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formative years. Assuming that two siblings are presented with the same external stim-
uli, they apparently choose to experience those stimuli very differently. The sarcastic
humor of the father one son adopts as his own and there is regular father-son bantering
that draws the two of them closer together. The other son, who perhaps views the world
in more humanist terms, interprets the sarcasm as a rejection of him and his world view,
eventually becoming estranged from the father, but not necessarily from his brother.
One son's map is filled with conflict, contradiction and humor. The tension of paradox
is resolved with humor, not with intellectual synthesis. Whereas the other son's map
seeks to reward compatibility and to isolate paradox, and the intellectual synthesis is
much stronger, but the humor is almost completely absent. The mental map of one draws
him to interacting with other people, whereas the map of the other leads to introspection
and understanding rather than sharing.
Understanding the psyche of an individual is not like understanding a physical pro-
cess. There are no laws to guide the exploration of the psychological domain. But wait; it
is not entirely true that there are no laws. In the middle of the nineteenth century, physics
was considered the paradigm of objective science. In their rush to understand individu-
als and the world in which they live, scientists invented
psychophysics
and
sociophysics
in attempts to apply the methods of physics to the understanding of social and psycho-
logical phenomena. On the whole, psychophysics was the more successful of the two
since it involved direct experimental verification of theory. Much of the theory was con-
cerned with
psychometrics
, which is to say, the construction of metrics to enable the
quantification of psychological phenomena. The theory of measurement, which is now
a rather sophisticated branch of mathematics, grew from the efforts to understand these
first experiments of their kind. Much of today's experimental design is concerned with
the formulation of experimentally accessible measures, which, more often than not, is
the most difficult part of the design of an experiment.
1.3.1
Power laws, prediction and failure
So let us return to the question of the utility of predictions. In the social and life sci-
ences the predictions do not have the quantitative precision of the physical sciences. It
might be argued that the precision is lacking because the natural laws in biology are
empirical, such as the allometric laws. But that would overlook similar empirical laws
in physics, for example, Boyle's law according to which the product of the pressure and
volume of a gas is constant; this is the same type of relation that Auerbach found for
urban concentration. When the temperature is kept constant Boyle's law can be used
predictively to interpret experimental results. However, Boyle's law does not stand in
isolation, but can be derived from the general theory of thermodynamics or from kinetic
theory. Consequently its predictions are constrained by a web of physical observations
and theory. This is usually not the case in the life sciences, where the allometric relation
does stand alone and consequently its predictive value is limited.
Complex webs described by hyperbolic or inverse power-law distributions are not
amenable to the predictions presented for simple physical phenomena. We shall find
that the more complex a phenomenon becomes the less predictable it becomes; less
