Category Archives: goodmath

Carnival of Math: The Spam Edition

To be honest, I haven’t been following the Carnival of Math much since it’s inception; my new job keeps me busy enough that I barely have time to keep the blog going, and so I haven’t really looked much at recent editions. In fact, I completely forgot that I was hosting it again until I started receiving

Much to my disappointment, it appears that spam has managed to invade even the carnivals. Close to half of the submissions that I received were blatant spam, including one for a penis-enlargement pill. But hey, when a theme hits me in the face, I run with it. So, welcome to the Carnival of Math: Spam Edition!

Get rich quick, by betting on the World Series! Just learn how to play the odds; we can show you how, with our entertaining and <a href=""educational probability puzzles! Once you’ve mastered that, just look at the batting averages, and place your bets!

Refinance your mortgage! Having trouble with rising interest rates? Is your bank balance in the red? Do you feel like no matter how much you scrimp, it never adds up to enough to pay your bills? Like
every time you save 2 dollars, you still have no money left? It’s not your fault: the real problem is the numbers you’re using! With primitive, old-fashioned numbers, if you’re not careful, 1+1=0! Just switch over to our new improved number system, Z2, where there are no negative numbers at all! Our prime polynomials and their relatives can solve your problems! But that’s not all – we’ll throw in a Catalan ring for free!

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The world is changing. Globalization is creating a new job market, where
old-fashioned skills aren’t enough to succeed. Even if your children are
the best and the brightest, standard education won’t give your
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For those of you who just want to be able to see the articles, here’s the list, in table form.

Author Title
Anne Glamore Beyonce and I Fail Long Division
Charles Daney Rings and Ideals
Dave Marain Educating our best and brightest: Alec Klein Interview
Dave Marain Last minute PSAT prep
David Eppstein Batting Averages
Eric Macaulay Equivalence
jd2718 Puzzle: last one left over
Mark Dominus The square of the Catalan Sequence
Mark Dominus Relatively prime polynomials over Z2
Martin Cooke Two “proofs” that 1 + 1 = 0
Slawomir Kolodynski Groups and neutral elements

Free Will and Fruit Fly Behavior

I’ve been seeing articles popping up all over the place about a recent
PLOS article called Order in Spontaneous Behavior. The majority of
the articles seem to have been following the lead of the Discovery Institute, which claims that the article demonstrates the existence of free will, which they argue is inconsistent with naturalism and darwinism.

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A Cool Movie of the Kaye Effect

I came across this while looking through the referrals to GM/BM. This is an incredibly cool video of a strange phenomenon called the Kaye effect. It includes high speed video of the effect, and a demonstration of their mathematical analysis of the effect, and their prediction and verification of the effect.

The Kaye effect is an incredibly bizarre phenomenon. Basically, if you take a substance like liquid shampoo, and allow a thin stream of it to pour down from a height onto a smooth surface, the stream will periodically “bounce”, producing a stream leaping up from the point of contact. Watch it – it’s seriously cool.

Strange Loops: Ken Thompson and the Self-referencing C Compiler

I’m currently reading “I am a Strange Loop” by Douglas Hofstadter. I’ll be posting a review of it after I finish it. A “strange loop” is Hofstadter’s term for a Gödel-esque self-referential cycle. A strange loop doesn’t have to involve Gödel style problems – any self-referential cycle is a strange loop.

Reading this book reminded me of my favorite strange-loop story. It’s actually
a story about software security, and the kinds of stunts you can play with
software if you’re clever and subtle. It’s the story of the Unix C compiler, and the virtually invisible back-door security hole inserted into it by Ken Thompson – a story he told in his Turing award lecture..

(Idiot that I am, I originally said it was Dennis Ritchie who did this… Leave it to me to link to the original lecture, and not notice that I got the author wrong!)

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The 2007 Abel Prize: Professor S. Varadhan and the Theory of Large deviations

As an alert reader pointed out, a major mathematical prize was awarded recently. Since
2002, the government of Norway has been awarding a prize modeled on the Nobel, but in
mathematics. The prize was originally suggested by Sophus Lie, he of the Lie group, back in
1897, when he heard that Nobel was setting up his awards, and was not including
mathematics. The prize is named after Niels Abel, the Norwegian mathematician who
discovered the class of functions that are now known as Abelian functions; the same person
that Abelian groups are named after, etc.

Anyway, this year, the Abel
prize was awarded to Srinivasa Varadhan
, an Indian mathematician who is currently a professor at the NYU Courant Institute.
Professor Varadhan’s specialty is probability theory – in particular, the theory of large
deviations. In honor of Professor Varadhan’s award, I thought it would be interesting to
very briefly explain what the theory of large deviations is, and why it’s so
important that it justified the award of a million dollar prize.

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Mathematical Study of Drug Interactions in the Evolution of Antibiotic Resistance

Orac has posted a really good description of a recent paper discussing how
interaction between different antibiotics effects the evolution of antibiotic resistance in
bacteria populations.

It’s a mathematical analysis of experimental results generated by combining drugs which normally interact poorly with one another, and analyzing the distribution of resistance in the resulting populations. It turns out that under the right conditions, you can create a situation in which the selective pressure of the combination of drugs – which are less effective when combined – can select in favor of the non-resistant variant of the bacteria!

Check out Orac’s post for details; I may also try to get a copy of the paper and post a more detailed look at the math later this week.

The Surreal Reals

The Surreal Reals

I was reading Conway’s Book, book on the train this morning, and found something I’d heard people talk about, but that I’d never had time to read or consider in detail. You can use a constrained subset of the surreal numbers to define the real numbers. And the resulting formulation of the reals is arguably superior to the more traditional formulations of the reals via Dedekind cuts or Cauchy sequences.

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The Second Carnival Of Mathematics: The Math Geeks are Coming to Town!

Please make sure you read to the end. A couple of late submissions didn’t get worked into the main text, and a complete list of articles is included at the end.

Oy. So I find myself sitting in my disgustingly messy office. And I’ve got a problem. The Math Carnival is coming to town. All those geeks, and the chaos that they always cause. Oy.

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Basics: Recursion and Induction

Time for another sort-of advanced basic. I used some recursive definitions in my explanation
of natural numbers and integers. Recursion is a very fundamental concept, but one which many people have a very hard time wrapping their head around. So it’s worth taking the time to look at it, and see what it means and how it works.

The cleverest definition that I’ve seen of recursion comes from the Hackers dictionary. In there, it has:

n. See {recursion}.

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Turing Equivalent vs. Turing Complete

In my discussion with Sal Cordova in this post, one point came up which I thought was interesting, and worth taking the time to flesh out as a separate post. It’s about the distinction
between a Turing equivalent computing system, and a Turing complete computation. It’s true
that in informal use, we often tend to muddy the line between these two related but distinct concepts. But in fact, they are distinct, and the difference between them can be extremely important. In some sense, it’s the difference between “capable of” and “requires”; another way of looking at it is
“sufficient” versus “necessary”.

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