[comp.ai] Can humans "understand" mathematics

ggast@peg.UUCP (12/17/89)

    I agree entirely that Searle is missing something.Everyone who has 
    learnt  a foreign language will know immediately what I  mean.When 
    you  start learning a foreign language your thought process is  in 
    your  mother  language, and each word of a sentence  you  want  to 
    speak  in the foreign language you have to translate according  to 
    memorized  rules  .This is a difficult and tedious  process,  just 
    like learning to play piano where you have to translate notes into 
    keystrokes consciously.
    Once  you  have practiced the foreign language  or  piano  playing 
    enough    the   translation   process   becomes   automatic    and 
    subconscious.This   increases   the   speed   of   the   operation 
    considerably and you start thinking in the foreign language.
    Following  Minky's  ideas I would say during learning  a  parallel 
    language agency with cross-connections to your mother language  is 
    created and with enough practice it runs just as smoothly as  your 
    old one.Semantics will result from these cross-connections.
    In that sense you "understand" the foreign language in the  moment 
    the prallel processing runs automatically and Chinese symbols  are 
    correlated automatically to English symbols.But I have to add that 
    you  " understand " English only because you have once  learnt  to 
    associate  acoustic  symbols with real things  (nouns),  processes 
    (verbs)  or attributes (adjectives and adverbs).This includes  the 
    naming  of  certain emotions and feelings too.You  will  associate 
    happiness  with a smiling face because your mother once  said  she 
    feels  happy  and smiled while doing so.To "understand"  does  not 
    only  imply  correct application of rules but  also  an  emotional 
    quality such as having a feeling of security in the application of 
    rules.This feeling of security gives rise to another feeling, that 
    is  satisfaction and it will arise once the application  of  rules 
    is performed on a subconscious level.

    Dr.Gert Gast
    Byron Bay 2481
    Australia

cik@l.cc.purdue.edu (Herman Rubin) (12/17/89)

In article <130200002@peg>, ggast@peg.UUCP writes:
> 
> 
>     I agree entirely that Searle is missing something.Everyone who has 
>     learnt  a foreign language will know immediately what I  mean.When 
>     you  start learning a foreign language your thought process is  in 
>     your  mother  language, and each word of a sentence  you  want  to 
>     speak  in the foreign language you have to translate according  to 
>     memorized  rules  .This is a difficult and tedious  process,  just 
>     like learning to play piano where you have to translate notes into 
>     keystrokes consciously.

This may be why there is so little understanding.  Certainly there is some
of this; even in one's own language, when one looks up words in a dictionary.
But understanding is not obtained in this way.  Even in languages which I
know poorly, there is considerable amalgamation in my thought processes with
my native English.  This produces difficulty mostly in trying to use the 
other language, as the translation process runs in the background, it at
all.

Understanding mathematics is somewhat different.  The ability to use
mathematical objects even with great facility has nothing to do with
understanding.  I maintain that it can even detract from understanding,
and make it difficult to acquire this understanding.  It is almost as if
acquiring the skills in manipulation, proof, etc., makes it difficult to
learn what is at the basis.  What makes it harder is that sometimes there 
is no known basis, and that it is mere accident.

A mathematical concept can even be learned without learning to manipulate.
It corresponds to the "leaning with understanding" a foreign language.  The
biggest problems that people, especially non-mathematicians, have is using
mathematics as a language to precisely express their ideas.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907
Phone: (317)494-6054
hrubin@l.cc.purdue.edu (Internet, bitnet, UUCP)

ladkin@icsib (Peter Ladkin) (12/18/89)

In article <130200002@peg>, ggast@peg writes:
>    I agree entirely that Searle is missing something.Everyone who has 
>    learnt  a foreign language will know immediately what I  mean.

i'm quite sure that searle is aware of most of these obvious points, and
has answered them. it seems appropriate, before deciding what potential
weaknesses his arguments have, to ask him about them.

peter ladkin

yamauchi@cs.rochester.edu (Brian Yamauchi) (12/18/89)

In article <20778@pasteur.Berkeley.EDU> ladkin@icsib (Peter Ladkin) writes:
>In article <130200002@peg>, ggast@peg writes:
>>    I agree entirely that Searle is missing something.Everyone who has 
>>    learnt  a foreign language will know immediately what I  mean.
>
>i'm quite sure that searle is aware of most of these obvious points, and
>has answered them. it seems appropriate, before deciding what potential
>weaknesses his arguments have, to ask him about them.

He replies to many of them in an article in Mind Design (edited by
Haugeland).  The article is worth reading if you're interested in the
Chinese Room debate, but I think a couple of his replies completely
miss the point -- in particular his reply to the robot reply and his
reply to the systems reply.

_______________________________________________________________________________

Brian Yamauchi				University of Rochester
yamauchi@cs.rochester.edu		Computer Science Department
_______________________________________________________________________________

ggast@peg.UUCP (12/20/89)

    In response 3 peter ladkin writes:
 
    > i'm  quite  sure that searle is aware of most  of  these  obvious 
    > points,  and  has  answered them.  it  seems  appropriate,  before 
    >deciding what potential weaknesses his arguments have, to ask him 
    >about them.
 
    So what would his answer be?
    Should  anyone be able to give me his or any of his co-workers  e-
    mail address I will be happy to ask him myself.
 
    ******************************************************************
    *  Dr.Gert Gast         e-mail:  ggast@peg.pegasus.oz [UUCP]     *
    *  95 Bangalow Rd                peg: ggast  [APC Networks ]     *
    *  Byron Bay 2481                                                *
    *  Australia       'Minds are simply what brains do'(M.Minsky)   *
    *  Tel (066) 856903                                              *
    ******************************************************************

markh@csd4.csd.uwm.edu (Mark William Hopkins) (12/30/89)

In article <130200002@peg> ggast@peg.UUCP writes:
> I agree entirely that Searle is missing something.Everyone who has 
> learnt  a foreign language will know immediately what I  mean.When 
> you  start learning a foreign language your thought process is  in 
> your  mother  language,...

I take issue with this.  When I learned Hungarian, I learned it on its own
terms.  More generally, the language is taught there to foreign students using
a text written entirely in Hungarian.

The results are what makes that nation the world's leader in language teaching.

The difficulty you experience are undoubtedly a by-product of the way foreign
language has traditionally been taught.

> Once  you  have practiced the foreign language  or  piano  playing 
> enough    the   translation   process   becomes   automatic    and 
> subconscious...

Therein lies the issue, there were frequently occasions where I could say
or read something in Hungarian and yet not know how to translate it into
English, though I knew what it meant.  Obviously my understanding of the
language did not derive from my understanding of my first language -- not
even from day 1.

Furthermore, there are often occasions where I use words in my own native
language, English, where I do not know their meaning but know exactly what
situation fits the word and just happen to use it where it's appropriate.

Language understanding is a process whereby language is "compiled" into real
or imagined neural-muscular and sensory signals.  You train the mind in the
knowledge of a language by establishing links between the most abstract
concepts, through the intermediate concepts, ultimately down to the base-level
concepts which are our subroutines for controlling our basic bodily functions
and signal processing (including vision).

There is a hierarchy in abstraction here that you progress through, and if you
are taught different aspects of a language in the wrong order your progress is
going to be greatly impeded and you'll end up having to compensate by
resorting to techniques such as "interpreting" the language in your native
tongue.  If you are taught the language abstracted away from the context of
its use (i.e. in the "disembodied state") the same effects likewise will result,
because the bottom-most level has to be "concretized" in terms of actual
base-level experience.

That's the lesson taught by my experience and numerous other experiences
of mine and of other people that I have observed.