Lect 12

Today we were going to look at a few problems about the discrete and the continuous regarding the chu and delanda text. Chu is obviously a proponent of the discrete as the basis for everything. Delanda is really a proponent of the continuous. Both are talking about genetic, that is, algorithnic systems. I'll get to that later. You're blog entries for this week were to discuss 1) the relationship between the algorithm and geometry and 2) to identify in any narrative form something about the discrete and the continuous. William offered a theory somewhat close to Newton's that where there is matter there is geometry but that algorithm as such isn't really connected. That is, it isn't an essence. One might want to ask what we mean about geometry as inhering in matter. It is after all a formal language. Bill offered an insight into the notion that algorithms are only always operations on geometry. But it raised an interesting point that although there may be axioms for geometry we can't say that, yet, for algorithm since it is not a formalized structure as such and so althought there may be infinite ways inwhich to construct a triangle there are limits to the definition of what is a triangle. Well, let's say this is a provocative idea. Frank suggested that in a way every schema of the algorithm has imbedded in it certain principles but that, surprisingly, these were topological if anything. Not geometrical. At a certain point we also discussed the question again of experience. I would like to edit my comments about that since I felt a bit rushed at the end of class to say something but I'm not at all satisfied with what I said. In any event, I would return to my previous claim that the experience of a system, say of language, is not the same as an explantion or even a definition of language. To say that we operate with rules is not yet to say whether and how we experience them and whether we intend them when we express certain things. If I give you a basice set of instructions to add 2 to the next number and you get to the 50th operation but come up with an odd number, for whatever reason, it is hard to say that I intended for you to carry it out such that you always get an even number after 50. This is something from Wittgenstein.
There were also provocative notions on the snowflake: geometry can describe it but can't account for the process by which it formed. And the question also of the operations of the coin toss when the coin is a sphere - the contrast between the discrete and the continuous.

I'll try to say more about this later. To return to chu and delanda, let me just emphasize two things: for chu. Material systems are themselves products of algorithm. Algorithm doesn't derive from dynamical systems. What does this mean? For Delanda, populational, intensive and topological thinking are essential to genetic algorithms. Why does he exclude the discrete? Finally, why in Leibniz are there no such thing as monsters?
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