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lightpurpledye comments on How to Convince Me That 2 + 2 = 3 - Less Wrong

53 Post author: Eliezer_Yudkowsky 27 September 2007 11:00PM

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Comment author: lightpurpledye 21 March 2011 03:58:34AM 12 points [-]

Woah, I think that's a little overconfident...

You're saying that in the mid nineteenth century (half a century before relativity), the anomalous precession of Mercury made it seem 99.999999% likely that Newtonian mechanics was wrong?

After all, there are other possibilities.

cf. "When it was noticed in the 1800's that the perihelion of Neptune did not match what Newton's inverse-square law of gravity predicted, did we change the way math works? Or did we change our understanding of gravity?" In this case we actually postulated the existence of Pluto.

Similar solutions were suggested for the Mercury case, e.g. an extremely dense, small object orbiting close to Mercury.

And that's leaving aside the fact that 99.999999% is an absurdly high level of confidence for pretty much any statement at all (see http://lesswrong.com/lw/mo/infinite_certainty/ ).

If I were a nineteenth century physicist faced with the deviations in the perihelion of Mercury, I'd give maybe a 0.1% probability to Newton being incorrect, a 0.001% probability to maths being incorrect, and the remaining ~99.9% would be shared between incorrect data /incomplete data/ other things I haven't thought of.

However, I agree that we can probably be more confident of results in maths than results in experimental science. (I was going to distinguish between mathematical/empirical results, but given that the OP was to do with the empirical confirmation of maths, I thought "mathematical/experimental" would be a safer distinction)