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# Posts

### March 31, 2015

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A recursive programming  Le Monde mathematical puzzle: Given n tokens with 10≤n≤25, Alice and Bob play the following game: the first player draws an integer1≤m≤6 at random. This player can then take 1≤r≤min(2m,n) tokens. The next player is then free to take 1≤s≤min(2r,n-r) tokens. The player taking the last tokens is the winner. There is […]
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Last March 25th, Sébastien Gouëzel gave the talk “Subadditive cocycles and horofunctions” at the Ergodic Theory and Dynamical Systems seminar of LAGA , Université Paris 13. As it is always the case with Sébastien’s expositions, he managed to communicate very clearly the ideas of a mathematically profound subject (and, by the way, this topic is […]
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Die Meldung ist zwar schon zwei Wochen alt, aber ich kann sie hier doch nicht unerwähnt lassen. Während Finnland Mathe und Physik als Schulfächer abschaffen will, macht man in Deutschland jetzt Nägel mit Köpfen. Die deutsche Mathematiker-Vereinigung DMV beklagt öffentlich Missstände in deutschen Grundschulen umd läßt durch ihren Präsidenten erklären Die DMV weist ferner darauf…
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It’s been a long time since I’ve written anything here; the blog was on hold while I was finishing my PhD and on the academic job market. Now that things have settled down a bit I plan to get back … Continue reading →
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but i never found the pages that the plot’s in. so all i’ve done is put a lot of blots in. you know, my meh, thuds, watson.
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cf the second, smaller, sketch is from desargues’ theorem in color (but let’s call it desargues’ rainbow from here on to match fano’s rainbow, posted the next day. in the first, newer, bigger sketch, i’ve used my mystical “projective geometry” powers to bend all the lines into circles. so we now (as you can see) […]
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An impressionist sketch So, one of those things we’re supposed to make much of is “recognition” principles, which is a bit of a funny name for a heap of algebraic/coherence data… One doesn’t so much recognise a very-loopspace as elaborāte a deloopable structure on a space. One clear advantage, though, is that “loopspaces are spaces of the form $\Omega^s X$” is tautologically irksome. We prefer algebra-like things. General Delooping works (when it […]
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3 / 3 = 1 * 1^5 Also: 3! / 3 = 1 * √(|1 - 5|) Also: 3 + 3 = 1 * (1 + 5)
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Filed under: pictures, Running, Travel, University life Tagged: Columbia University, Hudson river, New York city

### March 30, 2015

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Following the highly successful [authorised opinion!, from objective sources] MCMski IV, in Chamonix last year, the BayesComp section of ISBA has decided in favour of a two-year period, which means the great item of news that next year we will meet again for MCMski V [or MCMskv for short], this time on the snowy slopes […]
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We have seen in previous notes that the operation of forming a Dirichlet series or twisted Dirichlet series is an incredibly useful tool for questions in multiplicative number theory. Such series can be viewed as a multiplicative Fourier transform, since the functions and are multiplicative characters. Similarly, it turns out that the operation of forming […]
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The simplest quantum 3-manifold invariant is the Murakami-Ohtsuki-Okada (MOO) invariant. It comes from Chern-Simons theory in the way that the Reshetikhin-Turaev invariant comes from Chern-Simons Theory. It has a closed formula in terms of the order of the first cohomology class of the -manifold and an eighth root of unity. Witten’s Chern-Simons theory for gauge […]
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Simultaneous equations belong in elementary-school mathematics curricula. That’s been my mantra for many years, and I want to examine it now in the context of an interactive Web Sketchpad activity. When I say that elementary-age students should encounter simultaneous equations, I don’t mean that they should be instructed in the standard algebraic procedure for solving pairs of […]
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3 + 3 + 0 = 1 + 5 Also: 3 / 3 = 0 + 1^5
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Filed under: Books, Kids, pictures Tagged: Andrew Gelman, atheism, Friedrich Nietzsche, graphical novel, Maximilien Le Roy, Michel Onfray, Philosophenweg
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one can do only so much with fixed-size mantissa Each cycle of colours is about $256 e$ as many iterations ‘till escape as the cycle outside it.

### March 29, 2015

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A self-study question on X validated exposed an interesting property of the Beta distribution: If x is B(n,m) and y is B(n+½,m) then √xy is B(2n,2m) While this can presumably be established by a mere change of variables, I could not carry the derivation till the end and used instead the moment generating function E[(XY)s/2] […]
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An approximation from Justin Wolfers: “Quarterly growth ˜ 0.33 * this month’s growth + 0.67 * (t-1) + 1.0 * (t-2) + 0.67 * (t-3) + 0.33*(t-4)”. I stared at this one for a while. But it’s actually pretty easy … Continue reading →
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Yes, it’s that time of year again. Hide and Seek: Contacts you every day about the status of their application, then goes on radio silence the moment they receive an offer, never to be heard of again. The No Chancer: … Continue reading →
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I’ve done a little discovery today: Proximities are the same reflexive, symmetric, transitive funcoids. For now I leave to prove this as an exercise for a reader. But later I am going to include this theorem into the book I am writing.
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A short note on how the Graph Laplacian is a natural analogue of the Laplacian in vector analysis. For a twice differentiable function on the euclidean space, the Laplacian of , is the div(grad()) or the divergence of the gradient of . Let’s consider the laplacian in two dimensions: To get an intuition about what […]
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The idea is simple. Put these together:   Craig Venter’s Digital Biological Converter which could print molecular computers. That’s more than just teleportation. Suppose you want to do anything in the real world. You can design a microscopic molecular computer for that, by using chemlambda. Send it by the web to a DBC like device. … Continue reading Biological teleportation taken further →
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|3! + 2 - 9| = 1^5 Also: |3! - 2 - 9| = |1 - 5| Also: 3 = (2 * 9) - 15
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The goal of this post is to summarize some more-or-less standard facts about projective objects. A subtlety that arises here is that in abelian categories there are several conditions equivalent to being projective (we’ll list seven of them below) which are not equivalent in general. We’ll pay more attention than might be usual to this […]

### March 28, 2015

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I am off to New York City for two days, giving a seminar at Columbia tomorrow and visiting Andrew Gelman there. My talk will be about testing as mixture estimation, with slides similar to the Nice ones below if slightly upgraded and augmented during the flight to JFK. Looking at the past seminar speakers, I […]
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Are we just a service department? I don’t believe Princeton’s Mathematics department thinks so, neither does any Chemistry department on this continent. Yet, a Vice-President of the Canadian Mathematical Society wants us “to come to the realization that in almost … Continue reading →
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The following problem is apparently a bonus question for 13 year olds at a local girls school: Evaluate the sum $$\displaystyle \frac{1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4} + \cdots + \frac{1}{99} – \frac{1}{100}}{\frac{1}{1+101}+ \frac{1}{2+102} + \cdots + \frac{1}{50+150}}.$$ It’s not that easy if … Continue reading →
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Some things spotted recently: an absolutely star-studded conference in Zürich next june Jean-Pierre Serre giving strings of lectures at 88 Peter Scholze lecturing in Ann Arbor at 27 a pretty expensive set of compass and rulers and, finally, last week in the fine small city of Saverne : (Picture in the Public Domain)
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A latest article on bias issues for women in STEM by Harvard Business Review.  A slide presentation by AAUW related to their report: Solving the Equation: The Variables for Women’s Success in Engineering and Computing.  The full report can be downloaded for free here.
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the 7 points, as usual: {m, r, b, g, p, y, o}. Let P = {mud, red, blue, green, purple, yellow, orange}. wipe all traces of ROYGBIV away for now and consider the “colors of the rainbow” as MRBGPYO instead. the virtue of this renaming- -and-reordering is that i can now present the seven “lines” […]