  To take an example, let us suppose that we have analyzed a sequence
>  of numerals to have the form ...
...snip...
>... x20,
>  (2x20)+1, (2x20)+2, ...
>  i.e there are distinct number morphs for 1 to 4, and 20,

Now this I find indeed particularly interesting, because I cannot
imagine what may have been the source of having '4' as a base for
numeration. I mean we know about 5/10/20 (hand, both hands, all the
extremities), and one could at least propose evidence for an
underlying source for 3 and 7 as referent quantities. But where
does the 4 come from? There must have been some culture historical
circumstance for this, like that of '12' in counting in dozens, the
number of ounces in a pound, pence in a shilling (in pre-decimal times).
My first impression is, that this is an indication that the particular
numeration system is not at all a "primitivism", but a relatively late
development from an older quintal/vigesimal numeration (I won't say
"system"), that retained the 20, and lost the '5' (perhaps by a taboo?).
Just a speculation, like with the Javanese "trans-vigesimal" thing.

>  This quick coding sorts out the sheep from the goats, and prompts a
>  detailed look back at, say, Macassarese and Buginese, to see how and
>  why they differ in detail from nearby Tolaki.

I haven't had time to look up the Tolaki word for 'iron'. That in Bugi
and Makassarese is a (borrowed) cognate of Malay _besi_, suggesting
introduction from the West. The particularity in numeration analogical to
that in Malayic languages probably reflects the same historical influence.
Further north in Sulawesi, the word for 'iron' was apparently brought in
from the direction of the Philippines.
Well, to be frank, there actually is quite a lot more evidence for
influnce on Buginese/Makassarese from the direction of Malay, but the
word for iron just popped up in my mind at the moment.

Must stop here. sorry this got so long.

Aloha,
Waruno
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