Re: [spoon-discuss] Junk

[Zarpint Jeremy Cook <mcfoufou@xxxxxxxxx>]

Sorry, but my three-dimensional brain is not seeing this. Questions:

Aren't you just depicting some of the boards rotated? It's not the
topology that your twisting changes, but the way you represent the boards
on the paper. Isn't this just really a normal 4x4x4 cube?

Then you're adding more lines connecting the points, really. I can't
visualize this at all. How many neighbors does each point have?
And how is this hyper-anything? It's 64 points in a 3-D grid.

I also question "four in a row with three moves."
Say we have a 3x3 torus (2-D). If I play at (0,0), (0,1) and (0,2) does
this really count as "aleph-null in a row"? It's the same issue here...
I am tempted to say each point of "n points in a row" has to have a different
coordinate set than the others, or they're not n points.

Zarpint


On Mon, 29 Dec 2003, Glotmorf wrote:

> I tried this once with a 4x4 game, except I made it hyper-
> toroidal...
>
> . . . . | . . . .
> . . . . | . . . .
> . . . . | . . . .
> . . . . | . . . .
> _ _ _ _   _ _ _ _
> . . . . | . . . .
> . . . . | . . . .
> . . . . | . . . .
> . . . . | . . . .
>
> The idea is that the boards are rotationally above one
> another, with wraparound.  The upper left corner of the upper
> left board is above the upper right corner of the upper right
> board, which is above the lower right corner of the lower
> right board, which is above the lower left corner of the lower
> left board...which is above the upper left corner of the upper
> left board.
>
> Then I got carried away.  Imagine that the above board is
> intersected through its axes by two identical and
> perpendicular boards...that there exists an X plane, a Y plane
> and a Z plane.  This makes for a 4x4 board in three toruses at
> the same time, rotating through a different axis.
>
> Problem: Rotate through enough axes, and it's possible to make
> four-in-a-row in three moves...
>
> 						Glotmorf

-- 
Zarpint            "All thy toiling only breeds new dreams, new dreams;
Jeremy Cook         there is no truth saving in thine own heart."
mcfoufou@xxxxxxxxx       --W.B. Yeats, The Song of the Happy Shepherd
grep -r kibo /     "Movements are the problem, not the answer to problems."
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