John Fairbairn wrote:Now, reading a bit about anzan, I learned that they have discovered that expert practitioners use a completely different part of the brain - a visuospatial one - for anzan than the area (the lingusitic processing one) used for ordinary arithmetic.
It seems that this parallels other stuff I've read about experts in as diverse a range of skills as tennis, music and chess. I gather that these experts stimulate and develop a part of the brain that has nothing to with understanding what they are doing.
I don't think that we can draw that conclusion. Unless by understanding you mean the ability to verbalize what one knows.
Indeed, understanding can interfere strongly with what they are trying to achieve. Apparently this is the cause of choking in sport.
Shades of one mind and no mind in Zen.
Their goal is rather to develop automaticity and they do this by constant repetition of tasks imposed on them by a coach. Obviously they glean a vague idea of what they are doing and why (e.g. they understand what top spin looks like, or that control of the centre is usually good), but only in a superficial way. If greater understanding is required, for example to correct a fault, that's the coach's job, and he comes up with another set of repetitions. It seems to be well established that ten thousand hours is required for mastery by this method, in any discipline. But what struck me was that experts in anzan - a recent fad - were very unlikely to have spent that amount of time. It's not even a profession.
Very interesting.
And that brings me to my question, with the hope that the caffeine is working now. Whilst this is all very well for real experts, I think most of us would be satisfied with partial expertise, say 5-dan amateur, or 1-dan, or whatever, so: what is the best way for us to achieve that? Should we study and think, or should we just work out?
IMHO, we do not know the best go pedagogy for amateurs. It is an area that I would like to do research in.
I doubt if we can simply transfer the traditional training methods for pros.
Before reading up about anzan, I was inclined to think that for us halfway housers study and thought were probably best. They would never make us real experts. We'd accept that x-dan amateur would be the upper limit anyone could achieve that way (and even then it would probably have included some repetition). But it looks like a less painful and more enjoyable process - buy a few books, maybe discuss them with friends or on L19, and if we get stuck, buy another book. The holy grail is always round the corner, in our world.
Now I'm wondering about the alternative way. If 10,000 hours would get me to 9-dan, and maybe 5,000 hours, to 1-dan pro, could I get to amateur x-dan with, say, 3,000 hours of playing over games and doing tsumego?
The answer's almost certainly yes, because the top experts in sport have had to go through these various stages themselves, and they are clearly already pretty good when they've done only a few thousand hours. But the big difference seems to be that they are already highly focused at that stage and are doing nothing but repetitions. They don't let trying to understand get in the way.
Part of go is very much like math. For instance, to solve a tsumego is to construct a proof. But skill at math is not a matter of repetition. Understanding matters. (Even if it cannot be readily verbalized.) My girlfriend tells about, when she was in grade school, to multiply 18 by 5, she multiplied 5 by 20 to get 100, then multiplied 5 by 2 to get 10, and subtracted to get 90. Now, that was real math.
It showed understanding.
Unfortunately, she told the teacher what she was doing. The teacher, no mathematician, told her that she was doing it wrong. (!) Instead, she was supposed to go through the rote algorithm of multiplying 5 by 8, getting 40, writing down the 0, carrying the 4, then multiplying 5 by 1, getting 5, adding it to the 4 to get 9, and writing the 9 beside the 0 to get 90. (BTW, when I was learning arithmetic, nobody explained why that algorithm gets the right answer.
) Instead, our class
glean{ed} a vague idea of what they {were} doing and why . . . , but only in a superficial way.
Even for kids, arithmetic did not make sense. No wonder so many hated math or developed math anxiety. (Pavlov developed neuroses in dogs by giving them tasks that were beyond their ability.)
We less devoted souls, however, seem very prone to mixing up the methods. We might do a bit of repetition but then read a book for a change of pace. But is that actually harmful? Pure repetition can work. Pure study can work, although do a much more limited degree. But if we mix them, are we ending up with no, or reduced, benefits from either method?
Mixing methods is probably a good idea.
Go requires a number of different skills, and it is unlikely that they can all be best developed in the same way. Besides, there is likely to be a positive interaction between methods, IMO.
To return to the analogy with math, there is a new approach to math pedagogy which seems to hold great promise, called JUMP. I have only just heard about it, and know very little, but a few things are familiar. One thing that JUMP does is to identify a number of math skills and to develop each of them. An example is, if a kid has trouble subtracting 7 from 5, to ask the kid, suppose that you were playing a betting game, and won $5 and then lost $7, would that be good or bad? JUMP does incorporate repetitive practice, but not of poorly or superficially understood concepts. Both repetition and understanding are required.
Perhaps the number of skills in go is fairly large, in the dozens. Certainly the number of concepts in quite large, as the size of go terminology indicates. I expect that a sufficiently detailed course of study could be devised that would take most players to amateur dan level within a year or two.
A couple of years ago I did a small study of elementary tsumego to try to identify some concepts of life and death. I made some headway, but not enough to write a book. I do think that a concept based approach to tsumego would be effective.
can capture the White group on the right. Do you see why Black cannot capture the group on the left?