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What would be more true:
A position is consists of the grid and the occupation of each gridpoint
--OR--
Given the grid a position defines the occupation of each grid point.
The subtile difference becomes obvious when comparing a position of a square board with a position on a rectangular (non-square) board, or even a round board, a 3D board or the map of Switzerland.
When you are given the position in an abstract sense, does that also mean the grid is known?
A grid doesn't have to be a perfect square, as long as it is a series of interlocking lines I think you are ok.
ehm jeah, that's what i said, in fact that is exactly my point
Yes I misread, so you are asking what is the best definition of a position?
For a fully defined position you must know both the extent of the grid and the occupation of each intersection on the grid.
So how can we then say that the grid will be more important than the occupation.
Am I correct to say that you suggest to include the grid in the definition of position.
Or dou you agree with Herman that the position does not include the grid, but that a position is only valid within the context of a grid.
PS. What do you mean with "the grid is more important than the occupation" It seems to me that there is no hierarchy in importance. In fact, I do not understand the term importance in this context.
The evaluation of a position arising from a joseki on a 6x6 board is likely to be different from the same joseki on a 161x161 board. Therefore at times the grid is important. At times the grid will be of no importance - say a basic ko shape.
Are you unhappy with the definition of position on the page at the moment?
The position arising from a joseki on 6x6 cannot be the same position as the same joseki on 161x161. It can be the same local position, but position as used in this discussion (ie, in a rules/theory) context is a coloring of the entire grid, where "empty" is one of the colors (ie: a whole board position).
(Which is why I don't understand where all this is going :)
I don't really see the difference?
You mean it is irrelevant?
The difference, whether or not a position also defines the grid, seems clear to me.
Well, the position is the coloring of all grid points. I don't see how you can have a position without the grid? The only thing I can think of in this context is:
Go is played on a graph.
Here, I can image that you could specify position as:
Or as:
But the only point I could see would be if the game involved the addition/removal of edges. Otherwise, the information on the edges is static, and including it in the position is just redundant.
Yes, that was my question indeed, so your opinion is that position per definition does not the configuration of the edges of the graph.
Clear, I think I agree. This conclusion means that the following proposition is true.
Yes, it is simpler to define the graph as immutable and refer to it than to include it in the definition of every position. However, since every position must refer to the graph, I still don't really see where you're going with this.
the page should remain comprehensible to non-mathematicians, at least in my opinion (as an historian). s. definitionalism? ;-)
Yes, exactly, although this page was originally created by a mathematician. However, from personal interest I also like to see a sound mathematical definition here. That's why I attempt to split it up. At the introduction of the page, i tried to define position as it is used in colloquial language, and made a separate section for an attempt at formalism.
Feel free to improve upon making this page more comprehensible.