The Proizvolov Identity

Here is a simple card trick you can perform informally, courtesy of the British YouTube channel Numberphile. James Grady shares a simple prediction that can be accomplished thanks to something called The Proizvolov Identity. (Don’t worry, I hadn’t heard of it either.)

Take a look:

As an ex-mathematician, I find these small tricks charming. They aren’t well suited to performing in a show, but as something fun to share with friends, the offer a wonderful small pleasant mystery.

The concept of symmetry in math, where you can make changes that have no impact, is closely related to the idea of choice in magic, where you often get to make choices that don’t affect the outcome of the trick. (And providing a moderately irritating counterexample to proponents of free will.)

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.)

One of the world's most popular card tricks

If someone has shown you a card trick at some point in your life, odds are it was this one. It's not popular because it's necessarily the most miraculously astonishing thing you've ever seen. You probably wouldn't see it on a David Blaine or David Copperfield special, but it has the advantage of being one of those tricks that is knowledge-based rather than skill-based. 

Often after a show someone will ask me how much I have to practice certain things. Some of the pieces in my show are extremely difficult. If I don't practice for more than a day, I start to feel rusty. But in other tricks, the secret does absolutely all of the heavy lifting for me. Once I know the secret, I could put the trick down for years and pick it up again the next time. (Although I'd probably forget what I was supposed to say, the trick would still work!)

This trick (if you're interested in learning) is especially rewarding for kids to learn because you can learn the steps and remember them and when you try it, you get immediate feedback. (You either have the right card or you don't.) So if you're curious to add a bit of magical mind-reading to your next social gathering, you can try and pick up:

The Fabulous Twenty-One Card Trick

(Hope you like math nerds with British accents.)

You'll notice she mentions modular arithmetic, but for whatever reason, they skip that part of the explanation. Which is ok, because six years ago, they already explained it five years ago with a slightly more advanced version that requires a bit more mental arithmetic, but still manageable:

Magic with Physics

The extremely popular YouTube channel Numberphile (popular among nerds at least), they often tread into magical territory. Here one of their frequent guests Tadashi, explains an amusing technique for levitating a pingpong ball (and the physics behind it.)

When I was the host of Magic Tonight in Toronto, the comedy magician extraordinaire Wes Zaharuk used to use this as a bit in his show to great effect: 

Wes Zaharuk

Wes Zaharuk

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.