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There is a dimension to the human spirit that can never be satisfied. It is not something that has a definable goal or end point such as the craving for food or sex. It is always striving for something new even if what one has seems completely satisfactory. Why would evolution develop an instinct for creativity ? By investing some resources in exploring new possibilities just for the sake of exploring one occasionally hits on something that is of practical practical value. The roots of this instinct no doubt go back to how mutations are dealt with at the most basic level. More often than not mutations are bad but the best strategy is not to automatically eliminate them. Rather it is to allow a few to remain and see what happens.
Sexual reproduction was a great advance because it provides a means for trying out an enormous number of combinations of genes. Sex is a method to both speed up creativity and to support a higher level of diversity in a population. The latter can be important to adapt to recurring situations and the former to adapt to new situations. Just as introversion and extraversion have their roots in two basic strategies of survival the instinct for creativity and the freedom that is necessary for creativity have their roots in the creative mechanisms that are a part of reproduction.
There are potentially great advantages to an organism if it can build a model of part of its environment and, even to a very limited degree, predict how the environment will change over time. Higher animals invest many resources in sensation and in a nervous system to draw inferences from sensation. Gödel 's proof applies to this process. Higher animals are capable of higher levels of abstraction that determine a level of mathematical processing that the organism is capable of. At a low level the nervous system develops proportionate responses. If a prey is moving fast one strikes fast and in a direction and with a speed determined by the motion of the prey. At a higher level there is pursuit. One may not be able to capture the prey in a single swift blow but one follows it waiting for an opportunity. Pursuit provides the opportunity for more subtle strategies such as subterfuge and tiring the prey. Most importantly it opens the door to cooperation. Gödel 's result suggests that only a divergent process like evolution would be likely to evolve the mathematical sophistication of the human mind. Survival, by itself, is not enough. If the planet was smaller with less diverse climate then perhaps the development of anything approaching the human mind would be unlikely. Perhaps periodic global catastrophes like the event that destroyed the dinosaurs also played an essential role. By destroying less flexible life forms these catastrophes opened the way to greater diversity in the more flexible and creative species that remained.
In Chapter I described how the mathematics of the completed infinite might be interpreted as the mathematics of creativity. Is it possible to apply this mathematics to quantify constraints on evolution ? I believe this is possible and will happen in time. Can we apply the same mathematics to human institutions in which creativity plays such a vital role? I think this will happen also. We are a long way from being able to do any of this in a quantitative way. However we can begin to relate some of the things we already understand about creative institutions to the relevant mathematics. This may provide some insights of practical value now as well as point the way to developing a practical mathematics of creativity. In time we may be able to answer some political questions with mathematical or scientific rigor. They have calculable answers or answers that can be determined through experiments.
The ideas that can lead to such achievements are in a primitive state. We can begin to understand the tradeoffs between diversity and complexity in nature and how we might be able to quantify them not simply in turns of optimizing survival under fixed conditions but under conditions that change over time in an unknown way. That is the problem that evolution is faced with and has solved. In time these ideas can be made more rigorous and techniques can be developed to quantify some of these relationships. The mathematics of creativity is a profoundly important practical science because creativity is the principle business of life.
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