The latter point is quite interesting because group theory has played a very important role in modern physics in both relativity and quantum mechanics. Its importance lies in the fact that it provides a mathematical apparatus for dealing with invariance A very important theorem in group theory is Noether's Theorem which makes it possible to relate the conservation laws of physics (including the conservation of energy, of momentum, angular momentum, charge etc.) with specific transformation groups. Noether's Theorem has played a key role in the formulation of the basic principles of particle physics.
As it happens Albert Einstein who in his youth was drawn to Machian positivism in his maturity gravitated to the neo-Kantianism of Cassirer which he combined with a scientific realism. Having read a couple of Cassirer's books i know that he kept abreast of developments in modern physics including Einstein's work. That in turn raises the question of whether the two actually knew other and to what extent they may have interacted.
Jim Farmelant
On Mon, 10 Aug 1998 18:15:07 -0700 (PDT) Chuck Grimes <cgrimes at tsoft.com>
writes:
>
>Now people are critiquing Althusser's metaphors.
>
>Does anyone have an opinion on Levi-Strauss'
>claim to have isomorphism from Group Theory
>algebra in his "structures" ? I guess Althusser
>was a structuralist too .
>
>Charles Brown
>------------------------
>
>Well, well.
>
>What do you? No one, ever, in my hearing or reading has ever asked
>that question, and I've been waiting twenty years! Gawd damn.
>
>Sure, I've got an opinion. The whole foundation of structuralism as
>L-S and Piaget put it together was based on ideas they drew from their
>understanding of Group Theory. Guess where they got the idea? No one
>will know. Any votes?
>
>They got it from Ernst Cassirer, in his last collection of essays
>written in about 1944-5 just before he died. The essay is called,
>"Reflections on the Concept of Group and the Theory of Perception",
>found in _Symbol, Myth, and Culture, Essays and Lectures, 1935-1945_,
>Yerene, DP ed. Yale Uni Press, 1979. (The essay was published about
>1950 and appeared in other collections. This just happens to be the
>one I have)
>
>Cassirer's point was that there seemed to be something innate about
>perception, particularly the basic cluster that comprises the
>kinesethic perception of the body that shares a primary affinity with
>some spatial representations of abstract finite groups, in particular
>the Euclidean Group or E(8). The eight designates the eight possible
>motions of the square on a plane. For three dimensions, that becomes a
>subgroup of what's called the full symmetric group or S(24). These are
>the twenty-four motions or mappings of a basic tetrahedron--a
>symmetrical four cornered pyramid, rotated and reflected about a fixed
>center. In order to find these and make a multiplication table, you
>label the four vertices and imagine them rotating from vertex to
>vertex about axis through each vertex and then through the center of
>each face. The most important aspect is not the motions themselves, by
>the operations or transformations or 'rules' that turn one motion into
>another. All of this mathematical hardware, just reduces down to how
>the body can move and map space--say as in dancing.
>
>Cassirer goes on to say that the invariants, those things that remain
>unchanged by such motions become in some sense critical to both our
>perception and knowledge of space. Though extending or depending on
>this idea of invariants it is possible for us to make sense out of the
>world of perception. This abstraction from perception forms a primary
>foundation for knowledge, and in essence solves the epistemological
>(Kant) riddle of the manner in which we develop knowledge from
>perception.
>
>IMO, this is a pretty neat little theory, especially for 1945. What
>L-S and Piaget did with this interesting and undeveloped idea is
>another matter. If anyone is interested, we could go on.
>
>Chuck Grimes
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