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Posts

March 01, 2015

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Here is my calendar picture for March. The shiny fruit are images of an artwork based on concave circular mirrors in the Kampa Gallery in Prague, the art gallery which inspired the whole enterprise and provided the basic picture for … Continue reading →
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(Zum Vergrößern auf das Bild klicken.) Der einfachste nichttriviale (d.h. nicht unverknotete, vulgo: verknotete) Knoten ist die Kleeblattschlinge. Die wird, wohl in Anlehnung an das dreiblättrige Kleeblatt, im Englischen als “trefoil” bezeichnet und steht deswegen hier im Eintrag bei der 3. Der Sekans ist das Inverse des Kosinus (nicht die Umkehrfunktion, sondern das Reziproke), weshalb…
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זו הפעם החמש-עשרה שבה אצביע והפעם השלישית שאנו נמצאים לפני בחירות מאז שהתחלתי בכתיבת הבלוג. בעבר לא הבעתי בפומבי את הבחירה האישית שלי. עבורי יום הבחירות הוא יום חג, ההכרעות בין  תפיסות עולם ואינטרסים מנוגדים אינן קלות, ויש דרכים שונות, … Continue reading →

February 28, 2015

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I had missed these news that a frozen portion of the Niagara Falls had been ice-climbed. By Will Gadd on Jan. 27. This is obviously quite impressive given the weird and dangerous nature of the ice there, which is mostly frozen foam from the nearby waterfall. (I once climbed an easy route on such ice […]
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While Googling something or other, I came across Nine Chapters on the Semigroup Art, which is a leisurely introduction to the theory of semigroups. (While the document is labelled “lecture notes”, the typography is quite beautiful.)
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Yesterday my colleague Collin Bleak sent me an email containing the number 1247. I will explain why this made me so pleased. Automata Our problem concerns automata. If you know Collin, you may suspect that it has something to do … Continue reading →
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Once upon a time, I worked with a postdoc who shaped my views of mathematical physics, research, and life. Each week, I’d email him a PDF of the calculations and insights I’d accrued. He’d respond along the lines of, “Thanks … Continue reading →
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2 + 2 = 8 + 1 - 5 Also: 2 = 2 = 8 - 1 - 5
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For the second installment of this series of posts (which started here) on the first Bourbaki seminar of 2015, we will discuss Gilles Carron talk entitled “New utilisation of the maximum principles in Geometry (after B. Andrews, S. Brendle, J. Clutterbuck)”. Here, besides the original works of Andrews-Clutterbuck and Brendle (quoted below), the main references […]
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“Mi hanno proposto un quesito che mi sembrava facile, e invece…”.“Eh, succede spesso con le cose che sembrano facili. Uno dice dai, è semplice, si farà così e cosà, poi quando prova a risolvere si pianta”.“Già”.“Ma il quesito in questione qual è?”.“Questo: abbiamo dei dadi a sei facce numerate in un modo non standard, cioè con i numeri 0, 0, 1, 2, 3, 4. Ne lanciamo cinque e sommiamo le cifre che vediamo: quali sono le probabilità di ottenere i numeri da 0 a […]
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i hope y’all remember this thing? Anyway, brains are weird.

February 27, 2015

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It may be that weekends are the wrong time to tamper with computer OS… Last Sunday, I noticed my Bluetooth icon had a “turn off” option and since I only use Bluetooth for my remote keyboard and mouse when in Warwick, I turned it off, thinking I would turn it on again next week. This […]
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Boise Set Theory Seminar, Wednesday, March 4 from 3 to 4pm Abstract: Continous logic is a proper generalization of first order logic where the usual binary truth values are replaced by the unit interval \$[0,1]\$. The models for this logic are metric structures, which are metric spaces together with continuous functions and \$[0,1]\$-valued relations. Just as ordinary logic has typical applications in discrete math, continuous logic has applications in analysis. In this talk we will introduce just […]
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This is about parity subgroups and the spaces that (nearly) represent them in homotopy, and … other stuff… but the working tool is Blakers+Massey, in the aspect of connectivity estimates. Here \$P \simeq \mathbb{RP}^2\$ is a mod-2 Moore space. For whatever reason, we are considering the spaces \$[P,\Sigma^a P^{\wedge b}]\$ of pointed maps (appologies, in the unlikely event that anyone following is hoping to find this notation used consistently in earlier tmblpsts. I can’t […]
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On a set with an operation which has a neutral element, there is an algebraic axiom which is equivalent with both associativity and commutativity of the operation. I call it the shuffle (does it have a name?). It is this one (ab)(cd) = (ac)(bd)  so the middle terms b and c switch their position. Of … Continue reading The shuffle trick, or how to eliminate commutativity and associativity, for the benefit of better self-multiplication →
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Even in this corner of the galaxy, Captain, two plus two equals four.Incluso en este rincón de la galaxia, Capitán, dos más dos es igual a cuatroSeñor SpockEsta es una cita (extraída de Aperiodical) que el Señor Spock pronuncia en el episodio La conciencia del Rey de la serie Star Trek: la serie original.En ella se pone de manifiesto que las matemáticas son universales y que independientemente del lugar en que nos encontremos, siguen siendo ciertas.Tito Eliatron DixitPD: Esta entrada es […]
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For those readers who understand spoken French (or simply appreciate the musicality of the language) and are interested in the history of mathematics, I warmly recommend listening to the recording of a recent programme of Radio France Internationale entitled “Pourquoi Bourbaki ?” In addition to the dialogue of Sophie Joubert with Michèle Audin and Antoine […]
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It would appear that there’s a substantial academic literature on social groupings amongst adolescents at schools. I learned about this while attending a seminar by Robert Akerlof on Social norm formation: the role of esteem. The paper considers a simplified model of social interaction between adoloscents1 in which (in a 2-player version) each player makes 3 choices: effort at 2 activities (academic achievement versus rock music), which one to value, and whether to interact with the other […]
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Kick off your new blog or explore the fundamentals of photography with a supportive community of bloggers.
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This will be a talk for the CUNY Set Theory Seminar, March 6, 2015. I shall describe the current state of knowledge concerning the question of whether there can be an embedding of the set-theoretic universe into the constructible universe. … Continue reading →
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আমরা শোকাহত কিন্তু আমরা অপরাজিত [“We mourn but we are not out”]Filed under: Uncategorized Tagged: atheism, Bangladesh, blogging, Mukto-Mona
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2 / 2 = 7 - 1 - 5
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Combinatorics and More’s Greatest Hits First Month Combinatorics, Mathematics, Academics, Polemics, … Helly’s Theorem, “Hypertrees”, and Strange Enumeration I (There were 3 follow up posts:) Extremal Combinatorics I: Extremal Problems on Set Systems (There were 4 follow up posts II ; III; IV; VI) Drachmas Rationality, Economics and … Continue reading →
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Three approaches to defining equality.

February 26, 2015

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[Here is a reply by Heiko Strathman to my post of yesterday. Along with the slides of a talk in Oxford mentioned in the discussion.] Thanks for putting this up, and thanks for the discussion. Christian, as already exchanged via email, here are some answers to the points you make. First of all, we don’t […]
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The deadline is on April 22, 2015. From the webpage http://mfcs2015.di.unimi.it/ The series of MFCS symposia, organized since 1972, has a long and well-established tradition. The MFCS symposia encourage high-quality research in all branches of theoretical computer science. Their broad scope provides an opportunity to bring together researchers who do not usually meet at specialized […]
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Backstory: Lester Saunders Hill wrote unpublished notes, about 40 pages long, probably in the mid- to late 1920s. They were titled “The checking of the accuracy of transmittal of telegraphic communications by means of operations in finite algebraic fields”. In the 1960s this manuscript was given to David Kahn by Hill’s widow. The notes were […]
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Image reconstruction seems like magic because at first it’s not clear there’s enough information in the blurred image to reliable infer a less blurred image. It’s not surprising Bayesian statistics is a useful tool for doing this, but entropy which … Continue reading →
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Lyretail is a stunning visual treat for your personal site.
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The two languages of math Mathematics is communicated using two languages: Mathematical English and the symbolic language of math (more about them in two languages). This post is a collection of examples of the sorts of trouble that the two languages cause beginning abstract math students. I have gathered many of them here since they […]