Is Math a Gift From God?

I think my calculus students would probably not think so. But as John Allen Paulos reports, not everyone agrees:

Consider first a Baptist school in Texas whose description of a geometry course begins:

Students will examine the nature of God as they progress in their understanding of mathematics. Students will understand the absolute consistency of mathematical principles and know that God was the inventor of that consistency. They will see God’s nature revealed in the order and precision they review foundational concepts while being able to demonstrate geometric thinking and spatial reasoning. The study of the basics of geometry through making and testing conjectures regarding mathematical and real-world patterns will allow the students to understand the absolute consistency of God as seen in the geometric principles he created.

I wonder if the school teaches that non-Euclidean geometry is the work of the devil or at least of non-Christians.

As Paulos goes on to point out, some really sharp people have thought that the effectiveness of mathematics in describing nature is evidence of, well, something or other:

Of course, there are more sophisticated ideas that are vaguely similar, and there have been first-rate scientists who have taken mathematics to be some sort of divine manifestation. One of the most well-known such arguments is due to physicist Eugene Wigner. In his famous 1960 paper, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” he maintained that ability of mathematics to describe and predict the physical world is no accident, but rather is evidence of a deep and mysterious harmony.

Paulos goes on to explain how evolutionary biology can shed some light on the nature of mathematics. Worth a look.

Like Paulos, I am baffled by those who are baffled by the effectiveness of mathematics in describing nature. Our ability to describe the world with mathematics does not strike me as any more mysterious than our ability to describe the world using ordinary language. Mathematics is just the sort of language best suited for describing patterns and regularities.

I have even heard it suggested that the mere fact that nature is consistent and predictable is itself evidence of God’s existence. This strikes me as totally incomprehensible. A world in which supernatural entities can interfere in the workings of nature is also the sort of world in which we do not expect mathematical regularities. It is in a world devoid of such interference that regularities simply have to reign.

But this is all too philosophical for me. My occasional forays into the philosophy of math literature have left me even more frustrated than my forays into the philosophy of science literature. Most of the time I can’ t even figure out what the question is. Perhaps John Wilkins would like to wiegh in…

Comments

  1. #1 Tyler DiPietro
    September 3, 2007

    I think philosophy is math (or metamath or whatever) is good mental masturbation, but I can’t really think of any place it has enriched my understanding of basic math concepts. I read and think about it a lot because, like most philosophy, it’s really just nagging questions that demand your attention, even if they often fail to have practical value.

  2. #2 Blake Stacey
    September 3, 2007

    What Tyler said.

    The way I figure it, you can’t do philosophy of math without learning the math first. So, why not study the math for its own sake and then fret about the philosophical stuff when you’ve got the knowledge necessary to do so?

  3. #3 Tyler DiPietro
    September 3, 2007

    Exactly, Blake.

    Hell, it can also be a distraction in some sense. I have to figure out whether the Fourier transform of this function vanishes outside of a given interval….but really, what is the ontological status of this “Fourier transform”? Is it independent of my own cognition and subjective experience, or is it purely conceptual, or is it just a bunch of marks on a paper, or maybe…..

  4. #4 Tim Bartik
    September 3, 2007

    The Baptist School’s interpretations of math don’t seem necessary. However, it is somewhat amazing that nature is consistent and regular. I don’t know whether this is evidence that God exists, but we need to have the imagination to consider that the universe could have been quite different. Perhaps we could be in a universe where one day 2 + 2 would equal 4 and another day it would equal 5, or a universe in which physical laws would vary chaotically. It is somewhat surprising that human beings living on a minor planet of a typical star in a typical galaxy can understand the underlying patterns of the universe. Again, this may not mean that God exists, but it does mean that the universe is friendly to logic and regularity. It need not have been so.

  5. #5 shiva
    September 3, 2007

    Jason says, I have even heard it suggested that the mere fact that nature is consistent and predictable is itself evidence of God’s existence. This strikes me as totally incomprehensible. Is nature consistent and predictable? Or is it that the laws we have wrighted only help us make sense of what is consistent and predictable? I am not for a moment doubting the utility of the many physical laws that have been a source of all those millions of useful things that have made life easier. The difference between noise and information is purely a sentient invention. To think otherwise would be to mistake the description of a phenomenon for the phenomenon itself. I am very uncomfortable with professed freethinkers/atheists/rationalists who reject the scientific possibility of a supreme entity but yet find room for the self-same entity by attributing order and method to nature.

  6. #6 bigTom
    September 3, 2007

    I have mixed feelings about this whole development. One the one hand I understand that trying to “come closer to understanding the mind of god” was a very significant motivating factor for many great scientists of past centuries. It is probably not a fluke that advanced math and science developed among the Abrahamic religious societies, and not among the earlier (and contemporaneous) great civilizations elsewhere.

    So religion and science has a pretty mixed history. On the one hand, some religions have promoted a great appreciation for scholarship. On the other hand, when a religion comes to feel threatened by the results of scientific study, we have seen some pretty unfortunate results.

  7. #7 Tyler DiPietro
    September 3, 2007

    To be perfectly honest Tim, that reminds me much of the story of the puddle that contemplated why he fit so neatly into the pothole in which he was located.

    More specifically, I think you have things backwards. The universe isn’t friendly to logic, it is logic that is molded to assist our understanding of the universe. One might as well ask why such beautiful colors as blue and green find themselves in such abundance on this planet.

  8. #8 Craig Pennington
    September 3, 2007

    Why would one expect otherwise of mathematics? Quite the reverse seems intuitive to me: if a thing exists, it would be unreasonable for there not to be an effective mathematics describing its behavior.

    A favorite quote of mine is relevent:

    The fatal flaw of magic lies not in its general assumption of a sequence of events determined by law, but in its total misconception of the nature of the particular laws which govern that sequence. If we analyse the various cases of sympathetic magic which have been passed in review in the preceding pages, and which may be taken as fair samples of the bulk, we shall find, as I have already indicated, that they are all mistaken applications of one or other of two great fundamental laws of thought, namely, the association of ideas by similarity and the association of ideas by contiguity in space or time. A mistaken association of similar ideas produces homoeopathic or imitative magic: a mistaken association of contiguous ideas produces contagious magic. The principles of association are excellent in themselves, and indeed absolutely essential to the working of the human mind. Legitimately applied they yield science; illegitimately applied they yield magic, the bastard sister of science. It is therefore a truism, almost a tautology, to say that all magic is necessarily false and barren; for were it ever to become true and fruitful, it would no longer be magic but science.

    Sir James George Frazer, The Golden Bough

  9. #9 Leni
    September 4, 2007

    Jason wrote:

    Like Paulos, I am baffled by those who are baffled by the effectiveness of mathematics in describing nature.

    Maybe it’s the “Holy crap I get it!” moment.

    I’ve had several math related instances of this, and while I understand now what happened and don’t think it has anything to do with god, when I was in the midst of it it did seem almost spiritual. That’s just how powerful the feeling of clarity and excitement that comes with new insight is.

    It’s a rare and wonderful treat, really. (Especially considering how much of our time is spent wallowing in abject ignorance and confusion!)

    Anyway, unlike everyday language math has the ability to help us describe complex patterns and phenomena that we may barely understand in an exacting way that words just can not do justice to. Phenomena that is often really, really interesting, and sometimes downright beautiful.

    So I have a kernel of empathy for people who mistake that instantaneous insight for divinity. I can see why, at least intuitively, it would be easy and appealing to think of it mystical.

  10. #10 Richard Wein
    September 4, 2007

    Jason: Mathematics is just the sort of language best suited for describing patterns and regularities.

    I quite agree. But I think it’s fair to ask why the universe is describable in relatively simple maths. For example, why do so many natural laws involve squares and cubes rather than arbitrary non-integer powers, like 1.739547? I’d be very interested to hear an answer to that question. Anyone?

  11. #11 Ginger Yellow
    September 4, 2007

    “The study of the basics of geometry through making and testing conjectures regarding mathematical and real-world patterns will allow the students to understand the absolute consistency of God as seen in the geometric principles he created. ”

    I wonder how they approach Godel’s theorem.

  12. #12 Blake Stacey
    September 4, 2007

    Richard Wein:

    Often, exponents are connected with the dimension of a system. For example, Newton’s law of gravity falls as r squared because the number of spatial dimensions we live in is three. This isn’t an “ultimate” answer, but it does push the ignorance back one step.

    Then, too, if you want weird numbers, they’re never in short supply: take Feigenbaum’s constant, for example.

  13. #13 Blake Stacey
    September 4, 2007

    Oh, and if it’s exponents you’re after, check out the “critical exponents” observed in phase transitions. The equation for helium’s heat capacity near the superfluid transition has a power of 0.013, and the 3D Ising model of interacting magnetic spins involves an exponent of 0.110.

  14. #14 David D.G.
    September 4, 2007

    Is Math a Gift From God? I think my calculus students would probably not think so.

    I never even got as far as calculus, and when I was in school I was sure that math was a “gift” from the Other Guy, if anything. The lousy college counselors who talked me into taking trigonometry were surely his minions.

    ~David D.G.

  15. #15 Richard Wein
    September 5, 2007

    Thanks, Blake. Good points.

  16. #16 vanderleun
    September 19, 2007

    ” A world in which supernatural entities can interfere in the workings of nature is also the sort of world in which we do not expect mathematical regularities.”

    Why would supernatural entities feel forced to interfere with a world they created? Seems to me that that would be, at the very least, optional. Why couldn’t they set it up with math and evolution and natural laws and just set it running and then take a 14 billion year vacation? Seems to me a supernatural being would be interested in efficiency, especially if setting up universes was their work. If that was the case, it would seem that a universe much like this one would be the way to go.

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