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Matter or mathematics?

  1. Aug 21, 2005 #1
    Does matter follow precise mathematical laws or is mathematics simply a good approximation and tool used to describe matter ? If all there is is mathematical relationships, then matter and all physics actually doesn't even exist if only as a metaphor for equations. If matter only APPROXIMATELY follows mathematical laws, then there is room for a real metaphysical universe made up of non mathematical items. Could matter and reality simply be what remains after all the equations have been calculated as a sort of error ? Matter is the "error" in our calculations, or it could be that the quantum imprecision is what gives matter some "substance" as opposed as being only mathematical items. Any ideas ?, there is always some confusion as where matter, physics starts and mathematics ends.......
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  3. Aug 21, 2005 #2


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    However matter (or whatever) interacts and moves, there will be some mathematics that describes it.
  4. Aug 22, 2005 #3
    This is another example of irreducible complexity. Matter-physics can be described "completely ?" by math but math needs some "external" reference to exist, but the external reference can be described by math etc. So what came first math or matter ? Or maybe it is LOGIC, a subset of logic called MATH and a subset of math called PHYSICS ? It is very confusing, is the universe a complete sea of mathematical formulas, equations within which matter is floating on ? Is there something totally NON-MATHEMATICAL ? very confusing....
  5. Aug 23, 2005 #4
    I think I am on to something here. If matter only obeys mathematical rules, then reality doesn't exist at all and a complete simulation of a universe on a computer is just as real as our "real" universe. Is math just a refined , precision language to describe interacting items ? Is the basis of logic just relationships ? Then the elementary particles of physics and the theory of everything has ALREADY BEEN ACHIEVED AND IS JUST "THE MATHEMATICAL DESCRIPTION OF INTERACTING ITEMS" ! The details of these equations and formulas and how far or close they predict real phenomena is mostly IRRELEVANT! So I think I have finally conquered the theory of everything, or maybe I am really just confused on the relationship between math, physics and how math is used to describe physics....

    It may also be that we use math in a very narrow range of problems we need to solve, (like designing a rocket) and it is just a handy tool with absolutely no metaphysical importance whatsoever.
  6. Aug 23, 2005 #5
    Bottom line:

    Does matter exist or is it only a set of mathematical relationships ?

    Is physics simply a subset of mathematics ?

    What does it really mean when we cannot solve differential equations of physical systems ? Is matter following equations at all times ?

    I find it intriguing and confusing..
  7. Aug 23, 2005 #6
    I think you are asking good questions, and IMHO you are asking more than one. The question in your first post, "Does matter follow precise mathematical laws or is mathematics simply a good approximation and tool used to describe matter" is very different from "Does matter exist or is it only a set of mathematical relationships." If you don't mind I'll toss out a couple of thoughts about this until someone more capable posts.

    The question: "Does matter exist" depends of course on how you define matter and exist. Without spending paragraphs on the particulars, I would like to argue that matter exists. I say this with great certainty, as I experience it every moment of my life. For instance, I do a little amateur boxing. Every time I get punched in the face I consider it evidence that something material exists and that it just had a very direct affect on me. While it's true that the word "matter" becomes much less easily understood at subatomic levels, this shouldn't prevent us from saying that the concept of matter emerges as larger scales.

    As for your first question, I would like to propose this (roundabout) answer: science creates paradigms that predict observables. Just because a paradigm predicts an observable doesn't make it "real". You can argue that one should accept whatever paradigm predicts best as "real," but that still dissasociates it from a "true reality." When you say "If matter only APPROXIMATELY follows mathematical laws, then there is room for a real metaphysical universe made up of non mathematical items" I think you are not giving mathematics enough credit, because new math can be produced to fit new observations. However, because we can never say that our "laws" absolutely predict our observations perfectly, I think it does leave room for this "real mataphysical universe" you describe.

    However, just because it leaves room doesn't mean such a thing should actually be accepted. In fact, I would argue that while it leaves room for a greater metaphysical universe, little or nothing is gained by imagining one.

    You might be interested to know (or maybe you already do) that this habit we have here in the 21st century of assuming that mathetmatical models actually have a direct link to reality was not as prevalent in times past. In Galileo's time it was quite common for someone to believe that, for instance, Copernicus' heliocentric model was a superior predictor but did not actually depict reality.
  8. Aug 23, 2005 #7


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    (bolding mine)

    This is a perfect example of hypostatisation. You experience a phenomenon, the solidity of a punch in the face, and attribute it to a substance, which you call matter, and then claim to have direct experience of matter. But the nuclei in the boxing glove are far apart, and the solidity you experienced was caused by the forces between them, carried we are told, by massless particles that cannot be observed (virtual photons, carriers of the electromagnetic force). And some people call these virtual photons mathematical fictions! So where is your matter now? And surely you can't claim something exists on the basis of an experience you admit to be an approximation?
  9. Aug 23, 2005 #8
    Sure I can. I can claim matter exists just as much as I can claim that crowds exist and that forests exist. If examined carefully it is true that defining these things becomes extremely complicated. Yet, in each case there is a perspective where identifying them is straight forward.

    I admit, this rests somewhat on our definition of the word "exists." If you define exists as "real" then I guess I'll give you that I can't prove anything exists. However, I don't think people use the word exists in the same strict way they use "real." I think we say something exists when we are forced to treat it as real due to some circumstance. Is political pandering real? Does political pandering exist? Is electrical current real? Does electrical current exist? I can't accept that the words real and exist are the same.

    One definition of matter is anything that takes up space and can be detected. I argue that on classical scales matter by that definition exists. The fact that this becomes more complicated on smaller scales doesn't bother me; I don't need to show that matter exists at every scale any more than I need to show that one atom of gold is shiny.

    I do not accept that just because a system loses properties when we examine its consituents that we can no longer claim those properties exist.

    Looking forward to your reply, both to me and her.
  10. Aug 24, 2005 #9
    So any kind of new math can be produced to fit any possible observation. So math is a handy "invention" to fool ourselves into thinking we know the laws of nature. When nature is slightly out of line we just add some "corrective terms" and go on forever like this. This reminds me of the Feynman diagrams of QED (quantum electrodynamics) where the precision of the calculations increases by calculating ever higher number of integrals , like I think 4 loops can correspond to 30 million integrals. So you add it up on a supercomuter see results, see experiments, measure the differences and say OK the differences are corrective terms in further integrals. Let's calculate 5 loops and then maybe 6 loop etc. What is the complete equation of QED ? trillions of integrals ? Aside that we may never know, but is it safe to assume math really does have this one to one correspondence with reality ? Or maybe is it safe to assume that OUR MIND AND IT'S LANGUAGES (MATH AND NATURAL) HAVE A ONE TO ONE CORRESPONDENCE WITH REALITY-MATTER ?

    Just like natural language can describe, relate and encompass all reality, even math, although it would be very wordy (energy is equal to mass times light speed times light speed etc.) , so math does the same. So all reality is just a sequence of symbols and language, either mathematical or natural.

    It would seem that it really doesn't matter what the laws are just as long as they are mathematical laws, after which all and any other kind of laws can be discovered or invented. So in a universe that has completely different laws that allow a human mind to appear, that mind can reverse engineer the mathematical laws of the universe, and then invent all mathematical laws, and universes and simulate the laws of our particular universe as we know it.

    The problem if all reality-matter is math is very important because if in the future we can simulate complete worlds on computers, then these worlds are just as real as ours. We may even be able to create hyper-real worlds that are even more "real" than ours.
  11. Aug 25, 2005 #10
    Simply stated THIS THREAD IS PRESENTING A FALSE PROBLEM. Mathematics is matter-physics and matter-physics is mathematics. Our senses don't do anything but measurements, everything we see is a measurement, a mathematical operation etc. An object occupies space, has coordinates is present at a time t0 etc. We perceive proportions and geometrical relations and logical cause and effect. Natural language expresses these things in a more vague and abstract way, math is the precision language. We just zero in on some phenomena and apply a precision language to describe it. Everything has some regularity, order and math expresses this. There is no way to perceive matter or physics without somehow putting it in some reference system of time,space weight etc, hence math and logic.

    When physicists say that math seems miraculous in that it can explain things, they have it all wrong. We can ONLY EXPLAIN THINGS WITH MATH AND LOGIC, indeed only with some language that divides things into interacting items. Actually NATURAL LANGUAGE IS WAY MORE MIRACULOUS THAN MATH!.

    It is just that we split the object of observation from the language observing it and call the language a miracle. This is false, there is no miracle, even the ancients thought it was a miracle to dance and provoke rain. They where fooling themselves. Also math needs a material substrate to be written on and matter follows the mathematical laws. Which came first ? both because they are the same thing.

    As far as hyper-reality is concerned, any simulation that is indistinguishable from reality is just as real. Even a film, which is far from reality is very real to the viewer and even novels.
  12. Aug 26, 2005 #11
    Well, I'm not fooling myself into anything. How about you? :tongue2:

    No one said that math always has a correspondence with reality, only that in some situations it can be a predictor of observables. I can also produce any number of equations that aren't - that's part of what physics is, choosing the correct predictive system. On another note, consider this statement: it can be argued that it is safe to assume physics has a one to one correspondence with reality, whereas it is not safe to believe it does.
  13. Aug 31, 2005 #12
    When, in grade school, I was introduced to the principle of inertia, I was quite surprised at what I was being told. My teacher said all objects that are in motion will remain in motion unless a force is applied to it; when I asked him how could anyone say something as outrageous as that when any observation of the world reveals that any object in motion will eventually stop, he explained to me that it's only because friction is a force. But even as a child I clearly understood that friction was just a convenient hypothesis that allowed us to maintain belief in a completely arbitrary principle.

    But I didn't feel fooled, I was actually delighted to learn about the ingenuity of the human intellect, which allows us to make up fictitious rules that actually work despite their fictitiousness. Only after I grew up did I notice so many people erroneously believe those rules are anything other than figments of our imagination.

    Exactly. And that's the beauty of it. We can understand anything we want as long as we do not restrict ourselves only to what can be directly observed. If we do restrict ourselves that way, then we can understand absolutely nothing.

    No, that is not the case. On one hand, language is filled with concepts that have no real existence, such as forces, fields, and any invisible entity that can only be detected through its visible effects. On the other hand, our perception of reality is limited by our sense of vision, and we have no way to know about the existence of invisible entities which do not manifest themselves in a way that can be seen.

    There has to be more to reality than symbols, otherwise the symbols stand for nothing. But that thing itself cannot be represented by symbols. In other words, beyond the reality described by language and math lies the reality that is indescribable.

    Well, certainly the human brain is quite capable of creating worlds that appear more real than the ordinary world itself. Just talk to anyone who ever tried drugs such as LSD or ketamine. And sometimes the brain does it spontaneously, without the help of drugs. And that begs the question: if the brain can create different realities, how do we know this reality is not a creation of our brains? That is, by the way, a question with no knowable answer.
  14. Sep 1, 2005 #13

    Even if, for example, some mathematical theory of everything in physics were perfectly matching reality there is little hope that we would ever be able to justify that clearly. This is one of the the reasons of why modern physicists and philosophers of science make a clear cut difference between the laws of nature and the laws of science. Thus at most we can hope to find/jusitify approximately true physical laws/ physical theories/ theories of everything (providing also justification for that stance).

    To me this is still realizable as much as fallibilism is never dropped, for example if a successful 'theory of everything' is found and no serious empirically progressive alternative exist the only solution of 'bon sens', to quote Duhem, is to regard, provisionally, that TOE as being additionally approximately true. Modern physicists from Einstein onward have been, and still are, much more confident than me, for they not only it is possible to find such a TOE but is also possible to justify once and forever that this TOE is approximately true.

    However the developments in the philosophy of science in the last 45 years (especially from Kuhn and Feyerabend onward) cast a serious shadow over the claim that we can prove once and forever that such a TOE is approximately true. In my view all we can say is that at a certain moment we have sufficient reasons, upon the type of rationality accepted at that time, that such a TOE is approximately true, letting also the door open to strong, nontrivial, paradigm changes (thus in the future is conceivable that the standard of rationality will change and that that TOE will cease to be seen as approximately true; the same is valid if the standard of rationality remains the same and an equal, enough distinct, alternative approach is constructed).
    Last edited: Sep 1, 2005
  15. Sep 1, 2005 #14
    Especially since what we perceive as reality is only a given arbitrary organization of information in our minds. Given other sense organs and another body form and another kind of interaction with the external (?) environment we would have a completely different organization of information and hence reality. Are all organizations of information reducible to logic math as we know it ? This is not known. You can imagine extreme forms of life living inside stars as plasmas that perceive and are very sensitive to plasma patterns. They may even be very complex and evolved and have something analogous to our mind. Who knows reality, they or us ? Reality is a total function of how our mind is organized and interacts with the external world. Modified minds could have very different views that are just as valid (or invalid) as ours. Virtual reality worlds that may appear in computers some thousand years from now may be very different and may be the ultimate reality, our material world being something considered ancient.
  16. Sep 2, 2005 #15
    Well it's not so much how different or complex the mind is organized as how different all the emotional-sentiment-feelings-senses are organized with respect to the items the given mind perceives. The information content can be as varied as possible, it is the association with how the mind "feels" this information which can be very different. All items in the mind are simply tokens and symbols that activate emotional-sentimental states of some kind. Those are the really central circuits and manipulating them to any degree really means going into any REAL conceivable universe in it's deepest sense.
    Last edited: Sep 2, 2005
  17. Sep 10, 2005 #16
    Mathematics is a just a tool we invented. Also number theory has limitations. The numbers we use have identical properties, elements and particles do not.
    Last edited: Sep 10, 2005
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