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I've decided that I'm trying to do too much, too soon in Taxonomy III. I've decided to detach a small piece of it, and move the rest all the way down to Taxonomy VI. The old IV, V, VI will each bump up one.
The problem is that, to do the Varignon stuff the way I wanted to, I had to build up a great deal of machinery before getting to the payoff, and much of that machinery is useful, separately, for other things. So, I'll take a piece of the machinery and exploit it in the new Taxonomy III, discussing first-order pure classes. Another chunk will go into the new IV and V, covering various kinds of mixed classes. Then, when I get to VI, the remaining machinery will be of a digestible size.
I don't regret the work I put into III this summer; I've learned a bunch of new things which will illuminate the other papers. Still, it's a bit frustrating.
The problem is that, to do the Varignon stuff the way I wanted to, I had to build up a great deal of machinery before getting to the payoff, and much of that machinery is useful, separately, for other things. So, I'll take a piece of the machinery and exploit it in the new Taxonomy III, discussing first-order pure classes. Another chunk will go into the new IV and V, covering various kinds of mixed classes. Then, when I get to VI, the remaining machinery will be of a digestible size.
I don't regret the work I put into III this summer; I've learned a bunch of new things which will illuminate the other papers. Still, it's a bit frustrating.