Week 5: Syllogism and algorithm

I pointed out a few things about Aristotle's Categories: The generalization of subject and predicate and the question of what can be said about what. This was one important move. Rather than itemize what we have in the universe in terms of individual identities, or endless categories, we search for a simple terminology one that economically exhausts the notion of identity and inherence without having to list everything. But note that in the Categories we are really talking about the nature of propositions - literally what can be said about what. The syllogism is different. Subject and predicate now have almost algebraic values -- replaceable by whatever. The syllogism connects the universal to the predicate and back to a universal (in a new relationship) showing the inherence of the universal in the subject. Again, this is distinct from Plato. It is, moreover, an incredible invention of which there are 258 or so variations (we discussed later the relation between this and two term 1D cellular automata) some of which are valid, some of which are not (just like interesting patterns and homogeneous patterns in two term 1D cellular automata.

The other thing i discussed was the question of a model of meaning -- again. And i will continue to discuss it throughout. I remarked on the consistency of the topological model of meaning in Lynn, Eisenman, Ben van Berkel, and others. The point was: just as the sphere represented a geometrical ideality in Boullee, the manifold or the intensive surface consitutes a figure of topological thinking. . . . but one that seems reducible to an image of that figure. It is not entirely so in all cases -- nonetheless Cecil's use of Seifert surfaces for the UN Studio Arnheim transfer station, their topological diagrams as well as the global topological image, FOA's folding and unfolding bands, Eisenman's folds: all these seem to project a figure that is the pictorial geometrical object of topology or catastrophe.

What was different between this and a straightforward platonic or Euclidean geoemtrical model is that the mathematics in the first case point to an ontology of events rather than things. This was the silly demonstration with the water bottle. I'm just glad the cap was on.

In other words, i was trying to explain how the model of meaning shifted from thing to event. Again, the references are to calculus (first mathematics to quantify events), topology (thinking space, form, and continuity in terms that aren't possible with geometry), and catastrophe theory (which is a hybrid of calculus and topology). (Keep in mind that one of Thom's basic questions is really about modelling phenomena -- but specifically, how to quantify qualitative transformations, like phase change.)

With the subject of this afternoon we looked at Woolfram and his description of cellular automata and i wanted to get a basic feeling for what this idea consists of. But one of the main points in that discussion is of course the interest in complexity and emergent behavior. There is and will be a lot more to say about this. One point is that historically it has been impossible for philosophy to deal with this problem. In Metaphysics Aristotle calls this the accidental, for which he says there can be "no science." Cleary Wolfram is arguing that indeed this simple functions and our ability to see their operations points to a new kind of science. But as Matt pointed out, we have to let the programs run.

Ok, this also brings to discussion the Turing text -- one of the points i wanted to make here is that the very notion that this was a thought experiment about the decidability of any statement about numbers is such an incredible fucking thing. it isn't a computer, it is the idea of this process which hardly even seems mathematical. Again, the cross between logic and mathematics here seems important. Both Leibniz and later Frege were interested in this idea. If there is one thing that I am interested in it is not just the application of the results of computation for architecture -- ie the spinoff results of Wolfram et al, but rather the thought experiment itself. That is why i was asking for an analogy. I wanted to get at that in architecture. Maybe, though I'm not sure, that would mean that we look at architecture kind of like the Entscheidungsproblem in math. hmmm

The Rocker discussion was really about the problem of taking computation, cellular automata, and the other stuff in such a literal kind of mapping way. The spatialization of that information is neither a diagram nor an internal geometrical operation to the geometry of the images she is showing. Rather, it seems, it is a pictorial mapping -- which can certainly become something else, and so there is nothing intrinsically wrong with, but it seems to be a kind of red herring.

This is why i also pointed out in Wolfram's images, the strange idea that if we lay the series one after another of each iteration then we get the image of complexity and it seems that it isn't part of the computational function or a rule in the cellular automata that you take the first iteration and the below show the second and so on. When we see the image of the shell that Wolfram carries with him, we feel as though we have a complete correspondence between computation or cellular automata and Nature. hmmm