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Does the word exist as a mathematical structure?

  1. Jul 9, 2008 #1
    Max Tegmark develop a hypothese in which physical reality is equated as being a mathematical structure, and further it is proposed that every mathematical structure itself is a reality on it's own.

    To look up this idea, see these threads:
    http://en.wikipedia.org/wiki/Ultimate_ensemble
    http://en.wikipedia.org/wiki/Mathematical_universe_hypothesis

    Note that (although the form of the idea is quite new) this idea is not very distinct from the idea's of the Greek philosopher Plato.

    This idea has met many criticism.
    One important objection one could raise is that mathematical structures, as seen as information, can not exist on it's own merits, but needs to be denoted in some (material) form. Which would lead to the conclusion that at least something different then information must exist to carry the information.
    This would lead to the idea that reality = physical reality + information.

    Many other objections have been put forward, as for instance the objection that the universe is not a set or mathematical structure.
     
  2. jcsd
  3. Jul 10, 2008 #2
    Isn't mathematics just an unambiguous language with large component simplicity for describing quantities, relations and so on?
     
  4. Jul 10, 2008 #3
    Yes. Indeed it is. I would add "And it is an invented language".

    Max Tegmark's idea is nonsense. It is a Platonistic delusion of a kind that seems to be shared by many mathematicians. A mathematician correspondent of mine has told me that "Some people who discover mathematics in their young age immediately tend to see it as a reality on its own. These people usually become mathematicians. In my experience, every mathemacian is a Platonician. I don't know a single one who is not." I believe him. For example Roger Penrose's book "Road to Reality" supports this belief.

    Are we not all susceptible to delusions of a similar kind about subjects that we are proficient in, admire greatly, or that fascinate and mystify us? For example that polemicist Richard Dawkins has written an entire book about one such delusion, namely that of the Theist variety. It seems to me that reality is mysterious enough withot adding a mathematical dimension to it.
     
  5. Jul 10, 2008 #4
    I don't think that the idea of mathematics being the real reality is true, but then, how would one proof that?
     
  6. Jul 10, 2008 #5
    If you were out walking in the woods and a wild primary number, say "7", jumped out from behind a bush and bit you, you'd be justified in accepting the reality of mathematics. Otherwise, don't believe what you read about its reality.
     
  7. Jul 10, 2008 #6
    Yes, quite obviously.

    But that is not what I meant. The idea is based on the fact that mathematics has been very successfull in describing the reality in theoretical physics.

    But then the thought error is that physical reality does not equate to mathematical reality.

    But this then would involve proving that certain aspects about reality can not be described in mathematics, but I don't see an easy way to proof that.

    Besides the fact that mathematical structures, as regareded as information, must have some physical form, and if all reality would only be in the form of mathematical structures, there is obviously no 'place' to write that information on.
     
  8. Jul 10, 2008 #7
    Invented language? Of course it is an invention. All languages are! What would they else be? Also note that, that which mathematics describe is not an invention, just like that which natural languages describe are not invented.
     
  9. Jul 10, 2008 #8
    Apart from the (human invented) notation, are mathematically entities "discovered" (I guess most of them are) or are (some of them) "invented"?
     
  10. Jul 10, 2008 #9
    No matter how well mathematics can describe physical reality, it's accuracy would still remain a testament only to the quality of the language, not to a statement of literal fact. Therefor, there is no need to show any aspects of reality that cannot be described. Furthermore, even if we did find something that mathematics could not explain, a brilliant mind must simply invent a knew language (Issac Newton).

    The only 'discoveries' that a mathematician can make would be those lying within the existing invented framework of the language. You could discover aspects of a certain existing framework, but a new framework must be invented.
     
  11. Jul 10, 2008 #10
    About the existence of math...

    It seems clear that what does not exist does not matter to anything. The implication of course is that whatever matters must exist. And since mathematics matters (at least to mathematicians) then it must exist as well. This does not necessarily make it a "physical" reality, whatever that may be. But concepts do exist, concepts are real. What is arguable is the exact nature of concepts.
     
  12. Jul 10, 2008 #11
    "Chairs" and the mathematical equivalent are arbitrary social constructions. Chairs, and their mathematical equivalent, are not.
     
  13. Jul 10, 2008 #12
    Re: About the existence of math...

    Good point. Getting close to the crux of the matter I think.
     
  14. Jul 11, 2008 #13
    Exactly my sentiments. But mathematicians like to argue that their subject is not an invented language, but somehow part of 'reality', waiting out there to be discovered by any intelligence that happens to evolve. Which strikes me as sheer nonsense.
     
  15. Jul 11, 2008 #14
    Cats are real. In practice and in principle it is impossible to fully describe a cat with mathematics. Is this the proof you need?
     
  16. Jul 13, 2008 #15
    I think quantum mechanics would contest that, there is nothing intrinsically about a cat which can not be satisfactory described in quantum mechanics.
    But that deals only with the physical aspect of cats.
     
  17. Jul 13, 2008 #16
    Their notation (ie. the mathematical language) is invented, their subject might not be.

    There are some good arguments to assume that (part of) mathematics is merely discovered, not invented.
    Like we discover physical laws and physical elements and particles.
     
  18. Jul 14, 2008 #17
    Obviously the subject isn't. Math's primary purpose is to describe physical phenomena from the number of apples in a basket to the speed and trajectory of a particle.

    Once the basic rules were set down for the language the next step is obviously to explore its usability and look for interesting patterns. You can easily invent something and find that it has interesting uses and extensions you may not have thought of in the first place.
     
  19. Jul 14, 2008 #18
    Its not such a crazy idea. Quantum mechanics is basically matter/energy described in terms of mathematical probability. Before the superposition decoheres the measured particle has no definable properties; so it can be said the material itself does not exist.

    If we can express matter/energy in terms of not existing when in superposition, and we can accurately express all the physical laws with mathematics then perhaps the universe is a mathematical constuct.
     
  20. Jul 15, 2008 #19

    baywax

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    The operative words here are "we can express". Expression requires a physical state and a physical state is required to observe "superposition" as well as to express it in a mathematical model. This sort of duality of states (many worlds?) begs explanation.

    We can't observe a quantum state without the contrast and comparison of our emergent state, can we? So, which came first? Which is fundamental? Did we invent the quantum state through our observations of the emergent states and our overlay of maths on it?
     
  21. Jul 15, 2008 #20
    Hi baywax,

    "The operative words here are "we can express". Expression requires a physical state and a physical state is required to observe "superposition" as well as to express it in a mathematical model. This sort of duality of states (many worlds?) begs explanation."

    Okay perhaps i worded it sloppily using as "we can express". Howabout if the universe can be explained completely mathematically, then it seems logical that maths can actually create the universe. I personally don't buy MWI but what i would say is that a qm superposition even in standard Copenhagen is considered to be a probablity wave. So in esssence there is nothing there but abstract possibilities - until decoherence/wave collapse occurs.

    "We can't observe a quantum state without the contrast and comparison of our emergent state, can we?"

    No. I mean once we make the observation/measurement we get the emergent result.

    "So, which came first? Which is fundamental? Did we invent the quantum state through our observations of the emergent states and our overlay of maths on it?"

    Interesting. I think the real maths - whatever it is - behind qm is fundamental. Whether we only have an approximation of it i dont know. But what qm maths appears to tell us is that something can define itself into our sense of reality; having only an instance before been nothing more than a possibility. The reason why i point to qm maths as circumstantial evidence of the op is because it more or less describes matter and energy popping into and out of existence. If matter can be a maths abstract then so can the whole universe.

    Im not saying this is for sure just speculating :smile:
     
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