Mathematical vs Metaphorical Understanding

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This is a page to discuss two different ways of approaching and understanding the game of Go.

Mathematical
CGT path
Statistical analysis
Small board Go
Mathematical Bounds of Komi
Does Kami No Itte Exist
Semeai Mnemonic

Metaphorical
Anatomical terms
Flora Terms
Wildlife terms
Mineral terms
Aji
Shape
Metaphorical Names for the Game of Go
choshi

Naustin: I want to make clear that I think that neither is inferior though I have a bias. I also think it is interesting to recognize that they are different. These two approaches are often necessarily complementary but I do not think that they always are. There seem to be some concepts that are more aptly or easily conveyed in one way than the other. In order to express more clearly the division I see and to provoke discussion if possible I have provided links to illustrate the two sides of the coin and have begun the discussion below.

Naustin: Of course one of the first things that leaps to mind is the old left versus right brain discussion. Historically, there seems to be a deep tradition of metaphorical description of the game. In Kawabata's Master of Go the traditional Japanese view of Go emphasizing aesthetics is seen as passing with the passing of the Master. At the very least its ascendancy.

As far as I am aware, the mathematical approach has been a result of two factors: first, the intersection of the game with Western culture, and secondly, the advent of computers and the ability to carry out really large scale pattern searches and statistical analyses. The question would then become are these really two separate ways of looking at the game, or are they really just different names for the same thing? That is, do these two different viewpoints really imply a different way of "thinking" about the game or are they simply different name sets? Kami No Itte seems like a good example in a way because it is something that is expressed in a metaphorical or poetic manner but is being studied from the mathematical viewpoint now.

Another question of interest is, do different ways of thinking about the game actually translate into different styles of play? Are there certain styles of play that tend to be adopted by the more mathematically (metaphorically) minded Go enthusiasts?

Analogies are another relationship associated with the metaphor idea. It seems to me that there are lots of people out there who can find in Go analogies for all sorts of things in intellectual and general culture and life. A question that seems to spring out of this is: Does this proneness to analogy spring more from the nature of the human mind as it views any complex system or is there a particular character to this game which rewards such thinking?

starline: Maybe Go is an analogy for the working of the human mind itself!


ilan: I don't think there is a mathematical way to Go, except for small board sizes up to 7x7. My observation of other mathematicians who play Go is that they usually ignore the mathematical aspects. In fact, in almost all cases, Go players are much too caught up in improving their play to make the necessary abstraction and simplification for mathematics to work. It is not surprising then, that the mathematical theory was developed by a non-Go player (J.H. Conway).

This directly addresses the mathematical approach to Go, but I believe that you have confused "mathematical thinking" with "analytical thinking." Mathematics is about finding elegant universal results in very simple settings, e.g., a triangle. Playing Go well is about dealing with a mess of technical details and is intractable mathematically.

On the other hand, playing Go well definitely requires analytical thinking, in particular reading and counting, and playing the game without this is pretty much garbage. The "metaphorical" aspect you refer to is meaningful only when these analytical aspects are present.

Alex Weldon: Math underlies Go the way physics underlies, say, soccer. In both cases, the system is so complex and chaotic that the large-scale behaviour that results has little resemblance to the equations that are actually responsible for it, especially because of human involvement. Math might tell you which of two endgame plays is bigger, as physics can tell you the trajectory of a soccer ball... but approach Go from a purely mathematical point of view and you'll end up playing about as well as Stephen Hawking plays soccer. :-)

ilan: You can also consider billiards. There is a mathematical theory of billiards which has absolutely no application to the actual game of billiards, since friction is not considered in the mathematical theory. Of the thousands of mathematical articles written about billiards, there are only two which apply to the game: the book of Coriolis 1840, and a theorem of Euler (son), 18th century. Interestingly, most mathematicians and billiard players are unaware of this dichotomy.

Naustin-- On the other hand I think it is important to notice that as a complete information game no idealisation (i.e. departure from the true nature of the object of study) is required. Go is an ideal system in that sense.

It makes sense to me that a mathemetician might not try to solve go in a mathematical way when he plays particularly as there is no theory for go as of yet at the 19x19 size. However I think that though not completely seperate it does make sense to talk about how someone understands the game in a way that is not completely equivalent to talking about how they decide to make specific moves in games. One of the places I see this kind of thing is here at senseis in how different people study the game. Notice above how I stated I don't think these approaches are probably even possibly completely seperable.

This is one of the very enjoyable things about go to me. I can play games with other people which is great but studying go is also very enjoyable and in a way is a sort of solitaire.

I guess basically what I am trying to do is say that I think there is a more interesting definition of understanding than informs the replies above but that could still yield a meaningful discussion.


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This is a copy of the living page "Mathematical vs Metaphorical Understanding" at Sensei's Library.
(OC) 2004 the Authors, published under the OpenContent License V1.0.
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