Re: Telona number system

Since there's been such a lot of interest in the Telona numbers, (for
which many surprised thanks :) ), it's probably time for me to tell
you how they really work.  Actually, almost everything that's been
said about them so far has been pretty close to the mark.  I've posted
separately with regard to some of the pragmatic and usage issues, so
I'll restrict myself to explaining the rules underlying the system.

There are single words for the numbers 1 - 13, 15 and 17.  Other
numbers are expressed as combinations of these numbers multiplied
together, along with two other words meaning 'multiply by 2 and add 1'
and 'multiply by 4 and add 1'.  The rule to decide the choice and
ordering of factors is that the largest single-word number is put
first.

To be more precise: let the set of 'F factors' of a number N include
its prime factors, however large, together with all the composite
factors that are expressible as single words, possibly including the
number itself.  Then:

1. Write down the highest F factor of N.
2. Divide N by the number you've just written down - call this N1.
3. Go back to step 1, using N1 for N.
4. Repeat until the number is fully factorised.

For example, take the number 48.  Its highest F factor is 12 (a single
word, 'ite').  N1 is then 4, and the highest F factor of this is also
4 (again a single word, 'sur').  The expression for 48 is therefore
'ite - sur' which becomes (for reasons I'll have to explain elsewhere
or this post would be twice as long) 'ite ilcur'.  Solutions like 8x6
or 16x3 are vetoed by rule 1, 'highest F factor first'.

Now a more complicated example - 1914.  Its prime factors are
29.11.3.2, and therefore its highest F factor is 29 (not to be
represented by a single word this time).  The highest F factor of the
remainder is 11 ('lali', or in combination, 'allali'), and that leaves
6 ('dena' or 'eldena').  The expression at the end of step 4 is then
'29 allali eldena', which contains an inexpressible prime number.

Prime numbers are resolved by expressing them as 2n+1 or as 4n+1.  The
rules are as follows:

5. For each prime P in the resulting expression, replace it by 's'
followed by P minus 1.
6. Divide each of these numbers P-1 by 4 if possible, or else by 2.
7. Replace each 's' by 'ca' if you divided the following number by 4, or
by 'ru' if you divided by 2.

So, 29 becomes s28 -> ca 7, 'ca eso'.  Putting this in its place in
the expression for 1914 above, '29 allali eldena', gives '(ca eso)
allali eldena'.

What happens next?  There are two possibilities, and I haven't made my
mind up yet which I prefer.
- Option 1 involves marking the nesting structure of the expression as
it stands.  The syntax of Telona allows for a rather elegant way of
doing this, which again unfortunately I don't have space to show here,
but I certainly hope to do so before too long.  It basically relies on
diacritics over the words, realised as pitch accents in speech.  The
above example would come out as 'ca esò allali eldéna', for what it's
worth - note that two diacritics are needed.
- In option 2, the order of the words is rearranged to make the
nesting as simple as possible.  This works quite well for 1914, giving
'lali eldena asa esó' (with only one diacritic, note), although not
for every possible number.

I appreciate that all that probably looks very complicated.  It's only
really a natural development from simple premises, though.  Actually
the same could be said for Telona as a whole.  I hope I'll be able to
post more about the phonology and syntax soonish - maybe next week.

Hope you enjoyed that!  All comments and queries happily received...

Jonathan.

[reply to jonathan underscore knibb at hotmail dot com]
===
'O dear white children casual as birds,
Playing among the ruined languages...'
Auden/Britten, 'Hymn to St. Cecilia'
===
This post may contain the following characters:
á a-acute / é e-acute / í i-acute / ó o-acute / ú u-acute
à a-grave / è e-grave / ì i-grave / ò o-grave / ù u-grave