One of the more useful ways of classifying martial arts is into
external and
internal, sometimes known as
hard and
soft. External martial arts (like karate and taekwondo) emphasize the actual mechanics of punching and kicking (or blocking, or throwing, or grappling), whereas internal martial arts (like aikido and tai chi) are more abstract, focusing on things like listening, blending, and the flow of energy (chi, or ki, or ache, or ... if it helps, remember that this isn't energy in the physicist's sense, but something else with the same name. Like the physicist's energy, it's an abstract, derived concept, but that doesn't mean it isn't useful). I'll quote
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totherme here:
Of course tai chi is a martial art - the energy abstraction exists to facilitate martial application - but we learn it for its own sake - like learning to add numbers rather than learning to add apples. Apples are a great example, but they miss the point - if you add numbers then you can add bananas too :)
I've studied just enough martial arts to be extremely wary of making broad generalisations, so I'll hedge a bit and say that the ultimate aim of most established martial arts is to produce internal martial artists, which is to say those who intuitively understand the concepts taught by the internal styles (or possibly the deeper concepts behind them - the Tao that can be named is not the true Tao, of course). The difference is in the approach, and the stations you pass through on the way. Hard styles present you with a series of examples of correct technique, and leave you to deduce the underlying principles yourself; soft styles try to teach you the principles, and leave you to work out many of the fine details. Both approaches can produce both internal martial artists, and extremely effective fighters - believe it or not, tai chi can be very dangerous in experienced hands! It's notable that many arts seem to evolve towards internality as they age - karate's thought of as an external style, but it's much more internal now than it used to be. This progression is clearest in the history of aikido, which developed towards being an internal style as its founder progressed towards being an internal martial artist.
This distinction can be useful to bear in mind as an analogy. You sometimes hear mathematicians talk about "hard" and "soft" geometry, which strike me as similar in some ways to hard and soft martial arts - hard geometry has lots of coordinates, lots of differential forms, lots of linear algebra, whereas soft geometry is more abstract and topological.
totherme and I were discussing our respective ways of thinking about programming a while ago, and found this helpful in reaching some understanding: whereas the training I've received has all been about how to do specific things, his CS degree has taught him more explicit versions of what I (sometimes, unreliably) do in my head - things like proof of code correctness by invariants. Internal versus external, in other words - the Oxford CS course attempts to do the Tai Chi thing to hacking.
This is also one way of looking at category theory (I think this makes Attempt To Explain My Thesis No. 3...). An awful lot of modern pure mathematics is
implicitly categorical, but this can be hard to see because the details get in the way. Category theory attempts to extract the deeper principles from a large variety of techniques, and make it explicit, so it becomes easier to learn them (or work them out on-the-fly). Actually, this is how mathematics works in general: by identifying the implicit principles that underly things and making them explicit so you can think about them in their own right, thus (hopefully) making the original problem easier.
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