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> The problem is physicists tend to use "intuition" to prove things. That is not correct (or I am completely misunderstanding what you intended to say). There'

by privong 12y ago

> The problem is physicists tend to use "intuition" to prove things. That is not correct (or I am completely misunderstanding what you intended to say). There's a huge component of physics that is experimental, and those experiments are used to develop and test models and theories. Initution comes into play when developing theories or thinking about new directions to take experiments, but intution is not and cannot be a substitue for experimental evidence.

chriswarbo 12y ago
There's a distinction between "mathematical proof" and "empirical proof". Physicists are certainly good at empirical proof, but I think the 'appeal to intuition' complaint was aimed at the mathematical side (ie. the Maths in Physics isn't very rigorous). As a former Physicist and current Computer Scientist, I would agree with that complaint (although our use of empirical evidence is FAR below that in Physics). For example, in Programming Language Theory it's amazing how many different notions of "equal" there are (isomorphism, definitional, judgemental, propositional, extensional, etc.). In Physics, there's just "=" :)
- raverbashing 12y ago
  That "intuition" is what brought us Special and General Relativity "the Maths in Physics isn't very rigorous" Well, of course it isn't, because of the physical limitations. You can't expect to get Newton's second law and make it work with any kind of mathematical object. (if that's what you mean) > In Physics, there's just "=" Scalar equality? Vector equality? Magnitude equality? Also leptons are 'equal' following the Pauli exclusion principle?
  - j2kun 12y ago
    Nobody is criticizing the results of physics. But you can't call them mathematicians unless they're giving mathematical proofs.
  - chriswarbo 12y ago
    > That "intuition" is what brought us Special and General Relativity Yes. Intuition is a good thing. It just shouldn't be relied on for proofs. To compare, Mathematicians followed their intuitions to bring us all kinds of results (eg. ). It's a good thing. It just shouldn't be used to prone to making mistakes when but shouldn't be relied on for (Mathematical) proof. > You can't expect to get Newton's second law and make it work with any kind of mathematical object. That's not rigour, that's generality. For an example of rigour, compare the treatment of (infinitesimal) calculus in Physics and in pure Mathematics (eg. see http://en.wikipedia.org/wiki/Calculus#Foundations http://en.wikipedia.org/wiki/Calculus#Foundations ). >> In Physics, there's just "=" > Scalar equality? Vector equality? Magnitude equality? I would say the first two are "instances" of the same principle (in the same way that, for example, intensional equality can be "instantiated" for integers, arrays, matrices, etc.). Magnitude equality composes the absolute value operation with "the" equality operation, so I would call it a shorthand rather than a distinct equality principle. > Also leptons are 'equal' following the Pauli exclusion principle? What an excellent example of a non-rigorous statement ;) (ie. what is your model of leptons?) For reference, some of the examples I mentioned are described at http://ncatlab.org/nlab/show/equality http://ncatlab.org/nlab/show/equality
    - DougMerritt 12y ago
      >> Also leptons are 'equal' following the Pauli exclusion principle? > What an excellent example of a non-rigorous statement That is completely uncalled for. The difference between leptons (as a kind of fermion, which obey the P.E.P.) and bosons (which do not) is no more and no less than the different definition of identity/equality in the two cases. Rigorously. http://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_statistics http://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_statistic... http://en.wikipedia.org/wiki/Fermi%E2%80%93Dirac_statistics http://en.wikipedia.org/wiki/Fermi%E2%80%93Dirac_statistics

by privong 12y ago

chriswarbo 12y ago

There's a distinction between "mathematical proof" and "empirical proof". Physicists are certainly good at empirical proof, but I think the 'appeal to intuition' complaint was aimed at the mathematical side (ie. the Maths in Physics isn't very rigorous). As a former Physicist and current Computer Scientist, I would agree with that complaint (although our use of empirical evidence is FAR below that in Physics). For example, in Programming Language Theory it's amazing how many different notions of "equal" there are (isomorphism, definitional, judgemental, propositional, extensional, etc.). In Physics, there's just "=" :)

raverbashing 12y ago
That "intuition" is what brought us Special and General Relativity "the Maths in Physics isn't very rigorous" Well, of course it isn't, because of the physical limitations. You can't expect to get Newton's second law and make it work with any kind of mathematical object. (if that's what you mean) > In Physics, there's just "=" Scalar equality? Vector equality? Magnitude equality? Also leptons are 'equal' following the Pauli exclusion principle?
- j2kun 12y ago
  Nobody is criticizing the results of physics. But you can't call them mathematicians unless they're giving mathematical proofs.
- chriswarbo 12y ago
  > That "intuition" is what brought us Special and General Relativity Yes. Intuition is a good thing. It just shouldn't be relied on for proofs. To compare, Mathematicians followed their intuitions to bring us all kinds of results (eg. ). It's a good thing. It just shouldn't be used to prone to making mistakes when but shouldn't be relied on for (Mathematical) proof. > You can't expect to get Newton's second law and make it work with any kind of mathematical object. That's not rigour, that's generality. For an example of rigour, compare the treatment of (infinitesimal) calculus in Physics and in pure Mathematics (eg. see http://en.wikipedia.org/wiki/Calculus#Foundations http://en.wikipedia.org/wiki/Calculus#Foundations ). >> In Physics, there's just "=" > Scalar equality? Vector equality? Magnitude equality? I would say the first two are "instances" of the same principle (in the same way that, for example, intensional equality can be "instantiated" for integers, arrays, matrices, etc.). Magnitude equality composes the absolute value operation with "the" equality operation, so I would call it a shorthand rather than a distinct equality principle. > Also leptons are 'equal' following the Pauli exclusion principle? What an excellent example of a non-rigorous statement ;) (ie. what is your model of leptons?) For reference, some of the examples I mentioned are described at http://ncatlab.org/nlab/show/equality http://ncatlab.org/nlab/show/equality
  - DougMerritt 12y ago
    >> Also leptons are 'equal' following the Pauli exclusion principle? > What an excellent example of a non-rigorous statement That is completely uncalled for. The difference between leptons (as a kind of fermion, which obey the P.E.P.) and bosons (which do not) is no more and no less than the different definition of identity/equality in the two cases. Rigorously. http://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_statistics http://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_statistic... http://en.wikipedia.org/wiki/Fermi%E2%80%93Dirac_statistics http://en.wikipedia.org/wiki/Fermi%E2%80%93Dirac_statistics