Haven't blogged in a bit. Thought I'd toss this out.
I got a degree in engineering and computer science which involves a fair deal of math. I've met a lot of people since then that are very bright.
To be good at engineering and such, you need to know math, and to know math, you have to think in a certain way. Mathematical thought isn't easy for everyone, which is why everyone doesn't do it. However, the human mind is clearly able to manage and organize these abstractions.
At times, I must have thought like Mr. Spock. That there was a logical way to intuit the things you needed to know about math. If you worked hard enough, you didn't need creativity. There was an answer. Indeed, those who have avoided math or science often imagine these disciplines to be perfectly logical, reinforced by their high school classes that graded in terms of right and wrong.
Little did they know that such thinking was only for the convenience of the teachers who wanted something tidy and easy to grade.
Some people perceive programming in this way. Occasionally, I would be called up to a hearing over someone who had cheated in their program, mostly by copying some parts of their code from someone else. The case would often be presented to non-technical sorts of people and they had to try to pass judgment whether cheating had indeed occurred.
If they thought computer programs were all written as if there was one magical answer which they class would eventually converge on, that would have been a mistake. Programming is a bit like, say, catering a large event. Two caterers may be given a description of the event, the numbers of people, and so forth. They may be told to make Mexican food and to allow for vegetarians. But beyond that, you would hardly imagine two groups would handle things identically. There might be vastly different interpretations that satisfy the basic requirements. Writing programs is like that. There is some level of creativity in programming.
So people learn basic principles of programming and how to write code that is robust, safe, and extensible. This experience often takes years of practical programming to develop. In the process, one learns to organize one's thoughts, and how to deal with bugs in the code. A certain proficiency in problem solving results, and for some, it leads to amazing productivity.
Now, this skill can be developed in any number of neighboring fields including mathematics.
If an engineer or computer scientist or mathematician were asked how they do what they do, they might be hard-pressed to answer. They would undoubtedly agree that it takes a certain kind of "mathematical maturity", a way to reason about numbers and properties of mathematical elements.
Surely, you are now wondering, what any of this has to do with tennis.
Did the poor man forget what the blog was titled? Writing one title, and blogging on something else completely different?
Here's the deal. You get someone like this, and ask them to learn tennis. It doesn't have to be tennis, per se. Any sport of sufficient skill should do.
And what do you discover?
They have no idea how to proceed to learn the sport. Sure, some are OCD enough that they will read prodigiously on the topic, treating said problem like they do any other problem. With enough research, you can probably get some idea of what to do. The web, after all, is more than just a means to find solutions to your programming problems.
For some reason, however, the people who have tried to learn tennis (or similar sports) haven't always looked for the "right way" to do things. I remember I played table tennis about half an hour a day, five days a week, for nearly a year. I got pretty decent, at least, in a recreational sort of way. But my technique was awful. I hit the ball fine, but over time, it was quirky and therefore not totally reliable.
I could have looked on the web for lessons, but I didn't. I didn't fully realize this until I played tennis and tried to learn it as technically well as I could. I know, roughly, what I need to do on, say, my tennis forehand. I can show you slow mo video and break down the nuances I am seeing. To be sure, I miss at least as much as I see, but at this level, I think I am paying a lot more attention that most would.
Now I had the advantage of already playing tennis before, and with web resources growing ever more plentiful, there's a lot of resources to learn tennis from a technical viewpoint.
Yet people don't.
To give an analogy, there are people that play musical instruments, but because they are too shy, they don't sing. For some reason, plucking strings or pressing notes seems very objective. Controlling one's voice seems more mysterious and it activates a person's modesty meter. It's more revealing of a person to sing than to play a musical instrument, even if both are about music.
If math/science/programming is about how to organize your brain to solve problems, then playing sports is about how to get your body to do things, and much like music, it only comes from a lot of repetition, and repeating the "right things". You can certainly learn sports the "wrong" way and be quite proficient.
I say "right" and "wrong" in so-called scare quotes (I don't like that term because I think it implies I am trying to scare people, and I'm not) because with sports, there's a lot of latitude about what is right or wrong and people often discover, through trial and error, that there are other valid ways to do something. If you watch tennis over its long history, you'll discover a lot of changes in how players hit the ball, some of which has to do with the equipment.
Hitting a ball has evolved over time, and may continue to evolve, as players discover different ways to do the same thing.
But beyond hitting a technically sound stroke, there is the practice. You can think of tennis as a real time physical game. Balls are hit in very similar ways, some higher, some lower, some with spin, some without, some with more power, some with less, some over here, some over there, and you are constantly having to solve these problems in real time.
If players struggle, it's because they often solve a certain kind of problem, say, a flat ball deep, but not too deep, over and over, to the detriment of solving other kinds of problems. While there are the occasional a-ha moments, they aren't usually the same as in math problems where a clever trick can greatly simplify a problem, the right frame of mind making all the difference.
Learning tennis is a little like learning music. Musicians know, even as talented as they may be, that success comes with a lot of practice. There aren't a great deal of shortcuts. Learning a sport is learning to cope with one's own body, to make it do what the conscious mind says it should do and then to move beyond that so it comes without thought.
The body learns things by repetition. It takes a lot of convincing, especially if you've trained it to manage a different sport. Indeed, when people struggle learning a new sport it's because they apply principles from other sports. This makes sense. When someone is learning a new programming language, they often apply ideas from a programming language they already know. Now, as anyone who has learned a few programming languages knows, you can't always do that. You should learn a new language like experts in that language learn new languages. You should imitate them.
And that is also the same lesson about learning any sport. Rather than apply what you know from another sport, you should learn how practitioners of the sports learn it. But so many people prefer to side-step this. They learn it any old way.
Why? Well, they convince themselves, perhaps quite rightly, that they don't care about the sport that much, and so they don't need master it beyond a basic level of proficiency. I find that a bit odd since they have often mastered some other part of their professional lives with great mastery. But, much as playing music and singing music are two distinct skills, so are mastering mental proficiency and physical proficiency.
One reason I like tennis is because it allows me to apply some thought to a physical task. Since tennis is a physical sport, you want to get beyond constant analysis. The game moves too quickly, and you need the body to respond semi-automatically. This is one reason you rarely see a pro make major changes to their stroke. I've seen seniors play on the champion's tour that have made some changes, but nothing dramatic. John McEnroe, for example, isn't going to use a semi-Western grip and hit like Rafa. It's too dramatic a change when he hits the ball perfectly fine.
A player on my level, on the other hand, hasn't developed the same kind of technical proficiency that McEnroe has. That doesn't mean that it makes it any easier for me to make changes. Indeed, one might argue that McEnroe, being more physically gifted might adapt more easily. However, McEnroe has a much bigger downside. Since he hits so well already, he would have to develop the shot so that he could at least match his current level.
Meanwhile, my forehand isn't as good, so I can afford to spend time learning to play better.
In a nutshell, I find that tennis exercises a different part of the brain, in addition to being exercise. I like the strategy, learning to hit different shots, and trying to learn the "right" way to hit a ball.
Three opinions on theorems
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5 years ago