Can "Infinity" ever be more than a mathematical abstraction?

Discussion in 'Physics & Math' started by Seattle, Jun 24, 2018.

  1. Seattle Valued Senior Member

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    Can "Infinity" ever be more than a mathematical abstraction? Without any real world evidence, for me the answer would be "no".

    Yet, our Universe is thought to be flat and without a special topology that would seem to imply infinity. Many concede that the Universe likely is infinite. How can science so readily concede that infinity is a real possibility when there is no evidence of infinity outside of math?

    Here I'm speaking of infinity of space and time and not some situation where the infinity is just do to the framework imposed such as walking around the North Pole and calling space there a Singularity just because the time zones all converge or some such example.
     
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  3. James R Just this guy, you know? Staff Member

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    Everything remains a real possibility until it is ruled out. In addition, in the case of the size of the universe, theory suggests that infinity is a real possibility.

    Philosophically, I don't much like the idea, but I can't rule it out.
     
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  5. Seattle Valued Senior Member

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    Philosophically, I don't rule out unicorns but scientifically I don't place much weight on them because there is no evidence for their existence.

    The only "evidence" for "infinity" is in math and that's usually a marker for something breaking down.

    Theory suggests a "singularity" just before the Big Bang and most scientists consider that to be a break down in the theory and are looking for a quantum theory of gravity to correct that break down.

    It's the same with black holes, a quantum theory of gravity is being looked for to deal with singularities there.

    Yet, with the size of the Universe there doesn't seem to be as much skepticism regarding involving infinity.
     
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  7. Q-reeus Valued Senior Member

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    Haven't yet viewed part 2, but George Ellis is spot on imo with his critique of such, especially cosmological appeal to infinities, part 1 here:
     
  8. Speakpigeon Registered Senior Member

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    As I see it, for every property we can think of, and I would assume finiteness and infinity are both potential properties, we have the two logical options that either it exists or it doesn't exist. I would also assume that the rational attitude to have is to accept you don't know something until you believe you have evidence for it. So, as far as I am concerned, I don't think I or anybody has any evidence either for the existence of infinity or it's non-existence. That's the rational position to have in my opinion (and nothing to do with philosophy).
    Then scientists could try to decide what science is all about. There, it's a matter of consensus although I'm pretty sure you'll always have people with original views. So, yes, the consensus in science could be that infinities are assumed as not existing until proven otherwise. As long as you understand that this can only be a pragmatic move that for all you know may well have to be jettisoned as some point, you'll be fine. In other word, don't get dogmatic on this.
    One aspect of being pragmatic may be that assuming finiteness could be more productive. Possibly, this leads you to deduce potential observables and this may in turn gives you a chance to falsify your theory and therefore make progress. In other words, it may be pragmatically better to assume a limit to have a chance that it will be falsified by experience. But I'm not sure that would work in all circumstances.
    It's only natural for scientists to try to reach a consensus on various aspects of what they do, but it's also natural in my opinion that you will always have individuals who will disagree with the consensus opinion and do their own things. I would assume there's no problem with that. The consensus is what it is and should be proclaimed as such but individuals get to decide for themselves whether they agree with it or not. No need to get dogmatic about this.
    Personally, I believe our attitude to the notion of infinity comes down to our biology. We're apparently very finite beings and we tend to resent wastefulness. We don't like to think of an infinity of things if we can't see the usefulness of them. Then again, we think of the future as open ended. Most likely, that will be because we're unable to decide on any actual end of time, not only for the universe but more importantly for ourselves, at least in normal circumstances. So, we do have one clear notion of the infinite. And we also seem to take space as infinitely divisible by default. This is likely due to the fact that we are unable to perceive with our own senses any granularity in space. So, I would say that if evolution decided that it was somehow better for our survival that we should have at least two clear notions of the infinite, relative to time and to space, I think we should pay attention.
    Then again, perhaps scepticism has been historically the better option to further progress in the sciences. But I don't think anybody knows which way the chip falls as to regard infinities.
    EB
     
  9. mathman Valued Senior Member

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    Infinity is a mathematical concept. What does existence mean?
     
  10. Speakpigeon Registered Senior Member

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    ???
    Same as for everything else:
    The meaning of a word doesn't change when applied to the concept of infinity.
    EB
     
  11. Write4U Valued Senior Member

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    I have a problem with equating the physical Universe with infinity. If it were how could we even begin to speak of the size or shape of the universe, other than as a spherical object with an infinite and expanding 2D surface?

    I wonder if we can separate the universe from another external abstract condition which is basically non-dimensional and timeless, but permittive of an expanding universe, a kind of flexible membrane (for lack of a better word), capable of infinite expansion by the actual universal boundary?
     
    Last edited: Jun 25, 2018
  12. Sarkus Hippomonstrosesquippedalo phobe Valued Senior Member

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    Describing something as spherical implies a point of origin. The universe has no such point. Our observable universe is certainly spherical with us at the centre, but the observable universe is likely but one small, possibly infinitesimally small, part of the greater whole. Need the larger be spherical?? If so, where is the centre?
     
  13. Write4U Valued Senior Member

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    Ok, but then should we not always use the qualified term "observable universe" as being the expanding physical universe within a larger infinite metaphysical Universe?

    And a little aside; does a 3D infinity not have a logical (mathematical) center from which each dimension extends infinitely?
     
  14. someguy1 Registered Senior Member

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    It's interesting to me that modern physics depends crucially on using mathematical infinity. Quantum theory takes place in Hilbert space, an infinite-dimensional complete inner product space. Such a thing can't exist in the real world yet you can't do physics without it.

    Perhaps mathematical infinity is like non-Euclidean geometry. First it was considered impossible. Then it was discovered to be mathematically consistent, but irrelevant to the real world. Finally it turned out to be a vital tool in understanding the physical universe.

    Perhaps infinitary mathematics will come to be seen that way. The genius who figures out that the mathematical infinite is an actual part of our world hasn't yet been born. It's just a matter of time. From negative numbers to the square root of -1, "crazy" mathematics has a way of becoming essential in physical science.
     
  15. Speakpigeon Registered Senior Member

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    Could you explain in a few words what is an "infinite-dimensional complete inner product space" and why it's really necessary in QM?
    EB
     
  16. Seattle Valued Senior Member

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    I get how "crazy" math often becomes useful as an approximation or in the case of imaginary numbers allowing all section in a graph to be used (for example). Infinity can be a shorthand for (a lot of numbers to follow) rather than having to write them all down, infinity in optics means after this point everything further away will be in focus.

    It's when some theoretical physicists seem to (from time to time) take infinities as real that I have a problem...singularities, superpositions, infinite space, etc.
     
  17. Write4U Valued Senior Member

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    Check out Max Tegmark.
     
  18. Seattle Valued Senior Member

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    Max Tegmark is one of the theoretical physicists that I was talking about. He is interesting but ultimately off-base. Actually, I don't think he believes everything he talks about (I could be wrong about that however).
     
  19. Write4U Valued Senior Member

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    Yes , I saw him first briefly on a NOVA program;

    and was initially impressed, but after reading and watching some of his lectures I was becoming a little skeptical as well.
    However I still believe that the fundamental workings of the universe are based on a form of mathematical processing of inherent discreet physical values and functions, which we have been able to symbolize with a mathematical language, mathematics.

    The Fibonacci Sequence is just too pervasive to be ignored as a fundamental mathematical property or potential of spacetime. The Exponential Function is another.
     
    Last edited: Jun 25, 2018
  20. mathman Valued Senior Member

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    This discussion seems to be pointless. The original question asks if infinity can be more than a mathematical abstraction. As far as I'm concerned the same question can be asked of zero or any other number. Physically you can have one item of something, but you can' have one. All mathematical concepts are abstract.
     
  21. Write4U Valued Senior Member

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    Well, perhaps they are human abstractions of real universal values and functions.
    How else can mathematics be so spectacularly successful? We can even make predictons of events at the smallest scales by use of our symbolic mathematical language.

    Are there not many objects which have one value or function in common? Common Denominators?
     
    Last edited: Jun 25, 2018
  22. Seattle Valued Senior Member

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    The number one represents what we normally just call "one"...as in one apple. You can't have a physical number one but you can have one apple.

    Infinity represents something that is without limit but there is nothing in our physical world that is without limit. That is what the OP was about and that's hardly pointless.

    Rather than using infinity as a large approximation it is being used as "if anything can happen it will happen and it will happen infinitely many times". It's being used to suggest that there are infinitely many copies of "you" in another Universe. It's being used in Quantum Physics to suggest Superpositions, the Many Worlds interpretation etc.
     
  23. kx000 Valued Senior Member

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    Time is kept not counted, infinity is nhil.
     

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