3 ms·

You are being condescending and over simplifying the issues, try to not rush to judgment. I have spent a lot of work and time learning how to apply machine lear

You are being condescending and over simplifying the issues, try to not rush to judgment. I have spent a lot of work and time learning how to apply machine learning, so your comment was offensive and wrong. Applying mathematical theory is not just a matter of understanding the theory - in the real world there are a whole lot of reasons why you won't be able to apply the theory, even if you understand it perfectly. You will always have to make assumptions and approximations. I like learning, but I prefer learning for a purpose. Proofs don't really give you a practical understanding of the theory.

catnaroek 10y ago
> You will always have to make assumptions and approximations. The ability to determine when an approximation is good enough comes from a solid understanding of the underlying theory. For example, we understand that special relativity doesn't invalidate classical mechanics, because, in the limit, as speeds and energies become arbitrarily small, their predictions coincide. But, if all you have is a bunch of computational recipes, even the tiniest unexpected thing renders you unable to solve problems. Anyway, I'm not saying that examples of applications are a bad thing. But proofs are indispensable. Even for “intuitive” people, proofs are necessary confirmation that their calculations will match their intuitions.
- throw_away_777 10y ago
  You bring up an interesting example in special relativity. I am a physicist, and there isn't really a "proof" in the mathematical sense of special relativity. Googling it provides this quora answer: https://www.quora.com/What-is-the-proof-for-Special-Relativity https://www.quora.com/What-is-the-proof-for-Special-Relativi... There is no proof of special relativity, we believe it because it makes experimentally verified predictions. Your example of limiting cases of special relativity is how I wish statistics texts were taught - it isn't based on the "proof" of special relativity. Of course I know when special relativity is applicable and when it isn't (when beta = v / c is close to one, special relativistic effects are important, and gamma = 1 / sqrt(1 - beta*beta) indicates how good the approximation is). But I do agree that proofs are useful and needed, I think that complicated proofs could easily be placed in appendices and looked at after understanding why the theorem is relevant. Of course this is just my personal preference.
  - catnaroek 10y ago
    > There is no proof of special relativity, we believe it because it makes experimentally verified predictions. Right, that's because special relativity is a scientific theory. A scientific theory has two components: a mathematical theory (in which you can perform a priori physically meaningless calculations) and a physical interpretation (which turns the results of such calculations into predictions). However, statistics isn't a scientific theory. It's just math, and like all math, it's about itself and nothing else. It doesn't make sense to “experimentally confirm a mathematical theory”, because, without a physical interpretation, math doesn't make any predictions about the real world. > I think that complicated proofs could easily be placed in appendices and looked at after understanding why the theorem is relevant. Then you're looking for books on applications. That's fine. But a book whose subject matter is a mathematical theory (it even has “foundations” in the title!) can't relegate proofs to appendices.

catnaroek 10y ago

> You will always have to make assumptions and approximations. The ability to determine when an approximation is good enough comes from a solid understanding of the underlying theory. For example, we understand that special relativity doesn't invalidate classical mechanics, because, in the limit, as speeds and energies become arbitrarily small, their predictions coincide. But, if all you have is a bunch of computational recipes, even the tiniest unexpected thing renders you unable to solve problems. Anyway, I'm not saying that examples of applications are a bad thing. But proofs are indispensable. Even for “intuitive” people, proofs are necessary confirmation that their calculations will match their intuitions.

throw_away_777 10y ago
You bring up an interesting example in special relativity. I am a physicist, and there isn't really a "proof" in the mathematical sense of special relativity. Googling it provides this quora answer: https://www.quora.com/What-is-the-proof-for-Special-Relativity https://www.quora.com/What-is-the-proof-for-Special-Relativi... There is no proof of special relativity, we believe it because it makes experimentally verified predictions. Your example of limiting cases of special relativity is how I wish statistics texts were taught - it isn't based on the "proof" of special relativity. Of course I know when special relativity is applicable and when it isn't (when beta = v / c is close to one, special relativistic effects are important, and gamma = 1 / sqrt(1 - beta*beta) indicates how good the approximation is). But I do agree that proofs are useful and needed, I think that complicated proofs could easily be placed in appendices and looked at after understanding why the theorem is relevant. Of course this is just my personal preference.
- catnaroek 10y ago
  > There is no proof of special relativity, we believe it because it makes experimentally verified predictions. Right, that's because special relativity is a scientific theory. A scientific theory has two components: a mathematical theory (in which you can perform a priori physically meaningless calculations) and a physical interpretation (which turns the results of such calculations into predictions). However, statistics isn't a scientific theory. It's just math, and like all math, it's about itself and nothing else. It doesn't make sense to “experimentally confirm a mathematical theory”, because, without a physical interpretation, math doesn't make any predictions about the real world. > I think that complicated proofs could easily be placed in appendices and looked at after understanding why the theorem is relevant. Then you're looking for books on applications. That's fine. But a book whose subject matter is a mathematical theory (it even has “foundations” in the title!) can't relegate proofs to appendices.