A World Without Time: The Forgotten Legacy of Gödel And Einstein by Palle YourgrauMy rating: 3 of 5 stars
In the annals of twentieth century physical and mathematical thought there were a series of crises, and as a result of those crises, in many cases some kind of limitative result was derived.
Two of the figures involved in these results became deep friends in their late years at Princeton: the voluble Einstein and the strange reclusive Gödel, and this book dwells on the development of their philosophical views and the outcomes of some of that thought in the late work of Kurt Gödel.
Gödel, it is to be remembered, demonstrated a general approach that separated the concept of truth from the concept of provability from a set of axioms: every completely formal mathematical system possesses at least one true statement that cannot be demonstrated by it, regardless of what modifications you attempt. Gödel was extremely dubious of logical positivism, and essentially deriving his outlook from Plato, regarded formal methods as merely a rigorous way of arriving at fundamental, prexisting, intuitions of truth.
Einstein, more familiar to most readers, produced a geometrical interpretation of space and time not existing independently, but wholly determined by measurement, matter and energy.
Gödel became extremely interested in the aspect of time as psychological time, time that flows, and asked the question as to whether the intuition of time was something that should prove as reliable and fundamental as the notion of truth. Or was Plato's hint to be followed that time was not truly to be taken as real?
Gödel in exploring Einstein's general relativity came to the conclusion that time was an illusion, at least in the sense that we intuit it. Or perhaps one might say, it lacked the power and generality to become a fundamental intuition. It is odd, in that in his master work, his Incompleteness Theorem, he rigorously demonstrated the generality of the intuition of truth; yet in his work on relativity, he demonstrated deep flaws in the intuition of time.
Background: Unlike special relativity, general relativity allows the large scale distribution of matter to determine "average" or in some sense privileged observers at any region of space and time, in which it could be said time is to pass.
Gödel proceeded to
1. artificially imagine a universe in which the large scale distribution of matter is rotating about an axis
2. demonstrate that an observer could follow a path in which they would end up eventually in their own path
3. argue that in such a world time in the sense of a linear flow that we can intuit is an invalid concept
4. argue that if time cannot be validly applied to all possible worlds it has no true validity in any.
It may be noted that Gödel invented a totally new and completely valid solution of Einstein's field equations, but with very odd conditions clearly not followed by our actual universe. The argument from complete necessity in all possible worlds, may strike the reader as odd, or may seem to recall strange resemble to the Ontological Proof of the existence of God (Gödel played with formalizing the Ontological Proof, but never published it.)
I gave 3 stars to this book because (I have read the monograph on the Incompleteness Theorem, so trust me on this) I thought some of the explanations for the general reader, especially the Incompleteness Theorem were a little poor. It did give a very brilliant portrayal of Gödel's philosophical concerns. I also not that this is the non-technical companion to a much more rigorous exploration of Gödel's war on time, also by Yourgrau.
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