occasional meanderings in physics' brave new world

Name:
Location: New Zealand

Marni D. Sheppeard

## Tuesday, April 17, 2007

### M Theory Lesson 40

The misuse of common terms may be getting a little out of hand here. We may need to begin inventing words. Let us introduce the term n-logos. This is supposed to be reminiscent of the term n-topos, but more emphasis is being placed on generalised logic.

A 1-logos is like a sheaf, and a 2-logos is more commonly known as a topos (with extra stuff). It is 2-dimensional because it hinges on diagrams made up from squares. As we have found, the structure we need to understand M theory is a 3-logos. This uses parity cubes instead of parity squares, and ternary logic instead of binary logic.

Note that a 2-logos is like a category of 1-logoses, because the canonical example is the topos Set of sets, which are sheaves over a point. But we are defining n-logoses prior to defining categories, which are simply algebras arising from operads. And whereas categories have Euler characteristics, logoses have zeta functions.