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Does mathematics rule the universe?

  1. Nov 7, 2005 #1
    :confused: Is mathematics the grand design for the universe? Can everything be explained by a mathematical law or calculation that governs it? Are we humans simply in the process of discovering and trying to understand these laws or does maths simply reflect our attempt to make order out of a complicated world?

    Maths is based on conlusions we have drawn by watching the world around us. Therefore does this not mean that maths is already inherent in nature?

    We discover laws, when these laws break down does this show that nature does not conform the mathematical model we squeeze it into or simply that its mathematical laws are much too complicated and involve too many factors for us mere humans to understand?
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  3. Nov 7, 2005 #2

    Tom Mattson

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    If you look at physical laws in their mathematical form, you'll see that they don't really explain anything. Rather they describe our world and make predictions about it.

    I say the latter. Mathematical models of the universe are in every instance an idealization of it. Nowhere in the universe will you find an actual straight line, the number "2", a square root, or a derivative. The existence of these objects is identical to their definitions. Mathematical constructs are mental constructs.

    No, it isn't. Pure mathematicians (as opposed to applied mathematicians) conduct their research without regard to the applicability of their work. Some of it has been used by physicists, some of it has not.

    Even if I agreed that your premises were true, I still don't see how the "therefore" is warranted. If the inferences you made were logically valid, then it is not obvious to me. The remarkable success of mathematical knowledge in predicting physical phenomena is consistent with the point of view that mathematical laws are stricly descriptive.

    When people use Newton's second law to solve for the motion of a satellite in orbit around the Earth, they typically do not include the gravitational influence of Alpha Centarui, despite the fact that it's there. But the model still works for that purpose. On the other hand when people tried to apply classical particle dynamics to the atom, an irreconcilable contradiction was found (hence, quantum mechanics). Physical laws are not governing principles but rather descriptors, and they have restricted realms of applicability.
  4. Nov 8, 2005 #3
    I'm not sure, (even pure) maths is based on axioms, and these are based on observation of the world around us. For example, if you took one apple, then picked up another two, and looked and saw you had three apples, that would be normal. but if you picked up two, then picked up another one and saw that you had 4, then I'm not convinced we'd be using a + b = b + a as a rule; If addition wasn't commutative in the world around us, then why would we make it so in our maths?

    Clearly a daft example but just raising a point.
  5. Nov 8, 2005 #4


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    I am afraid you don't know much mathematics. From the time Menaechmus invented the conic sections, mathematics has been about things that are not derivable from observations of the world around us.
  6. Nov 8, 2005 #5


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    This is my belief about it:

    A non-linear brain evolved as a successful survival strategy in an inherently non-linear world. From that non-linear brain emerged a non-linear phenomenon we call mathematics. I don't mean "non-linear" mathematics like non-linear differential equations, but rather the geometry of mathematics itself, it's intrinsic geometry, is non-linear and because of that it successfully describes a non-linear universe.

    Some examples: Between every real number lies another. The Real number system is dense, a never-ending fractal.

    The operations of mathematics are "nested" say for example the Chain Rule: plans within plans, structure within structure just like the world we see around us.

    There is "sensitivity on initial conditions". Ever worked a long, several-page problem and somewhere on page one made a teeny-weeney mistake? What could happen to the answer if a plus sign is replaced with a negative sign at the start of a solution?
  7. Nov 9, 2005 #6


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    Since two apples aren't an apple, the world of apples isn't closed under "addition".:wink:
  8. Nov 9, 2005 #7


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    I think saying that mathematical objects are mental constructs ignores the fact that our brains are physical objects. Presumably, we do the math we do because of the way our brains are wired. Math is a property of nature in as much as our brains obey the laws of physics and, in doing do, discover math. A more interesting question is whether math is all there is to nature. That is, clearly math comes out of the laws of physics, but is math sufficiently powerful to describe those laws exactly?

    We evolved with brains that are compatible with doing math and logic, but all this means is that math and logic are robust enough to describe the physical world to a very (arbitrarily?) high degree of accuracy. Now, the laws of math and logic aren't wrong, because like I said, they come out of our physical brains. But whether there is someinthg more is impossible to prove or disprove beause, by hypothesis, it is not logical. One piece of evidence against math being the most basic language of the universe is that as we try to describe more fundamental physical laws, the math gets much more complicated, not simpler. But it's still to early to tell how this will turn out.
  9. Nov 9, 2005 #8
    i could also argue the universe is based on the english language, because everything can be explained in words.

    the universe is based on itself, independent of language and math which are just human attempts to describe it.
  10. Nov 10, 2005 #9
    I have commented alot on these, search some of my posts. Also oldtobor has written about these items. What I find amazing is how Einstein and others using pure math deduced general relativity! Now that is really something that makes you think. It is as if the fundamentals of the universe are abstract items, concepts, geometry, probabilites (quantum) and the details of the world are just big combinational quirks. Is physics really pure math-geometry? Very odd and paradoxical question......
  11. Nov 10, 2005 #10
    What we see with our five senses is a description of reality. The set of electrical signals that "describe" this reality can be considered a language that our mind-brain-consciousness interprets. Mathematics is just another, maybe simplified, language that "describes" this reality, just as "natural language" is. So there is a one to one correspondences between the "electrical signals" language and physics-reality, and just the same there is one to one correspondences between the "mathematical" or "natural language" language and physics-reality. A film in a DVD is completely described by 4.7 billion bytes, so this is another example of a complete description of a part of reality. I guess this is the best way to consider mathematics. A different description lets us see different aspects of reality, so this is how relativity was discovered. There may be an infinite number of different ways to encode or describe reality-physics, hence an infinite number of possible perceived universes.

    As far as the details of the universe this is interesting and very related, you may want to read this:

    Last edited: Nov 10, 2005
  12. Nov 10, 2005 #11

    Fantastic link !

    I especailly like the DVD example. So then, mathematics is a kind of compression algorithm upon physics-reality. In that case "Natural Language" is an even more powerful compression algorithm. In fact if you say "street", it is a simple functional concept, used within a grammar and syntax and in a universe of intentions. You completely wipe out all the millions of small pebbles and millions of quirk details present on the street, you don't see them anymore and you condense (compress) trillions of atoms and details (temperature of each point on the street, color, chemical composition of each pebble etc.) into one simple 6 letter word. We don't need or use the details, so it is with mathematics, we eliminate the details and compress physics into its largest common denominator. Bend down on your knees and look at all the details on a street. The earth's mantle is another example. It is more than 2,000 kms of trillions of stones, rocks and quirk details. For our mind it is only a 6 letter word.
  13. Nov 11, 2005 #12
    A very interesting link related to this is :



    Actually you could say that it is upside down, physics-reality is a "compressed" version of its mathematical description. If you were to discover and write down all the equations describing the entire universe with every conceivable corrective term of Quantum Electrodynamics etc. on a piece of "paper", this paper would be many trillions of times larger than the universe (actually 10 to the trillionth power larger maybe). So the real world-physics is a "compressed" version of these equations. When we do use equations to describe physics, we are using only the dominant terms and only describing a very small local part of the universe, or only some very general parts of the universe, and this gives the impression that we are compressing the information whereas we are simply extracting a very small part of all the equations operating in the universe. You could also say the same if, instead of using equations, you used an imaginary computer program simulating each particle in the universe. This program would be, just like the equations, many times larger than the universe it is simulating. You can also simply imagine the universe as a series of numbers, just like a DVD film, and the same thing happens, the number would be many times larger than the universe. Natural language is the ultimate compressed version of the universe-reality-physics.
  14. Nov 11, 2005 #13


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    "Addition" is in the world around us- we defined addition that way. We have also defined a number of other operations that aren't commutative.
  15. Nov 12, 2005 #14
    maths is just a power of putting feelings in nature to a world where people just think ,dont feel
  16. Nov 12, 2005 #15
    The idea that the universe is simply math-geometry and there is no matter is spooky and frightening. So then our goal is to escape any form of logic and get as far away as possible of any rational perception of the universe. This could be achieved by tricking math-logic to work for us by manipulating our minds-neural networks to perceive vastly more intricate-complex and confusing universe-feelings-emotions. We could reach a point with modified brains where we have totally escaped math-logic. Maybe extreme ART attempts to do this.
  17. Nov 12, 2005 #16
    And in fact nameta9 you are completely WRONG. MATTER is the only thing that exists, mathematics is a small ghost of symbols we use to explain only a very limited number of material items we set up in certain configurations and is totally dependent on our QUIRK intentions. We use mathematics to manipulate or describe matter according to our intentions which are, by the way, completely insignificant.
  18. Nov 12, 2005 #17


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    well i feel as if i am in a call - in segment of "best damn sports show". but here is 2 cents more: I may not understand math either, but I tend to agree with michael24 in post 3.

    i.e. to me the following rejoinder misses the point:

    "Maths is based on conclusions we have drawn by watching the world around us."

    "No, it isn't. Pure mathematicians (as opposed to applied mathematicians) conduct their research without regard to the applicability of their work. Some of it has been used by physicists, some of it has not."

    I think a pure mathematician can be inspired by observation, regardless of the applicability of his conclusions.

    Riemann for example was clearly inspired by physics in his work on the dirchlet principle, which he used for a pure discussion of the meromorphic functions on a desingularization of a curve in the complex plane, i.e. to prove the riemann roch theorem.

    his results in surface topology also appear to be inspired by observation of actual cuts in surfaces.

    All my own insights in pure mathematics, few as they are, (in complex algebraic geometry), seem inspired by visual imagination. I still remember my first discovery concerning factoring a period mapping through a "blow up" in 12 dimensional space, and simultaneously picturing a spiral staircase in my mind's eye, or a ride at an amusement park.

    I may be wrong here, but at least I am speaking from personal experience as a pure mathematics researcher, and not speculating about how other people think.

    I would say the most crucial tool in doing mathemnatics research for me, is the ability to draw creative analogies, and I guess real life experience can provide sources for analogy as well as anything.
  19. Nov 12, 2005 #18
    So could a blind person have discovered relativity or all the math involved ? Could a person who cannot see have discovered geometry and its laws ? Then is math dependent on what sense organs we have, how they are organized, how they encode information and how our mind decodes it or uses it (INTENTIONALLY) ? So math then is a pure invention and is valid just as much as abstract ART.
  20. Nov 12, 2005 #19


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    i don't know, but i have met at least one blind mathematician whose geometric ("visual") imagination and intuition was much stronger than mine.

    Another famous story (told in scientific american) concerns Bernard Morin who described to another mathematician how to visualize Smale's argument that a sphere can be turned smoothly inside out. Morin is blind.

    I am still a big advocate of speaking of something you know about, not speculating wildly about things you do not.
  21. Nov 13, 2005 #20
    But that's what makes philosophy so pretty. You can speculate and invent all you want and get away with it! It has no goal, no solid INTENTION like math does. So if in physics you say I don't know what is present at 10^-1000000 mm or you say it can't exist, well I can use philosophy to make up what is there and force reality to bend to my will, and it becomes true. Philosophy doesn't search truth as it is known in science, it is a completely different ball game. There are 2 kinds of materials in the universe, the minds-brains which are intentional and we all try to manipulate them with words and human communication and the rest of the material world where we mainpulate them with pre-constructed intentions. So if I change intentions I can achieve anything. You may want to read this :


    Philosophy has no given goal. It doesn't necessarily want to increase our understanding, some philosophers may want to decrease our understanding as "understanding" may not be such an interesting goal. Some philosophy likes the purely artistic view of things hence there is no relationship with science. Some philosophy likes to be completely wrong on everything because they are not using right and wrong concepts or non contradictions as taken for granted.

    Philosophy, in the wider sense, is very much more general and abstract than science, it questions every conceivable assumption, demolishes every conceivable logic and thought process. Real philosophy is truly non social and has no use whatsoever. It is this that makes it so much grander than science.

    One could say why search for the "truth" ? Why not search for the best lies, non-truths or try to get as far away as possible from the truth ? After all, searching for the truth is one of the assumptions we take for granted. Why not invent better and better lies ? why not contradict ourselves more and more ? Why is truth assigned a higher "value" than that which is "false" ?
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