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The point I'm trying to make is that just as those non-mathematical dancers presumably also had to learn the patterns at one point before gaining this freedom of movement and improvisation, and they probably stumbled and were quite awkward when doing so, so can go players in the long run benefit from learning the go patterns.
I don't think that many dancers learn patterns. At last night's dance I danced with a woman who did not know a dance called Elephant's Stampede. It's rather complex with some unusual movements, and done at a very brisk pace with lots of bodies all mingling at the same time (a stampede in effect). So she went into the garden and read a word description of the dance for a minute or so. She is a demonstration-level dancer (i.e. a "pro") admittedly, but even so I was rather surprised when she danced the long dance quite perfectly a few moments later.
Now, if you're curious, you can follow the link below, and the see static "crib diagram" associated with this dance. This sort of thing makes my brain do a wobbly. But the words are easily digestible - well, not maybe easily for people like me, but even these words can be pulped down into baby food. Thus, the first two lines of the written crib:
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1- 8 All circle 8H round and back
9-16 1s+3s advance nearer hands joined and with free hand join with 2s and 4s, retire into longwise set across the dance; all dance ½ parallel RSh reels of 4 across
can be pulped down into something like "circle, advance and retire and reel". The other fiddly bits intuitively get tacked onto that as extra movements in your brain. I'm not sure how to describe that but in large part it's because you can rely on the music to help you.
The crib diagram, however, cannot be pulped down, and (worse) you have to learn the definitions of all the many symbols first.
https://www.scottish-country-dancing-di ... mpede.html(a further link there will show you can example of the stampede being danced, if you want).
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Though, it's the transition from knowledge to instinct that may be a struggle for some.
My impression is that some people make it difficult for themselves by mistrusting or even attempting actively to suppress their instinct/intuition.
I'll additionally make two extra points:
(1) I think there is a difference between the way pros learn and amateurs learn, and most of the discussion here is ignoring pros. In the case of amateurs, possibly from having to make do with scarce resources, we suffer from having a mixture of shape and movement elements (and, as I've already said, a surfeit of the shape element in the western case). In part I suspect this is because amateurs learn too much from diagrams in books and not enough from the mixture of words and hand movements on the board that you get from a live teacher - the typical way a young pro-to-be learns. I have tried to redress the balance a little with my Go Wisdom format, i.e. dispensing with variation diagrams as much as possible.
(2) I have mentioned a couple of times that music helps us learn dances. It may seem there is no equivalent in go. But I wonder whether what is meant by whole-board vision is really the equivalent (like the "music of the spheres"). I have an impression that many amateurs think that acquiring whole-board vision simply means trying to remember to look at each part in turn, static portion after static portion. I suspect pros, in contrast, literally "see" the whole board at once, that is they have an awareness of what is going on everywhere simultaneously, and that's because they see it all as the "flow" of the game - or, if you like, they intuitively sense the moving "music" of the game.