Re: Steven Cullinane is a Crank



Steven H. Cullinane wrote:
> On the off chance that "Bob Stewart" is not "crankbuster" under another name, here is a reply:

You are paranoid!

> Your statement that "if each of the permuted objects has some geometrical symmetry, >then these resulting permutations will display symmetries too" is false,

What an idiot you are! If I arranged 16 identical objects in a 4X4
array and let the symmetric group S16 act on them then I would have 16!
"symmetries".

>as you would know if you had tried to find a counterexample... Such as (for instance) >the four diffent square patterns obtained by division of a square into black and white >halves by horizontal or vertical (rather than diagonal) midlines.

Why horizontal and vertical lines? Surely there are other shapes
possible. And more colors than just two. There are lots of examples
other than the one you have that would display symmetries. Silly!

> As for affine geometry, see
> http://log24.com/theory/geometry.html.
>
> This site contains an explanation, written for those with some mathematical maturity, of the role played by the affine group AGL(4,2) in the geometry of the 4x4 square.

There does not seem to be any natural association of AGL(4,2) with the
4X4 array. Why not just take any set with 16 elements? And by the way,
what does this have to do with T.S. Elliot's "Four Quartets"?! Yeah
right, the affine geometry of free verse! Crank!!

> That group, by the way, is where the number 322,560, quoted by the deeply confused "crankbuster," comes from.

No, it is you who are confused. The question was, why do you restrict
the complete symmetric group S16 to just this subgroup? In the 2X2 case
you take the complete symmetric group S4. Then you claim that the 4X4
case is a "generalization". Why a smaller group? Just to get the result
you want. You dont fool anyone! You dont have any generalization of
your silly trivial "Diamond Theorem". What about the nxn array? Why not
state the theorem for the nxn array? Because you cant! You have no idea
of how many elements the group will have because you have not defined
it!

Bob

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