M Theory Lesson 33
Let's have some more fun with pictures. A ribbon can be drawn on a boundary tube, even if the tube has to twist to keep up with the edges of the ribbon. 
Using the edges of the ribbon as boundaries for square pieces of tube, we could draw swiss cheese pictures on the cylinder. 
But instead of disc operad circles we could add in points and make a swiss cheese cubes operad picture. 
I apologise if I'm making up inappropriate names for these diagrams. According to Aaronson, M Theory will probably not be able to show that P = NP. This hypothesis is about packing cubes inside bigger cubes in polynomial time.
Using the edges of the ribbon as boundaries for square pieces of tube, we could draw swiss cheese pictures on the cylinder. 
But instead of disc operad circles we could add in points and make a swiss cheese cubes operad picture. 
I apologise if I'm making up inappropriate names for these diagrams. According to Aaronson, M Theory will probably not be able to show that P = NP. This hypothesis is about packing cubes inside bigger cubes in polynomial time.
posted by Kea | 2:21 PM
4 Comments:
I just realized that I do not know the core idea stimulating the attempt to formulate M-theory in terms of braids, ribbons, and categories.
Best,
Matti
03 27 07
Yes, I don't think I understand the core idea either Kea. And this is why I take ideas from all of the links you provide and come up with ideas from there. M theory does seem somewhat ill defined, but perhaps that is because of my own ignorance and not a failing on your part.
However, I do get the gist of what you are doing; you are trying to cast the nature of physics itself into a categorical framework. Why not? Category theory provides us with overall structure. P-Adics also provide structure as well, but the two structures needn't be at odds and this is where integration of ideas is so useful. Thanks:)
03 27 07
Kea:
Aside from my ignorance stated above, what a wonderful post! One thing that I wonder is that since the square is an approximation to the circle, extra space is added. Does that mean that extra guage degrees of freedom are added that can be modded out in these transformations? Assuming that these transformations are morphisms are have I misunderstood? Or does the square approximation to these circular boundaries have no affect on the outcome of categorization? If my question makes no sense, pls forgive, I am trying to digest all of this.
Thanks.
Hi Matti and Mahndisa. Yes, I have not elaborated on the principles here, although they are quite simple. Roughly, (1) the categorical heirarchy should canonically describe measurement geometry. This starts with Gray's analysis of the categorical comprehension scheme, as I mentioned to nosy snoopy, and (2) a Machian principle of inertia (this is why I appreciate what Louise has been doing).
Although CarlB is making great strides understanding inertia in the Bohmian view, I agree with Matti that this is just the tip of the iceberg, and it is better to view the Mathematical God as an emergent reality.
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