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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 expressivity. 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. <3, mungojelly


Michael Poxon <mike@...>