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Posts

August 03, 2015

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11:09 AM | Constructing an Ellipse with Web Sketchpad Tools
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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5:06 AM | An exercise gleaned from the proof of a theorem
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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5:06 AM | An exercise gleaned from the proof of a theorem on pseudocompact space
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 ...

August 02, 2015

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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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12:30 PM | 8/2/15
(8 / 2) + 1 = 5Also:8 - 2 = 1 + 5
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11:45 AM | Spaces of Dirichlet series with the complete Pick property (or: the Drury-Arveson space in a new disguise)
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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9:50 AM | MSRI Analytic Number Theory Semester in 2017
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.

August 01, 2015

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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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4:48 PM | Every ordinal has only finitely many order-types for its final segments
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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4:37 PM | Analytic Number Theory program at MSRI: Jan-May 2017
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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12:30 PM | 8/1/15
8 - 112 = 5
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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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1:57 AM | Also, does reading the nlab or n-category café make one a CT cultist?
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.

July 31, 2015

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10:15 PM | new tomatoes [update]
Filed under: Kids, pictures Tagged: garden, summer, tomatoes
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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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