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Here's the problem: I could easily make up another theory based on quantum mechanics and relativity, with the same amount of empirical support (none). The trivi

by guscost 12y ago

Here's the problem: I could easily make up another theory based on quantum mechanics and relativity, with the same amount of empirical support (none). The trivial other theory would not be in the form of math, but pure math is not a sufficient condition for scientific theories like quantum mechanics and relativity, and there would be no other meaningful difference.

deleted 12y ago
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Steuard 12y ago
> I could easily make up another theory based on quantum mechanics and relativity [...]. The trivial other theory would not be in the form of math[...] Can you clarify that at all? I honestly don't know how to reconcile your first sentence with your second one: you clearly mean something different by some of those words than I do, but I can't puzzle out what. Are you suggesting that you'd make up a theory that said, for example, "The universe looks behaves according to quantum field theory in the following set of circumstances: [long list of conditions], and behaves according to general relativity in the following distinct set of circumstances: [other long list], and consists of a troupe of dancing angels under all other circumstances [including, for example, black holes and the early universe]." Because I'd hesitate to call that (or anything like it) in any sense a scientific "theory". It has zero explanatory power, because it's an archetypical example of "overfitting the data": it's a description of reality, not an explanation, and there is literally zero reason to expect anything that you used to fill in the gaps between the observed data to be true. If that is the sort of thing you're talking about, then it sounds like your main claim is that there's no meaningful difference between that and (in our imagined case) a unique mathematical framework that gave rise to both quantum and gravitational observations as distinct limiting cases (while also making explicit claims about how the universe must behave in possibly-unobservable situations like black holes and the early universe). I don't really know how I would answer such a claim (if it's what you're trying to suggest), except to suggest an upgrade to a philosophical system that isn't deliberately obtuse. (I know that there is no a priori reason to expect the universe to have a mathematical description. But by this point, given the truly amazing success of those descriptions to date, the burden of proof really does have to rest on anyone who claims that those successes are just some sort of coincidence.)
- guscost 12y ago
  My main point is that there is only one meaningful difference: the presence of the unique mathematical framework. This alone would not be sufficient to put that theory in the category of science. Why? It comes down to the basic requirement that the theory should make some new and falsifiable prediction. Without that, the theory would at best be a mathematical unification (admittedly quite an impressive one). If using it isn't substantially better than using the older theories, all you've really done is invented a mathematical object that behaves like relativity in one context and quantum mechanics in another (and doing that without introducing loads of hidden variables seems to be enormously difficult). There is only something noteworthy and new in that mathematical sense. Is it interesting? Absolutely. Is it a scientific theory? Not really.
nilkn 12y ago
That is not the problem. Any predictive unification of quantum field theory and general relativity will be mathematical in nature. A unification which is not mathematical is guaranteed to never be predictive and to never aid in the construction of a unified theory which is predictive, because the problems to be solved here are indeed entirely mathematical (divergent integrals). String theory is a unification which is mathematical. Its direct empirical support is indeed currently none. However, as Hawking stated, it remains the only serious viable theory of everything right now. Every other competing theory has been found to have serious intrinsic issues, let alone lack of experimental support. People take string theory seriously not because it's some vague unification. They take it seriously because it solves extremely difficult mathematical problems. Even if it turns out to be wrong, it is fairly likely that the mathematical insight gained will be invaluable. Indeed, it has even led to at least one awarding of the Fields Medal for advances in pure mathematics, to Edward Witten.
- guscost 12y ago
  Your point about the need for prediction is relevant, but string theory is currently in the class of ideas which have no prospect of making meaningful predictions anytime soon. You might want to argue that the mathematical formulation makes the possibility that this will change in the future more likely, but I honestly don't see how that follows.

by guscost 12y ago

deleted 12y ago

[deleted]

Steuard 12y ago

> I could easily make up another theory based on quantum mechanics and relativity [...]. The trivial other theory would not be in the form of math[...] Can you clarify that at all? I honestly don't know how to reconcile your first sentence with your second one: you clearly mean something different by some of those words than I do, but I can't puzzle out what. Are you suggesting that you'd make up a theory that said, for example, "The universe looks behaves according to quantum field theory in the following set of circumstances: [long list of conditions], and behaves according to general relativity in the following distinct set of circumstances: [other long list], and consists of a troupe of dancing angels under all other circumstances [including, for example, black holes and the early universe]." Because I'd hesitate to call that (or anything like it) in any sense a scientific "theory". It has zero explanatory power, because it's an archetypical example of "overfitting the data": it's a description of reality, not an explanation, and there is literally zero reason to expect anything that you used to fill in the gaps between the observed data to be true. If that is the sort of thing you're talking about, then it sounds like your main claim is that there's no meaningful difference between that and (in our imagined case) a unique mathematical framework that gave rise to both quantum and gravitational observations as distinct limiting cases (while also making explicit claims about how the universe must behave in possibly-unobservable situations like black holes and the early universe). I don't really know how I would answer such a claim (if it's what you're trying to suggest), except to suggest an upgrade to a philosophical system that isn't deliberately obtuse. (I know that there is no a priori reason to expect the universe to have a mathematical description. But by this point, given the truly amazing success of those descriptions to date, the burden of proof really does have to rest on anyone who claims that those successes are just some sort of coincidence.)

guscost 12y ago
My main point is that there is only one meaningful difference: the presence of the unique mathematical framework. This alone would not be sufficient to put that theory in the category of science. Why? It comes down to the basic requirement that the theory should make some new and falsifiable prediction. Without that, the theory would at best be a mathematical unification (admittedly quite an impressive one). If using it isn't substantially better than using the older theories, all you've really done is invented a mathematical object that behaves like relativity in one context and quantum mechanics in another (and doing that without introducing loads of hidden variables seems to be enormously difficult). There is only something noteworthy and new in that mathematical sense. Is it interesting? Absolutely. Is it a scientific theory? Not really.

nilkn 12y ago

That is not the problem. Any predictive unification of quantum field theory and general relativity will be mathematical in nature. A unification which is not mathematical is guaranteed to never be predictive and to never aid in the construction of a unified theory which is predictive, because the problems to be solved here are indeed entirely mathematical (divergent integrals). String theory is a unification which is mathematical. Its direct empirical support is indeed currently none. However, as Hawking stated, it remains the only serious viable theory of everything right now. Every other competing theory has been found to have serious intrinsic issues, let alone lack of experimental support. People take string theory seriously not because it's some vague unification. They take it seriously because it solves extremely difficult mathematical problems. Even if it turns out to be wrong, it is fairly likely that the mathematical insight gained will be invaluable. Indeed, it has even led to at least one awarding of the Fields Medal for advances in pure mathematics, to Edward Witten.

guscost 12y ago
Your point about the need for prediction is relevant, but string theory is currently in the class of ideas which have no prospect of making meaningful predictions anytime soon. You might want to argue that the mathematical formulation makes the possibility that this will change in the future more likely, but I honestly don't see how that follows.