[jackson1372]

> we have to assume some sort of isomorphism between the map (our theory) and the territory (the world)

But a mathematical model != a theoretical model. The very same mathematical model will be compatible with uncountably many theoretical models. (By 'theoretical model' I mean something like 'an interpretation of what the math is representing'.)So you can't read off theoretical structure from mathematical structure. And so you can't read off the structure of the world from mathematical structure.

[lmm]

> (By 'theoretical model' I mean something like 'an interpretation of what the math is representing'.)So you can't read off theoretical structure from mathematical structure. And so you can't read off the structure of the world from mathematical structure.

Occam's razor favours a theoretical model that corresponds more closely to the mathematics, rather than one that adds a bunch of epicycles to arrive at a different interpretation. If you follow your logic then you can never reject geocentrism, because it's possible to create a geocentric model that generates the same predictions as a heliocentric one; nevertheless we would generally say that heliocentrism is "more true" and "more physically real" than geocentrism.

[alien_at_work]

What Occam's razor favours is irrelvant. It has no predictive power [1]. The more complex answer is just as likely to be the correct one.

[1] http://scienceblogs.com/developingintelligence/2007/05/14/wh...

[lmm]

Physics tends to be simpler than we originally thought, and Occam's razor correctly predicts this: electricity, magnetism, and light turn out to be facets of the same phenomenon, electricity and the nuclear forces turn out to conform to the same theory, electromagnetism, gravity, and spacetime turn out to behave in the same way. Your link's lazy "11 dimensions! OMG!!!1one" non-argument is in no way an adequate refutation of that history.

[alien_at_work]

You're cherry picking. You pick the places where Occam's razor picks the correct answer and ignoring all the places it doesn't. For any new situation we can't predict which of those possibilities the answer will fall. Hence my statement that Occam's razor has no predictive powers.

I just linked to the first article I found that talked about the subject. And it's interesting that you look for something lazy instead of addressing more serious issues like Newton's model vs Einstien's. Very clearly the (much!) more complex answer is more correct than the simple one. Here's [1] another link discussing the issue and gives 2 examples.

[1] http://neuralnetworksanddeeplearning.com/chap3.html Search for "Occam"

[lmm]

> I just linked to the first article I found that talked about the subject. And it's interesting that you look for something lazy instead of addressing more serious issues like Newton's model vs Einstien's.

You should give links you're willing to stand by. I didn't go looking for something lazy, I went looking for talk about fundamental physics (where Occam's Razor is appropriate, and what we're talking about) and found only the barely even wrong throwaway line about M-theory.

> Very clearly the (much!) more complex answer is more correct than the simple one.

Newton and Einstein don't make the same predictions. When you include the amount that you'd have to add on to Newton's theory to generate the predictions Einstein gives you about the behaviour of light, Einstein ends up simpler.

> Here's [1] another link discussing the issue and gives 2 examples.

The "new particle" example shows the opposite of what's claimed. Bethe's only reason to dismiss a new particle as an explanation was Occam's razor. The part about Newton/Einstein is just wrong about the history; relativity wasn't developed as an effort to explain the orbit of Mercury, it was developed out of Maxwell and Lorentz's work on electromagnetism. A universe in which the only reason to believe relativity was those deviations in the orbit of Mercury probably would be a universe in which the true theory was Newtonian gravity with small correction terms, not a universe in which relativity was true.

[alien_at_work]

>Bethe's only reason to dismiss a new particle as an explanation was Occam's razor.

Thank you for pointing out the other fault of Occam's razor: both sides of most arguments tend to assume the razor is on their side. This aspect was addressed in the second article I linked.

[jackson1372]

But what does 'corresponds more closely to the mathematics' mean? The relevant point is just that the mathematics, alone, doesn't settle the theoretical question.

In general, it's hard to use Occam's razor in a non-question-begging way.

[lmm]

Well, the mathematics describes reality. If humans can't agree about whether one way of interpreting the mathematics in human terms is more or less complex than another way of doing so, then that's a human problem and potentially insoluble. But I don't think things are actually that bad: people are generally capable of reaching consensus about what a given piece of mathematics "means", and the relevant cases here are pretty clear-cut: either we interpret the wavefunction as being physical reality, or we interpret some derived structure as being physical reality, and the latter gets us further away from the wavefunction.