Page 381 - Deep Learning

364 Conclusion

in the application to the design of a bridge or a rocket those equations generate
complex mathematical expressions, as even a brief look at an engineering text­
book will confirm. likewise, a concise statement of Darwin’s theory of evo­
lution belies the complexity of variation­selection explanations for particular
evolutionary phenomena like flight, kinship selection and vision. in general,
simplicity of theoretical expression is gained in return for complexity of artic­
ulation, the latter being easier to off­load onto cognitive support systems like
paper and pencil, computer software and research assistants.
one approach to complexity, advocated by positivist philosophers of sci­
ence, is to reduce phenomena at one level of description to phenomena at lower
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levels, with the levels ordered via part­whole relations: All physical objects are
made up of material substances, which are made up of molecules, which are
made up of atoms, which in turn are made of elementary particles, which are
made up of quarks, which are made of … we do not yet know what. once we
know, the theory of those ultimate building blocks will be a theory of everything
in the reductionist sense. The expectation that the parts and the parts­of­parts
will turn out to be simpler than the objects and processes at analytically higher
levels has never been fulfilled – there is nothing simple about so­called elemen­
tary particles – but analysis into parts is nevertheless a successful research strat­
egy. The substance­molecule­atom­particle and the organism­organ­tissue­cell
ladders of parts and parts­of­parts are very useful for understanding nature.
But analysis is not the scientist’s only handle on complexity, not even within
physics. simplification is also served by abstract principles that unify large swaths
of knowledge by codifying shared patterns. The great conservation laws of phys­
ics are the type specimens. other examples include the unification of terrestrial
and celestial mechanics by newton’s principles of mechanical motion and the
unification of various radiation phenomena – light, radio waves, X­rays – by the
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principles of electromagnetic fields. in other natural sciences, the unification of
biology by the theory of evolution, the unification of chemical reactions under
the principle of reorganization of atoms and the unification of the medicine of
contagious diseases under the germ theory are further examples. The key fea­
ture of abstract principles is that they are independent of particular objects, pro­
cesses or mechanisms. They specify constraints that all events of a certain type
satisfy. Analysis into parts and the identification of abstract principles are not
incompatible research strategies. The two­punch alternation between analysis
and abstraction has served the successful sciences well.
Although cognitive psychologists pride themselves on adhering to high
standards of rigorous, empirical science, the theoretical goal of research in
cognitive psychology is obscure. What does it mean to have a complete theory