building from primitives (was Re: Langauge Constets)
|From:||Pope Salmon the Lesser Mungojelly <mungojelly@...>|
|Date:||Wednesday, November 21, 2007, 23:50|
Quoting Jim Henry <jimhenry1973@...>:
> It seems you could make a good start, at least -- I'm not sure
> about deriving the whole of mathematics -- with one number, 1,
> and two operations, addition and subtraction. 0 is 1 minus 1.
I don't know much about mathematics, but I can tell you that it is
possible to build a Turing machine (and therefore all of computation)
from a single instruction. Several have been discovered, but the best
known is probably "subtract and branch if negative." See:
I'm not sure that human language has that same property of being
easily reconstructed from various equivalent fundamentals. I'm
finding it very educational to struggle with this idea of a very small
language, and to see exactly what the difficulty consists of.
I am coming to the conclusion that the difficulty of creating
something which feels anywhere near as powerful as a natural language
with a small set of symbols lies not in the combinative power of the
set-- which is naturally infinite in all cases-- but rather in the
**implicit knowledge** embodied in full languages.
Imagining that natural languages were merely very large categorization
schemes, it would be possible to indicate one of the concepts pointed
to by a 160,000 word language with just four words of a 20 word
language-- twenty to the fourth power being 160,000. If you had
160,000 words for the numbers between 1 and 160,000, for instance,
it's easy to see how twenty symbols could replace them.
But in fact, the words of natural language do not just pick out a
category from a natural set of categories available. Each word
carries a frame of implication which embodies irreducible information
about the nature of the world. You cannot either use or understand
the word "dog" without a shared frame containing numerous facts about
Canis lupus familiaris.
It's these shared frames of reference which allow the expressive power
of language. Having a lot of symbols is a convenient way to quickly
trigger the appropriate frames in each other, but it's the number of
underlying semantic spaces that most strongly determines the possible
Thus I have to conclude that in order to create a language which is
fully expressive within a very small set of symbols, it would be
necessary only to create an entire architecture of implication around
those symbols, so that they could be used to access a large number of
concepts. Combinations of symbols would have to be understood as
conventional gateways to preestablished meanings, as the English
phrase "make good."
If that is cheating, then every attempt so far has been cheating-- as
symbols such as "opposite of" rely very heavily upon our existing
frames of linguistic reference-- and furthermore I believe that the
exercise would then be impossible. I'm increasingly convinced that
the expressiveness of language does not reduce to primitive
constituent parts in any useful way.