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# Numerical language (was Chiming in (was Re: Evolving shades of meaning))

From: Didier Willis Wednesday, November 18, 1998, 18:24
```Douglas Koller wrote:
>
> Nik Taylor wrote:
>
> > There's no problem with repeating decimals, that's only because we
> > happen to use 360 degrees.  If we divided a circle into, say, 77
> > degrees, then there'd be no problem.
>
> But then the beauty of the rest of the system would be lost. I was
> just marvelling that so many numbers divide evenly into 360 - from
> 1 to 20, the only ones that don't are 7, 11, 13, 17, 19 (all prime I
> notice - a coincidence? I don't think so.). Perhaps this is why it
> was selected? 7, 11, and 13 all numbers associated with luck?...I
> think I'll stop free associating before my brain implodes.
Beside 2, constructible numbers (that is divisions of a circle that
may be constructed with a pair of compasses and a ruler) are prime
Fermat numbers and their multiples (The theorem was proven by
the mathematician Gauss -- There many other interesting things
about Fermat numbers, but it would be really too off-topic here.
I may just add that very few Fermat numbers are prime, though the
first ones all appear to be prime).

Fermat numbers are of the form (2^2^a + 1), e.g. 3, 5, 17, 257...
Incidentally, 17 (2^2^2 + 1) is constructible, so there is a
method (though quite complex, and presumably really too complex
for Old Babilonians:) to divise a circle in 17 exact parts with
a pair of compasses and a ruler.

Conversely, 7, 11, 13 and 19 are not constructible.
As an aside note, it is thus impossible to divise a circle
into 77 = 7 * 11 degrees (at least with an exact construction)
as Nik suggested in his post... <grin>

To switch to a more CONLANG-oriented discussion, did anybody
ever tried to design a 'numerical' language where the rules
(grammar, word formation...) would be dictated by numerical
considerations?

Architecture and paintings have the well known golden section
which is supposed to represent perfect proportions, and I
recently saw a program on the french TV where musicians
were relying on statitics and sound distributions to invent
a new kind of music (somewhat contemporary, but I have to admit
that it was quite pleasing).

As a conlanger, I just think that it would be great if an artlang
could claim to have a perfect numerical design :-)

Didier.
-- -
```