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This is Stephen Wolfram’s bet. He thinks the universe is based on simple computation rules. The emergence of complex traits from simple rules still requires ex

by d--b 4y ago

This is Stephen Wolfram’s bet. He thinks the universe is based on simple computation rules. The emergence of complex traits from simple rules still requires exotic mathematics to describe macroscopically.

eloff 4y ago
I’m just a computer guy, but I also see that as likely. When it comes down to it there’s less than 100 elements, made of a handful of forces and subatomic particles that make up the incredible universe that we live in. It seems somehow to get simpler as you go down. Until you hit all the quantum weirdness and then it’s all wave functions and probabilities. That maybe comes out of something simple as well.
- staunton 4y ago
  The first fundamental step in any physics model (or theory) is to separate the easily describable "laws" from the almost impossible to describe "state". The perhaps surprising question is why anything at all can be separated but if that wasn't the case, we wouldn't be having this conversation. "Going down" simply means identifying laws that are more universal in that they can underly models of different systems, ideally "any known system". Quantum weirdness isn't significantly harder mathematically than what came before (we don't have an objective measure of how "hard" some piece of math is), it's just harder to relate to everyday experience. It's similar to how we got used to "masses attract each other" or "things just keep moving in a straight line", which seemed ridiculous to most of Newton's contemporaries.
  - tsimionescu 4y ago
    > Quantum weirdness isn't significantly harder mathematically than what came before (we don't have an objective measure of how "hard" some piece of math is), it's just harder to relate to everyday experience. We absolutely have a way to measure how hard a piece of math is: computational complexity. And quantum mecanichs is more computationally complex than newtonian mechanics (while general relativity is significantly harder still than both of them).
    - Ar-Curunir 4y ago
      > And quantum mecanichs is more computationally complex than newtonian mechanics (while general relativity is significantly harder still than both of them) Is there a formal version of this claim somewhere? (Beyond theorems about quantum computers)
      - deleted 4y ago
        [deleted]
    - explaininjs 4y ago
      Is there any formal proof of this computational complexity ladder you mention? Saying quantum is more complex than classical seems to imply P != NP. I don’t know nearly enough about general relativity to know how complex that is, though I’d have assumed it’d be less than quantum.
    - deleted 4y ago
      [deleted]
    - staunton 4y ago
      Computational complexity is defined for programs with respect to a parameter in the limit where that parameter is large. What's the objectively correct parameter for this comparison that every theory of physics has, after you convert it to a program in the objectively correct way, which you supposedly have?
      - tsimionescu 4y ago
        The purpose of a physical theory is ultimately to derive a prediction of how a physical system will evolve after some time, within a given precision of measurement. The prediction can then be compared to a real measurement of the real system (or several, in the case of statistical predictions). So, we can represent a physical theory as some algorithm A(init_condition, time, precision) = final_condition. Let's call the Newtonian model N and the quantum mechanical model QM. My claim (which I think is completely uncontroversial) is that for the same init_condition, time, precision, you will need more computational steps to arrive at the same final_condition using QM than using N. This is the very definition of computational complexity. If you want instead to compute the asymptotic complexity, we can take either time, precision, or some combination of the two, to be the parameter in respect to witch we compute complexity as a function. Overall, this fact is quite uncontroversial since it is widely assumed that a classical computer requires an exponential amount of time to simulate a quantum computer running the same algorithm, for some algorithms such as Shor's. This is of course not yet proven, but it is widely considered very likely to be true. In fact, if it turns out to be false, it is quite likely that it will also turn out quantum mechanics is in fact reducible to classical mechanics (since the difference in computational speed is due to the special features of quantum mechanics as compared to classical, particularly the complex probability values that it arrives at).

by d--b 4y ago

eloff 4y ago

I’m just a computer guy, but I also see that as likely. When it comes down to it there’s less than 100 elements, made of a handful of forces and subatomic particles that make up the incredible universe that we live in. It seems somehow to get simpler as you go down. Until you hit all the quantum weirdness and then it’s all wave functions and probabilities. That maybe comes out of something simple as well.

staunton 4y ago
The first fundamental step in any physics model (or theory) is to separate the easily describable "laws" from the almost impossible to describe "state". The perhaps surprising question is why anything at all can be separated but if that wasn't the case, we wouldn't be having this conversation. "Going down" simply means identifying laws that are more universal in that they can underly models of different systems, ideally "any known system". Quantum weirdness isn't significantly harder mathematically than what came before (we don't have an objective measure of how "hard" some piece of math is), it's just harder to relate to everyday experience. It's similar to how we got used to "masses attract each other" or "things just keep moving in a straight line", which seemed ridiculous to most of Newton's contemporaries.
- tsimionescu 4y ago
  > Quantum weirdness isn't significantly harder mathematically than what came before (we don't have an objective measure of how "hard" some piece of math is), it's just harder to relate to everyday experience. We absolutely have a way to measure how hard a piece of math is: computational complexity. And quantum mecanichs is more computationally complex than newtonian mechanics (while general relativity is significantly harder still than both of them).
  - Ar-Curunir 4y ago
    > And quantum mecanichs is more computationally complex than newtonian mechanics (while general relativity is significantly harder still than both of them) Is there a formal version of this claim somewhere? (Beyond theorems about quantum computers)
    - deleted 4y ago
      [deleted]
  - explaininjs 4y ago
    Is there any formal proof of this computational complexity ladder you mention? Saying quantum is more complex than classical seems to imply P != NP. I don’t know nearly enough about general relativity to know how complex that is, though I’d have assumed it’d be less than quantum.
  - deleted 4y ago
    [deleted]
  - staunton 4y ago
    Computational complexity is defined for programs with respect to a parameter in the limit where that parameter is large. What's the objectively correct parameter for this comparison that every theory of physics has, after you convert it to a program in the objectively correct way, which you supposedly have?
    - tsimionescu 4y ago
      The purpose of a physical theory is ultimately to derive a prediction of how a physical system will evolve after some time, within a given precision of measurement. The prediction can then be compared to a real measurement of the real system (or several, in the case of statistical predictions). So, we can represent a physical theory as some algorithm A(init_condition, time, precision) = final_condition. Let's call the Newtonian model N and the quantum mechanical model QM. My claim (which I think is completely uncontroversial) is that for the same init_condition, time, precision, you will need more computational steps to arrive at the same final_condition using QM than using N. This is the very definition of computational complexity. If you want instead to compute the asymptotic complexity, we can take either time, precision, or some combination of the two, to be the parameter in respect to witch we compute complexity as a function. Overall, this fact is quite uncontroversial since it is widely assumed that a classical computer requires an exponential amount of time to simulate a quantum computer running the same algorithm, for some algorithms such as Shor's. This is of course not yet proven, but it is widely considered very likely to be true. In fact, if it turns out to be false, it is quite likely that it will also turn out quantum mechanics is in fact reducible to classical mechanics (since the difference in computational speed is due to the special features of quantum mechanics as compared to classical, particularly the complex probability values that it arrives at).