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The ideal



 

The ideal has a prominent role in Western science, culture and religion. We have the Platonic ideal of mathematical truth, culture icons of the ideal life and the religious ideal of God  . The ideal is a fixed absolute ultimate perhaps infinite goal or destination. Gödel 's incompleteness theorem  smashed Hilbert  's ideal of formalizing mathematical truth  . I doubt that any completed infinite totalities exist and thus I doubt that there is any Platonic heaven  of absolute mathematical truth. Is the ideal an illusion? The evolution of life seems to be a divergent process with no fixed goals. Evolution creates values such as human love. It is not a response to values.

Perhaps we should replace the notion of a final, ultimate or absolute ideal with the understanding that the universe is creatively evolving not to a fixed goal but to an ever more diverse and marvelous range of possibilities. To strive for a fixed ideal is ultimately to stagnate. That is one of the implications of Gödel 's theorem that we must apply not just to mathematics but to life itself. Many mathematicians (including Gödel ) have continued to cling to the ideal of ultimate mathematical truth existing in an idealized mathematical Platonic heaven of infinite structures. Mathematics is the purest expression of an intellect that wants to figure out the logical steps to obtain a specific goal. It is natural to idealize this process and think in terms of ultimate ideal goals. Up to a point this is necessary and useful. Perhaps intellect pushes it too far.

Intuition does not proceed by a series of steps. Intuition does not have a fixed set of goals. It is always on the look out for interesting relationships. It is always trying to make something out of them. Einstein was perhaps the most deeply intuitive 20th century physicist and perhaps the only prominent physicist for whom intuition and not intellect was the guiding star  . He accomplished more than any other physicists of this age even though he spent most of his professional career futilely searching for a grand synthesis of the revolutions in physics of relativity and quantum mechanics that he did so much to create. He was and is criticized and even ridiculed for this effort and for his refusal to accept that God plays dice. If the class of physical models I propose is at all close to the truth then Einstein will have his revenge with a vengeance.

More than the vindication of his ideas and intuition Einstein's revenge 

will be a vindication of the power of intuition when it is allowed to be one's guiding star.

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