Mathemagical Thinking

So maybe you’ve seen the Flash Mind Reader.  If not, go ahead and try it!  I wouldn’t dream of depriving you (especially as this is year’s MAM theme is mathematics, magic, and mystery awareness).  What you are asked to do is to think of ANY two digit number, add the digits together, subtract that difference from the original number, and then look up your number in a table of symbols.  Then the computer will read your mind and produce the correct symbol.  So the mystery is – why does it work?  We know it’s a trick, and it can’t be that hard since the computer did it.  So it’s bound to bug you until you figure it out, and there are a number of people who post things like “Flash mind reader revealed!!” and then proceed to expound on the method used to do this trick.  They make tables, they do a lot of writing, all to express some simple algebra.

Certainly this is the kind of magic that much of the public associates with math – fancy tricks with numbers.  And it does bear a passing resemblance to another kind of magic with which many of us are familiar.  When you’re turning a problem (a mystery) around in your head over and over again because you just can’t let it go, using symmetry to simplify and transform the ideas, you sometimes feel in a tancelike state.  This kind of sentiment is echoed in Vi Hart’s most recent post about creating Art Code.  She writes “One thing led to another and soon I had a simple animation I called Lost Memories of Desert Sand, and couldn’t stop staring.”  One might say that “magic” allows our thoughts to fit together just so and create something beautiful.  The gasp that follows many math tricks is also the gasp that sometimes follows a good presentation of a proof.  There’s a sense that magic has just been performed – you were following each movement of the performer ever so closely when all of a sudden they finished the proof – why yes they did!  And it was so clever!  And it made sense, right?  Or did it?  Wait a minute, what about that part over there?  There’s a sense of skepticism, excitement, and awe that accompanies the practice of mathematics.

Physics.org had a great post on Magic and Symmetry in Mathematics that speaks to this type of “magic” in math. One of this year’s Sloan Research Fellows, Dr. Ivan Loseu says “Any scientific discovery involves some kind of magic,” That is, various pieces that may seem to be completely unrelated eventually start to fit together through the fruits of one’s labor. “Since pure math is pure, all this magic is much more clearly seen.”

Ready for a fun video from Tadashi Tokieda, whose work I learned about from a guest post at Scientific American about this year’s recent Gathering for Gardener?

Dr, Tokieda from University of Cambridge likes to play with “Toy Models” that demonstrate certain unexpected, and one might say “magical” properties.  Check it out https://www.youtube.com/watch?v=f07KzjnL2eE, and you will probably find yourself spinning little tubes around and saying “paf, paf, paf!”.

So go ahead and work your magic this weekend!