Math Forum Discussions

crankbuster

Posts: 21
From: Srilanka
Registered: 7/5/05

Re: Steven Cullinane is a Crank
Posted: Jul 12, 2005 6:01 AM

Plain Text

Steven H. Cullinane wrote:
> See "Reply to my fan mail" at
> http://m759.freeservers.com/rough01.html.

Huh? Obviously, you cannot even begin to justify your dubious "Diamond
Theorem"! The questions asked in the original posting have not even
been addressed. Instead you are attacking other people again. Someone
is going to sue you one of these days. I quote you again:

Reference your dubious website:
http://m759.freeservers.com/

"The Diamond Theorem:
Inscribe a white diamond in a black square. Split the resulting figure
along its vertical and horizontal midlines into four quadrants so that
each quadrant is a square divided by one of
its diagonals into a black half and a white half. Call the resulting
figure D.

Let G be the group of 24 transformations of D obtained by randomly
permuting (without rotating) the four quadrants of D. Let S4 denote the

symmetric group acting on four elements. Then

(1) Every G-image of D has some ordinary or color-interchange symmetry,

(2) G is an affine group generated by S4 actions on parts of D, and

(3) Results (1) and (2) generalize, through intermediate stages, to
symmetry invariance under a group of approximately 1.3 trillion
transformations generated by S4 actions on parts of a 4x4x4 cube."

What does (2) mean? By Cullinane's definition of G, G is isomorphic to
S4, the symmetric group on 4 letters, with 24 elements. What does he
mean by saying G is generated by S4 actions? Every group generates
itself as its own subgroup! This is a theorem?

What does (3) mean? Generalize how? What is "approximately 1.3
trillion"? What "parts" of a 4x4x4 cube? Who is Cullinane trying to
fool?

See the "4x4 Case" following the "theorem". Cullinane states that "G is

a group of 322,560 permutations". Where does this number come from?
Going by his own definition, if 4x4=16 objects are to be permuted (this

is the only way to "generalize" his "theorem") then G should be
isomorphic to S16, the symmetric group on 16 letters, with
16!=20922789888000 elements. Why 322560? Huh?

No, Sir you are not a crank but a moron.

Andrew
for
Crank Watch International