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Mathematics
Set Theory, Logic, Probability, Statistics
Is Newtonian Mechanics as Correct as General Relativity?
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[QUOTE="andrewkirk, post: 6016291, member: 265790"] I think that good prediction must follow from good explanation, but not the other way around. If we have an intuitive, satisfying explanation of why something happens, which is consistent with all our other accepted theories, but the predictions that follow from that explanation are not borne out by observation, there is probably something wrong with the explanation. Indeed it is sometimes failures of prediction for well-understood and highly-trusted theories that leads to their replacement by more sophisticated theories with wider scope of application. But good prediction does not imply that we have a good explanation. It is much more satisfying when one has an explanation of a relationship, but there are many observed relationships that are widely used, for which we have [I]no[/I] explanations. For example there are plenty of approved drugs that have been repeatedly shown to be effective in treating certain ailments, and which are widely prescribed, but for which no mechanism is known about how and why they work. When building statistical models, the usual approach is to set the bar lower for inclusion of a factor that is called 'intuitive' - ie for which we can imagine a reason why it would affect the output in the way it has been observed to do. We might for instance set a lower confidence level or improvement in model score as the threshold that must be crossed for an intuitive factor than for an unintuitive factor. But sometimes the statistical evidence for inclusion of a factor is just too strong, even though we are unable to imagine a reason why it should affect the output in the way it has been observed to do. One reason unintuitive factors make their way into models is the existence of interaction effects between factors. When a model has several factors there can be many levels of interaction and the number of possible interactions explodes combinatorically, with many of them hard to conceptualise. But as long as we set a high enough requirement of impact before including an unintuitive factor, it would be counter-productive to rule that out. [/QUOTE]
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Is Newtonian Mechanics as Correct as General Relativity?
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