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Extending the standard model to include gravity, and thereby creating a "TOE" (Theory of Everything), is not I think going to be hurt by Godel. Because for TOE

by Allocator2008 18y ago

Extending the standard model to include gravity, and thereby creating a "TOE" (Theory of Everything), is not I think going to be hurt by Godel. Because for TOE to work, all it need do is make predictions over and above the standard model, which can be verified by experiment, but also be consistent with all predictions of the standard model. If it can do this, it will stand as a TOE, at least until it disagrees with prediction, if and when that would happen. In other words, a TOE need not be "provable to be consistent in all it axioms". All it needs to do is include the Standard Model's predictions, then, make a few new ones to include gravity. Like one nice prediction would be to have the value of 10^-120 plank units for the energy density of "dark energy" arising naturally and nicely from someplace. That would be a good prediction, just as an example. If a TOE (inclusive of the standard model, plus a description of gravitons which delt with infinities), could regurgitate all standard model predictions, plus just make one prediction more (like setting the energy density of dark energy without having to appeal to the anthropic principle, mind you), then we got a good TOE. "Provable?" No. But it lives to fight another day, which is the best we can ask of a theory anyway.

fauigerzigerk 18y ago
That's interesting, and I do think that something empirical needs to come into play in order to escape issues with formalism without cheating (Sorry about the incredible vagueness of this sentence). However, what makes me wary of proof by prediction is that it has failed in the past and it is all too obvious why. At the time, proponents of the Ptolemaic system were able to create a very complicated model that predicted the movements of planets reasonably well (don't know exactly who it was). So judging them by their predictions might have lead to the conclusion that the earth was indeed at the center of the universe. Also, just try to write unit tests to "prove" that some piece of code is correct with regard to concurrency. What if a particular problem occurs so rarely that it is very unlikely to be caught in any empirical test? What if its occurrence depends on factors that are not well known or hard to replicate? The problem with predictive models is that they sometimes break down unexpectedly. That doesn't make them useless, but it makes the distinction between logical proof and empirical proof all the more useful.

fauigerzigerk 18y ago

That's interesting, and I do think that something empirical needs to come into play in order to escape issues with formalism without cheating (Sorry about the incredible vagueness of this sentence). However, what makes me wary of proof by prediction is that it has failed in the past and it is all too obvious why. At the time, proponents of the Ptolemaic system were able to create a very complicated model that predicted the movements of planets reasonably well (don't know exactly who it was). So judging them by their predictions might have lead to the conclusion that the earth was indeed at the center of the universe. Also, just try to write unit tests to "prove" that some piece of code is correct with regard to concurrency. What if a particular problem occurs so rarely that it is very unlikely to be caught in any empirical test? What if its occurrence depends on factors that are not well known or hard to replicate? The problem with predictive models is that they sometimes break down unexpectedly. That doesn't make them useless, but it makes the distinction between logical proof and empirical proof all the more useful.