Only 7.8 Billion (was: 9 Billion. The Population Explosion Is At And End.)
From: Alfred Einstead (whopkins_at_csd.uwm.edu)
Date: 09/14/04
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Date: 13 Sep 2004 18:18:54 -0700
whopkins@csd.uwm.edu (Alfred Einstead) wrote:
> Things have become much more clear since then. The following mathematical
> regularity has emerged and has remained valid for the past 30 years:
> P(1989 + t) + P(1989 - t) = 10.39 billion +/- 5 million.
>
> Actual figures, millions (from mid-year estimates by US Census Bureau):
[see previous article for these]
[...]
> The best-fitting S curve, with 1989 as the inflection, fitting to
> 1950-2004, is given by:
> * linear fit against: population (1 - a exp(kt)) = b + c exp(kt)
> * k = 0.040785, 99.968% goodness of fit, 55 data points
> * Transition range of population in millions: 1160 -> 5194 -> 9229
> * Inflection time 1989
> * Maximum rate: 82.273 million/year
This does, in fact, fit very well. However, it shows small
deviations of about 10-20 million and is not a direct fit. A
closer examination shows a pattern in the deviations indicating
that even this coming to a halt fast enough to account for what's
been seen the past decade in the actual figures!
The proper way (but also more difficult) to do a fit is directly:
population vs. (b + c exp(kt))/(1 - a exp(kt)).
The results of fitting this to the above-mentioned regularity
1974-2004 are not only striking -- but shocking.
This is a slightly edited copy of a letter I sent recently to a Physics
professor and long-time ccrrespondant, which will also be of general
interest here, regarding the recent find -- also posted here -- on the
surprising recent development in the world population curve.
===============
Following up on the remarks I made in my last letter, the curve I mentioned
there should have read:
5.1 billion + 4.2 billion tanh((t-1989)/49).
I originally had 25, or about half of 49, where 49 is. This fits very
well over the past century going even back to the 1800's. However, looking
at the deviations in detail I noticed something very interesting: it's too
flat around the inflection point of 1989 and rises too fast afterwards,
going off by 10-20 million or so.
This may not seem like much, particularly given that estimates can be
off by around 10 million or so, but the deviations add up, and show
clearly (particularly with the more recent data) that the curve is
simply too straight.
In other words, what I'm finding is that the actual population is coming
to a halt MUCH FASTER than even the surprise I cited before (9.3 billion).
Fitting to the following curve:
P(t) = 5.198 billion + 2.577 billion tanh((t-1989.047)/30.415)
gives an EXACT fit for the 30 year range 1974-2004, where I had previously
noted the regularity
P(t-1989) + P(t+1989) = 10.39 billion +/- 5 million.
In fact, it is never off by more than 6 million.
This is, in fact, the difference between the actual population (as cited
by the US Census Bureau for mid-year world population) and the function
given above:
Difference (in millions)
1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988
-4 1 3 3 2 2 0 -2 -2 -2 -4 -5 -4 -2 0
1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
3 6 5 5 3 1 -1 -2 -2 -3 -3 -3 -2 -1 1
2004
6
I'm not sure if the 2004 datum cited at the US Census Bureau cite is an
actual figure or projected, since I haven't looked there recently.
This is beyond incredible. It's downright spooky. But the conclusion
that follows is radical:
Not only is the population explosion over, but
the population growth, overall, is nearly over ... NOW!
The asymptotic value of the function above is only 7.8 billion -- but
we're already at around 6.4 billion. In other words: we're already
almost at the stablization point.
Anyway ... that and the other material is what I've been working on
lately. The above information should be of interest to physicists in
general (which is how and why, for instance, the paper by Kapitza that
I mentioned before found itself in a Physics journal), because the
world population system is just another collective system that falls
properly under the study of statistical mechanics. The same phenomena
of phase changes, critical points, and growth processes apply here as
they would in any other collective system.
Kapitza's conclusion was based on the curve
P(t) = a arctan(b tan(c(t - d)))
which actually fits fairly well for the entire history of the human
race. He claimed that the population change is, in fact, a process
driven internally, rather than by external factors such as resource
limits, as a Malthusian account would have it. In this way, he fell
in line with other researchers in the demography field who are coming
to believe that the present-day demographic transition is actually
being brought about internally, independent of any resource limitations
that may exist.
Well, it turns out that there is now enough data present to refute the
Kapitza ansatz -- at least at the short-term level. It may still
provide a framework for a global history, but it doesn't fit the
short term.
In fact, with the most recent data that's come out since 2000, and with
the regularity that's emerged with 1989 showing itself to be the
inflection point and a near-perfect symmetry about 1989, it turns out
that it is mathematically impossible to make the Kapitza curve fit
while recovering the 1989 inflection point and the actual population
data from 2000 onward.
His original estimate was a asymptote of 14 billion. Fitting his curve
to more recent data reduces this to 10 billion. But it goes seriously
astray by the time you reach 2000. In contrast, the curve I cited above
fits exactly for the past 30 years.
The UN's estimate has always been 10-15 billion, with 10 being the low
end. They committed more to 10 billion in 1999, as did the US Census
Bureau. My findings completely blow all of this out of the water.
10 billion would have been a major surprise originally. 7.8 billion is
a complete shock, especially given that we're almost already there!
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