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

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

  1. billvon Valued Senior Member

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    No, the math always works. Models are based on math. The models are modified as needed. But an error in the model means you were using the math in the wrong way. You do not need to modify how math works to correct it; you need to use a different set of equations to better fit the model to the real world.

    The math underlying Kepler's laws of motion is 100% correct. It never needs to be changed. They provide a model that can be used to predict the motion of planets. Those models change as we understand more about the universe (i.e. changes due to warped space-time.)
     
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  3. exchemist Valued Senior Member

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    Yeah I do not know Tegmark's work but it does not look as if I would be likely to agree with his outlook. His idea that "all structures that exist mathematically exist also physically" strikes me as tosh. However I'm sorry to say I am not sufficiently interested in this metaphysics to spend the time required to understand how he reaches this bizarre conclusion. It is enough for me that plenty of knowledgeable people don't agree. I'm rather old and lazy I'm afraid - as an undergraduate I'm sure I would have eagerly read his ideas.

    As a general observation, it does seem to me there is a vogue in physical science, especially perhaps in the USA, that seems to elevate mathematics to a pre-eminent position in thought, inspiring a kind of holy reverence, that I do not think it deserves. It is an extremely powerful tool of human thought, but it should remain our servant, because it is only a man-made tool for thinking quantitatively.
     
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  5. danshawen Valued Senior Member

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    I haven't found the original text from which my post is based, but these are pretty close, if a bit more prudish in their descriptions:
    http://www.britannica.com/topic/number-symbolism
    http://mysticalnumbers.com
    http://home.anadolu.edu.tr/~bkelesoglu/GRA105/ders02.pdf
    http://www.hinduwebsite.com/numbers.asp

    And Pythagorus believed that numbers had souls.
     
    Last edited: Dec 4, 2015
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  7. DaveC426913 Valued Senior Member

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    Keplerian Laws do not model nature. Keplerian math doesn't either. It did in a Newtonian universe, it does not in an Einsteinian universe. If you measured out the areas of a segment of Mercury's orbit, it would not add up.

    Using what math, exactly? Can you demonstrate how to use any form of math that is not of human construction?


    What does it mean to have math 'existing' in nature? What do you mean by 'math' in this context? Define it.
     
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  8. rpenner Fully Wired Valued Senior Member

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    No they aren't. Your links are all to descriptions of numerology, concerned with the symbolism and/or magic properties of numbers. Your claim was about the origin of the shapes used in the Arabic language to write numbers (digits). As a claim, it was a claim in the field of historical fact not in contemporary symbolism or mysticism. As a rejection, my response was clearly tailored to your claim being in the form of a historical fact.

    Your weaseling about the claim can easily be seen to support my charge that you lack personal integrity.
     
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  9. rpenner Fully Wired Valued Senior Member

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    Keplerian laws approximately model the related aspects behavior of nature's phenomena. Newtonian Universal Gravitation does so more accurately and more generally. General Relativity does so more accurately and more generally.

    It's not that nature is mathematical, but it has every appearance of having a natural order which allows the behavior of phenomena to be precisely and accurately modeled with mathematics, regardless of nature's actual mechanism for giving that appearance of order.
     
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  10. DaveC426913 Valued Senior Member

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    And here we are talking about human-created mathematics. So I ask again, what does this 'natural, cosmic mathematics' mean?

    A planet experiences a pull toward 1 trillion other objects (easy enough to see: our galaxy is gravitationally bound over its 100,000 light years - we are demonstrably within the influence of every star and planet in it.) Do you think that nature applies formulae? Does it calculate each of these pulls, then add them together before deciding where the planet should next move?

    Or do you think the planet is simply passively responding to the local curvature of spacetime as generated by 1 trillion bodies simultaneously?
     
    Last edited: Dec 4, 2015
  11. rpenner Fully Wired Valued Senior Member

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    I think it has to include counting in that electrons show every indication of being quantized and indistinguishable so that the total electric charge is a measure not of which electrons are where but how many are there (relative to the number of positrons and protons). I don't think it necessarily includes Euclidean geometry, but I believe it may include a geometry which is Euclidean in the realm of human-sized spatial dimensions and in the limit of low relative velocities, so it's natural (in a different sense) for humans to initially assume Euclidean geometry is natural.

    But those are only provisional beliefs which are formed from an experience of phenomena in the universe which is necessarily incomplete. These are not positions which can be proven in the sense of mathematical truth because there are always alternative axioms which allow you to conclude the same evidence would come to light even with radically different underpinnings. Since the underpinnings of the actual universe are unknowable, I am extremely dubious that 'natural, cosmic mathematics' can be evidenced or defined in terms of evidence, in which case it is a sterile argument based on (all too human) metaphysics and aesthetics.
     
  12. exchemist Valued Senior Member

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    YES. Just so.
     
  13. danshawen Valued Senior Member

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    "Weasel words" used to mean something on Wikipedia before I took the editors to task for it. Their definition seemed to be that a weasel word meant that some statement was not an absolute: "many", "few", and "some" are on their short list of WORDS THAT CANNOT BE USED IN A WIKIPEDIA ARTICLE BECAUSE THEY ARE WEASEL WORDS. Not everything, or more to the point, ANYTHING that is not math is not going to be an absolute. The universe we live in is not an "all or none" proposition. It is unfortunate that this upsets a certain class of people.

    Take my word for it, I read that description of the origin of Arabic numerals somewhere, and it was an obscure publication I am not likely to remember. I wasn't reading it for academic research. My apologies if any of the ideas I related offended you.
     
  14. C C Consular Corps - "the backbone of diplomacy" Valued Senior Member

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    Like ordinary language, the system non-controversially "exists" in the sense of abstract symbols and the rules of their manipulation being recorded on a variety of mediums, humans discussing and using the applied aspects of it, architecture and devices and physics recruiting the services of the latter, etc.

    So perhaps what you're instead trying to ask (in a philosophical context): "Is there a prior-in-rank mathematical level which regulates the apprehended world (its spatial organizations and its appearance of being a process of unfolding changes)?" Which would only be part of nature if you want to extend the definition of nature to include all ontological possibilities, thus making the word into a redundant synonym for existence in general.

    One problem is how would such a Pythagorean "government" be realized and enforce itself, apart from just repeating the basic characteristics of our perceived / testable world that supervened upon it in one sense or another. IOW, that option would involve a relational structure configured to instantiating a system of mathematical properties, values, and tenets -- similar to a computer's organization, which can dynamically calculate or output quantitative-dependent products.

    But this "computer" approach to instantiating a super-external realism for "mathematics", even if the definition of "computer" is very broadly interpreted, still recruits space/time forms and mechanistic powers for its manner of being (i.e., computers don't float immaterially on their own).

    It introduces an endless situation of nested domains, since the constraints of the "cause" of our spatiotemporal manner of existence would just be the forms of our own condition duplicated at another ontological stratum (albeit with a strictly mathematical theme), and so forth ad infinitum. That is, if our perceived and understood environment implies such a regulatory or explanatory stratum for itself then so does the next. This "nested-doll" consequence of a stratified version of cause is terminated when a different manner of explanation (perhaps radically different) is introduced, which shugs off need for a cause and manager of itself.

    You could go with a non-scientific, immaterial option of asserting that mathematical principles are brutely potent powers that are hierarchically antecedent to the spatial / temporal template which gives "real-ness" to sensibly instantiated objects. Thus having no location themselves because they are prior in rank or are what makes possible that template, and "places" and their coordinates. Accordingly such "potent instructions" would then avoid having to be realized by another material system (computer, etc). However, by the very nature of being disembodied principles, their evidence would only be what they outputted: The original, putative claims of the universe process "behaving mathematically or as if undergirded by mathematics". What makes "empirical evidence" possible would thereby ironically resist being construed as real itself, or subject to being deemed an imaginative or unnecessary add-on.

    Also, another option is that any supposed principles "regulating the world" (whether a system of mathematics or otherwise) could be reified as the overall structural patterns of the extra-dimensional block universe (or whatever version of the spacetime continuum interpreters contingently feel falls out of general relativity during their particular era of thinking). Once presentism or the commonsense view of philosophy of time is eliminated, explaining how the world as an unfolding process behaves lawfully or coherently is no longer needed (IOW, the former's implication of all kinds of extra metaphysical baggage governing that process, to avoid the magical "maintenance of the inter-consistency of the procedure just happens over the whole sequence of one global moment of the universe being replaced by the next".).
     
    Last edited: Dec 4, 2015
  15. C C Consular Corps - "the backbone of diplomacy" Valued Senior Member

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    Deleted duplicate post here.
     
  16. DaveC426913 Valued Senior Member

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    I think you're agreeing with me, so +1.

    The problem here is what people mean when they talk about 'mathematics'. I think they are simply talking about the fact that natural forces that act one way in one circumstance (say, a mass m at a distance r from another mass) will act the same way in any other circumstance with m and r, assuming all other things the same. But that's not math, that's just forces constitently doing what they do. We apply math to model what is happening.

    The crux of this entire thread is dependent on what people define 'math' to be. And I haven't heard a lot of people lay down a satisfactory definition that can be said to exist naturally.
     
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  17. Daecon Kiwi fruit Valued Senior Member

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    Yes, and those forces follow the laws of mathematics.
     
  18. danshawen Valued Senior Member

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    Mathematics has come a very long way since its humble beginnings in simple commerce and sheep herding.

    But even if we had never worked out the details of something like Kepler's law, this would not mean that the universe would not obey this law just the same as it did millennia before humans saw their first dawn. Even our greatest discoveries in math are only descriptive of processes that would naturally proceed as they do without our knowing the mathematical details.

    Te order is there, even if we haven't managed to quantify everything about it.
     
    Last edited: Dec 4, 2015
  19. rpenner Fully Wired Valued Senior Member

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  20. Kristoffer Giant Hyrax Valued Senior Member

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  21. danshawen Valued Senior Member

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    Here is exactly what I said, and where I said it.

    https://en.wikipedia.org/wiki/Talk:Weasel_word

    WikiWeasels[edit]
    If Wikipedia could offer expert definition and information on any topic, this humble article certainly should have been the best among many. "Many" is of course, a 'weasel word'.

    An encyclopedia is, at best, a compendium of ALL knowledge that is worth knowing. "ALL" is not a 'weasel word', but "knowledge" most certainly is, for every finite mind, such as everyone who reads this. Notice that I am trying to define 'weasel words' without using them. It is difficult, and that's the point.

    Wikipedia contains some useful knowledge on a wide variety of topics. "Some", "useful", "knowledge", "wide" and "variety" are ALL 'weasel words'.

    Wikipedia contains an awful lot of useless knowledge, particularly in the subjects of geography and sport. "an awful lot", "useless", "knowledge" are all 'weasel words'. 96.255.108.117 (talk) 15:00, 25 March 2012 (UTC)danshawen

    Wikpedia is (or should be) the foremost authority on the term 'weasel words'. 'Should', 'foremost', and 'authority' are weasel words.

    An encyclopedia is a compendium of useful knowledge. 'Useful', and 'knowledge' are both weasel words.

    Wikipedia contains many useful articles on various topics. 'Many', 'useful', and 'various' are all weasel words.

    Widipedia contains almost as many useless articles on geography and sport as it does on useful topics. 'Almost', 'many', 'useless', and 'useful' are all weasel words.

    Any word whose meaning is ambiguous, any term that does not specify knowledge down to and including atomic structure, or any term that refers to another term in any human languge is a 'weasel word'. Humans are weasels, because all of their knowledge is necessarily incomplete or ambiguous. 96.255.108.117 (talk) 15:18, 25 March 2012 (UTC)Danshawen
     
  22. DaveC426913 Valued Senior Member

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    And what laws are those?
    What do you mean by mathematics?
     
  23. DaveC426913 Valued Senior Member

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    This is contrary to what others are saying. Many are saying mathematics existed before sheep - indeed Earth - existed.

    Of course, they can't define the term they are using...

    It doesn't obey this law. Never did.

    Yes it is.

    But order is not the word that this thread is about. Mathematics is the word that this thread is about.

    I'd like to hear the definition of this word that does not involve humans please.
    Here's one:
    " the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations"
     
    Last edited: Dec 5, 2015

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