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Our Mathematical Universe

  1. Aug 13, 2014 #1
  2. jcsd
  3. Aug 13, 2014 #2
    If you assert that everything mathematical is physical, then you run up against Godel's Incompleteness theorem, and physics becomes incomplete or inconsistent. Instead I prefer to think that we are only imposing a subset of math on physical concepts to produce the laws of physics. This would be something like math imposed on Euclidean geometry which is complete and consistent.
     
  4. Aug 13, 2014 #3

    MathematicalPhysicist

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    Friend, why should we consider it to be complete and consistent?

    Can we really know if the universe has an outside shape?

    Can you really assure me that QFT is consistent, and not trickery math?

    Anyway,we cannot prove either its consistency or its completeness, well if it includes Number theory as a subset of the mathematical theory of physical reality, then by Godel's theorem it's indeed incomplete.
    I really need to find time to reread Smullyan's book on Godel's theorems.
     
  5. Aug 13, 2014 #4

    Demystifier

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    I think nobody really thinks that this hypothesis is true. Well, perhaps only Tegmark, but I suspect that not even him believes it.
     
    Last edited: Aug 13, 2014
  6. Aug 13, 2014 #5

    marcus

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    Well put. I agree. Here's Hossenfelder's classic comment on it:
    http://backreaction.blogspot.com/2007/09/imaginary-part.html
     
  7. Aug 13, 2014 #6
    In other ontologically view point this would not be the case ? we can reach isomorphism betwen model and "realty" ?

    Patrick
     
  8. Aug 13, 2014 #7
    Maybe it's because there are two theorem of Gödel's incompleteness theorems ? This theorem are syntactic not semantic


    Patrick
     
  9. Aug 13, 2014 #8
    Nothing exists outside the universe. The universe is by definition all that exists. Therefore, the universe as a whole is complete by definition of the word universe.

    Nothing that exists in the universe contradicts anything else that exists in the universe. Therefore it is consistent.

    Now all we need is a math that describes this consistency between things that exist.
     
    Last edited: Aug 13, 2014
  10. Aug 13, 2014 #9
    We may already have a model that is isomorphic to reality. Either something exists or is does not, and this can be mapped to true or false. So I believe logic can be seen as isomorphic with reality/existence.
     
  11. Aug 13, 2014 #10

    micromass

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    You are using definitions of the word complete and consistent that are far removed from their mathematical meaning.
     
  12. Aug 13, 2014 #11

    micromass

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    Indeed, I see no reason at all to accept that Number Theory would be included in reality.
     
  13. Aug 13, 2014 #12
    Without language we can't build concept.

    Galileos `Book of Nature : “ The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word."

    Nevertheless I agree, map isn't the territory, even if the language concerned the map but the territory isn't the map. This is not a pipe.

    Patrick
     
  14. Aug 13, 2014 #13
    I'm not so sure. Complete and consistent have to do with axioms of a system being consistent and everything in the system being described by those axioms. That means all the axioms exist in logical conjunction with each other in that system, and no outside axioms are needed to proved anything about that system.

    How is the validity of using the terms completeness and consistency undermined if I choose to use the word proposition instead of axiom? Certainly an axiom is also a type of proposition. Then the system consists of only those propositions in that system, and those propositions exist in conjunction so each of them materially implies any other? As I recall, propositional logic has been proved to be "complete and consistent". If this is valid language, then all one has to do is replace the word proposition with the word fact of reality so that reality is seen as complete and consistent.
     
    Last edited: Aug 13, 2014
  15. Aug 13, 2014 #14

    MathematicalPhysicist

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    Im not sure if you understood me well enough. In one of godels incompletness. It says that if our mathematical theory includes as a substheory robinson's weak arithmetics then this theory is incomplete. Now i don't see any reason to believe that the mathematical framework for physics doesnt include number theory and thus it should be incomplete. As for consisteny of this framework,well we cannot prove a consistency of mathematical theory within that theory. You need a meta theory that will tell you this, and then youll need another meta-meta ad infinitum.
     
  16. Aug 14, 2014 #15
    Certainly we can say that the universe consists of all the facts in it, however you want to label them. But what is making them remain "consistent" with each other? Is the logic that holds them together part of that system? Or is that logic something other than the facts themselves?
     
  17. Aug 15, 2014 #16
    Via Gödel, a physics theory of course could still be a true theory that does correspond to the natural numbers even if you can't prove it.
     
  18. Aug 16, 2014 #17

    MathematicalPhysicist

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    Well first thing first, we have two theorems, one that states that a strong theory which includes number theory as a subtheory cannot prove its own consistency and the other theorem is that such a strong theory cannot be both consistent and complete.

    You mean that they are true statements in the theory that aren't provable in that theory, well, then yes I agree, it does follow from Godel.

    But then again we talked about completeness and consistency of a mathematical theory. (where the physical theory is modeled by sutiable mathematical theory which describes the observables).
     
  19. Aug 17, 2014 #18

    ftr

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    I don't understand what Godel or any mathematical philosophy has anything to do with MUH. We are doing physics just fine with mathematics. The only issue is to find a theory that naturally computes the experimental inputs. That would be sufficient to declare reality being only mathematics. The truth of mathematic and the truth of reality correspond, no other truth exist.
     
    Last edited: Aug 17, 2014
  20. Aug 17, 2014 #19

    MathematicalPhysicist

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    How do you know that there is no other truth? you have some background beliefs which are either believed without regrett as in faith or you are skeptical of.
     
  21. Aug 17, 2014 #20

    ftr

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    No, it is not based on faith it is based on 1000 years of doing science. Many phycisits conjectured such possibility based on evidence. We don't know any other truth in the same way we do science, we have no evidence for it.
     
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