Principles and Concrete Knowledge - Question to the Strong

[hyperpape]

How high are we talking here?

I've supervised maths students to Phd level and managed at post doc....

I'm still an undergraduate, but have been doing proof based courses for two years, and am starting with graduate courses later this month. I'm talking about anything at a similar level.

What would you say is the way to get better than math, if not to work through proofs, and write one's own?

Try to prove something new?

[Redundant]

How high are we talking here?

I've supervised maths students to Phd level and managed at post doc....

I'm still an undergraduate, but have been doing proof based courses for two years, and am starting with graduate courses later this month. I'm talking about anything at a similar level.

What would you say is the way to get better than math, if not to work through proofs, and write one's own?

Try to prove something new?

Trying to prove something new is way beyond the ability of most students. I just spent the entire summer trying to do so, and did not get very far. In math, it's not unheard of for a student's first publication to be their thesis.

[hyperpape]

Try is the key word. You don't have to succeed to learn something, right? But also I've talked to students who had proved something, albeit not the kind of results you could base a whole paper on. You're still learning something about problem solving and doing proper research as you do that sort of work.

I didn't mean to suggest that first year grad students learned by going out and attempting to find substantial results that develop their field. Even in philosophy, which has a substantial "make it up as you go along" component, that doesn't happen. In philosophy, I think it works like this: good undergrads write a 20 page paper criticizing someone's argument. As a first year grad student you write a short paper on the same subject. When you're dissertating, you spend a page on it.

As a tenured professor, you write one sentence on the argument, and you get it wrong. But if you're good, the whole of your work has enough insights that it doesn't matter that you're saying false things all over the place.

[Kirby]

... But if you're good, the whole of your work has enough insights that it doesn't matter that you're saying false things all over the place.

Just like some of the comments in forum discussions here, eh?

[Redundant]

Try is the key word. You don't have to succeed to learn something, right? But also I've talked to students who had proved something, albeit not the kind of results you could base a whole paper on. You're still learning something about problem solving and doing proper research as you do that sort of work.

That is true, but I'd say that it's more important while learning to actually work on problems with known solutions. It's like starting with tsumego with solutions before tackling that one from the igo hatsuryon.

[yithril]

For me it was always repetition and focusing on my strong points rather than my weak points, but then again I'm more of an instinctual player. I tend to let my intuition point out where the big spots are, and get a feel of where the big points are. I've done thousands of tsumego problems, but I have read little on strategy outside of "Attack and Defense" and "Lessons in the Fundamentals" which I think every Go player has read. For me, improving hinges ENTIRELY upon how well I can perform stone for stone reading. When I'm at the point where I just instantly know the vital points in a shape I start to go up in strength.

[Kirby]

... focusing on my strong points rather than my weak points...

Why do you think that this is important? It's an interesting comment, I think...

... For me, improving hinges ENTIRELY upon how well I can perform stone for stone reading. When I'm at the point where I just instantly know the vital points in a shape I start to go up in strength.

Can you explain what you mean by this? These seem like contrasting ideas here: intuition vs. reading. Can you elaborate?

[yithril]

1. My strong point is finding tesuji and shape weaknesses and steering the game to exploit them. I fumble with full board thinking and finding the big points on the board. I used to try playing games where I didn't fight so that I could try and resolve this weakness, but it didn't work out really well. Instead I got better at steering the game so that I felt comfortable.

2. When I pick my next move I literally just see the next spot in my mind like the point on the board is lit up, or a general area. Then I start working out the details. Whenever I feel more confident that the sequence I see in my head are good or are correct I am getting stronger. I'm a meticulous reader. I once spent 20 minutes a tournament reading out 5 different branches of one sequence. The fight was for the life of a group so it was important that I not screw up. I won because there was nothing he could do that I hadn't already planned for and hadn't read out 10-20 moves ahead.

[RobertJasiek]

I have been knocking at the door of shodan (measuring by KGS, which seems a reasonably stiff standard) for about 3 or 4 years, but with breaks in between. I think that I should be able to reach 3D, and perhaps higher,

Having reached 1k is a good indicator of a principle potential of becoming stronger because reaching 1k requires abstraction and reading abilities that are similar to those at higher levels. There is a major difference though: After 1k, the exponential growth of necessary effort and knowledge volume becomes relevant. (For some, it becomes relevant already at 5k.) Without much effort, you have little chance to improve. OTOH, 3d is still relatively easy. 4d+ is the really tough part. The knowledge required up to 1k doubles each time up to 3d, to 4d, to 5d.

A) Accumulate Knowledge
B) Learn (and Relearn) and apply general principles

Good, necessary and insufficient. You also need:
- reading ability
- problem solving accuracy
- positional judgement ability and accuracy
- improve your endgame
- psychologically overcoming of making blunders / big mistakes at all (average 5d means fewer than 1 per game on average)

Up to now, I have had the tendency to try to learn everything all at once, to attempt to read a week's worth of material in an hour and to do 25 tsumego instead of just a few. Recently, I started being kind to my short-term memory and began studying things in frequent short bursts,

Everybody has a preferred or most suitable learning style. Until a teacher knows your learning very well, you need to find out your best learning style by yourself.

1) Strength in go is a mixture of technical knowledge (tesuji, L and D, joseki) and strategic understanding

Strength is a mixture of knowledge, reading, strategy, judgement, time-control, psychological control and probably more.

2) You can improve by increasing knowledge
3) You can improve by deepening understanding

Sure... BUT strength is also blocked by your greatest weaknesses. Your 9p fuseki is useless if your reading is 1k - you will be 1k. To improve, you have to improve in MOST (or better: all) fields. All is not strictly necessary because each player has his relative weaknesses and strengths. Your strengths must be able to hide your weaknesses though. So a too great lag for weaknesses blocks your progress.

4) You can improve a lot by increasing knowledge AND by deepening understanding.

ONLY IF the above mentioned other fields are also improved AND none of your weakneses lags behind too much.

Besides extraordinary knowledge is useless if you cannot apply it.

also being able to come up with the technical vocabulary to express them,

That is part of the knowledge but does not cover all the other mentioned fields above.

5) You should not attempt to apply technical knowledge consciously,

Nonsense.

6) You should, however, attempt to apply strategic principles consciously and generally

Yes.

7) You cannot apply all general principles consciously all of the time,

Consiously or not - a priority making and selection is always necessary. (See Joseki 2, Strategic Planning.)

but you can choose one aspect (say a weakness identified through reviewing your games) and focus on that until it becomes "automatic" and then select another.

Insufficient. Almost always more than one aspect is necessary.

[RobertJasiek]

ez4u, to summarize a point of yours, more knowledge and analysis is required to then better reduce the information amount for the sake of choosing good moves.

I disagree WRT to mathematics. Mathematics is the most profound means to research in go theory. During a player's decision making, only results of mathematical research (propositions, procedures, values) are needed while the proofs can be ignored. It suffices to trust the mathematicians that their created results are correct and therefore truths. A player needs to apply some applied mathematics (e.g., when making positional judgement or endgame calculations).

[RobertJasiek]

the kind of thinking we call 'strategic' became more and more intuitive and subconscious as I grew stronger

[...] Technique [...] also becomes more and more important and pushes the 'strategic thinking' into the background

[...] Thus, as you grow stronger, reading will come to the forefront and 'strategic thinking' will become more and more intuitive

Anything else from you would have surprised me:) For me, of course, the opposite is true.

One of the beautiful elements of Go is that, ultimately, it has elements of both art and science.

As long as Go is not solved. Afterwards one can define what will have been Go art today.

Strength in Go is ultimately based on reading.

No, but on decision-making based on evaluating reading. (Unless of course, brute force is used.)

converging with the creative aspects of Go.

I would not say "converge" but "provide better ground for usage".

[RobertJasiek]

Acquiring new principles (or learning to understand old ones better) is not very useful in itself. It has to be done in the context of your game.

Learning principles during playing is inefficient. Principles become useful, after learning, when applying them during one's games.

One could probably come up with quite a handful of principles, good or not, but only some have the power to educate you and make you stronger.

All (good) principles make one stronger. Even efficiently so. (Although it could be that YOU don't become stronger from principles, I know I know:) )

do not take anything for granted!
This goes especially for any strategic principles you learn!

The power of good principles is told by themselves.

Go is such a wonderful game.

Oh, uh, ah, we agree on something! What a rare occasion! ;)

[RobertJasiek]

[principles] doubtful advisers when it comes to making a decision.

There are many principles that do make the decisions!

[RobertJasiek]

you could learn thousands of principles

Not their number is important but their quality. A powerful principle replaces several not powerful ones and is similar in contents and method to other powerful principles.

"Do you think there is any value for learning how to play go well in tackling strategy one principle after another?"

As Mr. Principle, I say: All good principles are worth learning and applying. Good means correct and as general as possible for the purpose according to current research insight and the purpose of application. At the same time, see my first reply message: besides knowledge (which includes principles), you need also the other fields for improving.

For instance, should one pay special attention to thickness for a time, and then having got that into their system, should they turn say to preserving aji or making good shape?

(Your) learning style is rather independent of the functioning of principles or strategic concepts. Principles for one strategic concept (like thickness) should not contradict those for another (like aji). Therefore you can choose learn both strategic concepts simultaneously or successively.

Usually principles are not at a standard of final truths in all cases though. Sometimes principle A can contradict principle B. In that case, methods or principles with mightier scope (typically: analysis methods or strategic planning) override the more specific principles. If even the higher level of abstraction does not provide answers, then reasonably complete reading cannot be avoided.

[RobertJasiek]

It may well be that I do not understand either mathematics or philosophy, being neither an mathematician nor a philosopher. However, my impression is that both disciplines are essentially about abstracting certain information about the world in order to understand it better. In both cases, the abstractions are the essence of the disciplines.

Mathematics can do different things: 1) Create an approximative model of a real world aspect. 2) Create a model of a real world aspect that is its identity. - Go mathematics has provided models of both kinds, depending on the studied object of go theory. I.e., type (2) models have already found the final, correct, complete solutions for some (specialized) aspects.

cdybeijing, therefore ez4u's statement is not the truth but a partial falsehood.

While we may often encounter abstract "principles", those are teaching tools at best.

No. They are teaching tools at worst. If a principle is of type (2), then there is nothing better (on the same level of generalisation and in the same manner of expression).

E.g., "A 'strong eye' of size 4 without shape defects and with the surrounding string not being initially in atari has as many liberties as 5 minus the number of inside, nakade-filling stones." is the final truth (except for greater precision as to the used terms).