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Have to disagree, there is nothing inherently "simple" or "complex" about the world. As humans, with limited reasoning capacity, we tend towards simple represen

Have 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 ago
Alright, 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 ago
  That 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 ago
    s/reducing/increasing. My bad
- orangecat 15y ago
  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. 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...
  - Locke1689 15y ago
    Your paper is interesting and now that I think about it you may be right about your formulation of entropy, however do you have any resources that are more rigorous? To be clear, I didn't mean to suggest that the universe itself had decreasing Komolgorov complexity, but that the laws that govern the increase in complexity are relatively simple. That is, the laws of thermodynamics concisely phrase the increasing entropy of the universe with a low Komolgorov complexity, suggesting that the mechanics of the universe operate with a low Komolgorov complexity.
    - orangecat 15y ago
      do you have any resources that are more rigorous? For light bedtime reading, there's An Introduction to Kolmogorov Complexity and Its Applications: http://www.amazon.com/Introduction-Kolmogorov-Complexity-Applications-Computer/dp/0387948686 http://www.amazon.com/Introduction-Kolmogorov-Complexity-App... That is, the laws of thermodynamics concisely phrase the increasing entropy of the universe with a low Komolgorov complexity, suggesting that the mechanics of the universe operate with a low Komolgorov complexity. I'd agree with that.
      - ignifero 15y ago
        That's only true at a macroscopic level, though. If one wants to predict exact states of the universe, the complexity is proportional to the entropy of the universe.

Locke1689 15y ago

Alright, 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 ago
That 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 ago
  s/reducing/increasing. My bad
orangecat 15y ago
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. 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...
- Locke1689 15y ago
  Your paper is interesting and now that I think about it you may be right about your formulation of entropy, however do you have any resources that are more rigorous? To be clear, I didn't mean to suggest that the universe itself had decreasing Komolgorov complexity, but that the laws that govern the increase in complexity are relatively simple. That is, the laws of thermodynamics concisely phrase the increasing entropy of the universe with a low Komolgorov complexity, suggesting that the mechanics of the universe operate with a low Komolgorov complexity.
  - orangecat 15y ago
    do you have any resources that are more rigorous? For light bedtime reading, there's An Introduction to Kolmogorov Complexity and Its Applications: http://www.amazon.com/Introduction-Kolmogorov-Complexity-Applications-Computer/dp/0387948686 http://www.amazon.com/Introduction-Kolmogorov-Complexity-App... That is, the laws of thermodynamics concisely phrase the increasing entropy of the universe with a low Komolgorov complexity, suggesting that the mechanics of the universe operate with a low Komolgorov complexity. I'd agree with that.
    - ignifero 15y ago
      That's only true at a macroscopic level, though. If one wants to predict exact states of the universe, the complexity is proportional to the entropy of the universe.