## Martial Mathematics

March 25th, 2009 | Categories: general math | Tags:

Over at The Endevour, John Cook considers the martial arts movie Redbelt which differentiates between martial arts competitions and real fights.  Competitions tend to have artifically imposed restrictions (aka ‘the rules’) whereas real fights don’t.  In his post, John likens this to the difference between real world maths problems and academic maths problems.

Taking the martial arts analogy one step further – I was reminded of a quote from Bruce Lee while reading John’s post.

‘Before I studied the art, a punch to me was just like a punch, a kick just like a kick. After I learned the art, a punch was no longer a punch, a kick no longer a kick. Now that I’ve understood the art, a punch is just like a punch, a kick just like a kick.’

I used to practise Taekwondo back in the day and I can relate to what Bruce was saying.  When you start Taekwondo you expect to be taught how to kick, and you are, you are taught how to do a ‘side kick’ and a ‘front snap kick’ and a ‘turning kick’ and an ‘axe kick’ and a…..well you get the idea.  A kick for every occasion.

All these kicks to learn with each one having its own set of detailed technical nuances.  I spent years developing the perfect ‘spinning reverse turning kick’ for example and got seriously good at it – everyone was impressed with my kick.  It was a beautiful, powerful, amazing kick and I was proud of it.

However, I rarely managed to hit anyone with it in a competition scenario.  Of course if I ever did score a point with it then the crowd would go crazy – it looked great and they loved it.  It just didn’t happen very often.  Futhermore, in a real fight I would be a moron to even think about using it.  It was too inefficent, too slow and put me at too much risk.  It involved briefly having my back to my opponent while doing the spin for pity’s sake.

Over the years of learning these fancy techniques I somehow missed the point…which was to learn how to plant your foot on your opponent as fast and powerfully as possible with the minimum of fuss.  All the tehncial paraphernalia was just a means to an end but I got caught up trying to develop the ‘perfect kick’ for its own sake.  The application didn’t concern me.

I never got very good at winning fights but I had a whole load of fun and that’s what I really did Taekwondo for.

Back to mathematics….

When solving a mathematical problem how do you go about it?  Do you insist on always using certain favourite techniques to get the job done?  Will you only accept and publish  the answer if you reached it by some clever, beautiful and impressive means?  In short are you perfecting the perfect spinning reverse turning kick which will only work occasionally but when it does everyone oohs and aaahs at your technical prowess.

On the other hand will you use any dirty, sloppy and downright underhanded method in your arsenal to solve the thing?  Who cares how you get the answer as long as you get it?  Street Fighting Mathematics maybe?

Personally, with both Mathematics and Martial arts, I don’t think that there is a ‘right way to do it’ just as long as you are aware of what you are doing.

1. Thanks for commenting on my post. I’ll have to remember your “spinning reverse turning kick” story. It reminded me of something Sir Michael Atiyah said.

He said when he applies theorems from other areas of math to his research, it’s often the simplest cases that are most useful, not the edge cases and variations that specialists work so hard on. He said a potter may be very proud of a bowl he made using only one hand, but that doesn’t matter to the person who just needs a bowl.

2. Hi John

Well thanks for the inspiration :) and for the Atiyah quote.

3. I believe that Bruce Lee quote is actually an old Zen saying.

“Before I was enlightened, a mountain was just a mountain. When I was enlightened, a mountain wasn’t a mountain anymore. After I was enlightened, a mountain was just a mountain.”

4. Just wanted to chime in and say this was a great post!

5. Thanks Maria :)