I just ran across an interesting idea in the autobiography of Andre Geim, Nobel Laureate in Physics http://www.nobelprize.org/nobel_prizes/ ... /geim.html . It is about solving physics problems, but it may be applicable to reading in go.



For go problems I don't think that guessing answers would mean guessing first moves, because that does not entail working backwards. Rather, I think it would be guessing final configurations.

This is not something that I have tried, myself, but it sounded interesting, so I thought I would just throw it out there.

Besides, Geim is an interesting fellow.

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I think that guessing possible final configurations is a great idea. I've never practiced it extensively but in retrospect I realized that I've dealt with life-and-death problems in games by imagining what the living shape would be and then seeing (reading?) whether I could get there. This same approach could work in other parts of the game; tesuji moves could be found by identifying a goal shape, for example.

Would this not be similar to looking at an eyespace and seeing where the potential eyes are going to come from and working your way back from there in life and death problems? I say this because I've often seen it remarked that weaker players see the surrounding stones but stronger players can see the future eyes.

This is an interesting idea, and might work.

It reminds me of when I first started getting into mathematical proofs. Given a proof I was supposed to construct, if I was spinning my wheels trying to prove that some expression X was the same as some expression Y, I'd try starting at Y and going "backwards" to get to X.

In my case, this sometimes worked, but even more important seemed to be the idea of making sure I was moving in some sort of... direction (if that's the right word for it).

In other words, I could spin my wheels starting from X to get to Y, or start from Y and go to X. But for anything non-trivial, it was really important for me to make sure I kept my eyes on the goal at each step.

I'm sure the proofs that I've done are a lot easier than what Geim was involved in, but I wonder what he'd think about the idea of making sure you're headed in the right direction for each of the logical steps he refers to.

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be immersed

That is funny. If you are asked to proof that X == Y you start backwards. So if you are asked to proof Y == X you would start forwards ???
For me, I used another method. I assumed that the assertion was false and tried to derive some contradiction from it.

BTW Dr Geim is dutch, so let us call it dutch reading!

In general proofs will involve the demonstrandum x->y. This is rather different from y->x. Proving both is twice as much work, unless you are able to rely on biconditionals at every step of the way.

I thought this was how everyone of a certain strength picked joseki, for example.

One would have to have a sense of what kind of result you are looking for and is likely. I could guess that all my opponent's stones will die, but I'm not sure that will help me find the line if that's not likely.

I think there is a decomposition of harder problems that is analogous to this, though. If you know a particular move is sente against a particular group, you might say, hey, that may be useful. Now I have to contrive a sequence where that same move is also sente against another group, and I'll be in good shape.

Any sequence that involves miai is kind of like working from both ends. I think it requires a higher level of reading/strategy than just looking for single forced lines all the time. I wish I could do it more, myself.

Usually I start with X and try to prove Y. But if I am spinning my wheels, I try from the other direction. That's what I was trying to express - sorry if it was not clear.

Of course, proof by contradiction is a nice method for proving things. I guess it already applies to go, too: assume that black cannot live in the area, and then contradict yourself by finding a living sequence :-p

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be immersed

Sometimes I do what Kirby is talking about too -- I think of it as "meeting halfway".

To me this is almost the only way for research. Indeed the kind of problem you can solve totally in a deductive way are from exams, not research;
First wou try to build an intuition with toy models, then you try to imagine what will change and what will stay the same in the real, complex case, and you make the relevant approximations to try to prove that the complex case behave like the simple one. If this fail you try to complicate teh toy model, but only a bit, and see in what direction the simpl case evolve.
But as we are all formated to solve the deductive kind of problems during our studies, it takes some getting used to to change the way of thinking. One crucial ability for a researcher, i think, is to try to know when to dig deeper and try to prove what he believes to be true, and when the inital intuition was wrong and you should, indeed, try to prove something else.

The most famous example perhaps of a physicst following is intuition a bit too far is Einstein adding a cosmological constant to force its general relativity theoroy to predict a stationnary universe. It was later proved wrong as we now know that the universe is expanding, but its a clear example of fitting a reasonning to the wanted result. I am certain that this kind of things are numerous in science, including a lot of brilliant people that are unsucessful because they are devoting their genius to prove someting that is unfortunatly untrue.

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In theory, there is no difference between theory and practice. In practice, there is.

There are different kinds of research; the kind you are describing refers to modelling a seemingly complex reality. As I have created two (or three) such models after long and hard research (Japanese 2003 Rules' life definition and the general ko definition), I can share my experience:

I started with much preliminary research (incl. fundamental research in the related study field) to approach the still unknown core from various directions and get an idea at all roughly what that core might be (getting this idea is the hardest and most creative part of research). When a core's shadow appears in the dust, I tried models to describe the core and tested them against reality. This is a sort of trial & error mixed with iterative approach, sometimes closer, sometimes farther from the goal. Early models tend to be cumbersome - the final model (when all known tests agree to reality) has beauty and elegance. Then I wonder why I had not seen the "obvious" solution immediately.