On Wed, 03 Nov 1999 20:36:01 -0800 (PST) Chuck Grimes <cgrimes at tsoft.com>
writes:
>
>What makes you think that a guy (i.e. Lacan) who didn't know the
>difference between an irrational number and an imanginary number would
>know anything about symbolic logic?
>
>Jim Farmelant
>-------------------
>
>Jim,
>
>Absolutely nothing. But I got fascinated by the idea that the
>structuralists in
>the early sixties were using groups as the underlying form to their
>theories.
>Piaget was probably the only one who knew what he was doing, since he
>had
>started off with a degree in the philosophy of science and probably
>had to take
>the courses. Ecco also might.
>
>In any event, I started off a post on quark theory to show that this
>theory is
>developed from a combination of elementary groups and partitions,
>built up by
>direct product and sum operators (SU(2), SU(3)). I have to wonder how
>much of
>that Sokal knows or cares about.
I suspect quite a bit since group theory is an essential mathematical tool for doing work in quantum mechanics and particle physics. Sokal's specialization is I believe in the area of quantum field theory which is very much built around group theory (Quantum electrodynamics around the U(1) group, the electroweak theory around the SU(2) X U(1) group and quantum chromodynamics which is the quantum field theory for gluon fieds around the SU(3) group).
> And, even if he does at least know
>these
>forms, does he understand how artifical they are? I mean, does he
>realise that
>given some arbitrary collection of elements, you can construct
>a group out them? That this construction will have symmetries as
>built-in
>features and that these will seem to be a discovered 'sense' to this
>arbitrary
>collection?
But in mathematical physics, you can all the beautiful equations you want and all the splendid math concepts that you could ever hope to dream of but in the end the theory must be able to give you experimentally confirmable predictions or it is of not much value. The reason why the concept of symmetry looms so large in modern physics is that theories built around this concept including relativity theory, quantum mechanics and quantum field theory have been such great successes in the laboratory. Noether's Theorem which links symmetries of action to conservation laws has been one of the single most fruitful pieces of mathematical formalism in all of 20th century physics.
Whether group theory can have similar successes in fields like linguistics or anthropology seems a bit doubtful to me.
Jim Farmelant
>
>Any way, it was fun to do.
>
>Chuck Grimes
>
>(PS. There was at least one mistake in that other post. If you make
>the
>triangle and label the vertices and center (00) (10) (11) (01), you
>have to
>count the points twice to complete all sixteen. For example the center
>with one
>path out is (00 01). But the center itself has to be counted by itself
>(00 00)
>also.)
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