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Posted: Sat Oct 04, 2003 5:38 pm Post subject: Stephen Hawking Lecture: "Godel and the End of Physics
On the newsgroup sci.physics.relativity, Jeff Krimmel wrote:
I just returned from a public lecture given by Stephen Hawking at Beckman Auditorium on the Caltech campus, and his talk was entitled "Goedel and the End of Physics".
In his talk, Dr. Hawking sought to take Goedel's Incompleteness Theorem and apply it to physics itself. Goedel's Incompleteness Theorem basically states that within any branch of mathematics, certain postulates will always exist that are unable to be proven true or false within the field's existing axiomatic structure. The most basic implication of this statement is that mathematics itself is incomplete (because of the fact that propositions exist that are patently unprovable).
If we follow this argument to its logical conclusion, we can begin to see the implications for the science of physics. As Dr. Hawking explained, the logical positivist approach to the philosophy of science holds mathematical models to reflect observed reality. In other words, physics relies on mathematics as the formal structure whereby scientists can make accurate, quantitative, and verifiable predictions. If this mathematical foundation is incomplete, what is the implication for physics? Well, one primary implication is that physics itself is incomplete.
Dr. Hawking took this conclusion one step further and speculated that no "theory of everything" will ever be discovered. Basically, no scientific structure with a finite number of axioms will be able to completely describe observed reality. As such, physicists will forever search for better tools to describe the world around us without ever reaching a final, finite physical description of the totality of the interactions governing the universe.
If physics is strictly defined as a search for the all encompassing "theory of everything", Hawking's statement, if it is indeed true, would mean an "end of physics", by definition. However, if physics is taken to be exactly what is today and what it has been for centuries in the past, the science of physics is truly endless as further investigations will continue to add useful tools to our ever-expanding descriptions of the universe, but this toolbox will never be full, or "complete". Again, Dr. Hawking simply gave a true gem of a lecture. An awe inspiring masterpiece.
Basically, I am curious if any of this has been presented in published form anywhere. The above synopsis is just from my own recollection of having sat through the lecture this evening, and I would sincerely appreciate having a much more authoritative and detailed account of Dr. Hawking's speculations. Also, please let me know if I have distorted anything in my above description.
Thanks,
Jeff
P.S. Not that anyone particularly cares, but a friend of mine was able to take a digital photograph of Dr. Kip Thorne, Dr. Hawking, and myself. It's a nice little reminder of the absolutely wonderful time I had this evening.
Jeff Krimmel wrote:
I would sincerely appreciate having a much more authoritative and detailed account of Dr. Hawking's speculations.
I don't think it's fair to call it "Dr. Hawking's speculations." I realized and spoke about the same application of Godel's incompleteness theorem to physics when I was a freshman math student in the early 1970's. And I can't imagine that I was the first person to envision the same infinite depth to the universe based on Godel's result.
Kurt Godel's incompleteness theorem is a mathematical certainty. Dr. Hawking is only presenting a highly plausible philosophy. I suggest that you do a google search for Kurt Godel incompleteness theorem and draw your own conclusions.
Stephen Hawking seems so sure we will need unprovable mathematical statements to formulate *the* theory of the universe. Can some guru formulate it again because I am not sure to really understand why it should be impossible to avoid it ?
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