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That is not what occam razor means. It doesn’t say anything about probabilities. It says that if two models give the same predictions, you should chose the simp

That is not what occam razor means. It doesn’t say anything about probabilities. It says that if two models give the same predictions, you should chose the simpler. If the models make the same predictions, neither can be said to be more true than the other. But if there is a difference in falsifiable predictions, this can be used to determine which model is best - but then occams razor does not apply. The most correct model wins, whether or not it is the simplest.

TeMPOraL 3y ago
> It doesn’t say anything about probabilities. It says that if two models give the same predictions, you should chose the simpler. Which is where it becomes probabilistic. The answer to what it means for one model to be "simpler" than another is part of information theory, and that is essentially the flip side of probability theory. Information is (unsurprisingly) counted in bits, and one way of defining "a bit" is as amount of information that cuts your uncertainty by half. > If the models make the same predictions, neither can be said to be more true than the other. But if there is a difference in falsifiable predictions, this can be used to determine which model is best - but then occams razor does not apply. The most correct model wins, whether or not it is the simplest. The point of applying the razor is that, if there's no evidence to support one model over other, your best bet is to chose the simpler one now, because when new evidence comes to light that will favor one over other, it's more likely to favor the simpler one.
- bazoom42 3y ago
  > The point of applying the razor is that, if there's no evidence to support one model over other, your best bet is to chose the simpler one now, because when new evidence comes to light that will favor one over other, it's more likely to favor the simpler one. I highly doubt that. The history of science has plenty of examples where more complex hypotheses turn out to be more correct. E.g Einsteins relativity is more complex than Newtonian mechanics, but nevertheless better matches observations. The current model of the universe is far more complex than the Ptolmaic model, the periodic system is more conplex than the four elements etc. Occams razor applies if two models make the same predictions and therefore neither can be more correct than the other.
  - TeMPOraL 3y ago
    > The history of science has plenty of examples where more complex hypotheses turn out to be more correct. E.g Einsteins relativity is more complex than Newtonian mechanics, but nevertheless better matches observations. Yes, but that's after people made observations that couldn't be explained by Newtonian mechanics. If you were living at the time the latter were formulated, and someone came to you with relativistic equations, showing that their result all line up perfectly with Newtonian ones, but otherwise offering no example of divergence, nor any explanation why the person chose these particular equations - you'd be right to call them a kook and ignore them. After all, there would be no way to distinguish between Newtonian formulation, Einstein's formulation, and an infinite amount of other formulations that also give the exact same results. Ockham's razor makes sense only if some two models in question, which today make the same predictions, can also make divergent predictions that you expect to be testable in the future. The Razor tells you to stick with the simpler one, because it's most likely to remain the best model. The more complex model has more moving parts, requiring more bits of information to identify among many possible variations of same or greater complexity - bits you don't have, because if you had them, you could use them to disprove the simpler model. In other words: the Razor worked for Newtonian mechanics despite Einstein, because a Newton's contemporary couldn't just randomly come up with the exact formulation of relativity we use today, given evidence available then. So whatever theory they would propose, it would overwhelmingly likely be wrong - as in, made bad predictions where Newtonian mechanics still made good ones. > Occams razor applies if two models make the same predictions and therefore neither can be more correct than the other. So to reiterate: Ockham's razor is future-facing; it applies to theories that can generate divergent predictions, but which you can't test just yet. If you expect the two models to always give the same predictions, now and in the future, then... they're literally the same thing, just expressed in different ways. There is no meaningful difference there, and you may just pick whichever one you like more, or whichever is easier to work with.
    - QuantumGood 3y ago
      Thank you both for a great thread.
    - deleted 3y ago

TeMPOraL 3y ago

> It doesn’t say anything about probabilities. It says that if two models give the same predictions, you should chose the simpler. Which is where it becomes probabilistic. The answer to what it means for one model to be "simpler" than another is part of information theory, and that is essentially the flip side of probability theory. Information is (unsurprisingly) counted in bits, and one way of defining "a bit" is as amount of information that cuts your uncertainty by half. > If the models make the same predictions, neither can be said to be more true than the other. But if there is a difference in falsifiable predictions, this can be used to determine which model is best - but then occams razor does not apply. The most correct model wins, whether or not it is the simplest. The point of applying the razor is that, if there's no evidence to support one model over other, your best bet is to chose the simpler one now, because when new evidence comes to light that will favor one over other, it's more likely to favor the simpler one.

bazoom42 3y ago
> The point of applying the razor is that, if there's no evidence to support one model over other, your best bet is to chose the simpler one now, because when new evidence comes to light that will favor one over other, it's more likely to favor the simpler one. I highly doubt that. The history of science has plenty of examples where more complex hypotheses turn out to be more correct. E.g Einsteins relativity is more complex than Newtonian mechanics, but nevertheless better matches observations. The current model of the universe is far more complex than the Ptolmaic model, the periodic system is more conplex than the four elements etc. Occams razor applies if two models make the same predictions and therefore neither can be more correct than the other.
- TeMPOraL 3y ago
  > The history of science has plenty of examples where more complex hypotheses turn out to be more correct. E.g Einsteins relativity is more complex than Newtonian mechanics, but nevertheless better matches observations. Yes, but that's after people made observations that couldn't be explained by Newtonian mechanics. If you were living at the time the latter were formulated, and someone came to you with relativistic equations, showing that their result all line up perfectly with Newtonian ones, but otherwise offering no example of divergence, nor any explanation why the person chose these particular equations - you'd be right to call them a kook and ignore them. After all, there would be no way to distinguish between Newtonian formulation, Einstein's formulation, and an infinite amount of other formulations that also give the exact same results. Ockham's razor makes sense only if some two models in question, which today make the same predictions, can also make divergent predictions that you expect to be testable in the future. The Razor tells you to stick with the simpler one, because it's most likely to remain the best model. The more complex model has more moving parts, requiring more bits of information to identify among many possible variations of same or greater complexity - bits you don't have, because if you had them, you could use them to disprove the simpler model. In other words: the Razor worked for Newtonian mechanics despite Einstein, because a Newton's contemporary couldn't just randomly come up with the exact formulation of relativity we use today, given evidence available then. So whatever theory they would propose, it would overwhelmingly likely be wrong - as in, made bad predictions where Newtonian mechanics still made good ones. > Occams razor applies if two models make the same predictions and therefore neither can be more correct than the other. So to reiterate: Ockham's razor is future-facing; it applies to theories that can generate divergent predictions, but which you can't test just yet. If you expect the two models to always give the same predictions, now and in the future, then... they're literally the same thing, just expressed in different ways. There is no meaningful difference there, and you may just pick whichever one you like more, or whichever is easier to work with.
  - QuantumGood 3y ago
    Thank you both for a great thread.
  - deleted 3y ago