November 18th, 2003

beartato phd

(no subject)

Grr. Don't really have time to think about it right now, but I think there is potentially something really interesting about internal strict n-category objects in the functor category N -> Sets. In general I would really like to see a definition of weak n-category that gives it as merely a strict n-category "with stuff". Maybe my hope is in vain, but...

Unless I'm totally wrong, Cat is equivalent to the category of skeletal-categories-with cardinals, where by "skeletal" I mean "any two isomorphic objects are equal" and by "with cardinals" I mean over every object hovers a set that keeps track of the size of the isomorphism class you just collapsed. It really seems like this trick ought to be possible to continue, somehow, displaying the strict n-category "skeleton" of a weak n-category in a more obvious way, and keeping track of precisely the "error" in the approximation.
beartato phd

(no subject)

Writing coming much more easily today. Count is at 18,109. Also having a good piano day. I love being totally owned by a chord progression, singing, screaming through it, over and over, each time different. Tried to read a little of the algebraic topology book I got from the Thackeray math library over at pitt last night --- not really getting anywhere. I find I don't really have a good sense of the typical problem of the field, so I can't really digest the tools too well. Something about category theory itself managed to make me motivated to learn it --- something about how it seems to appear everywhere --- without feeling a need to know how to use it or what to use it for. Maybe I saw that algebraic topology was "really everywhere" it would help. But maybe it just isn't.
beartato phd

(no subject)

Wrote over 3,300 words today, a new daily record, and broke 20k total. I enjoy measuring my progress by well-nigh meaningless numbers rather than quality!
beartato phd

(no subject)

(Man, you think you have it under control, and then you go through old music you haven't listened to for a while, and it starts, and you hear the guitar, and the metronome, and Paul singing, and the B minor dances so naturally into the E7, and the C falls into C minor like a winter sunset and you fall in love again, and it might as well be the first time you ever heard it, it might as well be every other time you've listened to it. Every moment of a year and change of your life sits and whispers in that song, and a dozen others, spread out across them, but densely, deeply bound up in each note. All the memories that stand a dream's-thought away from it light up in your brain with a hazy, bittersweet warmth. You can't go back, can't step in the same river twice, but neither can you forget it. But you can listen to it again, just once more, and sing along... all your life, you were only waiting for this moment to arise...)