Gödel's Rotating Cosmos
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Albert Einstein's General Theory of Relativity (1915) describes, with an impressive degree of accuracy, the nature of gravity and the large-scale structure of the Universe. Many different solutions have been found to the equations of General Relativity since its inception in 1915. A way to understand this is to say that the equations are a little like a garden maze and in this particular case there are many ways to escape the maze - that is, there are many different ways to solve the equations. There are many different solutions to General Relativity and their descriptions of the structure of space and time can vary from closely resembling the Universe we see around us to much more exotic and much less likely configurations of space, time, gravity and energy.
Some of the solutions are truly unique and quite fascinating. The mathematician and philosopher Kurt Gödel derived solutions to General Relativity which imply that the universe must in some sense be rotating. I am no theoretical physicist but I have always been quite taken by this idea. The solutions he arrived at were closely related to some of his ground-breaking work on the base of mathematical logic, the First Incompleteness Theorem (1931).
What Gödel's First Incompleteness Theorem establishes is that it is actually impossible to find a complete and self-consistent base upon which to build the towering edifice of mathematical proof and logic. So, although mathematics works for building bridges and calculating share returns, if you were to rely on it because you thought it was completely infallible you would be sorely mistaken. The beauty of Gödel's idea is actually related to recursion and self-reference. There is absolutely no way I can do it justice here so look at the link for more information. Douglas Hofstadter's "Gödel, Escher, Bach: an Eternal Golden Braid" is as good a place as any to start in attempting to wrap your mind around all this.
The basic point is that Gödel showed how it is possible that a Universe may in some sense rotate and that this is related to his results in mathematical logic, themselves based upon recursion and self-reference. The problematic issue is in attempting to consider what a Universe (- by definition as being the sum total of all that exists -) could possibly be rotating relative to. I think, however, that given the proliferation of self-organising complexity and self-reference in the mathematical patterns of nature - we should not be so very surprised to find, in the end, that the Universe is in some way rotating through itself.
