An average splits any set of data; half is less than average, half greater. The frequency distribution for ancestors is uniformly positive with a mean which is always quite small in relation to the range of the data, leaving the frequency distribution highly skewed. The following tabulation of the 512 ancestors of the 256 configurations of length 8 illustrates the point:

At one extreme, there is a large number of ancestorless configurations, for example all those containing the string 010 somewhere amongst the eight cells; the other end boasts an outlier -- -- with 89 ancestors. Indeed, some of the configurations account for half the ancestors.

The lesson to be learned is that even a few points on the high end must be compensated by numerous points on the low end, the very lowest of which come from the Garden of Eden.

Harold V. McIntosh