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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    20,043
    LOL, I did and you complained because I showed you that I was right.

    I understand very well what you are stating, but you are so far from understanding what I am stating that it is almost discouraging. You have a narrow vision, perhaps it is time to expand it.

    If you want to talk about infinity then you better treat the term and its implications with a little more respect and humility than you have so far.

    Infinity is not a number, it is a value.....and the human symbol for that value is:

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    Don't see that number in the decimal system do we?......

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    Last edited: Jul 15, 2018
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  3. Speakpigeon Valued Senior Member

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    Sorry, you're not making sense, here.
    EB
     
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  5. Speakpigeon Valued Senior Member

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    That's just not true. What carries "an infinite amount of information" isn't the physical number itself, which is just the physical quantity, but our particular representation of it in terms of symbolic numbers and in a way which isn't computable.
    It just means our representation isn't very good, which should not really come as a surprise since it's not the physical world itself.
    Elements in a continuum just come one after the other without a care about our mathematical distinctions. So, what could be the import of our distinction between integer, rational, irrational, computable, non-computable numbers on the elements of a physical continuum. Why would there be a difference in nature between those elements?
    No. That's not true.
    We do need an infinite amount of information to express a non-computable number in terms of a computable number. That's true but the reverse is also true. We need an infinite amount of information to express a computable number in terms of a non-computable number.
    Second, we in fact only need a finite amount of information to express a non-computable number, as long as we do it in terms of another non-computable number and provided it is properly selected (and there's at least a countable infinity of appropriate non-computable numbers to choose from).
    So, why exactly should non-computable numbers be of a different nature?
    All there is is a mathematical bizarrerie that has no effect on the physical world because mathematics isn't the physical world.
    And the bizarrerie is entirely due to our epistemological perspective. It's been just convenient for us to use numbers the way we have done so far. It's a practical problem. We started out counting on our fingers. That's all there is to it. We've extended our arithmetic beyond its provincial origin and now we find there is a bizarrerie? We can't properly describe the universe just by counting on our fingers? Well, too bad.
    No, I don't accept that premise because you still haven't explained what it would mean for a non-computable number to be instantiated and what would be the physical difference between an instantiated number that would be computable and one the wouldn't be computable.
    EB
     
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  7. Write4U Valued Senior Member

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    It's not a number, it is a symbolic representation of a value which has no beginning and no end. It is a value of the "Wholeness and the Implicate Order" as theorized by David Bohm, who called it "insight intelligence", but was speaking of a hierarchy of orders or pseudo-intelligent mathematical constants from which "enfolded" probabilities become "unfolded" in reality. The symbol we choose was for the value (1 possible workable model) of an endless continuity in the existence of the expressed physical and metaphysical reality and which yields an equation to the value of the Wholeness.
     
    Last edited: Jul 15, 2018
  8. Speakpigeon Valued Senior Member

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    1,123
    Could you give actual examples of the ""confusion" you're talking about?
    I want convincing quotes from well-known scientists with the appropriate link to check if necessary.
    EB
     
  9. Speakpigeon Valued Senior Member

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    1,123
    Sorry, you're not making sense, here.
    EB
     
  10. Write4U Valued Senior Member

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    20,043
    https://www.merriam-webster.com/dictionary/number

    OTOH:
    https://www.merriam-webster.com/dictionary/value

    I think this describes pretty well the areas which are common to both terms and definition, but also the areas which give each unique and independent aspects in and off themselves.
     
    Last edited: Jul 15, 2018
  11. Speakpigeon Valued Senior Member

    Messages:
    1,123
    Could you give actual examples of the ""confusion" you're talking about?
    I want convincing quotes from well-known scientists with the appropriate link to check if necessary.
    EB
     
  12. someguy1 Registered Senior Member

    Messages:
    727
    You make some excellent points. I don't claim to know all the answers or even understand the questions. I'll just toss out some thoughts.


    Hmmm, yes, I have to agree. If there are pointlike thingies "out there" and we agree that out measurements are not inherent in the things themselves, then this is a very good point. After all, you can take any noncomputable number and translate it (by a noncomputable distance) and bring it to a computable location on the number line. So the noncomputability doesn't actualy inhere in the point itself, but rather in our description of it.

    Now I happen to believe this, or at least believe that it's possible. That these "values and functions" that @Write4U talks about are not properties of things, but rather properties of our measurements. When we measure the frequency of red light, we're not measuring a quality of the photons, but just imposing our own minds and lab apparatus on reality, and telling ourselves we're measuring something "out there."

    This goes against a lot of what scientists believe, that we are measuring what's "out there." I don't know the answer to this one. But if we accept that there are undifferentiated mathematical points "out there", then it doesn't matter if we label some of them noncomputable. Perhaps you're right.

    I think the argument against the physical existence of noncomputable quantities is an argument against the CUH and the Church-Turing-Deutsch thesis. You noted earlier that these aren't necessarily true, and I agree. But a lot of people believe them; and to the extent that people believe them, it's fair to note that the idea of computability and the idea of continuity are somewhat at odds.


    Semantic quibble, between any two points there's another one. They don't come one after another. Think maple syrup, not bowling balls.

    Good point, if we agree that science doesn't describe reality, it's only something we're making up about things we can never name or understand. Your viewpoint is extreme here. Not wrong of course, but it will put you into some trouble with those who think science is about studying what's "out there." If we can't apply everyday notions of mathematics to the world, that undermines all of science. You should think about this and tell me if you take this as a reasonable criticism.

    Yes but I'm lost because you just denied that concepts like rationality or being an integer even apply to the real world. I hope you see that while you might be right, that position undermines science. You have to make sure you understand the implications of your own idea.

    Yes that's true, but plenty of pairs of noncomputables are NOT computable multiples of each other.

    If the noncomputability lies only in our minds or labeling or notation, no difference at all. So if math is only in our minds and not in the objects themselves, you are going to have an army of scientists to argue with. I'll just sit back and watch.

    Now you're joining me in arguing against Tegmark. I suspect your viewpoint and mine are not that far apart.

    I tend to agree. But Tegmark and many others think the math is "real" in some way. I'm arguing against that point of view and now you're arguing with me, so I'm pretty confused. But your points in this post are correct, or at least valid.

    I'll leave that to those who claim they can be.

    If there's a physically intantiated noncomputable quantity, we could never measure it and we could never even write a program to approximate it. I'd say that would be a problem for science and a fatal blow to the Tegmarkian "the world is mathematics" point of view.

    But I'm in way over my head now. I agree with most of what you said here.
     
  13. arfa brane call me arf Valued Senior Member

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    7,832
    Actually infinity is neither a number nor is it a value. You might be able to argue that infinity is uncomputable, but not that it's an uncomputable number (since it would then have a value, even an uncomputable one).

    I think it makes more sense to talk about the complexity of numbers, as Chaitin does, in terms of algorithmic complexity. That is, roughly, how complex an algorithm needs to be to specify a given number. Algorithms then describe those numbers we can obviously compute, so those numbers which are germane to science, to 'measurements' etc.

    But just as obviously, not all numbers. AC lets us throw the darts, type of thing.
     
    Last edited: Jul 15, 2018
  14. Write4U Valued Senior Member

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    20,043
    Well, you see, "if I can't speak directly to the scientist, I don't bother"; your words.
    I gave you Webster's definitions on both terms. Ibelieve that should suffice.
    What you are espousing here is Tegmark. Now do you understand the meaning of being confused about the difference between values and numbers?
    We don't observe the numbers, we observe the expressed values. What is the number of water, air, fire, earth, a square, a circle, a rectangle? Those are all properties of the elements and mathematical patterns. The value is the expressed reality as an object.
     
    Last edited: Jul 15, 2018
  15. Write4U Valued Senior Member

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    20,043
    Is that not what I said? Infinity's value is not a mathematical value, it's value lies in infinite potential or permittivity, it is a timeless uncountable physical state, which apparently resulted in the emergence of the universe.
     
  16. someguy1 Registered Senior Member

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    727
    Well as it happens that's another thing I have a mathematically-influenced opinion about.

    Now you claim that infinity apparently resulted in the emergence of the universe. That's quite a statement.

    But when you say that infinity is "a timeless uncountable physical state," first, you're ignoring the mathematical definition of infinity; and second, you are making yet another metaphysical claim: That you know what resulted in the universe. I'm sure you do. But that's not a rational position that can be argued against. It's essentially a theological claim. As such, it may be properly ignored in scientific discussions.

    But when you define infinity, you are saying either that "I know all about the work mathematicians have done on infinity in the past 140 years and I choose to completely ignore it." Or, you are simply ignorant of said work.

    Mathematicians can define what it means for a set to be infinite. They study a huge hierarchy of levels of infinity, transfinite cardinals and ordinals, infinite numbers so big they can't even be proved to exist.

    Now you might say, "Well, that's not the infinity I mean." Or you might say, "Oh really? Tell me more."

    So please tell me where you're coming from. Are you making an essentially theological point? Or perhaps you have not seen the mathematical definition of infinity.

    Here it is. A set is infinite just in case it can be put into one-to-one correspondence, called a bijection, with a proper subset of itself. So the natural numbers 0. 1, 2, 3, 4, 5, are infinite because as Galileo noted in 1638, they can be placed into bijection with the perfect squares 0, 1, 4, 9, 16, 25, ... And the set {a, b, c, d, e} is finite because there is no such bijection, as you should verify.

    So just let me know why you're waxing poetic about a concept that's been mathematically tamed and formalized for 140 years.

    https://en.wikipedia.org/wiki/Galileo's_paradox
     
    Last edited: Jul 16, 2018
  17. Write4U Valued Senior Member

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    It must have been bed-time......

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    But I must admit that I have never prayed in my life.. I am an atheist and stating that the universe apparently emerged from the implicated mega quantum event the instant of the BB, is not necessarily a theological claim.

    IMO, a theological claim must include a sentient motivation, else it is just an unknown permittive condition.
     
    Last edited: Jul 16, 2018
  18. Speakpigeon Valued Senior Member

    Messages:
    1,123
    Could you give actual examples of the ""confusion" you're talking about?
    I want convincing quotes from well-known scientists with the appropriate link to check if necessary.
    EB
     
  19. Speakpigeon Valued Senior Member

    Messages:
    1,123
    Sorry, you're not making sense, here.
    You appear to be terminally unable to explain yourself.
    EB
     
  20. Speakpigeon Valued Senior Member

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    1,123
    Infinity is initially an attribute. The attribute of a number. We say for example that there's an infinite number of points or that time is infinite because we assume there's no limit to the number of seconds in the future. It's the number of points or of second which is infinite, so infinity is first and foremost an attribute.
    As such, it may also be a proper quality, for example if there is an actually infinite number of points in time or in space. In this case, to the attribute of infinity that we ascribe to time or space would correspond an actual infinite number of points in time or space. In this case infinity would be something like a quality or property of the physical world.
    If so, there's also no difficulty in considering infinity as a number, provided we can conceive a consistent way of dealing with infinity as a number. We already have special numbers, such as 0 and 1, primes, Integers, Reals etc., so why not infinity. That's something for mathematicians to consider. No need to be dogmatic about that.
    But I agree infinity is not a value, except if by value we just mean number. For example, the value of the function 1/x when x tends towards zero could be said to be infinity.
    EB
     
  21. arfa brane call me arf Valued Senior Member

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    7,832
    I agree with the first, but not the second statement.
    For instance, where is the center of the "external" face of a planar graph?
    Where is the point at infinity on the Riemann sphere?

    Infinity looks a lot like a place, rather than a value, or any kind of number.
    Because of continuity.
    Yah. Or there might not be an actual infinity of points, space and time might be discrete, not continuous (after all, we will only ever know about real intervals of either, which means measureable intervals).
    A difficult task, since infinity is also some attribute of location (i.e. where is infinity? not how big is it).
    There ya go.
    Now you're talkin' (about limits of functions, and again, continuity).
     
  22. iceaura Valued Senior Member

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    30,994
    In an attempt to keep it as simple as possible with an example, this post:
    It's an honest question. One of the possible answers is "no" - that since the correspondence of the number 2 to some physical situation is contingent on assumptions or conventions known to be ad hoc or heuristic rather than theoretically unalterable and uncontradictable reality, the number "2" is a mathematical abstraction only.

    The relevance would be that "infinity" and "2" share the same reality.
    My own guess is that math works as material from which we can construct virtual sensory organs we lack, and that perception via math is essentially equivalent (in its relationship with reality, whatever that may be) to perception via sensory organ. So that we can "see" infinities - they are as real as densities, masses, temperatures, wavelengths, pitches, colors, etc.
     
  23. phyti Registered Senior Member

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    732
    Speakpigeon #255;
    ---

    Life is supported by the local portion of the universe and continues independently of the astronomically distant portions. There is no need of a larger universe.

    The mathematician will tell you a finite interval of the 'real' number line contains an 'infinite' number of points. The truth of the statement depends on the physical existence of a continuum

    corresponding to the mental concept of a continuum. Chemistry demonstrates matter is discrete, and measurements depend on physical objects as references. Energy is also quantized and does not have a continuous spectrum. This supports the conclusion that measurements will be finite. Plank solved the 'black body' problem with h. Where is the need for anything continuous?

    example:

    1. Divide a pile of 1000 seeds into 3 equal piles, the 'real' number fans will give you, 333.33 seeds per pile. The 'integer' fans will give you 2 piles of 333, and 1 pile of 334.

    Which answer is 'real'? The problem says divide the pile, not the seeds.

    2. Divide a metal rod 4" long into 2 equal length pcs. Are we sure there are the same number of molecules in each half? When a rod is cut, does the cut fall between molecules? (can't cut molecules)

    3. An engineer can specify a dimension to 3 decimals, but can it be formed to exact specifications? No, they only work with 'significant' digits.

    4. Approximations such as non-rational numbers, pi, e, ... etc, are always incomplete, and become meaningless after the decimal positions become smaller than the diameter of a fundamental particle.

    When we count, the integers correspond precisely to the quantity of things counted.

    So what is 'real' in the world of measurement?

    Hopefully this clarifies my position regarding infinity, it can't be quantified, nor conceptualized by the finite mind. The one ended stick can never be measured if the 2nd end can't be found!

    The continuum, you can't make something from nothing (unless you're a supreme being).
     
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