Hallo!

On Thu, 9 Jul 2009 02:21:48 -0400, Alex Fink wrote:

> On Wed, 8 Jul 2009 22:06:09 +0200, Jörg Rhiemeier <joerg_rhiemeier@...>
> wrote:
>
> >Hallo!
> >
> >I don't know how Leibniz addressed this problem, but my understanding
> >of such arithmographic systems (as I call them) is that the prime
> >factor encoding is meant to generate *roots*, which then could be used
> >as the starting point of an ordinary word formation machinery, from
> >semantic primes. And even that could indeed be fraught with the kind
> >of difficulty you mention. The arithmographic approach assumes that
> >semantic concepts form a lattice spanned by semantic primes which could
> >be mapped onto the divisibility lattice of natural numbers; it may well
> >be that this notion is misguided.
>
> Indeed, I'm very skeptical of it.

So am I! I have the intention to try it out some day, but I do not
expect it to work out well. Leibniz may have been one of the greatest
minds ever, but even the greatest minds sometimes make mistakes. It
tells a lot that he later realized that simplifying the grammar of
Latin may be a more practical solution of the "world language problem".

> Commutativity and especially
> associativity seem exactly like the sort of properties you want to _avoid_
> in your number-combining operation if you want a tractable sort of syntax
> (or word-internal morphological structure) to work with.

Sure. I realize that this is a problem, hence I said that it would
work at best for making roots - but even there, it is likely to fail.

> Taken together
> they just collapse everything into a multiset. And multisets of numbers
> will certainly give you these difficulties, that there's no natural way to
> say which given things in your multiset are closest bound to each other, let
> away any natural way to get a recursion.

Right. Meanings are not associative. This reminds me of a lightbulb
joke I found on this list a few years ago:

Q: How many Lojbanists does it take to change a broken light bulb?

A: Two. One to decide what to change it into, and one to find out which
kind of bulb emits broken light.

> There are plenty of injections from N^2 to N (N being the naturals; my
> naturals include 0) which avoid being broken in these ways. If I were
> designing a language of an arithmographic sort, I'd use one of these,
> perhaps something like
> f(x,y) = 1 + 2(x + (x+y)(x+y+1)/2)
> which hits all the odd naturals and leaves the even ones for use as
> primitives. Build up a sentence (/ word) with a binary tree structure with
> labelled leaves as usual, put an even number on each leaf, and put f(x,y) on
> each nonleaf whose children are x and y. Unambiguous and flexible enough.

Now that's an interesting idea.

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