Tuesday, November 07, 2006

the primacy of objectified reality, or how the thingy is us.

Despite the obsessive profligacies of the dime on the street objectivist, they do have a point which they utterly miss, because they are so concerned with just kind of lollygagging in their own insane foray into El Umero Nuno's "The Truth". It's as if they misunderstand their subject by proclaiming the object's primacy without the foggiest or faintest clue what they're doing. The tautologous logos reductase (or tautologase) is only one strobeframe, and probably one of the tricksiest to get stuck on: yes, it's a springboard for meditative practices, and I do not doubt that some objectivists have gone that route. The greatest stumbling block is the axiomatization. Once you have something atomic and axiomatic, then you are mired by it's in-your-face characterization. It's object primacy without relational ontophoresis, and thus, a car crash in the field, a wailing daisy in a blender, a propositional calculus elevated to the stature of savior: in short, it's a sotto voce attempt at intrinsicist goobledybbuk. Yes, apprehension of objects is important: but you've got to do the thing that Grothendieck did with points or otherwise you're just going to be stuck to your own flome. Once you recognize that a point or an object is essentially the same as an Ur-point or Ur-object in the topos that you're operating in (or context, if you will): the point is the same, the relations differ, you increase your awareness of this object and of the fabric which it's a component thereof. We are in the business of understanding objects: we are in the business of understanding points. While we percieve, or think we percieve the fabric of reality simultaneously: this is not true. Our understanding occurs because we can lay a fabric over reality: we are not in a position to understand that fabric in it's whole because a fabric cannot be its own metafabric, but we are in a position to abstract out the processes which we use to percieve that fabric (perceptases, etc.). This is probably more important in the short term than actually teasing out the fabric's structure because of our contextual limitation. Despite long and repeated attempts to find a philosopher's stone, it's not something which is going to be available within this context the same way the keyboard sitting in front of you is available in this context. This is a kind of weird message about magic and possibility: some magical things are impossible, and of those things, they are impossible only because they do not fit within this context easily. If I have the tensor product of a bottle of shampoo and a bottle of salt available to me, and the appropriate rotation, I can clean rotate this product so that the bottle of salt becomes the bottle of shampoo, and so forth. But these transformations aren't available within this scope. One imagines an infinity group that can transform any object into any other object. At that point, it would be unnecessary to carry anything else around but knowledge of that group. If you already have this group as an abstract object in your context, then things, that is, objects aren't your concern. Since such a group is inconcievable in scope, magnitude, character tables and so forth, then objects are our concern.
Whether or not this group is present, from awareness of its structure to the ability to apply it when the time comes, demonstrates the degree of object concern one has. And as human beings, or animals, or coelemates, we most decidedly not have this group available to us. If we did, our concern wouldn't be objects. But to generalize a little: yes, we are concerned with stuff, but the stuff which we are concerned with is transitive in character: we cannot and do not look at the flow because it is too dynamic and flexible and slippery. An analogy is appropriate here:
this context is a solid in an ocean of liquid: the solid both accretes and dissolves periodically. Within the solid are processes which eke solid from liquid. Insert reference to traditional Hindu mythology.

But isn't a relation just another type of object? That's an important point. Perhaps we have a Voronoi triangulation? There's a tricky type of duality here that needs to be considered before you get so far off the roost, Icarus. That is to say that mathematics has "point-line" duality as the basis of projective geometry. And we can employ a device to defocus our attention from the individual objects under our consideration in category theory. Important point: instead of talking about categories of projective spaces as "projective categories". Where the duality of import isn't "point-line duality" but "object morphism duality".

Let's start with the category of three objects, usually denoted 3. For abstraction's sake, and just to avoid any group theoretical entanglements with braid groups at the moment, we'll call the objects of this category a, b, and c. Without regard to the directions of the morphisms (modding those out for the moment, they're not important, we're going to assume commutativity and damn the Helicobacter Pylori, We've got at least nine morphisms to deal with: three identities, three going one way, and just that, making six morphisms total. Now we need to evacuate the objects without turning the category into a monoid. The dualization here transforms objects into morphisms and morphisms into objects. The next thing we do is to realize that the identity morphism essentially contributes no information about a given objects, so we've got three morphisms: morphism(a->b), morphism(b->c) and morphism(c->a).

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