A Mathematician's Pick-up Line

The winner of the MIT Nerdy Pick-up Line Contest:

Hey, baby, I don’t have a nerdy pickup line, but I can prove that one exists.

Via Quomodocumque.

The Infinite as an Approximation to the Very Large

Many years ago, when I was still at school, I remember one maths lesson in which a pupil had a heated argument with the teacher over the use of infinity in the calculus.  The pupil refused to accept that this was valid because infinite sets "did not exist", and the teacher didn't seem to to know how to answer this and instead got rather angry.  Well, after reading this post by Alexandre Borovik at A Dialogue on Infinity, I now know what the teacher should have said: that we use the infinite as an approximation to the very large.  Hence it does not matter whether infinite sets exist or not.  As Borovik explains, calculating with infinities is usually much easier than calculating with the very large.

The Miserable Wasteland of Multidimensional Space

From a review by Myles Aston of Life without Genes: the History and Future of Genomes by Adrian Woolfson, in the Balliol College Annual Record 2001:

The miserable wasteland of multidimensional space was first brought home to me in one gruesome solo lunch hour in one of MIT's sandwich shops.  "Wholewheat, rye, multigrain, sourdough or bagel?  Toasted, one side or two?  Both halves toasted, one side or two?  Butter, polyunsaturated margarine, cream cheese or hoummus?  Pastrami, salami, lox, honey cured ham or Canadian bacon?  Aragula, iceberg, romaine, cress or alfalfa?  Swiss, American, cheddar, mozzarella, or blue?  Tomato, gherkin, cucumber, onion?  Wholegrain, French, English or American mustard?  Ketchup, piccalilli, tabasco, soy sauce?  Here or to go?"

I know the feeling.

(Via Peter Cameron's website at Queen Mary College, University of London.)

The Pfaffian in the Grassmannian...

From a post by David Guarrera at Imaginary Potential:

One example that I do understand, since I’ve read the paper many times, is Hori and Tong’s “proof” of Rodland’s Conjecture: that the Pfaffian in the Grassmannian G(2,7) lives on the same kahler moduli space as a hypersurface Calabi Yau in a Grassmannian. The proof uses beautiful physical intuition about the dynamics of non-abelian gauge theories in two dimensions.

However, you may think that the kahler moduli spaces of Calabi Yau’s are useless. Fair enough, I say. But they’re quite beautiful.

Nomograms

When I first came across nomograms in my early teens I was mystified by them.  They looked interesting but the article on stellar evolution they accompanied gave no clue on how to use them.  They looked a bit like graphs, but had three or more graduated scales, and these scales didn't have to be at right-angles to each other, indeed, they might even be curved!  It was only a few weeks later that I discovered that you were meant to lay a ruler or straight-edge across the graduated scales, and by doing so you could perform various calculations.  Nomograms are a sort of graphical generalization of a slide-rule, and like the slide-rule they became extinct following the introduction of pocket calculators.

Anyhow, these long dormant memories were triggered when I came across the following awesome series of posts by Ron Doerfler at Dead Reckonings:

• The Art of Nomography I: Geometric Design
• The Art of Nomography II: Designing with Determinants
  
• The Art of Nomography III: Transformations
  
• A Zoomorphic Nomogram
  
• A 4-Variable Nomogram (by Liunan Li and Ron Doerfler)