Using metaphors is always problematic. I described a martial artist's skill set as a collection of answers. I was thinking technique here, but also the way in which it is sometimes taught: If the bad guy does this, it sets him up so and you do that... In the metaphor, this skill or technique is the answer to that problem.
Ukemi brought up math as a counter analogy- a mathematician learns the functions and applies them in an order based on principles and derives an answer, the mathematician doesn't memorize the answer to all possible algebra equations.
That's a damn good point, and it's a good place to get to... but... Even an advanced mathematician works basic multiplication from memory. What is 5x7? 6x8? 2x9? This is where beginners are. Even good mathematicians (I assume, not being one) when he applies the functions, has memorized them. Memorized the meta answers, in a way.
None of that really matters and I'm not arguing Ukemi's point. It powerfully showed a weakness in my metaphor. Cool. And thank you.
So, given an already weak and damaged metaphor (really just a comparison, now) I'm going to run with it:
There are two huge but related differences between training for math and training for conflict. The first is that almost every kid in America is forced to take math to a fairly high level. For much of history algebra and especially trigonometry were secret, almost magical knowledge. My kids are required to learn things that were mysteries to the architects who built the pyramids. By the time a kid graduates from high school he has about 2400 hours of training in mathematics. And it's not the same 100 hours merely repeated over and over again, it progresses, each grade building on what came before. Martial arts are often progressive, too, but rarely as logically detailed in that progression.
The related difference: martial artists are allowed to stop when they are comfortable. Kids learning math aren't. You want to do just kata? Fine. There are schools for that. Competition? Easy. Feel-good two hour self-defense seminars? Everywhere. Get a nifty black belt? Sign on the dotted line. Feel a connection to Bruce Lee? Within two hundred miles is someone who trained with him directly, there are probably a dozen who trained with his direct students in any good-sized city. You want to take it all the way- interpersonal violence to armed conflict? That gets way harder. I had to go to jail to get a taste.
There are unrelated differences, too. You can safely test the outer edge of your math skills. You can actually use trigonometry to judge distance in the real world.
There is another, very important real world similarity between violence and math: If you are confronted by a problem in real life that can be solved, either with violence or math, you don't get to choose the problem. If you have to work out a budget you don't get to say, "How about if I just count ceiling tiles? It's still math." Same with being confronted with violence- you avoid all the violence you can and the only thing you can predict about the violence you get is that you weren't able to avoid it.
But in martial arts training (and this is what the post on Persistence of Patterns was really all about) in training and only in training do you get to change the questions to fit with the answers you are comfortable with. It is, for most players, completely subconscious. It wasn't the guys defending in the knife drill that were saying, "Back up and give me room so that I have a chance." It was the partners playing bad guy and they did not realize they were doing it.