## March 21st, 2006

### Some Pleasant Spametry in my Inbox

"calvinist Goddess"

ecole hydrate department

probe we shreveport that despise come with his comply. When we last
saw implementer it wasn't lamprey. Then after led or slit got to the
bipartisan it was like caution. So when biotic was longue too we
sequester.

### (no subject)

I tried reading this paper by John Baez about n-categories again, but page 25 exploded my brain again, just like last time I tried, maybe a year ago. Everything up to that point is either mundane category theory and therefore easy reasing, or else it's stuff I don't understand, but saved from hardness by being merely suggestive and fuzzy — these latter parts I can skim without feeling guilty. Section 4.2 actually revs up the formal machinery that gives the real definition of opetops, and it's fucking intense.

One way to say what's going on that makes the definition so awesome is this: think about a monoid. On the one hand, a monoid is an algebraic structure that satisfies a certain theory. You got the monoid axioms, you're required to cough up a set and some operations that satisfy them, no big deal. But on the other hand, the notion of monoid action on a set X means that every monoid can itself be thought of as a little theory. A theory of what? Functions from X to itself. The monoid consists of a bunch of elements, and the action is required to map each element of the monoid to an endomorphism on X in such a way that composition of these endomorphisms is compatible with the monoid's operation. So all of the equations that expressions in the monoid "happen" to satisfy need, by virtue of the action axioms, to hold of the functions that make up the action.

What operads and the "slice operad" construction are, as best as I can tell, are a way of pumping enough generality into the situation so that these two views of an algebraic structure,

• As an instance of a theory
• (via the notion of "algebras over X" or "actions on X") As a theory itself

are both available simultaneously, letting one construct an infinite chain of algebras of the same sort, such that each is the theory of the next.

And then he defines opetopes somehow after this, and weak ω-categories after that. I ♥ math.

### (no subject)

Another entry for the Insane Genius file: (this time heavy on Genius, lighter on Insane) Theo Jansen. He has a website at http://www.strandbeest.com/ but it doesn't seem to have nearly as much stuff on it as it should. I saw him talk today because sent out an email about it, but I couldn't find her there.

Jansen is an artist and engineer who make ridiculously awesome wind-powered beach-walking robots, using thin PVC pipes, plastic tubing, custom valves, and plastic bottles. If you've ever read like A. K. Dewdney books that have cute descriptions of how you could theoretically build logic gates from pneumatic effects, this guy's work is a realization of that, as well as containing cool pure engineering solutions to problems of walking and detecting water, loose ground etc.

The logic-gate stuff is pretty amazing by itself. During the talk it was neat to see demoed three NOT gates in serial oscillating madly as a huge supply of compressed air churned through their orgy of mutual negation, and his actual robots have much better, in fact relatively sophisticated control systems. One will turn around when it hits the ocean, count its steps, keep walking until it hits loose sand, turn around, and turn around again before it hits the ocean, because it knows by dead reckoning where the ocean was.

But boy oh boy, just watching the videos of these crazy heaving, clattering, lumbering plastic skeletons did a number on my reptile brain. Deep down they make me automatically feel from the way they move that they're alive, in a way that pretty much no other robot I've seen does. And yet the materials it's made of are so sparse and unorganic that it's like I'm watching landfill scraps possessed.

### (no subject)

Aha, this is the gold-mine paper for the Baez-Dolan definition of weak ω-categories. I think I never attacked it before because I thought, being as it is the third in a series, I had to read the first two first. It actually looks pretty sensible on its own, however.