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Creativity and Evolution

Nervous systems and sense organs evolved to control an organisms actions taking into account likely consequences. Reason, logic and the capacity for mathematics evolved because they were useful in determining likely outcomes. Central to mathematics is induction on the integers and its generalizations. Induction allows one to derive a potentially infinite number of conclusions from a single proof. Mathematical induction is a product of cultural evolution, but the mind that can think about iterative and self reflective generalizations is a product of biological evolution. Gödel's result established that there is no finite limit to the generalizations of induction that are theoretically useful in predicting the consequences of ones actions.

The levels of induction derivable from ZFC seem adequate for every practical problem we currently encounter.2 A Gödelian limit must be something it is hard to see beyond, so it is not surprising that we do not see a clear need to extend the foundations of mathematics. However, I suspect ZFC is far from the Gödelian limit of the human mind combined with the culture and technology that mind can lead to. A philosophy of mathematics that focuses on the combinatorial structure of axioms and uses computers to do experiments on that structure may lead to much stronger generalizations of induction than can be derived from ZFC.

Evolution faced many major obstacles as it evolved the extraordinarily complex human brain. Some of these could be interpreted as Gödelian limits. They were only overcome by the immense diversity of life, the enormous time that was available and perhaps some good luck. The end of the age of dinosaurs is one example. They dominated the earth far longer than we have. They would probably still be dominant if not for that terrible wonderful meteor that destroyed them and a large percentage of all species. The world dominated by dinosaurs was less diverse then the planet repopulated with small mammals. A dinosaur dominated planet may not have had the diversity needed to evolve a mathematically capable brain. The human mind is the best example of overcoming a Gödelian limit. The structure of that brain has given us the capacity to create technology and transform the planet.

Unlimited creativity, at least in mathematics, requires both ever more resources for each viable path and an ever increasing number of paths. These are exemplified in the diversity of life and the complexity of the human brain. The inherent conflict in these two requirements is reflected in cultural and biological evolution. Carl Jung, in defining the modern usage of the psychological terms, intravert and extravert, observed that it applies to these psychological dispositions and to the fundamental strategies for reproductive success.

There are in nature two fundamentally different modes of adaptation which ensure the continued existence of the living organism. The one consists of a high rate of fertility, with low powers of defense and short duration of life for the single individual; the other consists in equipping the individual with numerous means of self-preservation plus a low fertility rate. This biological difference, it seems to me, is not merely analogous to, but the actual foundation of, our two psychological modes of adaptation [intraversion and extraversion][6, ¶559]

Jared Diamond in Guns, Germs and Steel[4] observed a similar creative dialectic between diversity and concentration of resources in cultural evolution. He investigated why certain cultures came to dominate the planet while others remained relatively stagnant. One needed an appropriate balance between diversity and concentration of resources for modern civilization to arise. A culture dominated by a single ruling elite, like China, inevitably failed to pursue possibilities essential to future development. In contrast, a region, like Africa, with so many small communities, could never marshal the resources needed for certain kinds of progress. Europe presented the ideal combination of diversity and concentration of resources.

There are many reasons why a good tradeoff between diversity and concentration of resource is important.

The above reinforce the need for diversity. If you do not know what is going to happen or how to create large institutions, hedge your bets. The problem of creating effective human institutions may ultimately require new mathematics. It involves the capabilities of the human mind and how those minds interact in a particular culture. In the near term, expansion of mathematics is unlikely to help us make better decisions. However, no matter how much progress we make in predicting and controlling our world through the exponential expansion of technology, expanding diversity will remain an irreducible logical requirement for unlimited creativity. The limits of mathematics will be of practical importance eventually, if we are able to survive the immediate problems we are creating for ourselves.


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