The name is absent

ON THE ANALYSIS OF LIBRARY GROWTH

growth phenomena related to society do not in general behave
logistically. For instance, neither the holdings growth of the Li-
brary of Congress (Figure 1) nor the growth in the number of
universities (Figure 5) are well represented by logistic curves.
Numerous attempts have been made to fit the data of civilization
to logistic curves and to successions of logistics (cf. Ref. 2, 6, 7, 9,
10,11, and 16).

If it is found that some data can be nicely fit by a sequence of N
logistics, this means that at least 4N -1 parameters are involved
(as well as some additional ones to describe where consecutive
logistics are to be fit together, but this can be ignored since this
problem is common to all piecewise fitting processes), since each
logistic requires three parameters, giving 3N, and all but one
(and sometimes that last one also!) must be shifted up or down,
which requires an additional constant. For instance, if data can
be fit by two logistics, as shown in Figure 7 taken from Pearl
(Ref. 10), then eight parameters are required. Only 11 data points
were available to Pearl, so it is no surprise that an eight-parameter
function could be found that would provide a good fit; it is not
clear that other functions might not provide an equally good fit
with the use of fewer parameters. Indeed, Pearl’s data is shown
on a Semilogarithmic scale in Figure 8, from which it is readily
seen that the leftmost four points are well fit by the two-parameter
exponential, the next three could be fairly well fit, and the remain-
ing four are again well fit by an exponential. Therefore three ex-
ponentials, requiring a total of six parameters, appear to dp
about as well as two logistics requiring eight parameters. One dif-
ference is that there is no evident place to transfer from one
logistic to the other; Pearl arbitrarily does this at 1855. The
exponential fits of Figure 8 immediately suggest that something
happened between the adjacent data points for 1840 and 1855,
and the fact that the lines representing the earliest and latest
exponentials in the graph are nearly parallel suggests that what-
ever occurred to change the population growth rate between 1840
and 1855 had returned to “normal” by 1870. The revolutions and
turmoil of 1848 and the following years could have affected the
birth rate, and it might have taken a generation—about 20 years—
to recover the rate loss, thus accounting for all of the features of
this graph in an informative way that the logistic interpretation
does not permit. Indeed, it is precisely the fluctuation from ex-
ponential growth that is of interest in this case ; the logistic curves
smooth that fluctuation so as to make it invisible.

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