On Wednesday, March 27, 2002, at 04:56  PM, [EMAIL PROTECTED] wrote:

> On 27 Mar 2002 at 22:43, Eugene Leitl wrote:
>
>> On Wed, 27 Mar 2002 [EMAIL PROTECTED] wrote:
>>
>>> I don't recall ever having read of this type of structure before,
>>> but it seems so obvious that I'm sure it's been discussed before.
>>> So is there a name for it? Does anyone use it? has it been
>>> shown to be utterly worthless?
>>
>> You don't mean something like this:
>> http://www.perfdynamics.com/Papers/Gnews.html do you?
>>
>
> Yeah, I think what I was describing was more or less what
> they call a hypercube, or maybe just a cube.
> I'm not one of those people that
> can actually envision multidimensional structures, so I only
> know "this is a 4-cube" if I see the coordinates.

No need to "visualize" 4D spaces, 5D spaces, and so on.

Think in terms of how many nearest neighbors a point is, a la my last 
post:

-- in a 1-dimensional space/topology, 2 nearest neighbors (left, right)

-- in a 2-dimensional space/topology, 4 nearest neighbors (left, right, 
above, below)

-- in a 3-dimensional space/topology, 6 nearest neighbors (6 faces of a 
cube)

-- in a 4-dimensional space/topology, 8 nearest neighbors

-- in an n-dimensional space/topology, 2n nearest neighbors

(all using the definition of distance in terms of unit vectors, not 
diagonals)

Actual machine hypercubes are just made in the obvious way: by 
connecting vertices/nodes the way a physical hypercube would be 
connected.

In fact, since wires are small [though not infinitely small, and 
certainly not of zero propagation delay], it's possible to connect every 
node to every other node.

--Tim May
"That the said Constitution shall never be construed to authorize 
Congress to infringe the just liberty of the press or the rights of 
conscience; or to prevent the people of the United States who are 
peaceable citizens from keeping their own arms." --Samuel Adams

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