Hmm. I'm not sure that's the case. Sure, it's preferable, if possible, to describe a mathematical idea in such a way that makes it completely obvious and trivial. But at a certain point, there are some ideas that will not be obvious and trivial; there is a huge amount of foundation which is needed to understand them.
Can Grigori Perelman describe to you his proof of the Poincaré conjecture in a way that is completely obvious and trivial? Well, no, otherwise he probably would have done that. Rather, he explained it as succinctly as possible, in a series of papers totaling about nearly 70 pages of fairly dense math, building on nearly a century of earlier work on the problem.
Does the fact that he was not able to express this completely obviously and trivially mean that he is not brilliant? No. It means that it's a really hard problem, which doesn't have a really obvious and trivial solution.
Now, it's absolutely true that mathematical complexity has nothing to do with how correct a theory is. You can have a complex, difficult mathematical theory that is bullshit, and you can have a complex, difficult mathematical theory that is a damned good approximation of reality (remember, in all of science, we are building models or approximations of reality, so even the best theory is never expected to be "right" in some absolute sense). And likewise, you can have a simple, easily explained theory that is bullshit, and you can have a simple, easily explained theory that is a damned fine approximation of reality.
Part of the beauty of physics is that since you are just studying the most fundamental of forces and interactions in the universe, it's a lot easier for a simple mathematical theory to model it quite accurately. Newton's laws are a damn good approximation of many physical phenomenon that we can observe directly, even if we now know that at large scales and high speeds they are not quite accurate due to relativistic effects.
It's just hard to find that kind of beauty in economics. The systems involved are just so much more complex; remember, you are trying to model not just the a single human, but a complex system of humans operating in both cooperative and competitive ways. So, asking that they boil down theories into something completely obvious and trivial may be asking too much. It may be the case that no obvious and trivial theory provides anything close to an accurate model of reality.
Now, the issue seems to be that there are a lot of theories in economics that are simply not grounded in any sort of empirical evidence at all, and are merely more mathematical manipulations applied to other theories that haven't been well substantiated. And this may be a problem; it's also a problem in physics, where ideas like string theory take hold and lead to complex, opaque mathematical manipulations that seem to be almost entirely independent of any kind of empirical evidence.
This does not mean that better theories will necessarily be simpler. There are plenty of theories in physics which have been well tested which are quite mathematically complex and non-obvious, like quantum electrodynamics.
> You can have a complex, difficult mathematical theory that is bullshit, and you can have a complex, difficult mathematical theory that is a damned good approximation of reality (remember, in all of science, we are building models or approximations of reality, so even the best theory is never expected to be "right" in some absolute sense).
One quibble. Unlike the empirical sciences, mathematics doesn't have to agree with reality, only with the rest of mathematics. Mathematics need only be internally consistent, where successful empirical science theories need to be both internally and externally consistent, i.e. they must agree with established theories* as well as survive reality-testing.
* = Or overthrow them entirely, as relativity did to the ether theory
> This does not mean that better theories will necessarily be simpler.
Yes, true, but Occam's razor favors simple theories, and there's plenty of empirical support for the idea that a simple explanation is more likely to reflect reality than a complex one.
Sorry, when I used "mathematical" in the quoted paragraph I did not mean an actual theorem in mathematics, I meant a scientific theory that involves heavy use of mathematics to describe some aspect of the world.
> Yes, true, but Occam's razor favors simple theories, and there's plenty of empirical support for the idea that a simple explanation is more likely to reflect reality than a complex one.
All Occam's razor tells us is that all else being equal, the simple theory is more likely to be correct than the more complex. I was not objecting to this observation, just pointing out that in only applies when all else is equal. There are some cases in which Occam's razor does not help you; when the problem being modeled is complex enough that you really do need a difficult, complicated model to accurately model it.
I think the big issue that OP has with economics is that it is neither beautiful, like much of pure mathematics, nor particularly grounded in empirical results, so it essentially winds up being a bunch of complexity for complexity's sake. That's the problem, not just the fact that a theory is complex and difficult to understand.
> Sorry, when I used "mathematical" in the quoted paragraph I did not mean an actual theorem in mathematics, I meant a scientific theory that involves heavy use of mathematics to describe some aspect of the world.
Yes, that's different, and for that case, my reply was misdirected. A theory in mathematical physics must certainly acquire empirical support, and must remain falsifiable in perpetuity.
> I think the big issue that OP has with economics is that it is neither beautiful, like much of pure mathematics, nor particularly grounded in empirical results, so it essentially winds up being a bunch of complexity for complexity's sake.
I agree completely, and the consequences are sometimes severe, as when quants use questionable economic theories to make phony risk estimates that backfire.
> That's the problem, not just the fact that a theory is complex and difficult to understand.
Yes, both difficult to understand, and difficult to test in any meaningful sense.
Can Grigori Perelman describe to you his proof of the Poincaré conjecture in a way that is completely obvious and trivial? Well, no, otherwise he probably would have done that. Rather, he explained it as succinctly as possible, in a series of papers totaling about nearly 70 pages of fairly dense math, building on nearly a century of earlier work on the problem.
Does the fact that he was not able to express this completely obviously and trivially mean that he is not brilliant? No. It means that it's a really hard problem, which doesn't have a really obvious and trivial solution.
Now, it's absolutely true that mathematical complexity has nothing to do with how correct a theory is. You can have a complex, difficult mathematical theory that is bullshit, and you can have a complex, difficult mathematical theory that is a damned good approximation of reality (remember, in all of science, we are building models or approximations of reality, so even the best theory is never expected to be "right" in some absolute sense). And likewise, you can have a simple, easily explained theory that is bullshit, and you can have a simple, easily explained theory that is a damned fine approximation of reality.
Part of the beauty of physics is that since you are just studying the most fundamental of forces and interactions in the universe, it's a lot easier for a simple mathematical theory to model it quite accurately. Newton's laws are a damn good approximation of many physical phenomenon that we can observe directly, even if we now know that at large scales and high speeds they are not quite accurate due to relativistic effects.
It's just hard to find that kind of beauty in economics. The systems involved are just so much more complex; remember, you are trying to model not just the a single human, but a complex system of humans operating in both cooperative and competitive ways. So, asking that they boil down theories into something completely obvious and trivial may be asking too much. It may be the case that no obvious and trivial theory provides anything close to an accurate model of reality.
Now, the issue seems to be that there are a lot of theories in economics that are simply not grounded in any sort of empirical evidence at all, and are merely more mathematical manipulations applied to other theories that haven't been well substantiated. And this may be a problem; it's also a problem in physics, where ideas like string theory take hold and lead to complex, opaque mathematical manipulations that seem to be almost entirely independent of any kind of empirical evidence.
This does not mean that better theories will necessarily be simpler. There are plenty of theories in physics which have been well tested which are quite mathematically complex and non-obvious, like quantum electrodynamics.