The name is absent



ON THE ANALYSIS OF LIBRARY GROWTH

73


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.



More intriguing information

1. Insurance within the firm
2. SLA RESEARCH ON SELF-DIRECTION: THEORETICAL AND PRACTICAL ISSUES
3. The name is absent
4. The name is absent
5. The name is absent
6. Design and investigation of scalable multicast recursive protocols for wired and wireless ad hoc networks
7. EU enlargement and environmental policy
8. The name is absent
9. Importing Feminist Criticism
10. Contribution of Economics to Design of Sustainable Cattle Breeding Programs in Eastern Africa: A Choice Experiment Approach
11. Ability grouping in the secondary school: attitudes of teachers of practically based subjects
12. Changing spatial planning systems and the role of the regional government level; Comparing the Netherlands, Flanders and England
13. Publication of Foreign Exchange Statistics by the Central Bank of Chile
14. ADJUSTMENT TO GLOBALISATION: A STUDY OF THE FOOTWEAR INDUSTRY IN EUROPE
15. The duration of fixed exchange rate regimes
16. Bird’s Eye View to Indonesian Mass Conflict Revisiting the Fact of Self-Organized Criticality
17. CAPACITAÇÃO GERENCIAL DE AGRICULTORES FAMILIARES: UMA PROPOSTA METODOLÓGICA DE EXTENSÃO RURAL
18. Climate change, mitigation and adaptation: the case of the Murray–Darling Basin in Australia
19. The name is absent
20. The name is absent