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The idea is that the simpler hypothesis is more likely to be true, given that it explains the data equally well. It doesn't mean it is true. Also, I believe ell
by 6ren 15y ago
The idea is that the simpler hypothesis is more likely to be true, given that it explains the data equally well. It doesn't mean it is true. Also, I believe elliptical motion predicts the observations of planetary motion more accurately than circles.
A problem with defining "simpler" is that it depends on the language that you use to express it. If you lack the right concepts for it, it may seem more complex. And if these concepts are quite difficult to understand (require a lot of training), it's kind of cheating to say that a theory expressed in them is "simple". A bit like a 1k demo that uses multi-megabytes of library code.
And now, my conjecture for why Occam's Razor seems to work: it is because we pre-select simple theories. That is, there are lots of complex theories out there that are the truth, and some of them are so complex, that we actually can't understand or even conceive of them (and never will - they are not susceptible to hierarchical decomposition). Therefore, correct theories turn out to be simple (they are more correct than the slightly more complex theories they compete with; but are never compared with the actually true theories that are bizarrely complex).
Plus, our language (including mathematically) notation is constantly being refined for how we use it - by adapting it to what we know. So it is overfitted to our present theory (the first thing a scientist or mathematician does when confronting something too complex is invent a notation for it that makes it simpler - the notation absorbs some of the complexity, which it borrows from our massive stores of analogies and ideas - and sneaks complexity in via the back door).
The Unreasonable Effectiveness of Mathematics in the Natural Sciences, Wigner, http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html
THE UNREASONABLE EFFECTIVENESS OF MATHEMATICS, Hamming, http://ned.ipac.caltech.edu/level5/March02/Hamming/Hamming.html http://ned.ipac.caltech.edu/level5/March02/Hamming/Hamming.h...
(these are perennial favourites relevant to the topic - not claiming they support my conjecture).
- olavk 15y agoIt's philosophically problematic to say that one theory can be truer than another if they both explain the same facts and yield the same predictions. This would mean that there is a notion of truth which cant be verified or falsified experimentally, which really opens the door for all kinds of metaphysics.
- Retric 15y agoLet's suppose you have three theories that fit all known observations. F=MA vs F = (M+1/(10^300))A vs F = (M+1/((10+M)^300))*A If you can't build an experiment that shows that tiny constant perhaps it's meaningless complexity and in some ways less true.
- ignifero 15y agoAll 3 formulas are equally true then. Occam suggests you use the simplest. Just like in programming, where one prefers to write as little code as possible.
- 6ren 15y agoLet's say I have a theory that can explain the complete works of Shakespeare so well, that an algorithm based on it (written in C) can generate the complete works. Now, it turns out that my "theory" is just a printf with a loong string... containing the complete works of Shakespeare. You can measure how "simple" this theory is, by the information content. What if there was another theory (algorithm) that could also generate the works exactly, but was shorter - would you say it's a better theory?