problem solving

On Practice

Before being a magician, I studied math at the University of Toronto and in those days, I also made most of my income as a martial arts instructor.

Suffering for art - Photo by Michael Kostiuk

Suffering for art - Photo by Michael Kostiuk

Through math I learned how to break down tasks into smaller manageable parts; to problem solve. Through martial arts, I learned how to practice.

In a recent article, master jazz musician Wynton Marsalis offered up twelve tips on practice to be employed by musicians, but also athletes or just about anyone. The list is fairly straightforward but the full article helps put it into perspective:

  1. Seek out instruction: A good teacher will help you understand the purpose of practicing and can teach you ways to make practicing easier and more productive.
  2. Write out a schedule: A schedule helps you organize your time. Be sure to allow time to review the fundamentals because they are the foundation of all the complicated things that come later.
  3. Set goals: Like a schedule, goals help you organize your time and chart your progress…. If a certain task turns out to be really difficult, relax your goals: practice doesnʼt have to be painful to achieve results.
  4. Concentrate: You can do more in 10 minutes of focused practice than in an hour of sighing and moaning. This means no video games, no television, no radio, just sitting still and working…. Concentrated effort takes practice too, especially for young people.
  5. Relax and practice slowly: Take your time; donʼt rush through things. Whenever you set out to learn something new – practicing scales, multiplication tables, verb tenses in Spanish – you need to start slowly and build up speed.
  6. Practice hard things longer: Donʼt be afraid of confronting your inadequacies; spend more time practicing what you canʼt do…. Successful practice means coming face to face with your shortcomings. Donʼt be discouraged; youʼll get it eventually.
  7. Practice with expression: Every day you walk around making yourself into “you,” so do everything with the proper attitude…. Express your “style” through how you do what you do.
  8. Learn from your mistakes: None of us are perfect, but donʼt be too hard on yourself. If you drop a touchdown pass, or strike out to end the game, itʼs not the end of the world. Pick yourself up, analyze what went wrong and keep going….
  9. Donʼt show off: Itʼs hard to resist showing off when you can do something well…. But my father told me, “Son, those who play for applause, thatʼs all they get.” When you get caught up in doing the tricky stuff, youʼre just cheating yourself and your audience.
  10. Think for yourself: Your success or failure at anything ultimately depends on your ability to solve problems, so donʼt become a robot…. Thinking for yourself helps develop your powers of judgment.
  11. Be optimistic: Optimism helps you get over your mistakes and go on to do better. It also gives you endurance because having a positive attitude makes you feel that something great is always about to happen.
  12. Look for connections: If you develop the discipline it takes to become good at something, that discipline will help you in whatever else you do…. The more you discover the relationships between things that at first seem different, the larger your world becomes. In other words, the woodshed can open up a whole world of possibilities.

The Science of Thinking

Many people are quick to offer their explanations for why magic tricks "work"; why people of average intelligence — and in fact many well above average intelligence — aren't able to decipher the method behind them.

The main reason is simply information a-symmetry. If the magician knows something you don't (in this case one single something out of all the possible somethings that could be known) then you are at a significant disadvantage. It's the same reason that encrypting and decrypting coded messages is much easier when you know the method of encoding and the key than when you don't.

But the other reason is this. Derek Mueller, the creator of Veritasium, describes how your brain has two methods of operating; "System 1" and "System 2". 

While there is no hard line distinction, what we largely think of as "intelligence" and "problem solving" lie in "System 2". (Although Daniel Dennett's concept of competence without comprehension certainly needs to be part of that conversation.) But "System 2" spends most of the day dormant, like an iPad with a dark screen, it sits there conserving battery until some stimulus jars it into action.

And that's where the magic happens!

The secrets to most tricks lie in the space where your serious problem-solving intellect hasn't had a chance to switch on yet. Many tricks have as a selling point of their modus operandi "the work is done before the audience is even aware the trick has started."

But knowing that isn't of much help. Because, as described in the video, maintaining that level of analytical alertness requires energy and concentration — both scarce resources which can't be deployed continuously. Your brain yearns to turn them off, so after a while the iPad screen goes dark. 

So when the next magic trick begins, you're ready to begin the process all over again. 

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.

A Test of Confirmation Bias

The New York Times posted a quick puzzle test which you can try here. If you enjoy this sort of thing, it's a fairly standard number puzzle you may have seen before. But the results are extremely counterintuitive. Go try the test and see how you do before reading any further...

I'll wait... Promise.

I've known the answer since university (Math professors throw these things out all the time) and it highlights that the way most of us go about trying to solve problems the wrong way.

Everyone usually starts out right trying to generate some possible solutions - guesses at what the right answer might be. But then when it comes to choosing the best one, things get messy. The common belief is that we search for evidence which confirms our theory. It doesn't work, since one piece of evidence can be consistent with many different possible solutions, the fact that the piece of evidence agrees with any one solution, doesn't help picking one solution over another. Counter-intuitively, piling on more evidence that agrees with your hypothesis doesn't help distinguish one solution over another; it doesn't move you forward.

The correct path is the opposite direction. You go out in search of evidence which would go against your hypothesis. And if you try hard to find it and come up empty, then you can be confident. When it comes to deciding, one piece of inconsistent evidence is more valuable then a thousand pieces of consistent evidence.