The Evolution

The Evolution
25

Now earlier it was noted that shifting from a Type II intersection
to a Type III intersection, or vice versa, altered memory's expectations
by a large factor. This factor will be termed the shift ratio (S. R.)
and will be defined as the Type III ratio divided by the Type II ratio:

S.R. ₌ P(N∣Y)∕[P(I∣X) + P(IlY)] ₌ P(I∣X)
P(Y)P(N∣Y)∕P(I∣X)       P(Y)[P(I∣X) + P(IlY)]

If one then assumes that P(I∣X) and P(l∣Y) are approximately equal,
which roughly they would tend to be, then the above equation yields
the formula:

S.R, ₌    1

2P(Y)

Since human experience encompasses tens of thousands of recognizable
percepts, it would be common for P(Y) to be less than .0001, which means
that shift ratios of 5000 or more would be common. This means that a
memory that treated Type II and Type III intersections alike would fre-
quently incorrectly estimate probabilities by a factor as high as 5000,
and that still larger errors would be inevitable as well.

Needless to say, such a poorly designed memory would have a hard
time competing for survival with well-designed memories that took advan-
tage of part-whole and whole-to-whole linking in order to treat Type II
and Type III intersections properly. It follows that one is justified
in expecting that it is likely memory treats Type II and Type III inter-
sections differently, inasmuch as such an expectation is supported by a
mathematical analysis of the physical world in which memory evolved, an
analysis that also supports the more particular conclusion that memory
stores its information in part-whole and whole-to-whole links.

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