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The only way that mathematics should be used to signal intelligence is if you can explain a mathematical idea in a way that makes it completely obvious and triv

by j2kun 13y ago

The only way that mathematics should be used to signal intelligence is if you can explain a mathematical idea in a way that makes it completely obvious and trivial. The kind of "signalling" that the author describes in macro (by obscurity and complexity) is the opposite, and it makes me sad.

losethos 13y ago
I got a C in partial differential equations. That was the semester I went to jail at nights. I took PDE because I got introduced in electrical properties of materials. Shrodinger's Equation and probability density functions. I got an A in electrical properties of materials. Potential wells, periodic crystals. I got an A incomplex analysis. We looked at integrating line integrals around the RHP to to count poles and zeros. Complex math is good when you want to transform stuff. Bilinear transformsa, I think. I did a whole bunch of Z and Laplace transforms over the years. I had to learn the ten properties of Vector Spaces about 4 times as a start of various classes. I used MATLAB. Xdot=AX+BU Y=CX+DU I like singular value decompositions. SVD. I'll bet you don't know routh horwitz. http://www.youtube.com/watch?v=WBCZBOB3LCA http://www.youtube.com/watch?v=WBCZBOB3LCA I'll bet you don't know root locus.
cynicalkane 13y ago
The only way that (X) should be used to signal intelligence is if you can explain an idea in a way that makes it completely obvious and trivial This is the opposite, unfortunately, of academia in general, not just economics.
- j2kun 13y ago
  I think mathematics at least strives to achieve that goal. But then when I say obvious and trivial I mean it in a mathematical sense: it's obvious and trivial if you understand all of the obvious and trivial groundwork needed to understand how obvious and trivial the idea at hand is.
lambda 13y ago
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.

by j2kun 13y ago

losethos 13y ago

I got a C in partial differential equations. That was the semester I went to jail at nights. I took PDE because I got introduced in electrical properties of materials. Shrodinger's Equation and probability density functions. I got an A in electrical properties of materials. Potential wells, periodic crystals. I got an A incomplex analysis. We looked at integrating line integrals around the RHP to to count poles and zeros. Complex math is good when you want to transform stuff. Bilinear transformsa, I think. I did a whole bunch of Z and Laplace transforms over the years. I had to learn the ten properties of Vector Spaces about 4 times as a start of various classes. I used MATLAB. Xdot=AX+BU Y=CX+DU I like singular value decompositions. SVD. I'll bet you don't know routh horwitz. http://www.youtube.com/watch?v=WBCZBOB3LCA http://www.youtube.com/watch?v=WBCZBOB3LCA I'll bet you don't know root locus.

cynicalkane 13y ago

The only way that (X) should be used to signal intelligence is if you can explain an idea in a way that makes it completely obvious and trivial This is the opposite, unfortunately, of academia in general, not just economics.

j2kun 13y ago
I think mathematics at least strives to achieve that goal. But then when I say obvious and trivial I mean it in a mathematical sense: it's obvious and trivial if you understand all of the obvious and trivial groundwork needed to understand how obvious and trivial the idea at hand is.

lambda 13y ago

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.