Even gravity has exceptions—yes, really, this is a standard topic in philosophy of science because the Laws Of Gravity are so clear, yet in practice they are riddled with exceptions and errors.
No, you did not. Your examples are all consistent with our best current exceptionless theory of gravity (general relativity) and knowledge of the composition of our solar system (Uranus, Neptune, and Pluto). You merely hinted at the existence of additional examples that perplexed the Newtonians. In fact, since our current understanding of gravity is better than the Newtonians’, hinting at the existence of examples that perplexed the Newtonians fails to even suggest a flaw in our best current theory, not to mention suggesting the existence of “exceptions to gravity”. Please give at least one real example.
Nobody brought up relativity as the issue; the fact remains that every theory is incomplete and a work in progress, and a few errors is not disproof especially for a statistical generalization. You would not apply this ultra-high standard of ‘the theory must explain every observation ever in the absence of any further data or modifications’ to anything else discussed on LW, and I do not understand why either you or army1987 think you are adding anything to this discussion about cities exhibiting better scaling than corporations.
You said that gravity has exceptions. I’m not quite sure what that’s supposed to mean, but the only interpretation I could think of for that statement is that our current best theory of gravity (namely, general relativity) fails to predict how gravity behaves in some cases. I did not mean to suggest that any theory must explain every observation correctly to be useful, nor did I mean to imply anything about how well cities and corporations scale. I was merely pointing out that you falsely asserted that you had given examples of exceptions to gravity, when you had in fact you had only given examples of exceptions to Newtonian gravity as it would operate in a solar system similar but not identical to ours.
I have never heard of any observation showing that gravitation as described by general relativity (and, so long as you aren’t very close to something very massive and aren’t travelling at a sizeable fraction of the speed of light, excellently approximated by Newton’s law) might have “exceptions” on Solar System-scale, except possibly the Pioneer anomaly (for which there is a very plausible candidate explanation) and similar. When I read “errors” I hoped you meant measurement uncertainties, but I can’t make sense of the rest of the paragraph assuming you did.
There are no examples of failures of general relativity in that entire article. So far, of the two of you, only army1987 has given an example of an even slightly perplexing observation.
What are you talking about?
I gave multiple examples and specified the field interested in how such a naive formulation is completely wrong; please ask better questions.
No, you did not. Your examples are all consistent with our best current exceptionless theory of gravity (general relativity) and knowledge of the composition of our solar system (Uranus, Neptune, and Pluto). You merely hinted at the existence of additional examples that perplexed the Newtonians. In fact, since our current understanding of gravity is better than the Newtonians’, hinting at the existence of examples that perplexed the Newtonians fails to even suggest a flaw in our best current theory, not to mention suggesting the existence of “exceptions to gravity”. Please give at least one real example.
Nobody brought up relativity as the issue; the fact remains that every theory is incomplete and a work in progress, and a few errors is not disproof especially for a statistical generalization. You would not apply this ultra-high standard of ‘the theory must explain every observation ever in the absence of any further data or modifications’ to anything else discussed on LW, and I do not understand why either you or army1987 think you are adding anything to this discussion about cities exhibiting better scaling than corporations.
You said that gravity has exceptions. I’m not quite sure what that’s supposed to mean, but the only interpretation I could think of for that statement is that our current best theory of gravity (namely, general relativity) fails to predict how gravity behaves in some cases. I did not mean to suggest that any theory must explain every observation correctly to be useful, nor did I mean to imply anything about how well cities and corporations scale. I was merely pointing out that you falsely asserted that you had given examples of exceptions to gravity, when you had in fact you had only given examples of exceptions to Newtonian gravity as it would operate in a solar system similar but not identical to ours.
I saw what sounded to me like an extraordinary claim (though it turns out I misunderstood you) so I went WTF.
I have never heard of any observation showing that gravitation as described by general relativity (and, so long as you aren’t very close to something very massive and aren’t travelling at a sizeable fraction of the speed of light, excellently approximated by Newton’s law) might have “exceptions” on Solar System-scale, except possibly the Pioneer anomaly (for which there is a very plausible candidate explanation) and similar. When I read “errors” I hoped you meant measurement uncertainties, but I can’t make sense of the rest of the paragraph assuming you did.
http://en.wikipedia.org/wiki/Philosophy_of_science#Duhem-Quine_thesis may help you a little bit. You should probably read the entire article, since you seem to think there were no errors or exceptions, and that some exceptions could disprove a power law.
I think I know what you mean, but if I’m right, “gravity has exceptions” is, let’s say, a very bizarre way of putting it.
EDIT: yeah, you meant what i thought you meant.
There are no examples of failures of general relativity in that entire article. So far, of the two of you, only army1987 has given an example of an even slightly perplexing observation.
Why should I give one? I never brought up relativity, army1987 did.
You brought up the Laws Of Gravity (capitals yours), which among insiders are known as the Einstein field equations of general relativity.