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Is the geometry of the world the source of what we call math ?

  1. Aug 27, 2008 #1
    Is the geometry of the world the source of what we call "math"?

    I keep thinking about this lately, think about how we know this is different from that without having to consciouslly think about it.

    For instance this T is different from the background it sits on. The only way we could know that is if we already did the comparisons unconsciously so we know there is inequality (or inequalities) on a surface, that is, a distinction.

    Think about how we detect things, in order to think, or do anything, we first must be able to observe/detect something is there and get feedback from it in a feedback ring, binary logic, yes something is there or no, without binary logic we can't even have a single perception.

    It seems that the act of detection between real world surfaces (energy/light/etc) in and of itself, is where we get the concept of object, and hence the concept of 1, or "one distinct object", this is not that.

    It seems to me numbers are just shapes in the real world, but in our minds we call these distinct shapes "numbers". So there is an equivalence between geometric shapes and numbers in the real world, at least that seems to be the case to me.
     
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  3. Aug 27, 2008 #2

    CRGreathouse

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    Re: Is the geometry of the world the source of what we call "math"?

    I would be careful to distinguish numerals from numbers.
     
  4. Aug 27, 2008 #3
    Re: Is the geometry of the world the source of what we call "math"?

    that would be a 'thing'. then 'things' break down into subthings. each subthing is a set of 'things' which resemble each other more closely than can be explained by chance. reptiles resemble other reptiles. mammals resemble other mammals. but theres not much in between reptiles and mammals.

    its all about finding patterns that cant be explained by chance.

    that 'T' in your example could have been a random stain on the paper. yet you know that it isnt. how?
     
    Last edited: Aug 27, 2008
  5. Aug 27, 2008 #4
    Re: Is the geometry of the world the source of what we call "math"?

    Numerals are basically symbols of the 'alphabet' of the concept of one object though, when we say one, we say 'one object', that is distinct from all other objects.

    When we look at two circles on a piece of paper, we call them 'circles' but they are merely two distinct shapes in the real world.

    If it is an object, it has boundaries, and is distinct from other thoughts, so it must be a shape, because it is distinct from other concepts (not equal to).
     
    Last edited: Aug 27, 2008
  6. Aug 27, 2008 #5
    Re: Is the geometry of the world the source of what we call "math"?

    Things are objects, i.e. they are distinct from other things, there is distinction between them, this thing is not that thing

    I think you misunderstood, what I'm saying is the concept of object in our minds, is an instance of distinction we get from the process of detection in the world, i.e. the t could be a random blob, but that doesn't make it NOT a distinct object.
     
    Last edited: Aug 27, 2008
  7. Aug 27, 2008 #6
    Re: Is the geometry of the world the source of what we call "math"?

    I understood you.

    how do we distinguish a 'thing' from another 'thing' or for that matter from a nonthing? that is the question.

    a stain would certainly be a thing. but it wouldnt be a 'T'. and how would we distinguish a stain from a generally chaotic background?

    furthermore each set of subthings has its own actions that they perform or that can be performed on them and has its own rules. in other words, its a field.
     
    Last edited: Aug 27, 2008
  8. Aug 27, 2008 #7
    Re: Is the geometry of the world the source of what we call "math"?

    Self recursion, self-reflection, reality processing itself. i.e. we make distinctions because reality is constantly bombarding us with information about itself. Photons bounce off objects and hit our eyes, etc. That is the only way we could detect ourselves, not only that, if we don't believe it we undermine knowledge completely and should just give up. i.e. if you don't believe things "out there" exist or you "in there" exist, then why should anyone listen to that kind of person? right? Not only that your conception is based on a flawed understanding of "nothing" in reality, nothing as it was conceived was conceputalized before modern understandings of physics. Space is a surface of a kind, i.e. similar to the ocean. We could also prove it from logic: You can't throw a ball across a non-existent entity, therefore space exists, and nothing is merely 'empty-space-surface'

    Consider if you were giving an object to another person at the bottom of the sea, the water between you still exists. There wouldn't technically be 'nothing'
     
    Last edited: Aug 27, 2008
  9. Aug 27, 2008 #8
    Re: Is the geometry of the world the source of what we call "math"?

    This discussion reminds me of G. Spencer-Brown's "Laws of Form"; there he would recreate boolean logic starting from the concept of a boundary, where one of its sides has been deliberately marked to distinguish it from the other. See f.i. here,
    http://www.lawsofform.org/ideas.html
    or the Wikipedia page which is even more cryptic than the book.
     
  10. Aug 28, 2008 #9
    Re: Is the geometry of the world the source of what we call "math"?

    Check this out:

     
    Last edited by a moderator: Sep 25, 2014
  11. Aug 28, 2008 #10

    atyy

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    Re: Is the geometry of the world the source of what we call "math"?

    Maths is biology. If our brains were different, we might make different maths, or at least what we'd consider a natural construction might be different.
     
  12. Aug 28, 2008 #11
    Re: Is the geometry of the world the source of what we call "math"?

    I wonder how the boy from the documentary would perform (or feel) doing arithmetic in a base other than 10.
     
  13. Aug 28, 2008 #12
    Re: Is the geometry of the world the source of what we call "math"?

    I wonder that as well. I'd love to look at the research they did. But it goes to show we hardly know anything about the brain, i.e. people can have innate knowledge and abilities and not be able to explain the process of how it occurs.

    Which rubs right against the scientific method.
     
    Last edited: Aug 28, 2008
  14. Sep 2, 2008 #13
    Re: Is the geometry of the world the source of what we call "math"?


    ok I get it. I dont know that I MISunderstood you and I dont think that what I said actually contradicts what you said but I did indeed miss your point.

    so 'thing'=distinction? well I'll have to think about. it sounds possible but at the same time distinction to my mind is more about the process of distinguishing rather than that which is distinguished if that makes any sense. A 'thing' certainly gets distinguished, but is that what it 'is'? but you may be right though. I'll have to think about it.

    BTW, as far as numbers being shapes, there is an interesting discussion on the successor function being the basis of numbers/math in this thread:
    https://www.physicsforums.com/showthread.php?p=1857233&posted=1#post1857233

    heres my take on it:
    since the successor function is the basis of math then maybe we shouldnt think in terms of one, two, and three but rather first, second, and third. 2+3 becomes the second after the third. 2*3 becomes the second third. its just semantics but it might make the underlying fundamental idea clearer.

    after all, what does three even mean anyway? thirdness?
     
  15. Sep 2, 2008 #14
    Re: Is the geometry of the world the source of what we call "math"?

    Well here's how I think about it.. imagine you had a piece of paper over two lumps (bubbles) out of the same surface, the surface would be a single surface, and yet you'd have two bubbles (two humps), so we get the concept of object from inequalities, i.e. in this example it is the flat vs raise/height.

    http://www.boundarymath.org/

    I know I'm doing research into computational logic. You may find this interesting:

    http://www.lawsofform.org/aum/prolog.html


    Thirdness? - three distinct objects. But consider the "hidden" subtext - all 3 numbers are actually subdivisions of a dinstinct thought, not '3 seperate thoughts', i.e. consider a fractal pattern, shapes within shapes, numbers within numbers. See this cool program, to sit and think on it for a bit. This is how I came around to these ideas, when I was thinking about the patterns in fractals.

    http://www.ultrafractal.com/

    I think we've got it backwards, for instance we observe the universe from 'outside' (pretend it's in a bubble), we are fractions of the universe, but when we look at 'objects', 'outside' of our minds, they are actually fractions of a single entity, i.e. part of a big fractal surface, but our senses give us the optical illusion that they are 'separate', but in the ultimate sense they are not, they are all part of one surface of reality.
     
  16. Sep 2, 2008 #15
    Re: Is the geometry of the world the source of what we call "math"?

    or better still a surface with a great many bubbles of all sizes and shapes and 2 bubbles much larger than the rest. clearly the 2 stand out represent something distinct from the rest. they arent just random.

    distinguishing things is exactly what I was talking about in post 6.
     
  17. Sep 2, 2008 #16
    Re: Is the geometry of the world the source of what we call "math"?

    you are thinking in terms of real bumps while I am thinking in terms of bumps in a distribution. plot each of the random bubbles by its characteristics (shape, size) and most would fall into a Gaussian distribution but the other 2 (I should have made it many more than that) clearly fall outside that. thats a distinction. thats what I was talking about when I mentioned the random stains.

    I know what 'three' means. I am suggesting that it is an 'empty' word, as the chinese say, derived in some bizarre and meaningless way from the root idea of being 'third'.

    I tend to believe that only nouns, verbs, and possibly conjunctions are 'real' words. all others are derived from those or they are 'empty' words.
     
    Last edited: Sep 2, 2008
  18. Sep 2, 2008 #17

    Hurkyl

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    Re: Is the geometry of the world the source of what we call "math"?

    If you want to discuss epistemology, then please do so in the philosophy forum (which is where I have moved this post). If you want to discuss a more scientific topic, such as the psychology of observation or the mathematics of detecting patterns in raw data, then please start a new thread on that topic, and try not to diverge into overly speculative posts.

    (Of course, one must refrain from overly speculative posts in the philosophy forums as well)
     
  19. Sep 2, 2008 #18
    Re: Is the geometry of the world the source of what we call "math"?

    The problem is you have it backwards, the bumps are what is real. Your distribution is a reflection (an image, a photograph) of what is i.e. think of the order of operations, photon bounces/is ejected from object (carrying information) hits your eye, eye translates the signal. The signal reaches your mind, mind derives a thought from the information your eye has received, therefore when you 'self generate' ideas, you got those ideas from the outside world first. Therefore in our minds we're really just manipulating 'holographic' reflections of what is on the outside. If you actually had to make your bumps in a distribution out of real stuff in the real world, you would find out things. This is why I always transport mathematical reasoning back into the 'real world' I think terms of "What would it be made of?".. if this is 'infinite' in terms of our thoughts (i.e. if we had infinite strings of data), but if we actually had to make say pi out of stuff in the real world. We would run out of stuff to make distinct numbers from, therefore. Pi is "infinite" only in imaginary space, in the real world, pi ends (i.e. when you make pi with stuff).

    In a computer pi would have to be stored somewhere, pi would fill up any amount of memory, hard disk space, and processing power you could throw at it, therefore, pi in the real world is truncated, it eventually ends somewhere when you consider the real world is made of stuff.
     
  20. Sep 2, 2008 #19
    Re: Is the geometry of the world the source of what we call "math"?

    All science begins with thought, I fail to see how our discussion of detection is unscientific. i.e. if you don't think you can see stuff you can't move around objects, if you believe what you are seeing is subjective, you're getting an objective outcome (movement around an object) from a 'subjective' experience, seems a little off to me. Would you sit there thinking you were experiencing 'subjective hotness' and let your hand burn off? I wouldn't personally, the whole point in asking these questions is to discover errors in the philosophy of science and the method of science itself. Men conceived what we call 'science' if there are errors in conceptualizations, then there are errors in everyone who claims to know what 'science' is. Men derive their concepts from the world, if they conceptualized their concepts incorrectly we should demand these errors be exposed, that is the scientific way.

    It is the duty of philosophy to destroy the illusions which had their origin in misconceptions, whatever darling hopes and valued expectations may be ruined by its explanations. My chief aim in this work has been completeness; and I make bold to say, that there is not a single metaphysical problem that does not find its solution, or at least the key to its solution, here. Pure reason is a perfect unity. (Immanuel Kant, Critique of Pure Reason, 1781)
     
    Last edited: Sep 2, 2008
  21. Sep 2, 2008 #20
    Re: Is the geometry of the world the source of what we call "math"?

    anyway, my point was that the successor function, which is the basis of all mathematics, doesnt give us one, two, and three. it gives us first, second, and third. so the whole question of what is a 'number' may be meaningless.

    for the record, I consider that very relevant to 'math'.


    you have to distinguish between 'types' and 'instances'. instances are real world objects. types are not. distinguishing an instance is in theory no different from distinguishing a type.
     
    Last edited: Sep 2, 2008
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