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> 3) When you have sufficient evidence, you upgrade your hypothesis to a theorem. A theorem is a mathematical result: something proved logically from (possibly
by taejo 14y ago
> 3) When you have sufficient evidence, you upgrade your hypothesis to a theorem.
A theorem is a mathematical result: something proved logically from (possibly physical) assumptions.
- danparsonson 14y agoSuch as the four colour theorem? en.wikipedia.org/wiki/Four_colour_theorem
- archivator 14y agoEspecially the four colour theorem - the first mathematical theorem to be proved with software. That said, I believe this discussion pertains to the hypothesis -> theory "upgrade", not to theorems.
- danparsonson 14y agoThe point I was hinting at was that some theorems can be proven by a sufficient body of evidence rather than requiring logical deduction - the four colour theorem being a good example as it was proven by 'brute force' rather than analytically.
- andrewaylett 14y agoDoesn't a logical proof count as evidence? To my mind, these two methods are demonstrating the same thing: considering all the possible inputs, we can show [using logic|by testing them all] that the output meets our criteria. To my mind, in this context, the difference between maths and physics is that maths is exhaustive while in physics we don't usually have exhaustive evidence so we have to work with what we've got.
- danparsonson 14y agoInteresting question - to me, the distinction is that 'evidence' of the validity of something is expected output(s) given known input(s), whereas 'proof' (at least in the mathematical sense) is a logical transformation that is applied to make it obvious that the theorem must be true. I'm not sure you could call a proof 'evidence' because it's not an output of the theorem - it is the theorem. I'm less certain than I was before I read your post, though - so I stand to be corrected :-)
- snprbob86 14y agoI meant to say "theory", as in gravity.