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

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

  1. Write4U Valued Senior Member

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    7,591
    Tegmark does not clain that the universe is math. He proposes that it has only mathematical properties.....difference. On the face of that sounds reasonable to me. I cannot conceive of a universe which does not have mathematical properties. Even chaos is a mathematical term.
    Well, as bookkeeper my maths were an accurate accounting and reflection of the real assets and liabilities of the company, as verified by our yearly inventory count and cash in the bank. This is not trivial.
    I would not compare mathematics to a game, but more to the rules of how a game is played....difference.
    Tegmark says that the universe could not exist unless it followed some form of mathematical function because all physical things in the universe have values and values interact through mathematical functions.
    As to our ability to represent the mathematical values and functions with a symbolic language is considered to be our greatest evolutionary asset. But humans are not the only ones who can perform mathematical calculations. A Lemur and many other species can tell the difference between more and less, and are able to do a form of rudimentary calculus based on that mental ability.
    It is not necessecary for our symbolic language to be reality as long as it can represent universal functions accurately.
    Thank you and suit yourself if you do wish to pursue this perspective.
    I have problems myself with some of Tegmarks presentations, but as have dealt with mathematics for a greater part of my life, I find the concept of a certain mathematical aspect to the very creation and evolution of the universe.
    David Bohm called this progreesion as the "enfolded order" (potential values and functions) becoming expressed in the physical world as the "unfolded order". The word "order" being key.
    Well , perhaps they are right, I am not qualified to judge, but many scientist seem to accept the premise and I can only ask, "how does the universe function if not by some form of mathematics?"
    I haven't read his book either. But I see no other option to his premise and I haven't read anything that can replace the power of mathematics in all of reality.
    All patterns are fundamentally mathematical in essence, as are equations which merely show that one thing has the same value as another thing, but seen from a different persective.
    And to say mathematical structures are very abstract, I recommend this short but delightful Ted Talk by Roger Antonsen, who clearly demonstrates the connection between ratios and reality.
    https://www.ted.com/talks/roger_antonsen_math_is_the_hidden_secret_to_understanding_the_world
    Thank you for the link, I now feel compelled to read it, just to confirm if my first impression is correct.

    And I agree with you that any assumption of a mathematical nature to the universe has nothing to do with infinity per se.
     
    Last edited: Jun 28, 2018
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  3. someguy1 Registered Senior Member

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    Ok I power-watched most of the second half. I confess that I much prefer written text. I can absorb info in text a lot faster than sitting through a lecture.

    I gather that in the end he rejects physical infinity as untestable hence not science. So I'm glad I watched because he's agreeing with me!

    He also did a couple of things typical of the genre that I find annoying. One, he repeated that infinity is "unreachable." But in fact in the past 140 years mathematicians have a very deep and beautiful theory of actual infinity. You cannot in my opinion legitimately talk about infinity without acknowledging what's been going on in modern set theory. And since set theory underlies the formal structure of virtually all modern math; and modern math is the foundation of physics; it's not possible to give a complete account of infinity in physics without incorporating the modern foundations of math. The entire subject is ignored in all these multiverse conversations.

    Second, he repeated the misunderstanding that in an infinite universe you must have infinitely many duplicates. He misunderstands or deliberately ignores infinitary probability, in which an event with probability 0 may still happen, and one with probability 1 might fail to happen. The best you can actually say with certainty is that SOME state recurs infinitely many times, but probably not the state representing you or me.

    So all in all a good summary of the state of the subject, and he agrees with me. Thanks for pointing me at the vid. I'll try to watch more in small doses, there's a lot of good stuff in there.
     
    Last edited: Jun 28, 2018
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  5. someguy1 Registered Senior Member

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    That doesn't mean they ARE the mathematical symbols, or the abstract mathematical objects the symbols describe. You're imbuing notation with ontological power.
     
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  7. Write4U Valued Senior Member

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    7,591
    They don't have to be human symbols, and yes human mathematics are the abstract symbolic representation of values and functions. But even here we need not stay with numbers per se. We can use the decimal system, the english system, the binary system, or morse code, or colors, or even sound waves, or even a geometric object or a pattern to represent a number. This is the power contained in mathematical equations.

    Do see the Roger Antonsen clip. It is short and really entertaining as well as profound in content.

    It makes no difference what symbols we use as long as they are consistent and represent a specific value or function. An abacus works just as well as a computer, it's just slower.
     
    Last edited: Jun 28, 2018
  8. NotEinstein Valued Senior Member

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    1,496
    Yeah, Write4U does that all the time. Coupled with a few misconceptions of reality here and there, and a complete disregard for traditional definitions of words, this leads to a whole bunch of seeming word-salad. It's not, though; Write4U simply hold an atypical philosophical position. He just has severe trouble expressing himself in wording that others can understand, and seems to be unable to change this. Note too that Write4U often doesn't explain things himself; he refers to clips and videos, often misinterpreted by him due to his own views. But using his own definitions, it does make sense, and the clips and videos do support his position.

    So don't be too harsh on the guy; the way you are interpreting what you read, is almost 100% certainly not what Write4U meant to write. He can't help it; he simply has his own language.
     
  9. Speakpigeon Registered Senior Member

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    318
    This is what Tegmark says:
    ..."our physical world is an abstract mathematical structure"?!
    To me, that's pure gobbledygook. So, could you explain what that could possibly mean?
    Here is a clue as to the problem. The definition of the word "abstract":
    Which definition did Tegmark had in mind exactly?
    I guess he might just as well have said that the universe doesn't exist for real. That it's just an idea.
    I would say that before you get into serious stuff you better learn your English.
    And that's just one word, line 4 in the abstract... Not a good start.
    EB
     
    Last edited: Jun 28, 2018
  10. Write4U Valued Senior Member

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    7,591
    I admit that like every one else I use my own language and if, as you say, the links and clips I provide do support my posits, then what is the problem, unless you want to dismiss the links and clips as well?

    If I just post the links and clips I am told to put it into my own words and when I do I am told I don't make any sense except the links support my posits? Now that's weird.
     
  11. Speakpigeon Registered Senior Member

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    318
    Yes, I've given up on trying to make sense of the "word salad" but it appears Tegmark is doing it as well. See my previous post.
    EB
     
  12. NotEinstein Valued Senior Member

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    1,496
    Actually, most people use the same language (i.e. definition of words).

    They only support your position when using your definition of words. They often don't support your position when using the traditional definitions of words. And because you are often unable to give your definition of words, it's difficult for others to see this and understand you.

    This is the exact opposite of what I've said, so I don't know where you got that idea from?

    It's not weird for the precise reasons I just gave. Putting things "into your own words" doesn't really help us understand your language; it is very difficult to learn Chinese when the other person only speaks Chinese. It'd be much more helpful if the other people also spoke English...

    You should try putting things in other people's words; that the best way to get your ideas across.
     
  13. NotEinstein Valued Senior Member

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    1,496
    I don't doubt it; one can always find somebody with weird and inconsistent ideas, and that's certainly not helpful in understanding, no. It's the deliberate cherry-picking of using only that person's views to support oneself (which is an argument from authority as well) that, to me, is more problematic.
     
  14. Write4U Valued Senior Member

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    7,591
    I understand that sentence to mean; the essence of the spacetime fabric contains a form of mathematical logic which determines how physical objects attain actual and potential values (Tegmark identifies 32 values) and how these values interact via certain functions (Tegmark identifies a handfull of equations). I see no inherent problem with that perspective.
     
  15. Write4U Valued Senior Member

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    7,591
    That's funny...and I agree...

    Please Register or Log in to view the hidden image!

     
  16. Write4U Valued Senior Member

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    7,591
    But I also agree that this does not have much to do with the concept of infinity.
     
  17. Speakpigeon Registered Senior Member

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    Your "essence" here is ambiguous:
    I assume you're no philosopher so I would guess you mean "essence" as per the first of these two definitions. So, we're talking not about the reality of the universe but about the way human beings characterise it. The essence of space-time is just the intrinsic or indispensable quality or qualities that serve to characterize or identify the universe. The essence is indeed an abstraction, not the real thing itself, but our representation of it. An essence in this sense is necessarily an abstraction, an idea, not something that would exist out there in the physical world.
    Yet, Tegmark actually says the physical universe is abstract: "our physical world is an abstract mathematical structure".
    So, again, even according to your own interpretation, he says the physical universe is just an idea, not a real physical universe, which of course makes the whole sentence contradictory.

    So, no, the physical world isn't an abstracty structure, mathematical or not, and Tegmark should learn his English or pass for a moron.
    EB
     
  18. Seattle Valued Senior Member

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    3,434
    https://blogs.scientificamerican.co...-insider-tips-for-criticizing-the-multiverse/

    Here's an interesting post/article/response by Max Tegmark addressing comments that his book is "empty" or whatever the various criticisms are. There is nothing earth shaking in this link. It just shows that Tegmark is aware of the issues and shows his state of mind.

    Even in this article however he still misstates (at least in my understanding) some of the choices. Such as "A fourth argument, made in my book, is that if there’s an external reality completely independent of us humans, then there’s a fourth type of multiverse realizing all mathematically possible universes."

    There can be an external reality independent of humans without that implying a "multiverse realizing all mathematically possible universes".

    Of course, when you read his hypothesis you know what he means but without the entire context some of his comments are very misleading.

    Here is a Wiki article (mainly criticisms)...

    https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis

    I realize that the OP was about infinity and it referenced Wegmark and the thread now seems to be mainly about his book but that's fine with me as well (it's better than talking about aliens) and I've included these links to be informational (since I just ran into them myself while looking for criticisms/reviews of his book).
     
    Last edited: Jun 28, 2018
  19. Write4U Valued Senior Member

    Messages:
    7,591
    The way things seem to work in accordance to recurring natural imperatives?
    David Bohm called it the "Wholeness and the Implicate Order"
    https://plato.stanford.edu/entries/qm-bohm/

    But I realize this is now way off from the OP question.
    I read post #4 and was impressed with logic why infinity cannot exist in reality.
    And as I understand the concept, if an equation yields a result of infinity, it is flawed
     
  20. Q-reeus Valued Senior Member

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    3,052
    Yes but goes further. And imo convincingly argues that multiverse advocate claims that bubble universes are born with infinite size ignore restrictions imposed by quantum physics. In particular Heisenberg uncertainty principle. This attention to physically imposed limitations vs assumed idealizations means that our universe, as a presumed 'typical' bubble formed ~ 14by ago, cannot be infinite in size!
    I don't see where that is relevant. Extremely doubtful Ellis is not thoroughly familiar with set theory and much much more. The whole aim is to show that recourse to what he terms essential use of infinities in physics is automatically suspect and should be discarded ab initio.
    Ellis's reference to the 'infinite copies' argument relies on iirc that:
    1: There is no infinitely small i.e. quantum physics means a finite number of possible states in any given finite region.
    2: Large scale homogeneity and the same general physics applies everywhere in a 'genuinely infinite universe'.
    3: Given an infinite number of such regions, 1 & 2 implies infinite repetition of all possible state spaces is inevitable.

    Leaving aside the de facto assumption of a truly infinite universe, I see there is arbitrariness in assigning sufficiently large regions effectively isolated from each other. In GR one could I suppose appeal to cosmic horizons i.e. observable universe as setting such a 'natural' boundary. Horizons per se don't exist in Yilmaz gravity but maybe effective ones can be defined. For either choice there, one thorny issue is how can any such arbitrary region remain even effectively isolated if the time taken for all possible state configurations to repeat is vastly larger than the light crossing time of such an arbitrary region? Which it surely always will be. The relevant Hubble expansion rate has to factored in, unless an unrealistic static infinite universe is assumed. Accelerated expansion may take care of isolation in GR setting, but then you have a heat death and continued matter dilution within any horizon bounded region setting a natural cap on what can occur in a finite effective time.
    Even in an unrealistic boundless static universe setting, in my view natural abiogenesis won't occur in any finite time. See e.g. http://inference-review.com/article/animadversions-of-a-synthetic-chemist
    The statistical 'miracles' that pure chance combinations can work have imo absolute caps no matter how much time and space and entropy gradients etc, is/are allowed.
    Quacker Ellis disagrees, as of course do the great majority of scientists. I have no disagreement re repetition of realistically possible chance arrangements.
    So I searched for infinitary probability and found http://philsci-archive.pitt.edu/1245/1/fim.pdf
    Started reading but quickly lost interest. Maths is only of interest to me as it relates to physics and even then mostly applied physics. The paradoxical examples you cite presumably contain 'hidden clauses'. At any rate I think your criticisms have misread Ellis in all but that 'infinite copies' piece, which as you know he rejects the idea as an actuality anyway.
    Agreed.
     
    Last edited: Jun 28, 2018
  21. Speakpigeon Registered Senior Member

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    318
    What was wrong with the definitions of "essence" I provided? You didn't say.
    So you're just confirming you want to speak your own private language.
    And I don't see that the notion of essence could possibly be tied up with your "recurring natural imperatives". You would need a more general definition, unless you want to exclude the possibility of anyone talking about the essence of God or some such. See?
    Making up definitions on the hoof can't be the easy and trivial task you seem to assume. Dictionary definitions relies on usage by many people over a long time and this is good insurance against ineptitude. You should try it.
    Further, "the way things seem to work" isn't a good start either. How could that possibly fit in with your understanding of Tegmark's sentence? The essence of the spacetime fabric contains a form of mathematical logic which determines how physical objects attain actual and potential values...
    So, apparently, you can't articulate your views. You have to refer us to linked papers.
    You must be kidding.
    EB
     
  22. Speakpigeon Registered Senior Member

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    318
    As I see it, this notion of necessary repetition can only be understood as based on the assumption that the number of all possible states of any given region of space is finite, and this in turn would be based on the assumption that a certain kind of laws apply to the universe as a whole and that these laws can only result in a finite number of different states.
    Yet, the justification for this assumption seems to me to be only that our own model of the universe is what it is. So, at best, all you may be able to say is that any model, of the kind of models we happen to have now, is self-contradictory if it includes infinity. Yet, I don't think that's even what Ellis is saying. Rather, he seems to be arguing on broadly common-sense grounds, i.e. that the idea of a universe with an infinite repetition of identical regions and histories is not appealing to him and shouldn't be appealing to anyone with minimal common-sense, or that in effect it's a finite universe.
    Now, beyond what Ellis may be saying, as I see it, that the particular kinds of models of the universe we may have now implies repetition is irrelevant as to the whole universe. If the universe was effectively infinite, our model itself would be finite in essence anyway because based on our observation of a limited region of the universe. But then, there doesn't seem any good reason to just assume that the models we happen to have now are valid beyond the limited region of the universe we are able to observe.
    And on the more general idea of the reality of infinities, beyond the models of the universe we may have now, I fail to see why we would need to have a repetition of states or histories of states over distant regions of space and time. There's just no logical reason to think that an infinite universe would need to feature repetition.
    There's a similar situation I think with the particular question of whether space may be infinitely divisible. As I understand it, there's no scientific experiment proving the existence of something like the shortest distance between two points in space. Now, if space was infinitely divisible, i.e. continuous, then even a quantified physics wouldn't necessarily lead to repetition.
    EB
     
  23. C C Consular Corps - "the backbone of diplomacy" Valued Senior Member

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    1,882
    The term is just an unnecessarily obfuscated or mysterian way of declaring that "more" can be added / outputted either continually or intermittently upon the "need" of the process, user, etc. If the "indefinite magnitude which does have a definite and fixed orientation toward endless growth" is converted to something concrete or ontological, then obviously it can't refer to a completed, static condition without being contradictory. As it then becomes finite: A definite boundary or set measurement no matter how ludicrously large in extent or quantity.

    From a purely practical standpoint, one might refer to whatever principle, algorithm, formulaic operation, systemic procedure, etc it is that is open to perpetually engendering "more" amount, extension, division, nested patterns, etc as... "infinity". Since in an abstract kind of way it would contain the potential of all the endless _X_ that is falling out of it or could be engendered by it. But "real-world" wise the expression otherwise cannot refer to a static, completed condition or final product unless it is one of us everyday, rational dunce "you, me, or theys" being blithely unconcerned about conflating two opposite characteristics in conversation. I..e, being too dense to be receptive to or affected by what otherwise be the stressful effects of cognitive dissonance. No professionals, including scientists and philosophers, are devoid of such rational dunce moments or even prolonged worldviews wallowing in the "ecstasy" of internal conflict.

    ~
     
    Last edited: Jun 28, 2018

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