>Eric wrote:
>>[1] Could we possibly start up a discussion here on Hofstadter's
definition
>>of meaning -- namely that meaning emerges because of an isomorphism? Is
>>this concept related to David's meaning=effect (which itself illustrates
>>the meaning of "meaning" with an isomorphism)?
>
>*****
>i-so-mor-phism n.
>1. Biology. Similarity in form, as in organisms of different ancestry.
>2. Mathematics. A one-to-one correspondence between the elements of two
>sets such that the result of an operation on elements of one set
>corresponds to the result of the analogous operation on their images in
>the other set.
>3. A close similarity in the crystalline structure of two or more
>substances of similar chemical composition.
Thanks, I was afraid I'd have to break out GEB again for a refresher.
>So H. sees meaning arising because two similar things are compared?
No, H. is a mathematician, he's using #2 above.
One example he uses is from music. A piece by a composer such as Bach or
Mozart can be said to have a self-contianed (isomorphic) meaning--there are
relationships between the notes in the piece which could be decoded by
anyone, regardless of cultural substrate--a one-to-one relationship between
the piece and its meaning. He compares this with a piece by a composer such
as John Cage, John Zorn, or Paul D. Miller (aka DJ Spooky, whose _Viral
Sonata_ has a wonderful little explaination of memes in the liner notes,
BTW). Where the Bach piece derives its meaning directly from its structure,
a Cage or other post-modern piece is entirely context dependent. The
structure of the piece alone is not enought to establish its meaning, it
must also be seen within its culture in order to decript its meaning(s).
Hofstadter (as I remember it) uses the example of an alien finding
recordings of both Bach and Cage. The Bach record the alien could recognize
as having meaning from its patterns (even if it did not share our
aesthetic), but it could not find the same meaning in the Cage recording
without sharing our cultural framework
.
The Bach has isomorphic meaning, there is a one-to-one relationship between
the piece and its meaning. The Cage has a contextual meaning, it must be
seen with its culture for the meaning to be realized. Math has isomorphic
meaning, Art has contexual meaning (increasingly so since the 19th century).
I suspect many of our arguments here stem from conflicts between those who
(implicitly) believe "meaning" must be isomorphic and those who (implicitly)
see "meaning" as including the contextual.
-Prof. Tim