Bucky Fuller's formula is either wrong or grossly unclarified. Consider a
matrix of dimensions N x N. Let each side be indexed by the "event set"
(or any other set). Let a 1 appear in the matrix cell if a specified
relationship is present between the left hand index and the top index.
Let a 0 appear otherwise. Then for any specified relationship, you can
count the number of instances by counting the 1s in the matrix, less the
redundant 1s on the main diagonal.
The number of cells in toto is N squared. Now subtract those on the main
diagonal and you have N squared minus N. If you choose to assume that
there are no cycles, then you wipe out half of the cells (those on the
right of the main diagonal). What is left is the formula quoted from
fuller, N squared minus N, all divided by two.
Going at it this way, you see the major problems with the formula:
(1) It assumes either (a) only one type of relationship or (b) one
overriding composite relationship,
(2) It presumes that everything is hierarchically related, with no gaps.
(3) It ignores cyclic relationships which, our own experimental data
show are almost always present.
Other than that, Bucky was right.
JOHN WARFIELD
Jwarfiel@osf1.gmu.edu