Re: Steven Cullinane is a Crank

Ah, I just found an interesting old post on one of Steven Cullinane's
gazillion websites that proves that the statement of his "Diamond
Theorem" is totally and outrageously false! I am quoting the post
verbatim:

What follows is attributed to:
Jed Pack
packj@xxxxxxxxxx
18:35:25 04/17/02 Wed

Steven Cullinane,

I wonder how you got the number 322,560.

I suggest the number is at most 30^2=900.
Please let me know if you find the error in my logic.

In the original four diamond configuration. The matrix indicating which
squares have the black corner either at top-right or top-left is:

0 0 0 0
1 1 1 1
0 0 0 0
1 1 1 1

Similarly, the matrix indicating which squares have the black corner
either at top-right or bottom-right is:

1 0 1 0
1 0 1 0
1 0 1 0
1 0 1 0

These two matricies fully describe the configuration. Swapping columns,
rows, and quadrants can change these matricies into any of the
following other 30 matricies (there are no other possibilities):

0 0 1 1 | 0 1 1 0 | 0 0 1 1 | 1 1 1 1 | 1 0 1 0 |
0 0 1 1 | 0 1 1 0 | 1 1 0 0 | 0 0 0 0 | 1 0 1 0 |
0 0 1 1 | 1 0 0 1 | 1 1 0 0 | 0 0 0 0 | 0 1 0 1 |
0 0 1 1 | 1 0 0 1 | 0 0 1 1 | 1 1 1 1 | 0 1 0 1 |

0 1 0 1 | 0 0 0 0 | 0 1 0 1 | 1 0 0 1 | 1 1 0 0 |
0 1 0 1 | 1 1 1 1 | 1 0 1 0 | 0 1 1 0 | 1 1 0 0 |
0 1 0 1 | 0 0 0 0 | 1 0 1 0 | 1 0 0 1 | 0 0 1 1 |
0 1 0 1 | 1 1 1 1 | 0 1 0 1 | 0 1 1 0 | 0 0 1 1 |

0 1 1 0 | 0 0 1 1 | 0 1 1 0 | 1 0 1 0 | 1 1 1 1 |
0 1 1 0 | 1 1 0 0 | 1 0 0 1 | 0 1 0 1 | 1 1 1 1 |
0 1 1 0 | 0 0 1 1 | 1 0 0 1 | 1 0 1 0 | 0 0 0 0 |
0 1 1 0 | 1 1 0 0 | 0 1 1 0 | 0 1 0 1 | 0 0 0 0 |

0 0 0 0 | 0 1 0 1 | 1 0 0 1 | 1 1 0 0 | 1 0 0 1 |
0 0 0 0 | 1 0 1 0 | 0 1 1 0 | 0 0 1 1 | 1 0 0 1 |
1 1 1 1 | 0 1 0 1 | 0 1 1 0 | 1 1 0 0 | 1 0 0 1 |
1 1 1 1 | 1 0 1 0 | 1 0 0 1 | 0 0 1 1 | 1 0 0 1 |

0 0 1 1 | 0 1 1 0 | 1 0 1 0 | 1 1 1 1 | 1 0 1 0 |
0 0 1 1 | 1 0 0 1 | 0 1 0 1 | 0 0 0 0 | 1 0 1 0 |
1 1 0 0 | 0 1 1 0 | 0 1 0 1 | 1 1 1 1 | 1 0 1 0 |
1 1 0 0 | 1 0 0 1 | 1 0 1 0 | 0 0 0 0 | 1 0 1 0 |

0 1 0 1 | 0 0 0 0 | 1 1 0 0 | 1 0 0 1 | 1 1 0 0 |
0 1 0 1 | 1 1 1 1 | 0 0 1 1 | 1 0 0 1 | 1 1 0 0 |
1 0 1 0 | 1 1 1 1 | 0 0 1 1 | 0 1 1 0 | 1 1 0 0 |
1 0 1 0 | 0 0 0 0 | 1 1 0 0 | 0 1 1 0 | 1 1 0 0 |

Consequently, any pattern that can be obtained through such
transformations can be described by a pair of these two matricies.

There are 30^2 such pairs, and hence can be no more than 30^2 patterns
obtained through the mentioned transformations.

.