Does mathematics really exist in nature or is math just a human construct?

Discussion in 'Physics & Math' started by pluto2, Dec 2, 2015.

  1. Write4U Valued Senior Member

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    I do try to be objective. But I don't see how that translates into,
    Allow me a question: is the Universe an expression of logic (a reasoning system) or mathematics?
     
    Last edited: Jan 26, 2016
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  3. expletives deleted Registered Senior Member

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  5. Write4U Valued Senior Member

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    Sorry, I was late in editing my previous post. I'll ask that question again; Is the Universe an expression of logic (a reasoning system) or mathematics?
     
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  7. expletives deleted Registered Senior Member

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    Sorry, Write4U, but my last response got mangled by the system when I tried to edit to include the further response to your own edit addition. Will rewrite it all again (the system won't let me copy-paste what I wrote before, so it will take a few minutes to write it all out again). Here is that lost post again:

    That last sentence in your quoted reference states clearly that Logics is indispensable to making the mathematical axiomatic and definitional work properly to output logical and consistent proofs and resultants. Else mathematics, as a distinct and independent system would be just another il-logical and arbitrary system of unreasoning without any rhyme or reason to its process and results.

    Neither. Consistent with my previous argument and opinion, the Universe is a Natural expression of fundamental Physical Relativities between natural physical states and potentialities.

    Mathematics and Logics seem to be reasoning systems invented by and used by humans to put the observations and relativities into some form of order as to cause and effect and proportions over time and space variability, to whatever detail or aspect necessary or achievable by our instruments and analysis methods. In short: The Universe is a Physical expression of the natural universal actions and evolutions; which we humans investigate and make sense out of via our invented mathematical and logical reasoning systems. Nature has no need for either il-logical or logical, un-mathematics or mathematical rules and programming considerations: it does what it does and we use whatever means at our disposal to make sense out of it in form, function, time and space terms which our logics and our mathematics can manipulate and give some sort of qualitative and quantitative grasp and scale to it all. Physical first; mathematical or logical expression only in the context of our observing and reasoning constructs.

    Is that enough to answer your own questions satisfactorily, Write4U?
     
    Last edited: Jan 26, 2016
  8. Write4U Valued Senior Member

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    Impressive reasoning, I must admit.
    However, the following statement you made is not entirely satisfactory, IMO.
    Ok, as layman in Cosmology and Physics (ex-accountant) let me explain my point of reference and why I am arguing for a Universe that must follow certain mathematical laws and functions, regardless of an observer.

    When I saw this National Geographic presentation, "Decoding The Universe The Great Math Mystery" narrated by by Max tegmark and Mario Livio, who argue that the Universe does not have some mathematical properties, but that it has only mathematical properties and that the Universe "cannot do what it does" without mathematical functions as dictated by physical interactions. How else could we formalize these functions into logical mathematics? Mathematicians themselves express a sense of *discovery* rather than *invention* of the mathematics in nature

    https://www.youtube.com/watch?v=ZfPXeJ4iu9c

    Would you care to comment on Tegmark's proposition and if he is wrong, why?
     
    Last edited: Jan 26, 2016
  9. expletives deleted Registered Senior Member

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    The nub of my reply is already imbedded in the last few words of your above quote: "...mathematically as dictated by physical interactions."

    Like I said previously, it is the natural physical states and potentialities in action which determine what the universal states are at any one moment in its evolution from one moment to the next via quantum scale uncertain transitions and macro scale less uncertain processing in the bulk forms which the aggregated quanta collectively manifest when bound up in large scale processes where quantum scale uncertainties are less immediately effective compared to the macro scale interactions with other macro scale features. So our mathematics and logics, as applied to the analysis and understanding of universal physical expression of natural relativities and states at all scales, are the human tools we use to make sense of what physical interactions determine will occur, in form, timing and transitional states at every scale we examine and analyze using our logics and maths constructs.

    Those last few words in the above quote says it all, in my opinion. Maybe in their enthusiastic pop science way of popularizing themselves and the theoretical sciences which they make money from in these TV appearances, they missed the telling import and relevant implications of those last few words. But that's what pop science is all about: the actors rather than the facts?

    Cynical, I know; but that's what I honestly think of pop science writers, bloggers and TV presenters, regardless who the popularizers may be. Sorry if I have offended anyone with that opinion. It is only my opinion.
     
  10. Write4U Valued Senior Member

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  11. exchemist Valued Senior Member

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    I agree with you, as do several other contributors.

    Write4U however has apparently been seduced, by Tegmark and possibly others, into thinking the universe either is mathematics or carries out mathematical operations, i.e that mathematics is itself physical. (At least that is my understanding of his or her position.)
     
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  12. Q-reeus Valued Senior Member

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    Agreed also. Show me a working computer that is 'pure software'. Anyone with an ounce of common sense realizes there has to be a package deal - always both hardware AND software present. Likewise, I reject the evident philosophy behind J.A.Wheeler's famous slogan 'it from bit'. For there to be any kind of physical world, from the outset 'things' simply exist and necessarily behave and interact according to 'laws'. How could it possibly be otherwise?

    I can't judge the true motivation of the likes of Tegmark, but it's a fact that 'deep thinking' expertly packaged helps to differentiate one from the crowd in a crowded field. Also tends to sell very well.
     
  13. exchemist Valued Senior Member

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    yr 2) Well of course E=mc² is a mathematical equation, but so what? That is not a definition of energy, any more than E = -μe⁴/8ε₀²h²n² (which if I've got it right is the formula for energy of successive electronic states of the hydrogen atom.) Both are relations, expressing the physical quantity called "energy" in terms of other physical quantities. A definition of energy requires words. And actually it is quite a hard concept to express concisely. As the opening of the Wiki article says, "In physics, energy is a property of objects which can be transferred to other objects or converted into different forms, but cannot be created or destroyed.[1] The "ability of a system to perform work" is a common description, but it is difficult to give one single comprehensive definition of energy because of its many forms.[2]"

    yr 3) Lots of things are geometrical structures. A football, for example. But if you say a football is "mathematical", what do you mean? You may mean it is approximately spherical, or that its surface is made of a pattern of polygons. But you cannot deny it is a physical object as well, with properties that its geometry alone does not account for. So if you were to say "a football is a branch of mathematics", most people would ring for the men in white coats.

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    yr 4) OK, one property of the universe is that it contains matter. What mathematical expression would you use for that? As for "function", as I've said before, I do not believe there is any evidence that it has a function.
     
  14. expletives deleted Registered Senior Member

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    I recall seeing that and other similar productions before, so I just scanned quickly through it. The same arguments I heard before in many versions and hushed tones about the mystery of it all. The upshot is that even in that video the mystery remains despite all the hushed tones and surreptitious urgings to believe that we both invent and discover mathematics. The discovery is true, as is the invention of the system from axioms which when followed we discover consistent relationships and patterns and entities and so on which flow from logical consequence of those axioms and construct. At no stage did they actually demonstrate that the universe is aware and or following such mathematical axioms let alone the logical processes that lead to results consistent with axioms and not just the natural physical relativities and forms which arise spontaneously during the universe's natural physical interactive evolutions. Recall how we had to invent a non-linear recursive chaos fractal mathematics to describe the very natural uncertainties which exist in the natural system of physical interactions. At no stage does the universe know mathematically what is going to result from such non-linear processes. It just gets on with it and out pops the physical consequences of the physical processes which involve physical inputs and interactions which may or may not be totally known as to energy levels or effective impact on whatever stage the process is at in any one moment during its unceasing evolutions. If nature itself does not know what will result from fractal, non-linear, chaotic and recursive processing of its physical quanta, then how can we claim that it knows mathematics and follows it according to mathematical rules. Of course in macro scale and in well behaved processes there is easier prediction of input and output, but in quantum scale and in unpredictably behaved processes there is no mathematics for nature to follow, it just does it and whatever the fractal/unpredictable result is then that is what it is. Mathematics describes and predicts the describable and predictable, but in no way does mathematics describe and predict that which nature herself cannot. Mathematical is post hoc human overlay on nature's physical process; nature is physical pre-existing process, mathematics is abstract analytical construct for making some sense of that pre-existing physical process. That's my opinion according to my own understandings. I hope I havent offended you or anyone else by voicing and supporting my opinion as I have? If I have I apologize.
     
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  15. exchemist Valued Senior Member

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    There's a rather funny, waspish review of Tegmark's recent book, by a sceptical mathematics don at Columbia called Peter Woit, here: http://www.math.columbia.edu/~woit/wordpress/?p=6551

    I don't pretend to be expert on Tegmark (or Shapiro as we should really call him), but a lot of what Woit says sounds like sense to me.
     
    Last edited: Jan 26, 2016
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  16. Q-reeus Valued Senior Member

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    Nice reference. Just reading the first few paragraphs is enough for me to wish the likes of Peter Woit a long and healthy and high visibility life.

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  17. Write4U Valued Senior Member

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    I never claimed the red highlighted sentence, nor did Tegmark or any of the scientists who made comments in the clip. It could be a simple matter of probability, efficiency, and limitations.

    The rest of this paragraph (green) tends to support a universe with certain recurring and essential constants in forms and functions.
     
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  18. expletives deleted Registered Senior Member

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    That paragraph opening comment in that part of my post was intended to forestall any further descent into mystery and mysticism which was the undertone of the video and many others like it. That video was pure theater and salesmanship for profit and self advancement without a shred of actual demonstrable case for what that mystery is supposed to be. A mystery which remained at the end of that video; despite all those hushed allusions to all sorts of wishy washy subjective takes on what the universe is and what mathematics may be involved in its existence and evolutions. The rest of my paragraph you quoted only supported the observed forms and interactions which the physical states and potentialities end up in at every iteration of processes at every scale and location. Whether mathematical forms, constants and functions recur over time scales and space expanses is again a consequence of the potential interactive dispositions of the energy in that space at any one stage in local physical process having local possible states and potentials for whatever results naturally. We can use pattern recognition, logics and abstract mathematical labels and symbols, avatars and pseudo entities to model everything we observe, but its the natural physical interactions which produce what we observe; and even nature itself, at quantum scale and in fractal/chaotic situations, cannot know what we will observe until it is produced for us to observe by the natural playing out of the physical factors involved. My opinion is as before, and for the reasons previously stated. That's all I can say, Write4U; it's only my opinion, though, you don't have to agree with it! I wont be offended if you dont. I enjoyed our conversation. Must say good night now.
     
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  19. exchemist Valued Senior Member

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    There's also a more deeply considered scepticism from a philosopher here (referenced in the Woit piece) : http://www.science20.com/rationally_speaking/mathematical_universe_i_ain’t_convinced-127841

    Seems that, among other reasons for scepticism, Goedel's Incompleteness Theorem presents some difficulties for Shapiro/Tegmark......

    There is also something suspiciously trendy and self-promoting about all this........Emperor's New Clothes?
     
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  20. Q-reeus Valued Senior Member

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    A few words of friendly advice. It's a good idea to put ones point of view over in as compact and structured a form as possible. Long sentences often containing multiple thoughts and often lacking punctuation, detracts from the poster's intent. Also, specific, relevant statements made from a position of working knowledge have more impact than generalized philosophical arguments. Nothing wrong with philosophy per se but imo this place is overrun with armchair philosophy.
     
  21. Q-reeus Valued Senior Member

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    Yeah, I like Penrose (author of Emperor's New Clothes) in general but he too leans to the Platonic ideal, though not near to the extreme of Tegmark/Shapiro (must look into that last bit!). Pigliucci in that linked to article well voices essentially everything I see wrong with 'relationships all the way down' philosophy. At the end there Tegmark suggests the gap is not as wide as made out, but closing it would require much shifting of ground imo. Hmm... maybe I am ignoring my own advice to expletives deleted.

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  22. exchemist Valued Senior Member

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    Haha, actually I was simply meaning "Emperor's new clothes" in its classic meaning, rather referring to Penrose's book (my mistake for putting it in capitals). To be honest I have not spent a lot of time on this sort of thing in recent years. (I read Barrow and Tipler's Anthropic Principle about 20 years ago.) Nowadays I am content with a more empirical - and less speculative - approach to physical reality. I do however have a visceral distaste for what I call "gosh-wow" popularisation and also for anything that seems to use science to create an air of mystery about the world, as it seems to me the job of science should be diametrically opposite.

    P.S. I was pleased to see Jim Baggott got a mention in the Pigliucci article. He and I once worked in the same office at Shell and used sometimes to talk about QM in the pub. Jim's recent dig at physics losing touch with reality ("Farewell to Reality") is something I can relate to, though I have not read that book.
     
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  23. sweetpea Registered Senior Member

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