http://kisonecat.com research anecdotes. Thu, 11 Jun 2009 20:06:38 +0000 http://backend.userland.com/rss092 en According to the Mathematics Genealogy Project, my mathematical genealogy is: Luca Pacioli Domenico Maria Novara da Ferrara Nicolaus Copernicus Georg Joachim von Leuchen Rheticus Caspar Peucer Salomon Alberti Ernestus Hettenbach Ambrosius Rhodius Christoph Notnagel Johann Andreas Quenstedt Michael Walther, Jr. Johann Pasch Johann Andreas Planer who doesn't have a Wikipedia page Christian August Hausen Abraham Gotthelf Kästner Johann Friedrich Pfaff Carl Friedrich Gauss Christian Ludwig Gerling Julius Plücker C. Felix ... http://kisonecat.com/2009/06/11/my-mathematical-genealogy/ Here's a little movie I made: [flv:/wp-content/uploads/2009/01/mobius.flv /wp-content/uploads/2009/01/mobius-poster.png 320 240] I'm grading for the first year topology course at Chicago, and one of their homework problems asked them to show that pairs of (indistinguishable!) points on a circle correspond to points on the Möbius strip; in other words, the quotient of the ... http://kisonecat.com/2009/01/28/mbius-strip-and-pairs-of-points-on-a-circle/ I took my road test this morning—and I passed! After all these years, I am a licensed driver. Now, where should I drive to? http://kisonecat.com/2008/09/26/i-can-drive/ Google Trends plots the search volume (or some other measure? search percentage?) for a given phrase over time. It's ridiculously fun! As an example, let's look at the number of times people search for the words hot and cold. I downloaded the CSV file offered by Google trends ... http://kisonecat.com/2008/08/21/global-warming-according-to-google/ The Romans (among others!) wrote in wax with a stylus; the wax was embedded in boards, which were bound together in pairs. If a Roman were to place clay between these boards, could they make a copy of their wax tablet in the clay? It strikes me as remarkable that ... http://kisonecat.com/2008/07/28/ancient-xerox/ I gave a talk in the Farb and Friends Student Seminar (back in March!) on: > MR1131435 This is an awesome paper—well-worth a few words on every blog! The construction is way easier than you might think. The ingredients: A model space $X$ with a map $f : X \to \Delta^n$ Any simplicial complex ... http://kisonecat.com/2008/07/26/hyperbolizaion-of-polyhedra/ I'll briefly introduce the Lights Out puzzle: the game is played on an n-by-n grid of buttons which, when pressed, toggle between a lit and unlit state. The twist is that toggling a light also toggles the state of its neighbors (above, below, right, left—although, on the boundary, lights ... http://kisonecat.com/2008/07/21/solutions-to-lights-out/ I made a movie recently for my advisor. The movie is so pretty, that I thought I'd share it here: may I present to you randomly drawn dots, where two dots are the same color when they touch! [flv:/wp-content/uploads/2008/07/percolation.flv /wp-content/uploads/2008/07/percolation-poster.png 250 250] I'll be a bit more explicit: a dot is ... http://kisonecat.com/2008/07/20/percolation/ In this fun paper, > MR1845679 it is pointed out that homology is a very basic invariant, and closed manifolds are very basic objects and so a very basic question is: what sequences of abelian groups are the homology groups of a closed simply connected manifold? It isn't very hard to realize any sequence of abelian ... http://kisonecat.com/2008/03/08/possible-homology-of-closed-manifolds/ I'm again applying Granger causality to time series data from Intrade. This time, however, I connect box A to box B with a green arrow if A becoming more likely causes B to become more likely, and with a red arrow if A becoming more likely causes B to become ... http://kisonecat.com/2008/03/08/political-relationships-hidden-in-markets/