Untitled, 2011 by Thór Vigfússon
Posts tagged with knots
William Thurston, geometrizer of manifolds
Sometimes I like to spend an hour looking at something I barely understand. The inside of this guy’s mind has got to be so interesting, but it’s been shaped by geometry rather than words, so it’s very hard for him to express it. The geometry shaping it is also quite less limited than the square space we hit baseballs in, so it’s hard to draw as well.
I can offer some help on grokking what he’s saying, but there’s simply no way to absorb this stuff quickly. That said, I wouldn’t mind being able to imagine the platonic forms inside Bill Thurston’s head.
3!ways. No, they don’t all sound the same, but when I use the word “triad” I am equivalence-classing over the kind of sameness that they do have.
&&surjects the source onto the target—which means it can be inverted. (By contrast, a non-monotonic, up-and-down-looking function, re-uses values, so going in reverse you couldn’t tell which usage the 3 had come from.)
That’s functional in the sense that the data of interest forms a mathematical function or curve, not in the sense that flats are functional and high heels are not.
So say you’re dealing with like a bit of handwriting, or a dinosaur footprint [x(h), y(h)], or a financial time series $(t), or a weather time series [long vector], or a bunch of electrodes all over someone’s brain [short vector], or measuring several points on an athlete’s body to see how they sync up [short vector]. That is not point data. It’s a time series, or a “space series”, or both.
The problem you’re always trying to solve is the “big p, small n problem”. Lots of causes (p) and not enough data (n) to resolve them precisely.
You can see all of their examples, with code, at http://www.springerlink.com/content/978-0-387-95414-1.