An aside about inflection points:
On Wed, 30 Oct 1996, A. Gunder Frank wrote:
> ALAS, one, perhaps the main thing, that it says is that 1500 was NOT
> a break/inflection time [except of course for the Americas and Europe's
> ability to become any kind of player], and/but that it defintiely was NOT
> the inflection that WSNers, following Marx Weber and Wallerstein
> [i think wrongly] ATTRIBUTE to it.
> ...
This aside is directed at the issue of breaks/inflections that
Gunder Frank raises here, and *not* necessarily at his treatment of
it.
One thing I noticed when looking at the literature in sociology
and other areas about technological diffusion was a basic confusion about
the stereotypical growth logistic. This was often presented as if it had
three "phases" of growth: a slow growth phase, accelerating into a rapid
growth or "take-off" phase tapering off into a slow growth, tapering off
to saturation.
But, of course, there are only two phases: an initial phase of
nearly exponential growth, when the critical limiting factor in
reproduction is the reproducing population (people who have already had
experience in using an agricultural technique, etc.), and a decelerating
phase when the limits of expansion begin to be the factor limiting
growth. In a pure logistic, the "take-off" has lower growth *rates* than
the initial period.
So we should be careful of classifying the significance of a
change strictly by the magnitude of the immediate impact: that works
well enough for mechanical models, but can be deceptive in dealing
with cumulative and circular causation.
Virtually,
Bruce R. McFarling, Newcastle, NSW
ecbm@cc.newcastle.edu.au