The nick Hypatia comes from a greek woman who is considered the first woman mathematician. One of her famous quotes is: "Reserve your right to think, for even to think wrongly is better than not to think at all".
In addition to playing Go and studying Math, I'm also a haiku writer.
Despite being a game with simple rules, Go is very hard to learn. So I've decided to give some thought to the learning process itself.
We can see that in most games we automatize simple moves once we get used to them. In the beginning we must choose carefully, considering each possibility that lies ahead. As we learn the implications of one of these possibilities under a given circumstance, we don't have to go through the whole line of reasoning again to know whether it's good or bad. Shortcuts are created in our brain.
Usually people try to achieve strength in Go by means of a lot of study, ranging from life and death problems to review of games. Of course, they also need to play. My question is: how much thinking is needed to become a good player?
Not so much. There are many skills a player develops to get stronger, but in the end all that matters is playing at the best spot. How you got to the point where you know how to play doesn't make you a better or worse player. In the beginning I said this is the result of a regular learning process, but now I want to suggest this sort of intuition could also arise naturally with experience.
Psychological behaviorism is one way to explain it. The classic example is of a rat in a cage that is given food when a lever is pressed. After some time, it always presses the lever when it is hungry. Behaviorists explain this by saying that hunger is a stimulus, pressing the lever is a response and receiving food is a positive reinforcement. The rat associates the response to the stimulus through the positive reinforcement. The same could happen during a Go game. If under a given situation (stimulus) you make a move that is good (response) you'll be in a better situation and may even win (positive reinforcement). Rationalizing it won't make any difference. If you try this move again and it works, chances are you'll use it more often. You don't need to know why it's good. In fact, even people who did not consciously try this approach of learning many times can't tell exactly why they chose a move. And if they can, they unconsciously chose a path to prove it.
If Skinner's behaviorism wasn't very convincing to you, let's see what an artificial intelligence researcher from MIT would say. Get a copy of Brook's paper Intelligence without representation. Basically, he says that the truth is we have little idea about how our intelligence works. We use a lot of symbols in our reasoning, but "it may be the case that our introspective descriptions of our internal representations are completely misleading and quite different from what we really use". So, when constructing the "creatures" (intelligent robots that walk around his AI lab), he never tried to develop a central representation that would choose the behavior of the robot. Instead, the robots are composed only of activity layers that may receive an input, do very simple processing and send an output. He says this is the basis of intelligent behavior. There is no need to create symbols and do complex processing over them.
If we go deeper in human intelligence, skipping the high level issues we can't understand, we'll reach the neurons (or maybe the molecules, atoms or quarks). Their rules seem quite simple. They receive a chemical neurotransmitter, propagate the impulse and send it to the next synapse. This simple action happening millions of times is responsible for every thought of the human brain. So, while playing Go, wouldn't it be easier to just go through the correct path of neurons, without the effort of creating a conscious understandable representation of what is going on?
We could go one step further and ask: should we think so much? Douglas Adams has written an interesting observation about this subject in his book "Hitchhiker's Guide to the Galaxy". He says:
"It is an important and popular fact that things are not always what they seem. For instance, on the planet Earth, man had always assumed that he was more intelligent than dolphins because he had achieved so much - the wheel, New York, wars and so on - while all the dolphins had ever done was muck about in the water having a good time. But conversely, the dolphins had always believed that they were far more intelligent than man - for precisely the same reasons."
Consequently, should we play Go with just our intuition, letting the game flow without analyzing each move? Maybe not. The fact is we do have fun thinking. When playing Go, studying the moves is part of the game.
Minue : Your guess is true partly. But, "without firm understanding of principles, and theory of Go" ( For example, efficiency of stones, the concetp of overcentration, thickness, Miai, the recogintion of the value of center. balance and speed in opening,..) all of those "blindly" training is not so much useful. At least, not so much useful to get dan rank...
The probability of Kami No Itte
After realizing how difficult it was to be a good Go player I started wondering what was the probability of playing it right by pure chance.
The result I got, using permutation, was 361 against 14379232588848906548323625114998633547 54907538644755876127282765299227795534389618856841908003141196071413794434890585968 38396823330432160771380883705655787966919248618270978003589902110057945010733305079 26277717227504122680867752813688505752654181204350215062346630264344267363262709276 46433025577722695595343233942204301825548143785112222186834487969871267194205609533 30641393571063519720072147337873382698030853510431742036536737798872175655134500412 91061650506154496265581102824241428406627054585562310156375289289992485738831664768 71652120015362189137337137682618614562954409007743375894907714439917299937133680728 45900003449642033706644085333700128428641265439449505077395456000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000000 (this big number is the factorial of 361).
Of course, this is a very simplistic model. A few things should also be considered:
- the average number of moves in a game
- how the number of valid moves evolve during a game
- decreasing as the board is filled
- increasing as stones get captured
- equivalent moves
It would also be fun to consider:
- the strength of the player
- the probability starting from a certain layout of the board instead of just its initial state
Some of these itens are addressed at Number Of Possible Outcomes Of A Game
Alex Weldon: Except for very strong players (high dan amateurs and pros), going with moves one knows to be good probably makes stumbling on kami no itte less likely than if one was choosing points completely at random, because of bad habits. Whereas a completely random move has at least a 1/361 chance of being kami no itte, I'm sure there are situations where my instincts pretty much guarantee that I won't make the right move.
This is a wiki, so feel free to add your comments below.
What is the best move? A, B or C?
Alex Weldon: Given that there is no diagram here, this is a very Zen question. I'm going to go with "C", on the grounds that in questions of this form, tenuki is usually the last option given, and in Go, tenuki is correct more often than not. :-)
ilan: My best guess for you would have been "A", since Canadians like to play, eh.
marker: For some reason, my stones don't seem to have letters. So I never know what the best move is. Explains my random play.
Zenmaster: If you answer either A, B or C you lose your Buddha-Nature. If you do not answer, you miss the path to Eternity.
So, if you meet the Buddha in you, just punch Him on the nose, as He's not a 9p, the Dirty Trickster.
Buddha: You fool, how dare you post such nonsense! Go and clean your room instead.
iopq: Meet your father, beat him at Go. Meet your mother, beat her at Go. Meet Buddha, beat him at Go.
A is a move you think is good. B is a move you think is bad. C is a move that you don't know if it is good or bad. Which should you play? A, B or C?