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

From:Didier Willis <dwillis@...>
Date: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. -- -