Yee Review of my Book

Thu, 14 Sep 1995 11:23:27 CDT

I would like to thank Danny Yee for his thoughtful and thorough review
of my recent book, *A Scientific Model of Social and Cultural Evolution*
(Kirksville, MO: Thomas Jefferson University Press, 1995). With Hugh's
prior approval, though, I would like to clarify two matters. First,
while Yee correctly stresses the accessibility of the mathematics used,
I would like to specify that it is elementary algebra--what
college-bound students usually learn in high school (except, as he
notes, for the calculus appendix); I regret, however, his reference to
the mathematics as "trivial for anyone who understands basic calculus,"
since the word"trivial" could be mistaken, in this context, to mean
gratuitous--which I hope he did not mean, and which I would utterly
refute by pointing out that the math, though easy, is applied to topics
hitherto treated almost entirely--and inappropriately--qualitatively
rather than quantitatively. Second, Yee finds implausible my assumption
that inhibition of geographical expansion exerts a linear (and inverse)
influence on societal proliferation, but concedes that the assumption
does generate archaeologically testable hypotheses. While I am glad
that he noted the empirical implications, I want to stress that the most
important of these implications, conveniently tabulated in Chapter 8 (a
non-mathematical concluding chapter), *do not depend on the linear
assumption he finds implausible*; they depend only on the elegant
assumption that by the time geographic expansion is fully inhibited (but
area is not shrinking), the tendency for societies to proliferate with
population growth will have turned into a tendency to *deproliferate* at
the rate of population growth. Suffice it to say, here, that my grounds
for assuming linearity, which I chose not to detail in the book, have to
do with what happens in cases where area inhabited is either shrinking,
or growing even faster than is population. (The obvious alternative to
straight-linearity would be a curvilinearity modeled by a cosine
transformation, which, unlike the straight-line assumption, is
intuitively unacceptable for these extreme cases. The likelihood that
more refined modeling of political evolution will require truly
non-linear math is considered in Chapter 6's lengthy endnote 1.) In conc
lusion, I repeat my appreciation for the review in general, and for the
reviewer's stressing the tentativity with which I am proposing several
related laws of social and cultural evolution. --Bob Graber