British mathematicians teach more magic

The UK-based recreational math channel Numberphile is still on a magic spree. Here they explain a card trick made popular by the Scientific American columnist (and pretty much hero to nerds everywhere) Martin Gardner. 

Again, it's one of those tricks that young aspiring magicians often show me, albeit with different phrases. It's nice for kids because it doesn't require any manual dexterity, but rather remembering a sequence and when to use it. It also provides some immediately feedback. (Either the cards match or they don't and you know right away.)

Space is Big

As the saying goes:

Space is big. Really big. You just won’t believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it’s a long way down the road to the chemist, but that’s just peanuts to space.
— Douglas Adams - The Hitchhiker's Guide To the Galaxy

[A note for North American readers, the "chemist" is a pharmacy.]

This clip from BigThink by NASA Scientist Michelle Thaller tries to put that bigness in perspective:

These numbers are hard to imagine. VERY hard to imagine. That's one of the reasons I'm such a strong proponent of math education for everyone of all ages (beyond my own personal bias as a math major shining through.) The only way to learn to cope with these kinds of numbers is through training. Otherwise you'll be caught in the paradigm of JBS Haldane:

My own suspicion is that the universe is not only queerer than we suppose, but queerer than we can suppose.
— JBS Haldane

Math becomes the key that allows you to do all that hitherto impossible supposing. Or, if you'd rather think of the world in terms of awe and wonder, it gives you access to entirely different domains in which to be astonished.

Questioning Assumptions or... proof that math teachers are evil

Magic teaches us to be constantly be looking at the world around us with a critical eye and to always be giving a second thought to things which appear, on the surface, to be completely obvious. Rushing through a problem trying to get to the solution as quickly as possible carries the risk of missing something important; something you believed to be true without realizing it. (And because you weren't consciously aware of believing it, you never gave yourself the opportunity to question it!)

For some, this exercise will be a delightful exercise in testing and challenging assumptions. For others, it will simply be the long-awaited proof that all math and science teachers are inherently pure evil. 

How to practice

In addition to my performing career, I've had lots of opportunities to work with students in different fields. For years I taught martial arts (which was mostly how I paid for university where I studied math... not the fast track to popularity you would think it was) and for nearly as many years tutored math (primarily for high school students). Now I teach magic several times a year through a children's community outreach program called My Magic Hands

One of the things which often needs to be included in that training is an instruction on how to practice. This short animated clip summarizes things quite nicely. It's important, because once you learn strategies for effective practice, they transfer almost immediately to any discipline. 

While they gloss over it briefly towards the end, particularly effective is the idea of starting slowly and building up speed over many, many repetitions. I remember both for students of martial arts and magic, when something is not working, the tendency was to attempt to do it faster or more vigorously. In fact, speed early on just diminishes the amount of control that you have and tends to make things worse.

When it came to math, the equivalent was for the student to try to do as much work in their head as possible. I believe the unstated premise was that the method which had the least amount of writing in the page was the most effective because it got to the solution "faster". In fact, trying to juggle lots of pieces of information behind the eyes slowed them down, increased their chances of making a mistake and making it impossible to find later. What proved the most valuable the most often was the method which left the most steps visible on the page (in accordance with the cliche dictum of showing your work). 

Another early magic mentor highlighted another important phrase: practice doesn't make perfect, practice makes permanent. So effective practice becomes extremely important. 

More Magical Mathematics

This will be the first of a series of three posts dedicated to mathematics, for no other reason then the coincidence that they all appeared in my life more or less at the same time. I'll begin with an interview with Persi Diaconis on The 7th Avenue Project. It's actually a little bit out of date (over a year old) and it relates, ostensibly, to his 2011 book Magical Mathematics (co-written with Ron Graham) Professor Persi Diaconis is a remarkable figure in magic who falls into that category of "greatest magicians no one has ever heard of." Provided you're willing to allow being interviewed for podcasts, being a published author and appearing on the front page of the New York Times never being heard of.

The interview is fascinating (and long). Perhaps it's the confirmation bias talking, but he seems to spend a great deal more time discussing magic than math — not that I would think of complaining. It also highlights the important but subtle difference between magical mathematics and mathematical magic. I noticed when the interviewer tripped up on the title and realized that there really is an important difference.

The stories involving Dai Vernon and Ricky Jay are also moving. Enjoy.