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I agree with the thrust of your post, but not with: Occams Razor is not a statement about the world. It is a tool for thinking. In a world where everything is
by ced 15y ago
I agree with the thrust of your post, but not with:
Occams Razor is not a statement about the world. It is a tool for thinking.
In a world where everything is best fitted by a fifth-order polynomial, scientists who encounter a seemingly linear relationship will think "Oh, what a coincidence. I bet that if we had better observations, those higher coefficients wouldn't be exactly 0." [1]
We live in a world that has:
- Very simple fundamental rules
- A ton of emergent complexity arising from those rules
That's why Occam's razor has a good track-record. Because the world is reducible to simpler laws.
[1] Similarly, Occam's razor does not hold in worlds where gods intervene, because every "coincidence" can have epic, Iliad-sized explanations in terms of Zeus getting mad at breakfast.
- olavk 15y agoIt might be that simpler theories are more often true due to the nature of our universe - but that is not what Occams Razor is about. So its really two different issues.
- ced 15y agoAh, I did not know that the systems of Tycho and Copernic were the same. I think that when most scientists (and bravura above) invoke Occam's razor, it's to pick one of two non-equivalent theories. For instance, the Ptolemaic system made predictions that were, given the limited accuracy of the instruments at the time, indistinguishable from the Copernician system. But I'm quite sure that scientists felt justified in "betting" on Copernic because the equations are simpler, and use fewer arbitrary constants.
- ignifero 15y agoHave to disagree, there is nothing inherently "simple" or "complex" about the world. As humans, with limited reasoning capacity, we tend towards simple representations because they are easy to reason about. So we have to choose our theories to be as brief as possible, but not briefer. There is also an aesthetic element in simple solutions, they are just more beautiful (or maybe we define beauty by the power of its simplicity)
- Locke1689 15y agoAlright, let's pause here and be scientific (i.e., have some semblance of mathematical formalism in this discussion). Do you have any reason to believe that the universe tends towards greater complexity as defined by Komolgorov complexity? It seems that the second and third laws of thermodynamics would suggest the opposite. Edit: pjscott has restated my point more formally lower in this thread.
- ignifero 15y agoThat is true, the universe's Kolmogorov complexity is reducing every moment. The complexity of our theories, though,is a whole different thing. The laws of thermodynamics don't apply to them: they dont become simpler just by time passing. What i was trying to say is that the laws of the universe are not "out there". They are models that live in our brains and are limited by our perceptual capacity. And that "complex" and "simple" are properties we ascribe to our brain processes, not properties of the world.
- deleted 15y ago[deleted]
- ignifero 15y agos/reducing/increasing. My bad
- orangecat 15y agoDo you have any reason to believe that the universe tends towards greater complexity as defined by Komolgorov complexity? It seems that the second and third laws of thermodynamics would suggest the opposite. Kolmogorov complexity is largely the same as entropy, so to the extent that "complexity of the universe" is meaningful, it should be increasing. There's a difference between Kolmogorov complexity and what we think of as useful information: a random sequence of bits has high complexity because it can't be compressed, but it's "useless" because we can't learn anything from it. There are concepts of "logical depth" and "effective complexity" that try to address this: http://tuvalu.santafe.edu/research/publications/wpabstract/200812046 http://tuvalu.santafe.edu/research/publications/wpabstract/2...