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From: zhu@ogcvax.UUCP (Jianhua Zhu)
Newsgroups: sci.lang,comp.ai,comp.ai.neural-nets
Subject: Re: Infinite alphabets - (Turing via Berke)
Message-ID: <1454@ogcvax.UUCP>
Date: Thu, 15-Oct-87 16:21:47 EDT
Article-I.D.: ogcvax.1454
Posted: Thu Oct 15 16:21:47 1987
Date-Received: Sat, 17-Oct-87 23:05:52 EDT
References: <154@Aragorn.UUCP> <114400001@exunido.UUCP> <364@su-russell.ARPA> <417@russell.STANFORD.EDU>
Organization: Oregon Graduate Center, Beaverton, OR
Lines: 64
Xref: mnetor sci.lang:1570 comp.ai:905 comp.ai.neural-nets:15

In article <417@russell.STANFORD.EDU>, nakashim@russell.STANFORD.EDU (Hideyuki Nakashima) writes:
> In article <8583@shemp.UCLA.EDU> berke@CS.UCLA.EDU (Peter Berke) writes:
> >
> >By Turing's above remarks, I think by his definition, Chinese cannot
> >succeed at having an enumerable infinity of symbols.  It can only
> >"attempt" to have them.  Unless you "go down a level" and consider
> >"things that make up" Chinese symbols "the symbols."  Then, there
> >must be a finite number of them.  Does anyone know if this is true
> >about Chinese?  It would seem that even in English it does not apply to
> >orthography, though it apparently does to letters, 
> >since we use in hand-writing no fixed "alphabet" of strokes, etc.  Well, 
> >I meant only to introduce Turing's words, forgive me for going on.
> >
> 
> The comparison between Europian alphabetical system and Chinese
> character system is very interesting.  Chinese can DO have infinite
> characters.  What they do is to assign one character to each concept.
> Of course, they don't have infinite characters now.  But I say it is
> possible to have them if they want.
> 
 ...

> 
> each concepts, is one of the examples.  I further think that digital
> computer follows Europian way.  I want to come up with Eastern
> equivalent of digital computer (not an analog one, though).
> Connectionism is one of the possibilities.
> 

It looks like a symbol is defined as a finite set of discrete points in
a *finitely bounded* square (otherwise, the number of symbols would be
infinite). According to this definition, I cannot image how Chinese can
have infinite symbols. On the other hand, if one is allowed to use certain
operators operating on symbols to introduce new symbols, then the number of
symbols in any language can potentially be infinite.

As far as written languages are concerned, the main difference between Chinese
and English (or any Europian language) is that English words are composed
of letters from an finite alphabet in a one-dimensional manner (namely,
concatenation), whereas Chinese words are composed of *strokes* from a finite
stroke set as two-dimentional pictures. (YES the stroke set is VERY finite,
in fact not that bigger than English alphabet.)

Although we do have one more degree of freedom by which we can build words
from elements of one level down, we wouldn't want to go too far in this
other direction (we still want to have neatly printed document in our
language). As a matter of fact, currently nobody is inventing new words
by piling up existing words any more, and new words are added, as new
concepts come along, almost exclusively in a form of *word combinations*,
whose English analogy would be hyphenated words.

Yes I quite agree with Mr. Nakashima in that digital computers follow
Europian way. But I don't see how Connectionism in particular can lead
to digital computers (or equivalents) of Eastern way (I do know that
Connectionism architecture can do extremely well for tasks such as
pattern recognition), and would be delighted if someone could provide
further information.


-- 
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