In _The Savage Mind_, Levi-Strauss has a picture of crystalline structure that might fit your rotating, dancing tetrahydrine below.
At a simpler level, thinking of the Leninist theory of reflection, and Marx and Engels references to the _camera obscura_like inversion of our eye lenses in reflecting to the brain, might not an elementary natural difference between concept and percept be the inversion or turning upside down ? The elementary first level difference between a symbol and a real,external object is turning it upside down in your head , or imaginary practice. Would this touch your thought on Kant's riddle of how we can know things-in-themselves ?
This also may be why Hegel had to be turned rightside up.
At any rate, the focus on the UNchanging aspects the INvariants as the structure, makes structuralism formal logic and not dialectics.
Charles Brown
>>> Chuck Grimes <cgrimes at tsoft.com> 08/10 9:15 PM >>>
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