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In a prior blog post, I described the pins-and-string approach to drawing an ellipse: Press two pins into a corkboard, place a loop of string around the pins, pull the string tight with a pencil, and trace the pencil tip’s path as you pull the pencil around the taut string. Guaranteeing that the traced path is […]

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8:23 AM | The Point Of The Banach Tarski Theorem

There's a classic "Limited Audience" joke/riddle that goes:
Q: What's an anagram of "Banach-Tarski"?
A: "Banach-Tarski Banach-Tarski."
Now, if you already know what the Banach-Tarski
theorem says, that riddle is really funny. If
you don't then you're simply not in the audience,
and you'll just go: "Huh?" In this article we
have a look at why the Banach-Tarski theorem is
more than just a curiosity.

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Filling in the gap is something that is done often when following a proof in a research paper or other published work. Authors tend not to prove or justify every statement or assertion. The gap could be a basic result … Continue reading →

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Filling in the gap is something that is done often when following a proof in a research paper or other published work. Authors tend not to prove or justify every statement or assertion. The gap could be a basic result … Continue reading →

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1:37 AM | The Other Other Rope Around The Earth

There's a classic problem: Upon stretching a rope around the Earth,
you find that you have 6 metres excess. So you join the ends, and
then go around the Earth propping up the rope equally everywhere.
How high will it be? An alternative that's been suggested is that
instead of propping it up equally everywhere, just prop it up as
high as possible in one place. But now Bill Mullins has asked me
yet another variant ...

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10:15 PM | Laplace great⁶-grand child!

Looking at the Family Tree application (I discovered via Peter Coles’ blog), I just found out that I was Laplace’s [academic] great-great-great-great-great-great-great-grand-child! Through Poisson and Chasles. Going even further, as Simeon Poisson was also advised by Lagrange, my academic lineage reaches Euler and the Bernoullis. Pushing always further, I even found William of Ockham along […]

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6:00 PM | Bits, bears, and beyond in Banff

Another conference about entropy. Another graveyard. Last year, I blogged about the University of Cambridge cemetery visited by participants in the conference “Eddington and Wheeler: Information and Interaction.” We’d lectured each other about entropy–a quantification of decay, of the march of … Continue reading →

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5:51 PM | Carmella Kalai (1926-2015)

My beloved mother Carmella Kalai passed away last week. With me, 1956 My father Hanoch Kalai, my mother Carmella, My sister Tamar (Tami) and me around 1957). Photos from the 80s and 20s. Chess-set based on masks

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1:19 PM | Four Weddings And A Puzzle

An unusual voting problem? “Four Weddings” is a reality based TV show that appears in America on the cable channel TLC. Yes a TV show: not a researcher, not someone who has recently solved a long-standing open problem. Just a TV show. Today I want to discuss a curious math puzzle that underlines this show. […]

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12:59 PM | Vertical Learning

Last week I had the opportunity to visit a Downers Grove middle school for #samricamp. I’d like to give an appreciation shout-out to the DG58 staff and administration for putting on another excellent PD event. I’m always impressed with their ability to organize events and invite all interested educators and administrators to their school. All […]

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12:56 PM | Sieve Of Eratosthenes In Python

One of the things we need to do when finding Perrin Pseudo-Primes is to recognise prime numbers so we can see if the numbers predicted by the Perrin test to be prime, are. So we need to generate primes. For small primes (for some definition of "small") this can be done quickly and efficiently by using the Sieve of Eratosthenes. Here we use a dynamically generated collection of filters, one for each prime, and run down the list of all numbers, filtering as we go.

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John McCarthy and I have recently uploaded a new version of our paper “Spaces of Dirichlet series with the complete Pick property” to the arxiv. I would like to advertise the central discovery of this paper here. Recall that the Drury-Arveson space is the reproducing kernel Hilbert space on the open unit ball of a dimensional […]

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11:27 AM | Performing truth

The title of this blog entry could be yet another proposed synonym for mathematics, one that hints at an alternative to the sterile but persistent opposition between discovery and invention. Or it could be an allusion to the practice of mathematicians by which what corresponds to our intuition is made to be true by a […]

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As already indicated by T. Tao on his blog, there will be a semester-length program on analytic number theory from january to june 2017 at MSRI, co-organized with C. David, A. Granville, Ph. Michel, K. Soundararajan. The mathjobs page for applying to the semester is now open (until December 1; because, apparently, of NSF data-gathering […]

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7:01 AM | Fast Perrin Test

So we've got scaffolding to look for Perrin Pseudo-Primes (PPPs), assuming any exist (which they do) but as we run the existing code we find that it's spending pretty much all its time in the test as to whether n divides k(n). Now we look to speed that up ...

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7:01 AM | Russian Peasant Multiplication

Sometimes simply called "Peasant Multiplication," sometimes called "Ancient Egyptian multiplication," sometimes called "Ethiopian multiplication," sometimes called "Multiplication by Doubling and Halving," this algorithm is well-known to some, a mystery to others, and more useful than you might think, being applicable not just to multiplication of numbers, but also useful for exponentiation, and for matrices.

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10:15 PM | weird bug

Filed under: Kids, pictures Tagged: beetle, bug, garden, ladybug, raspberries

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8:33 PM | A long time ago

I worked hard since my last post a year ago, mostly on isomorphism of finite groups which is a decidable problem. Isomorphism problem is a hard problem which is known to be decidable for most groups since it is decidable for hyperbolic groups (see arXiv:1002.2590 ”The isomorphism problem for all hyperbolic groups” from François Dahmani, Vincent Guirardel). However we […]

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8:22 PM | Math and Physics Summer Camps

With the kids shipped off to NSA summer camp, now is the time for mathematicians and physicists to head off to their own summer camp experiences. Some of these have websites where the rest of us can participate a bit … Continue reading →

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5:39 PM | Lenguajes internos

This file is licensed under the Creative Commons Attribution-Share Alike 2.5 Spain license. Para celebrar la publicación en línea de las notas de mi curso sobre las curvas de Shimura, para la escuela AGRA 2015 en Cusco, Perú, sobre aritmética, grupos, y análisis, he decidido escribir este post sobre los lenguajes internos en castellano. Si […]

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I was recently asked an interesting elementary question about the number of possible order types of the final segments of an ordinal, and in particular, whether there could be an ordinal realizing infinitely many different such order types as final … Continue reading →

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Chantal David, Andrew Granville, Emmanuel Kowalski, Phillipe Michel, Kannan Soundararajan, and I are running a program at MSRI in the Spring of 2017 (more precisely, from Jan 17, 2017 to May 26, 2017) in the area of analytic number theory, with the intention to bringing together many of the leading experts in all aspects of the […]

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2:56 PM | Finding Perrin Pseudo Primes, Part 2

So now we've got the scaffolding of a program to find these Perrin Pseudo-Primes. The timing shows that it overwhelmingly spends all of its time in the routine to test whether or not a number passes the "Perrin Test." So there are a few things we need to do.

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2:05 PM | Finding Perrin Pseudo Primes, Part 1

A while ago I was asked: Consider the sequence k(n) with k(1)=0, k(2)=2, k(3)=3, and k(n)=k(n-2)+k(n-3). Why is it true that n divides k(n) if and only if n is prime?" My immediate response was "Well, it's not true." So I was challenged to find a counter-example.

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6:50 AM | August

This picture came about quite by chance. I had taken the picture from Hungerford Bridge on a misty morning, and the whole scene was in pale shades of gray. I decided to increase the contrast just a little; but, as … Continue reading →

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Does the sentence “intersections of subobjects are fiber products of the corresponding monics (which are ordinary products in the relevant overcategory)” look like a good explanation of the intuition that “intersections are a kind of product”? If so, yes.

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3:58 PM | Another definition of pointfree reloids

In previous post I stated that pointfree reloids can be defined as filters on pointfree funcoids. Now I suggest also an alternative definition of pointfree reloids: Pointfree reloids can be defined as filters on products of atoms of posets and . In the case if and are powerset lattices, this definition coincides with the definition […]

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Filters

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di diffusione della scienza e rivoluzioni cc @aubreymcfato @CristianCantoro Utilizzare i dati sulle citazioni in Wikipedia per misurare la diffusione dell'open accessScrivevo all'inizio del 2011 per i festeggiamenti del wiki-decennale di una rivoluzione irreversibile. E' stato piuttosto interessante leggere il titolo che technology review ha utilizzato per raccontare dell'ultimo degli articoli dedicati all'enciclopedia libera: Why Wikipedia + Open Access = Revolution.L'idea degli autori, Misha
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Nielsen, F. (2007). Scientific citations in Wikipedia, First Monday, 12 (8) DOI: 10.5210/fm.v12i8.1997

Heather Ford, Shilad Sen, David R. Musicant & Nathaniel Miller (2013). Getting to the source: where does Wikipedia get its information from?, Proceedings of the 9th International Symposium on Open Collaboration, DOI: 10.1145/2491055.2491064

Misha Teplitskiy, Grace Lu & Eamon Duede (2015). Amplifying the Impact of Open Access: Wikipedia and the Diffusion of Science, Wikipedia Workshop at 9th International Conference on Web and Social Media (ICWSM), arXiv: 1506.07608v1

Citation

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After (or before?) @StartsWithABang's balloon animals' post? A couple of week ago Ethan Siegel published a post about ballon animals, so I decide to repost an old piece that I wrote in 2011 for my italian blog: the english version is lost, but it is magically reposted here! Two one-balloon constructions and their associated graphsI recently discovered this interesting site, vihart. In the site there are some interesting paper and today I want to write something about Computational Balloon
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Demaine E.D., Demaine M.L. & Hart V. (2008). Computational balloon twisting: The theory of balloon polyhedra., Proceedings of the 20th Canadian Conference on Computational Geometry (CCCG2008), 139-142.

Bryś K. & Lonc Z. (2009). Polynomial cases of graph decomposition: A complete solution of Holyer's problem, Discrete Mathematics, 309 (6) 1294-1326. DOI: 10.1016/j.disc.2008.01.054

Citation

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Supponiamo di doverci confrontare con un animale, ad esempio un cane o un lupo (o più in generale con un animale, addomesticato o selvaggio). Secondo Konrad Lorenz il comportamento aggressivo di un cane viene influenzato da due stati d'animo differenti: l'ira e la paura.Si può allora provare a prevedere il comportamento del cane in funzione di quale dei due stati domina: nel caso in cui l'animale è dominato da paura o da ira, proporre una previsione è abbastanza semplice; nel caso in cui il […]

Zeeman E.C. (1976). Catastrophe Theory, Scientific American, 234 65-83. DOI: 10.1038/scientificamerican0476-65

Jean Petitot (2013). Complexity and self-organization in Turing, The Legacy of A.M. Turing, (E. Agazzi, ed.), Franco Angeli, Milano, 149-182. arXiv: 1502.05328v1

Citation

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Non prevedevo di scrivere la versione italiana di un post sull'ultima news proveniente dal RHIC, ma mi è stato gentilmente chiesto, e provvedo ben volentieri. Inizio, però, con un piccolo cappello, alla fine del quale saprete che c'è anche un piccolissimo pezzetto (il doppio diminutivo è perché i firmatari del papero su arXiv sono veramente tanti) d'Italia in questa interessante scoperta.Tutto nasce da un post, nel flusso twittero, di Annalisa Arci, in cui racconta, in maniera e con un […]

Belavina A.A., Polyakova A.M., Schwartza A.S. & Tyupkina Y.S. (1975). Pseudoparticle solutions of the Yang-Mills equations, Physics Letters B, 59 (1) 85-87. DOI: 10.1016/0370-2693(75)90163-X

Hooft G.'. (1976). Symmetry Breaking through Bell-Jackiw Anomalies, Physical Review Letters, 37 (8) DOI: 10.1103/PhysRevLett.37.8

Hooft G.'. (1976). Computation of the quantum effects due to a four-dimensional pseudoparticle, Physical Review D, 14 DOI: 10.1103/PhysRevD.14.3432

Fukushima K., Kharzeev D.E. & Warringa H.J. (2008). The Chiral Magnetic Effect, Physics Review D, 78 (7) DOI: 10.1103/PhysRevD.78.074033

Kharzeev D.E. & Yee H.U. (2011). Chiral Magnetic Wave, Physical Review D, 83 DOI: 10.1103/PhysRevD.83.085007

STAR Collaboration (2015). Observation of charge asymmetry dependence of pion elliptic flow and the possible chiral magnetic wave in heavy-ion collisions, arXiv, arXiv: 1504.02175v2

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A new clue about the #quarkgluonplasma from @RHIC_STAR at @BrookhavenLabWithin the particles that constitute atomic nuclei, protons and neutrons, there are the quarks, the elementary particles with fractional charges, linked to each other thanks to the gluons, bosons that carry the nuclear interaction. Thanks to the gluons it is impossible to observe, at present, free quarks, but it is expected that in the very first stage of the universe, matter was in a state called quark-gluon plasma. Thanks […]

Belavina A.A., Polyakova A.M., Schwartza A.S. & Tyupkina Y.S. (1975). Pseudoparticle solutions of the Yang-Mills equations, Physics Letters B, 59 (1) 85-87. DOI: 10.1016/0370-2693(75)90163-X

Hooft G.'. (1976). Symmetry Breaking through Bell-Jackiw Anomalies, Physical Review Letters, 37 (8) DOI: 10.1103/PhysRevLett.37.8

Hooft G.'. (1976). Computation of the quantum effects due to a four-dimensional pseudoparticle, Physical Review D, 14 DOI: 10.1103/PhysRevD.14.3432

Fukushima K., Kharzeev D.E. & Warringa H.J. (2008). The Chiral Magnetic Effect, Physics Review D, 78 (7) DOI: 10.1103/PhysRevD.78.074033

Kharzeev D.E. & Yee H.U. (2011). Chiral Magnetic Wave, Physical Review D, 83 DOI: 10.1103/PhysRevD.83.085007

STAR Collaboration (2015). Observation of charge asymmetry dependence of pion elliptic flow and the possible chiral magnetic wave in heavy-ion collisions, arXiv: 1504.02175v2

Citation

rmathematicus tweeted: @rmathematicus

RT @AlexiBaker: Register by Aug 15 for Medicine of Words: #medieval Literature, Medicine & Theology @UniofOxford Sept 11-12: http://t.co/U4…

2015-08-03 18:56:07

evelynjlamb tweeted: @evelynjlamb

RT @kevin_sauter: @TmathC @ExploreMTBoS Anyone know resources similar to #MTBoS or #tmc15 for science teachers?

2015-08-03 18:53:52

DrMathochist tweeted: @DrMathochist

RT @punchycritic: New Trailer for Neil LaBute's 'Dirty Weekend' starring Alice Eve and Matthew Broderick ~ Punch Drunk Critics http://t.co/…

2015-08-03 18:41:08

MindAfterMath tweeted: @MindAfterMath

Hidden Markov Models: The Baum-Welch Algorithm http://t.co/OjrC89VsQl #compsci #datascience #math #stem #mathchat

2015-08-03 18:38:03

rmathematicus tweeted: @rmathematicus

RT @ResearchUGent: Today's history lesson: e-readers are nothing new (via @Europeanaeu) http://t.co/TbiUtIDOpS http://t.co/8qahkSQHED

2015-08-03 18:37:16

rmathematicus tweeted: @rmathematicus

RT @DollyJorgensen: Insightful roundtable review of Smith-Howard's Pure & Modern Milk https://t.co/BlZmrXVGqr #envhist #aghist #foodhistory…

2015-08-03 18:35:52

rmathematicus tweeted: @rmathematicus

RT @historybeagle: Good post on exchange of medical knowledge. MT @penandpension: Letters b/w sisters typical of mid-c18 middling women. ht…

2015-08-03 18:35:01

j_lanier tweeted: @j_lanier

2015-08-03 18:23:31

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