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 It's actually a little bit out of date (over a year old) and it relates, ostensibly, to his 2011 book Magical Mathematics (co-written with Ron Graham) Professor Persi Diaconis is a remarkable figure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.

Stories as tools of deception

There's a wonderful article in the New Yorker by Maria Konnikova (available online free here). A research topic that has been recently in vogue (and thankfully so) is the study of how easily humans are deceived. I've read a substantial amount about the various biases that we are prone to, but this article highlighted something I hadn't really considered before; that facts become more deceptive simply by being arranged in a narrative. The entire article is nicely summed up by this:

As the economist Robert Heilbroner once confided to Bruner, “When an economic theory fails to work easily, we begin telling stories about the Japanese imports.” When a fact is plausible, we still need to test it. When a story is plausible, we often assume it’s true.

The irrationality of humans is not a controversial thing (it's how I earn my living!) I have said before that when most people use the phrase "let's think logically (or rationally) about ______" what they really meant to say was, "let's make a series of educated guesses and stop when we reach a result which is consistent with our intuitions." Irrationality really does seem to hinge on tricking people into stopping thinking too soon.

The upside is it seems that Konnikova has a forthcoming book on the subject which I'll try to read when the opportunity presents itself.

Multiple Realities

In my spare moments over the holiday, I've been reading Max Tegmark's Our Mathematical Universe. There, in one of the chapters, he makes the distinction between the external reality and our internal reality. That is, there is a distinction between the world we live in and the information that makes it past our sense perceptions into our brains.

He's quick to stamp out those motivational-quantum-woo-guru impulses which make you want to think that your internal mindset determines your external surroundings. It's a common plot device in children's stories where, "if you only believe with all of your heart" you can manifest changes in the outside world. But it's an important point that what we see is not all there is. [1]

What made me linger on the chapter is the terms he used — internal reality and external reality — precisely mirror the terms used by Arturo de Ascanio[2] when describing the performance of magic tricks. The two terms refer to the different states of knowledge possessed by the audience and the magician.

So, if you were to imagine that you were Mr. Burns, then the external reality might be that you are reaching inside of your pocket to find your pen. The internal reality might be that you are in your pocket to press the button on the remote to release the hounds.

At the centre of most magic is the act of appearing to do one thing while actually doing another. (There is a more difficult way of doing magic which that of doing something while appearing to do nothing at all, which he calls techniques with no external reality.) So magic is excellent practice in multi tasking, since a magician has to simultaneously juggle two different versions of reality; the version the audience sees and what they are actually up to. Those who fail to parse the distinction wind up as lousy magicians.

That's one reason that magic is so difficult to teach to children. They find it difficult to accommodate the second reality. Often when "performing" what they do is explain the secret working of the trick as they go because to them that's just what's happening.

For me, that's one of the reasons magic (not that Harry Potter stuff) is so useful to have around. We need reminding constantly that the world is not guaranteed to be as we reflexively perceive it; that there's more going on than meets the eye.[3]

The book itself is well worth reading. It begins with a very thorough primer that will bring just about anyone up to speed on the developments in physics of the twentieth century, through relativity and quantum mechanics, as well as the discovery of the Big Bang and Inflation. It then goes on to ideas which are not the mainstream consensus of scientists (but he never claims that they are.)

[1] "What you see is all there is" is actually the name of a cognitive bias explored in Thinking Fast and Slow.

[2] Arturo deAscanio, The Structural Conception of Magic, Paginas, 2005

[3] Someone clearly wanted a Transformer for Christmas and didn't get one :(

Mystery Solved

On my second day at the University of Toronto in a course called Introduction to Proof (which really was a life-changing course that I heard they stopped offering) the Professor gave this question (actually a variation with 100 people and no aliens) and (owing to the fact that all math teachers are inherently creatures of pure evil) neglected to provide the answer.

In the dozen or so years it's been this is the first time I've seen that problem and so here's the answer. Now you don't have to wait quite as long as I did.

Confirmation Bias: Big Think

In case you didn't know what it was, this is a nice short description courtesy of BigThink and Social psychologist Heidi Grant Halvorson: 

Stephen Pinker - We only think we are free

Well that's the most intellectually stimulating thing I'm going to listen to all month.