Bad Math Education: Math does not need God

Once upon a time, I wrote about a jackass who was criticizing his college math instructor, because the instructor couldn’t explain what made the calculus class christian, or why it was different from what would be taught in a math class at a secular college.

That kind of thinking is quite strong in certain segments of the conservative christian community, and that disgusts me. Let me show you an example, and then I’ll explain why is annoys me so much. A reader
send me a link to the math curriculum for a Baptist high school, and it seriously bugs me.

Here’s their explanation of a high school geometry class:

GEOMETRY
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. Students will demonstrate an awareness of the structure of
a mathematical system, connecting definitions, postulates, logical reasoning, and theorems while exploring
attributes of geometric figures. Students will make and verify conjectures about angles, lines, polygons,
circles, and three-dimensional figures through coordinate and transformational approaches. Through the
knowledge of conditional statements and their converses, constructing and justifying statements about
geometric figures and their properties, students will begin understanding the concepts of constructing
geometrical proofs. Students will be able to solve problems with the use of formulas for the areas and
volumes of polygons and circles while applying them to real-world situations; in addition, they will
develop and improve their spatial visualization and reasoning skills with three-dimensional figures. As
they investigate properties of parallel lines, students will write deductive arguments to justify their
conclusions and apply those properties to real situations. Students will apply their knowledge of triangles
to develop properties of parallelograms, trapezoids, and kites as they continue developing their
mathematical reasoning abilities and their algebraic skills by learning to write coordinate proofs.
Right-triangle trigonometry will be introduced in the area of sine and cosine ratios and vectors. Finally,
students will study circles from an algebraic point of view by writing equations of circles in the
coordinate plane.

As I’ve mentioned before, I’m a religious reconstructionist Jew. I’m sympathetic to the idea
of religion. So I’m not just ranting because I dislike religion. What I dislike is the
use of religion to promote ignorance – and the perversion of legitimate knowledge to try to
turn it into support for religion.

Math is based on logic. It doesn’t matter whether you believe in God or not. It doesn’t matter whether you’re in our universe, or some radically different one. Math wouldn’t change. Math is the product of
pure abstract reasoning. First order predicate logic will always work in exactly the same way in a universe created by a benificent deity, a universe created by a malevolent deity, a universe created by a gaggle of insane elves, or a universe created by absolutely no one. It doesn’t matter what you believe. Math is going to be math. A theorem in FOPL will be a theorem in FOPL. No formal system is going to be both complete and consistent. The axiom of choice is going to be independent from the other axioms of set theory.

There are two ways of looking at math. In one of them, basically what I said above, math is a kind of pure and eternal truth. It doesn’t matter who you are, where you are, what you are: if you start from the same premises, the same things will always be true, and there is nothing you can do to make
them false.

In the other point of view, math is purely a creation of the mind. It’s one of the only things you can do from first principles. In this point of view, there’s no way that a deity can affect structure of
math – because math is entirely a creation of the mathematician. But once again – it’s a pure product
of the mathematicians mind. The mathematician picks a set of axioms and a set of rules of logic, and that defines the kind of math s/he can do. Without his or her choice of axioms and inference rules, there is no math; and the math is entirely determined by that choice. The existence or non-existence of a deity is completely irrelevant – whether a deity exists or not, it’s the axioms and inference rules that make it work.

Studying math isn’t exploring the nature of God. Math doesn’t demonstrate anything about God. God didn’t make geometry consistent – geometry is consistent, because it’s defined from predicate logic with a consistent set of axioms. And that’s true whether there’s a God or not. And God couldn’t make
geometry be inconsistent.

Teaching kids that you can’t understand math without God is lying – deliberate lying that will
reduce students ability to understand math. Just like inserting God into a discussion of physics,
it’s just introducing irrelevant information that, at best, adds nothing; and at worst, detracts from
the students ability and motivation to understand the material.

69 thoughts on “Bad Math Education: Math does not need God

  1. CRM-114

    They probably got their start in high school, introducing God to shop class. It might have been interesting, explaining losing fingers to a bandsaw as an act of God rather than a safety rule violation.
    If this keeps up, kindergarteners are going to have Christian finger painting. Well, God did invent colors, right? Unless of course they’re using Satanic colors.
    BTW, what if they get a Jew or Muslim in the geometry class? Do they get alternative instruction fitting their religion?

    Reply
  2. chaos_engineer

    BTW, what if they get a Jew or Muslim in the geometry class? Do they get alternative instruction fitting their religion?

    Of course. Christians would be taught real geometry, with the Euclidean version of the parallel postulate.

    People who practice flawed religions would naturally be more comfortable studying flawed, non-Euclidean geometries. Jews could learn Riemann’s version of the parallel postulate, Muslims could learn Lobachevksy’s, and atheists could learn H. P. Lovecraft’s.

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  3. Mark C. Chu-Carroll

    CRM-114:
    To be fair, it is a Christian school run out of a Baptist church. So they’re not going to have any Jewish or Muslim kids in the class.

    Reply
  4. Mark C. Chu-Carroll

    chaos_engineer:
    Can I sign up for the Lovecraftian geometry, even though I’m Jewish? I really want the unspeakable angles!

    Reply
  5. Blake Stacey

    I finally got around to reading some Lovecraft a little while ago, and I have to say, I was pretty underwhelmed. Like Conan Doyle, he appears to be a writer whose books people love as teenagers, and whose ideas are then re-crafted by more talented artists drawing upon their fond childhood memories: Gaiman, Borges, even Charlie Stross.
    (Of course, my personal aesthetic judgments are perfectly aligned with the absolute artistic standards of the Cosmos. Perish those who think otherwise!)
    We’ve probably already run through all the jokes about how in Christian math, 1 = 3 = pi. . . .

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  6. Davis

    math is a kind of pure and eternal truth

    I think this gets to the heart of why I assert that math is something distinct from science. Mathematics is the search for a set of necessary truths — assuming FOPL and a set of axioms, the results hold no matter what. Science is the search for the contingent truths of our universe — there are other conceivable universes where physics, chemistry, and biology work differently.

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  7. BangaloreCoolie

    Students will understand the absolute consistency of mathematical principles and know that God was the inventor of that consistency.”

    Muhahaha.
    All your jobs are soo belong to us.

    Reply
  8. Boosterz

    I thought if anyone mentioned “The Great Old Ones” then PZ would show up in the thread. You know, like in the movie Candyman. ūüėČ

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  9. ollie

    You might enjoy Underwood Dudley’s book “Mathematical Cranks”. One of its chapters is about how a college president (who was also a Catholic Priest) wrote a tomb which was supposed to have shown that Euclidian Geometry was the only “true” geometry (that is, you could prove the so called parallel postulate from the previous ones).

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  10. Torbjörn Larsson, OM

    math is a kind of pure and eternal truth

    I think this gets to the heart of why I assert that math is something distinct from science.

    math is purely a creation of the mind.

    I think this gets to the heart of why I don’t assert that math is something distinct from science. (>_<)
    But then again, maybe my Lovecraftian math is just from another dimension. (√Ķ_√≥)

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  11. Michael R. Head

    I’m all for God-is-in-the-numbers, because anyone that pins their belief in a creator to the beauty of arithmetic is going to really have some tough theological questions to answer once they come across G√∂del’s theorem (if they get that far).

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  12. Joseph Hertzlinger

    When they get to modern logic, they’ll probably decide to base their theology on Henkin sentences.
    They might even decide to go further. I’ve seen higher set theory described as “exact theology.” Presumably, anybody who doesn’t believe in the Axiom of Choice would be a heretic…

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  13. gg

    #9: You’ve made my morning with that comment! I nearly spewed Dr. Pepper all over the computer screen…
    Blake wrote: “[Lovecraft] appears to be a writer whose books people love as teenagers, and whose ideas are then re-crafted by more talented artists drawing upon their fond childhood memories…”
    Maybe to some extent, but I don’t think that’s completely the case. Lovecraft wasn’t a perfect writer, but he was a groundbreaking horror writer (drawing ideas from the most up to date biology, physics, and anthropology), he had a devoted following of (adult) writers in his era, and most of the major horror writers after him have written at least one pastiche. His quality varies from story to story, so you have to be careful in picking what to read: two of my favorites are The Shadow Over Innsmouth and At the Mountains of Madness.

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  14. Boosterz

    If you like Lovecraft you may also like to check out the Titus Crow series of books by Brian Lumley. He gets a bit carried away with it towards the end, but I still found them very enjoyable. The Necroscope series by Lumley is also very good.

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  15. Mark C. Chu-Carroll

    Blake:
    You need to see Lovecraft as a writer of his time. His prose style is very distinctly 1920s pulp, and with a very upper-class New England tone to it. That comes off as very stilted to modern readers.
    The other thing you need to remember was that he was really breaking new ground. The idea of the Mythos, and the kind of existential horror that he wrote about, were almost entirely new. They’ve been so widely copied in the time since then that a lot of it that was just on the edge at the time has become so common that its shock value disappears.
    If you go back and read some of Lovecraft’s inspirations – like Arthur Machen – you can see just how much he changed the field, and how great his writing is compared to what came before in the genre.

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  16. Mary

    Math does not need God. But God might need math.
    Giving these people a little more credit than they probably deserve, but… I think if you’re going to study theology, seriously, in the old Thomas Aquinas style, you do need to learn math. You need to learn to write proofs. You need to learn about assumptions and conclusions and consistency. Geometry will give you that. And it will also give you a different kind of appreciation of, for lack of a better word, beauty. Ideal, perfect forms, patterns, relationships. Harmonies, subtleties.
    Studying God won’t help you understand math, but I can see where you might think studying math would help you understand “the mind of God,” as Einstein put it. It feels that way for me sometimes, and I’m not even religious.
    So if I tell myself that these people actually went to college to learn theology, and the college is just trying to explain to them why they should learn math as a part of those studies, then I have no problem with this course description.

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  17. Susan B.

    Sometimes when I’m filling out a form and it asks for my religion, I’m really tempted to put “set theory”…

    Reply
  18. Giacomo Dorigo

    Premises:
    (P1) A certain being x is omnipotent if and only if x gets whatever x wants.
    (P2) A certain being x is merciful if and only if x wants all beings not to suffer.
    (P3) There exists at least a being y on this planet which suffers.
    Theorem:
    (T) If (P1), (P2) and (P3), then NON(there exists an omnipotent and merciful being x)
    Demonstration:
    For the demonstration of the theorem T we use a reductio ad absurdum:
    Let’s assume (P1), (P2) and (P3) to be true
    combining (P1) and (P2) it follows that
    (C1) “If there existed an omnipotent and merciful being x, then x would want all beings not to suffer and gets this”
    now let’s assume that
    (P4) “there exists a general being G that is omnipotent and merciful”
    combining (C1) and (P4) it follows that
    (C2) “NON(There exists at least a being on this planet which suffers)”
    combining (C2) with (P3) it follows a
    __contradiction
    so (P4) is false and we can derive the theorem.
    Of course we can change our premises, for example we can assume that there is no suffering on this planet, or we can change the definition of merciful, for example it would be interesting to see that if we will change (P2) in this
    (P2′) A certain being x is merciful if and only if he wants no other being to suffer.
    Then the theorem is proved if and only if we change (P3) in this
    (P3′) There exists at least a being y on this planet which suffers and y is different from x
    PS
    I am sorry my logic not being so rigorous as it should…

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  19. p

    So if I tell myself that these people actually went to college to learn theology, and the college is just trying to explain to them why they should learn math as a part of those studies, then I have no problem with this course description.
    IMO, the “theology” taught at most modern evangelical schools is like a cartoon compared to the heights of reasoned passion the medieval theologians like Aquinas and Ibn Arabi reached. And not a good cartoon. One of those ones that was written to sell candy bars by turning the brand names into robots.
    Metaphysics is not taught at all, or is reduced to determining the dimensions of Heaven from Revelations, rather than attempting to unite the unitive principle of creation with reason and logic, as it used to.

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  20. Mark C. Chu-Carroll

    Giacomo:
    That’s a version of one of the shallowest anti-religion arguments. Personally, I find it as disingenuous as many of the pathetic pro-religion arguments.
    There are anti-religion arguments than are very good; but that’s not one of them. It’s almost (but not quite) as bad as Descartes wretched gambit.
    Can an omnipotent being make the axiom of choice be provable from the other axioms of set theory? Can an omnipotent being create a complete, consistent formal system which doesn’t fail per Gödel’s theorem?
    Omnipotence is a word whose meaning can easily be played with to create contradictions. That argument is based
    solely on playing with the definition of the world.
    The moment you discard the idea of “being who can do anything he wants”, and recognize that there can be constraints on what’s possible – that argument falls apart.
    There are plenty of arguments against the existence of
    a deity that don’t rely on playing games with words. The best of them is the simplest: no one has ever found any objective evidence that indicates the existence of anything like a deity. You don’t need to play word games; that argument pretty much squashes anything except subjective arguments.

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  21. Jonathan Vos Post

    Off the top of my head, oversimplifying greatly, the
    standard metaphysical stances towards mathematics are:
    (1) Platonic/Pythagorean Idealism: Math is all there
    is. Minkowski space, tensors, Klein bottles, e, pi,
    triangles, categories, inaccessible cardinals, Hilbert
    space, are more real than thee, me, and the galaxy;
    (2) Formalism: Mathematics is devoid of meaning. It
    is a game played with scribbles by pen and pencil and
    chalk, or ink in shaped blots on flattened bleached wood pulp.
    (3) Social Constructionism: Mathematics, and Physics,
    are cultural domains where people and shifting
    associations of people duel with each other for
    wealth, power, attention, and sex.
    (4) Realism: for deeply mysterious reasons,
    Mathematics sometimes (not always) helps us to
    understand observations, to design experiments, and to
    make predictions which sometimes come true.
    Two people with different stances can argue until the
    spherical cows come home, and never convince each
    other of anything.
    Like the man and wife fighting and throwing bowls of
    alphabet soup at each other, hot words pass between
    them.

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  22. Harald Hanche-Olsen

    I am reminded of an anecdote I heard recently. Unfortunately, I cannot remember any specifics, like names or where I did hear it, but here goes anyway:
    Some mathematician who happened to be an orthodox Jew was talking about how fortunate he was to live within walking distance of his office. For then, since he could not drive a car on Saturday, he could still walk to his office and do mathematics. But isn’t that work? No, he said, doing mathematics is not work – it’s serving God, and so a perfectly acceptable activity for the Sabbath.

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  23. Douglas Mallory

    Mark, how are you defining “formal system”? It seems first order theories should qualify, and they’re certainly complete and consistent…

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  24. John Marley

    Re: Mark and quibbling over the definition of omnipotent.
    It’s true that Giacomo’s argument depends on what is meant by omnipotent. But clearly the author of the text you quote in your post meant exactly what Giacomo did.
    After all, “God was the inventor of that consistency.”
    So, at least in this case, the argument does apply.

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  25. Lucas V. B.

    I’m an atheist but I always say that if there’s something that gets close – if not over – our definition of God, that thing is mathematics.
    With an added bonus: at least we can be sure it is there, and that we can use it. All we have to do is learn it.

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  26. Lucas V. B.

    I’m an atheist but I always say that if there’s something that gets close – if not over – our definition of God, that thing is mathematics.
    With an added bonus: at least we can be sure it is there, and that we can use it. And all we have to do is learn it.

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  27. Stagyar zil Doggo

    Michael @ 13:

    I’m all for God-is-in-the-numbers, because anyone that pins their belief in a creator to the beauty of arithmetic is going to really have some tough theological questions to answer once they come across G√∂del’s theorem (if they get that far).

    I never got that. My (admittedly marginal) understanding of G√∂del’s Theorem is that it proves the existence of unprovable statements in every system of formal logic. This is done by constructing self-referential assertions of the form “this statement is false”, which become false if true, and vice versa. But proof of unprovability should advance nobody’s agenda. Both believer and skeptic should be equally impeded.
    Of course, this hasn’t stopped theists from making arguments that go something like this – G√∂del showed that reason alone fails to give all the answers. Hence you must look beyond reason and logic and accept the blindingly obvious infinite compassion of (insert random belief/deity here). The obvious objection to this is that the belief under question needs to consist solely of “unprovable statements” of the type described by G√∂del for the theorem to apply. Not to mention what it says about your deity if it can indeed be described thusly.
    But you’re saying the G√∂del presents problems for the theists. Could you (or anyone) elaborate.
    PS: Statements of the type “this statement is unprovable” also show up in G√∂del, but I can’t recall where.

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  28. PZ

    could any of you prodigies prove marks mullet in non-euclidean space?
    nice stuff…. business in the front, hilbert in the back.
    MaRk Is BrInGiN ThE 80’s PaCk.
    -PZ

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  29. Torbjörn Larsson, OM

    But you’re saying the G√∂del presents problems for the theists. Could you (or anyone) elaborate.

    Hmm. I have always assumed that this is about showing that gods can’t be all powerful.
    Btw, there seems to be an inherent conflict in assuming this power and trying to use it in “proofs of gods”. (And “proofs of gods” seems to rely on this power.) The logic enforces constraints that the premise declares void.
    For example, I just toyed with an old apologetic “math proof of creation” on another thread about this school. It was straight forward to deduce a paradox, such that gods aren’t necessary as assumed, nor do they exist. These things are ridiculous from the outset, but they are also internally self-defeating.

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  30. spudbeach

    I’m with you, Mark CC — math is a creation of either logic or mathematicians, not of the world or of god. Math is math, whether or not it relates to the real world. Calculating pi to 1 billion decimal places is cool, although long beyond any application to any physical problem. (Heck, either quantum uncertainty, the warping of space by the mass inside of a circle or the [possible] quantization of distance will make any measurement of pi disagree with math over more than 70 decimal places or so.)
    It really bugs me when people say that math is part of science. How can it be, when one can not do an experiment to prove or disprove a purely mathematical statement?
    If god exists, any evidence will be in science, not math. Math may help you see the evidence, but math won’t be the evidence.

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  31. Torbjörn Larsson, OM

    It really bugs me when people say that math is part of science.

    That could be said for a number of reasons. Math is part of science methods. Or math inspires and are inspired by its use, for example in theoretical physics. Or they go Chaitin’s way and see part of math proper as semiempirical.

    How can it be, when one can not do an experiment to prove or disprove a purely mathematical statement?

    Hmm. To get to that conclusion, we would have to see math as water tight from formal methods, and not based on empirical models of integers, geometry et cetera, or idealizations compliant with them such as points and infinitary methods. Seems like a difficult proposition to me – or perhaps assuming what we want to prove.
    Besides the question of how to look at formal math, every time we successfully test a theory we have also tested the chosen methods. That would include the math, and eventual mistakes. (Which never seems to happen in practice, because mathematicians are too good. :-P) Doesn’t this mean that the question above assumes that part of its answer in relation to the similarity to science?

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  32. gg

    MCC wrote: “The moment you discard the idea of “being who can do anything he wants”, and recognize that there can be constraints on what’s possible – that argument falls apart.”
    You may be familiar with his work, but if not you might find the philosopher Charles Hartshorne interesting. He wrote a text titled, “Omnipotence and Other Theological Mistakes,” in which he argues that the idea of an omnipotent god is not a traditional idea and one which results in a lot of the theological paradoxes (omnipotent loving god + bad things = paradox). I’m not a terribly big fan (to put it mildly) of his ‘modal proof’ of the existence of god, but his attempt to bring essentially Buddhist moderation into Christianity (“Wisdom as Moderation”) was somewhat refreshing.

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  33. Coin

    But you’re saying the G√∂del presents problems for the theists. Could you (or anyone) elaborate.
    Hm, well I don’t know about “theists”. But it seems to trivially pose a major problem for certain American Christian sets, who claim the Bible to be both complete and consistent ūüôā

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  34. Giacomo

    Mark thank you very much for the passionate reply, but I was quite joking ūüėÄ and I didn’t suspect I would be taken seriously…
    I am neither a mathematician nor a scientist and I don’t believe in God just because I don’t believe in God ūüėČ
    Anyway, you tried to reply seriously to me, so I will try to do the same.
    Incidentally you got the impression I was playing for this very reason: I was actually playing with definitions!
    But I had an underlying reason for doing that, it was in order to show that we can work on our premises in a reasoning. Starting from those premises, as I formulated them, we arrive to a contradiction and to a conclusion, I never said that conclusion to be definitive on the whole argument, I said “Of course we can change our premises”. I meant that work on them. If we arrive to a contradiction in our reasoning we have to come back to the premises and change them in order to see what will happen.
    Cleared this point, let’s come to omnipotence. I am not an English mother tongue so I am not so good in explaining high language subtleties… my definition of omnipotence were took from Dante Alighieri’s Divine Commedy:
    “Vuolsi cos√¨ col√† dove si puote/
    ci√≤ che si vuole” (Inf III 95-96)
    Anyway, if I can understand a little your argument, it is that if there are some constraints to what is possible, then we can define a kind of omnipotence inside that boundaries, so omnipotence is the possibility of doing everything which is possible, let’s say in this way “if it is possible to do that, He will be able to do that” or we can formulate also in a still different way “if it is possible to do that, and He wants to do that, he will do that”, for me this is quite ok, it is a change in the premises. If we redo the reasoning from these new premises we will find that it is impossible to have all beings not to suffer. So we will have an omnipotent being for whom is impossible to avoid suffering let’s say “totally”. Personally I would have not called this kind of power omnipotence, but I will not quarrel on words, let’s call it omnipotence… so I will call my own omnipotence super-omnipotence and my own God, Super-God, so it seems that just Super-God is contradictory :_)
    Note that you can change also the second premise, I mean the premise of mercy keeping unchanged that of omnipotence:
    let’s say that God is not merciful, in the sense that he left us the possibility to choose to be happy or not (of course you have to take in consideration also the after-life), in this way we are working on the definition of merciful (or more precisely on the definition of happiness).
    Let’s call the first God naive-merciful God, and the second one liberal-merciful God.
    Anyway coming back to the original argument, I have to be honest, I have taken that argument from the letter of a child who wrote to a magazine some time ago telling the journalist that he would have not believed in God any more because there was too much suffering in the world.
    It is an old argument and, as far as I know, it was faced for the first time by St.Augustine who had some difficulties to believe in God because he wasn’t able to explain to himself why if God is the Good and everything is created by Him, there is also the Evil?
    I admit that I have never understood the explanation he gave, but he was very happy of it and now he is one of the holy fathers of Catholic Church…
    Lastly, about the non-finding of objective evidence: that will never be a proof of anything, the believer can always reply to you, He don’t want to be found by you, because He wants you to have faith, and so on.
    That’s metaphysics!

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  35. Torbjörn Larsson, OM

    Lastly, about the non-finding of objective evidence: that will never be a proof of anything, the believer can always reply

    Well, the “proof” is for the empiricist. But if you reject empiricism, you can prove anything, superstitions among them, and specifically any number of magical beings. I’m not sure how that satisfies the believer.

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  36. KKairos

    I admit to seeing a certain beauty in numbers and, yes, thinking of God. I’ll admit that’s more a romantic thought than a complete logical train, though. I’m not about to formulate a new teleological argument based on the beauty of numbers. I’m not sure I quite agree with the statement that “Math does not need God,” which is partly because I am for theological reasons wary of saying anything does not need God–yet at the same time I’m conscious of mathematical arguments having greater philosophical certainty than God’s existence…
    Essentially, I’ll need some time to think about that one.
    Also, Mark already made the point of Giacomo’s quite mechanical and strictly logical problem-of-evil argument not working. While there’s better versions even of the Problem-of-Evil argument than that one, the version posted has been taken down by Alvin Plantinga’s “Free Will Defense” already. I still think it’s a decent argument, but just about the same level I think the teleological argument is still a decent argument.

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  37. Giacomo Dorigo

    Yes, this is the problem. When you enter metaphysics you can say whatever you want till it is logically consistent with your premises, which you can always try to patch in order to get the conclusion you want… or you can also abandon logical coherence so to say really whatever you want.
    Note anyway that usually believers claim to have proofs of what they believe in, for example the Gospel is full of proofs and witnesses, but what I was trying to show is that if you want to believe something you can always find some ways for justifying your belief even if you have not any proofs, for example basing your belief just on your faith. Of course this attitude gives rise to the “social” problem that everyone believes something different, a problem that you can solve both asking everyone not to try to impose their own beliefs upon others or establishing an authority which is the “real” source of truth (a Prophet, a Church, etc.) and which impose its own truth to everyone.

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  38. JeffE

    Hm, well I don’t know about “theists”. But [G√∂del] seems to trivially pose a major problem for certain American Christian sets, who claim the Bible to be both complete and consistent ūüôā
    Sorry, Coin, but this is not a contradiction. G√∂del’s theorem merely implies that if the Bible is complete and consistent, then it is not powerful enough to model arithmetic, the book of Numbers notwithstanding.

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  39. Jonathan Vos Post

    I’d like to iterate that “Proof” and “Truth” mean somewhat different things in the 5 major cases. As I said on or about 5 Feb 2007 (Sal and Friends butcher…):
    Scientists use Math, but are
    not mathematicians.
    (1) “Axiomatic truth” [as with Euclid] is foundationally different from
    (2) “Empirical truth” [the Scientific Method].
    These in turn are both different from
    (3) “Legal-Political Truth”, from
    (4) “Aesthetic truth”, and from
    (5) “Revealed religious truth.” The whole Creationist agenda is to conflate “Empirical truth” with “Revealed religious truth.”
    The ID scam tries to hide the connection with religion, in this case by incoherently stirring in “Axiomatic truth” as with K.G√∂del, A.Turing, G.Chaitin, J.Von Neumann to hide the flavor of burning bushes and The True Cross.
    Young Rene Descartes started so long and often at a crucifix in his Jesuit school, that it may have led him to the crossed x and y axes of Cartesian Geometry, but that’s merely my speculation.

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  40. Torbjörn Larsson, OM

    KKairos:

    the teleological argument is still a decent argument.

    In some circles perhaps. It is indecent in science because fundamental models lack it. And it is confusing for students.
    So I take a whack at it every opportunity I get.
    Giacomo:
    That is my thought as well. Tolerant “faith” is, well, tolerable, as opposed to for example pushing teleology onto cosmology. (But respect is always earned.)

    Reply
  41. Kenneth Schilling

    I find Mr. Chu-Carroll’s commentary silly. If you believe that God created everything that exists, since mathematics exists, of course you believe that God created mathematics. (In particular, if mathematics is an invention of the mind of man, since God created … ; you see how the argument goes from here.) It is important to note that the quoted course description says that mathematics will be used to study God, not that God will be used to study mathematics, so the obsevation that a nonbeliever will have the same mathematics as a believer is true, but entirely beside the point. Personally, I’m in favor of everyone, even Baptists, studying mathematics, and if “understanding God” is motivation to do so, I say “amen.”

    Reply
  42. paradoctor

    That Baptist high school is treating its math students the way a church soup kitchen treats homeless people; they subject them to a sermon before getting down to business. It’s also like the movie theaters, which play ten minutes of ads before the flick starts. It’s about marketing. After all, if they put the ads after the movie, or the sermon after the free meal, or God after the math, then nobody would sit through it.

    Reply
  43. rodolfo

    great!
    in the next generation, america’s scientific leading edge will be rocking in to the sky!
    yeah, great!
    you’re doing fine, folks, just fine, keep it that way…

    Reply
  44. r4d20

    Looks like they’re re-inventing sacred geometry.
    Maybe now they will understand why Jesus caught exactly 153 fish!

    Reply
  45. Jonathan Vos Post

    Why 153 fish? Obviously (as I’ve preached) because 153 is the 17th triangular number, i.e.
    17*18/2 = 17 * 9 = 153.
    This codes for the holy Trinity, especially as it is in the Bible at John 21 (since 21 is the 6th triangular number 6*7/2). Three triangular numbers in one verse. What are the odds?
    I’ve written on my own blog as follows:
    JOHN 21
    And after eight [8 is 3-almost prime] days His disciples were again inside, and Thomas with them…. But the other disciples came in the little boat (for they were not far from land, but about two hundred cubits [200 is 5-almost prime]), dragging the net with fish…. Simon Peter went up and dragged the net to land, full of large fish, one hundred and fifty-three [153 is 3-almost prime], and although there were so many the net was not broken…. This is now the third [3 is prime] time Jesus showed Himself to His disciples after He was raised from the dead…. He said to him the second [2 is prime] time, “Simon, son of Jonah, do you love Me?”…. He said to him the third [3 is prime] time, “Simon, son of Jonah, do you love Me?” Peter was grieved because He said to him the third [3 is prime] time, “Do you love Me?” ….
    This is the disciple who testifies of these things, and wrote these things, and we know his testimony is true. And there are many other things that Jesus did, which were they written one by one [in linear sequence, or in a 1×1 matrix?], I suppose that even the world itself could not contain the books that would be written [a Cantor diagonalization proof of higher infinity?]. Amen.
    http://magicdragon2.livejournal.com/3457.html?nc=225&page=1#comments
    One version of a famous anecdote is:
    Diderot, the French Encyclopedist, visited the Russian court, invited by the Empress. Amused by his witticisms, she told him that she has a mathematician who has mathematically proved God’s existence and would demonstrate this in front of the whole court if desired so. Diderot agreed. So, to make a long story short, the great Euler advanced towards Diderot and in a tone of perfect conviction said:
    “Monsieur, (a^n + b^n)/n = x, therefore God exists!”
    Another nice connection between math and the Miraculkous is:
    “Every mathematician worthy of the name has experienced … the state of lucid exaltation in which one thought succeeds another as if miraculously… this feeling may last for hours at a time, even for days. Once you have experienced it, you are eager to repeat it but unable to do it at will, unless perhaps by dogged work…”
    Andre Weil, (6 May 1906 – 6 August 1998)
    The Apprenticeship of a Mathematician.
    Another math and God quote:
    “I tell them that if they will occupy themselves with the study of mathematics they will find in it the best remedy against the lusts of the flesh.”
    — Thomas Mann, (6 June 1875-12 Aug 1955) The Magic Mountain. 1927.
    MathWorld has pages on:
    Religious Terminology
    Angel Problem
    Archimedes’ Cattle Problem
    Beast Number
    Calvary Cross
    Croatian Cross
    Cross
    Cross Curve
    Cross of Lorraine
    Cruciform
    Cube Duplication
    Devil’s Curve
    Devil’s Needle Puzzle
    Devil’s Pitchfork
    Devil’s Staircase
    Devil on Two Sticks
    Evil Number
    Eye of Horus Fraction
    Gaullist Cross
    Greek Cross
    Integer (“God made the integers…”)
    Latin Cross
    Maltese Cross
    Maltese Cross Curve
    Papal Cross
    Pascal’s Wager
    Patriarchal Cross
    Saint Andrew’s Cross
    Saint Anthony’s Cross
    Square Cross

    Reply
  46. SouthernMyst

    Funny for me to trip upon this today, on the heels of this press release made yesterday, for a 2005 book.
    I wonder if they’re really going to link God to math in any of their curricula, or if they’re just saying that in the course descriptions so the parents have less of a problem ponying up the thousands in tuition to send their children to the school?

    Reply
  47. John Green

    A belated response to #23.
    Jonathon’s post is a nice classification of the metaphysical stances towards mathematics, but he is too pessimistic about the prospects for dialogue. My own position is about 75% Realism and 25% Social Constructionism, but I’m British so I don’t have to worry about foolish consistency.
    More useful is Eric S. Raymond’s thought-provoking essay (www.catb.org/~esr/writings/utility-of-math/) which helps to demystify the topic.

    Reply
  48. RootX

    “The good Christian should beware of mathematicians and all those who make empty prophecies. The danger already exists that mathematicians have made a covenant with the devil to darken the spirit and confine man in the bonds of Hell.”
    — St. Augustine (354-430)
    from [http://www.sci.utah.edu/~weiss/quotes/science.html]
    A really good article!
    Since, I also have similar views, and so I thought about creating my own modern society…
    It’s hard to live with ignorants >

    Reply
  49. Mark

    So where does Goedels incompleteness proof fall under Christian Math? I don’t think these C.M. people are familiar with that result as it kinda makes Christian based math approach…. inconsistant? It’s like they’d be saying ‘God is inconsistant’ or imperfect or something.

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  50. Chris

    So, I’ll go out on a limb here and probably embarrass myself. I have had only minimal contact with Godel’s theorem as yet, though I intend to rectify this asap as I found it extremely interesting. My question is this: If I believe in a single coherent reality that exists independent of my ability to perceive it (that is, I’m not making it up and it would continue in my absence), does Godel’s theorem pose a problem for my belief or just my ability to describe it?

    Reply
    1. Marius

      “My question is this: If I believe in a single coherent reality that exists independent of my ability to perceive it (that is, I’m not making it up and it would continue in my absence), does Godel’s theorem pose a problem for my belief or just my ability to describe it?”

      At most the latter! In fact, G√∂del was a hardcore mathematical Platonist and he was always disappointed that his incompleteness theorem was misunderstood as implying that no absolute mathematical truths exist. What *he* believed to have shown, was that in any “sufficiently complex” axiomatic system (those that can produce ordinary whole number arithmetic), it is possible to create a statement that *we*, from our point of view “outside” the system, *know* to be true, but which is unprovable within the system.

      He essentially does this by using arithmetic to encode a statement that says, “This statement is unprovable in this system”, which, *if* the system is consistent, necessarily has to be true, or else we would have derived a contradiction in the system.

      From the point of view of the system, this is a statement about arithmetic, saying something about prime factors of some humongous number, which the system is not able to prove or disprove. From our point of view, as humans outside the system, the statement has a double meaning which we have encoded in it, which enables us to say for sure that it must be true, if the system is consistent.

      Hence, any sufficiently complex (i.e. useful) axiomatic system is either inconsistent or incomplete. Hence, in any useful and consistent (an inconsistent system isn’t very useful!) mathematical system, there are *true* statements that cannot be proven. Hence, mathematical truth and provability are not the same – truth is independent from formal provability.

      For this reason, Gödel also believed statements such as the Continuum Hypothesis have an absolute truth value despite their independence from our usual axioms of set theory (he believed the Continuum Hypothesis to be false and at some point I think he conjectured that the cardinality of the continuum is aleph_2).

      It is interesting, in light of this, to ponder how difficult it is to prove seemingly simple statements in number theory that everybody believe to be true, such as the Goldbach conjecture.

      Reply
  51. Torbjörn Larsson, OM

    Chris:
    I’m not an expert either. But AFAIK some say that G√∂del’s different theorems doesn’t tell us anything about physics.
    Personally I think G√∂del shows us that our formal theories may be seamlessly appended with those theorems that simpler systems lack, in case nature is more extravagant than we expect. (We expect simple theories, and so far we haven’t been dissatisfied.)
    Btw, my 2c:
    With respect to “a single coherent reality” physics place us on pretty shaky ground IMHO. What we are used to think about as classical objects are contingent. For example the number of particles observed varies with the observer. (Specifically, IIRC an accelerating observer sees more particles in a more energetic vacuum than a comoving observer.)
    Isomorphisms and equivalences between theories makes this phenomena explicit. (For example AdS/CFT equivalence.)
    So if theories (which are revisable forms of “reality” anyway) aren’t always singular, what remains is the observed processes (phenomenas) under their different guises. Nature exist by observation, it is a singular universe (phenomena) that we observe, but it doesn’t look like it is observable or describable in a singular way except in the trivial form: we see it, therefore it is.

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  52. Mark C. Chu-Carroll

    Chris:
    Gödel’s theorems say nothing about whether or not there is a single objective reality. They just say something about formal reasoning systems: any particular consistent formal system has limits – things which cannot be proven within the bounds of that formal system.
    That doesn’t say anything about the universe: the universe isn’t a formal reasoning system.

    Reply
  53. Norm Breyfogle

    Mark CC,
    “Math doesn’t need God” is true, in terms of typical and traditional language and concepts. However,if “God” is defined (non-traditionally, for most) as the ineffable ground of all being (existence in its infinitude), then such is indeed the necessary predicate for everything, including math.
    And this from you, alluding to ominipotence, “And God couldn’t make geometry be inconsistent,” presumes upon omnipotence in a way reminicent of your claim that reality can’t be based on an infinite fractal. I’m not convinced at all that even my most certain logical faculties aren’t essentially constructs of convenience based on our circumstantial experience in this particular reality or universe. The fact is that math and our version of consistent logic would not exist at all without ineffble existence itself.

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  54. Torbjörn Larsson, OM

    The fact is that math and our version of consistent logic would not exist at all without ineffble existence itself.

    As far as I can see this can all be derived from the question “Why is there something rather than nothing?” As Stanford Encyclopedia of Philosophy asks: “Well, why not?”
    For a more deeper discussion why scientists are skeptical to apply observations from an ensemble (universe(s)) outside it (no universe), see here.

    Reply
  55. Xanthir, FCD

    Norm:
    Depending on your definition of ‘exists’, math and logic certainly would exist even if our universe didn’t. They are simply patterns, which may not (under particular ontologies) require manifestation to exist. This is implicit for anyone who assumes that new mathematical ideas or logical proofs are ‘discovered’ rather than ‘created’ or ‘invented’.

    And this from you, alluding to ominipotence, “And God couldn’t make geometry be inconsistent,” presumes upon omnipotence in a way reminicent of your claim that reality can’t be based on an infinite fractal.

    It ‘presumes upon omnipotence’? Dude, the point is that you can’t make contradictions, even if you’re omnipotent. Is it presumption to assume that an omnipotent being can’t make a stone so heavy he can’t lift it? That’s essentially the same thing. Just replace ‘stone’ with ‘geometry’ and ‘so heavy he can’t lift it’ with ‘that is inconsistent’.

    “Math doesn’t need God” is true, in terms of typical and traditional language and concepts. However,if “God” is defined (non-traditionally, for most) as the ineffable ground of all being (existence in its infinitude), then such is indeed the necessary predicate for everything, including math.

    And if “God” is defined as “my grandma”, then it is indeed true that God is dead. By playing with definitions you can say anything. Stick with commonsense definitions. God, as understood by everyone except apologists and certain philosophers, is not defined as “the entirety of existence” or anything like that. He’s just a powerful magic dude in the sky who loves us as long as obey his rules totally.

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  56. Norm Breyfogle

    If I stuck with only common sense definitions, I might more regularly use common slang like “dude.”
    =)
    Read me more closely, Xanthir. I didn’t write that math and logic wouldn’t exist if our *universe* didn’t, I wrote that math and logic wouldn’t exist if *ineffable existence* didn’t. Our universe is probably only one of many possible ones in the infinity that comprises all of existence.
    And I did write this in my very first sentence: “Math doesn’t need God” is true, in terms of typical and traditional language and concepts.
    I am partial to the idea that math and logic is so universal that it “describes the mind of God” (if you’ll allow the poetic reference).
    Re contradictions: they are contingent on definitions, and definitions may vary between minds and universes and mathematical systems. Math itself has certain conundrums, mysteries, and definitional inner contradictions, and all axioms are arguably a matter of choice.
    Re definitons: yes, one can define “God” any way one wants, but very few define “God” as their grandmother. (Although, being a mystic, I’ll allow it; lol.) Ineffable existence, OTOH, is held as a fine definition of “God” by a very large fraction of humanity, and possibly, arguably – implicitly, and not fully consciously – by an actual majority.

    Reply
  57. Xanthir, FCD

    I didn’t write that math and logic wouldn’t exist if our *universe* didn’t, I wrote that math and logic wouldn’t exist if *ineffable existence* didn’t. Our universe is probably only one of many possible ones in the infinity that comprises all of existence.

    I didn’t mean to imply that you said it required our specific universe to exist. If you wish, you can take my language to be assuming that there is only one universe in all of existence (however true that may be).
    My point was that math, logic, and so on don’t have physical existence. Insofar as they can be said to exist at all, they would do so whether or not existence, um, existed. At least for convenience’s sake, I’m willing to grant that they exist, so they are independent of the universe’s existence quality.

    And I did write this in my very first sentence: “Math doesn’t need God” is true, in terms of typical and traditional language and concepts.

    Nod, and then you go on to redefine God. That’s the part I was arguing against. The sentence you refer to is uncontroversial.

    Re contradictions: they are contingent on definitions, and definitions may vary between minds and universes and mathematical systems. Math itself has certain conundrums, mysteries, and definitional inner contradictions, and all axioms are arguably a matter of choice.

    Exactly. And geometry, by the definitions that we use, cannot be made contradictory no matter what a theoretically omnipotent being does. If you define it in some other way, then of course there may be contradictions. I (and Mark, presumably) aren’t referring to the set of all possible definitions of geometry, but rather to the common one that we use.

    Re definitons: yes, one can define “God” any way one wants, but very few define “God” as their grandmother. (Although, being a mystic, I’ll allow it; lol.) Ineffable existence, OTOH, is held as a fine definition of “God” by a very large fraction of humanity, and possibly, arguably – implicitly, and not fully consciously – by an actual majority.

    Ignoring the contradiction this presents with your previous comment… ^_^
    Defining god as the whole of existence is much more pantheistic than most people are willing to do. And even then, just because god is existence doesn’t necessarily mean that he is math (see previous sections of this post).
    In any case, I certainly consider that question begging. You can’t just say, “God isn’t math? Oh yeah, well what if I say that God is EVERYTHING!? What about then?”. Part of the failing of the concept of “God” is that your redefinition is completely valid, because the concept is vacuous and can thus be said to be anything at all.

    I am partial to the idea that math and logic is so universal that it “describes the mind of God” (if you’ll allow the poetic reference).

    I agree only in the sense that Spinoza and Einstein meant ‘God’. In any case, you’ve just implicitly agreed that God cannot allow contradictions, if he himself is described by logic. ^_^

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  58. Norm Breyfogle

    Again, I largely agree. *Largely.* However, existence does indeed contain “contradictions.” To say that math “describes the mind of God” isn’t to say that such a description is perfectly accurate or exhaustive.
    I’ll grant that math and geometry is very, very consistent in this universe … for now (lol). But no one can be absolutely certain that the rules, laws, and even our own consciousness and thinking won’t change, that the depth of unknown infinite existence doesn’t contain such deep existential suprises that it might literally change even the present absolutes of thought, reason, and logic. After all, math is a language we’ve devised (or discovered) to model the universe *as we presently know it,* and this category includes our own thinking (i.e., the universe as we presently know it includes our minds and therefore it includes our mathematical systems with all their axioms and equations).
    I don’t mean to belabor any of this; to do so might appear to be inscrutable nonsense (and may *actually* be so). My only intention is to couch verities in the most universally true semantics possible. It’s not really a cumbersome burden to do so, though it may appear to be so at first, until an improved semantics is developed. In the long run, a more universal semantics would and does eliminate many unnecessary arguments.
    To wit: my point about “God” is that the typical definition of such includes omnipresence, omnipotence, and omniscience. Seems to me that such characteristics necessarily describe ineffable existence itself, not a separate individual.

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  59. Torbjörn Larsson, OM

    Norm:

    To wit: my point about “God” is that the typical definition of such includes omnipresence, omnipotence, and omniscience. Seems to me that such characteristics necessarily describe ineffable existence itself, not a separate individual.

    I suspect you mean that general properties aren’t amenable for personalization. But those properties you mention are inconsistent with their own existence or each others existence, and inconsistent with observed existence. Which makes it difficult to accept your description even for the sake of the argument.

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  60. Norm Breyfogle

    Torbjörn,
    Yes, “general properties aren’t amenable for personalization.” Thanks; I wish I’d been that concise.
    As for your difficulties with my semantics: I understand,but I see the definitions of those words characterizing “God” in a much more flexible manner than you undoubtedly do. Presumably, for you, the words “omnipresence, omnipotence, and omniscience” are necessarily anthropomorphic, but they aren’t for me. My point, in fact, is that they *can’t* be anthropomorphic (as per your concise statement opening this very post), i.e., no specific consciousness can fit that bill. So we agree on that. So what’s left of “God”? Well, only general existence comes close to exhibiting those characteristics; only existence is everywhere at once (omnipresent), only existence is all powerful (omnipotent), and only existence is all knowing (omniscient).
    Of course, the last adjective is the one most clearly carrying anthropomorphic connotations, but because anthropomorphic omniscience is literally impossible (due to the fact that any internal map of any individual mind or consciousness – even that of a traditional “God” – can never perfectly equal the territory of all of existence), the only referent coming close to exhibiting omniscience is the overarching interconnected web of information comprising the universe(s).

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  61. Torbjörn Larsson, OM

    Norm:
    Ah, i see, I didn’t understand that part.
    Well, I would say that “omnipresence, omnipotence, and omniscience” only makes sense for a set of independent agents (individuals, persons), which is what I was discussing.
    When we transform these properties, whatever we would like to characterize them as, onto non-agents it becomes pantheism I think. Somewhere here I lose interest in calling it religion and start calling it mysticism. I might not care much for anthropomorphizing, but I sure like my labels. ūüėõ

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  62. Norm Breyfogle

    You’re saying that omnipresence, omnipotence, and omniscience are basically nonsense words because they refer to impossible qualities of individuals. And I agreed that individuals can’t possess these qualities. But millions or even billions of mystics view “God” not as an individual per se (a fact to which you correctly alluded), so for the sake of clearer commuication it’s apparent that “God” needs to be defined more intelligently, and engendering a better semantic grasp of these concepts in religious minds – and even in nonreligious minds – goes a long way toward opening such minds to the inherent contradictions in their own assumptions.

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  63. Owlmirror

    @#48: Regarding Euler and Diderot, I serendipitously was researching this today, and found that (a) It probably was not Euler (the original version of the anecdote, written down some decades after it allegedly happened, says only “A Russian philosopher”), (b) It probably did not happen at all, and (c) Diderot was rather well versed in math, having written several papers before visiting Russia, including proofs that by the use of a circle and its involute, one could square the circle, trisect the angle, and double the cube. Or at least, so says the paper.
    In searching out Diderot’s works, I noticed that Euler’s name appears in his first paper, on acoustics. Since I don’t actually read French, I am not sure what it says, but he seems to be referencing something Euler wrote about flutes.

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  64. Torbjörn Larsson, OM

    Norm:

    goes a long way toward opening such minds to the inherent contradictions in their own assumptions

    You are assuming that a semantic analysis is necessary to reject flawed assumptions.
    I don’t agree, I think observations are key. So when I note that properties are inconsistent with existence I am pursuing an empiricist program, not a philosophical one.
    There is no outward difference here. But in other instances there will be.

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  65. scineram

    Math is based on logic. It doesn’t matter whether you believe in God or not. It doesn’t matter whether you’re in our universe, or some radically different one. Math wouldn’t change. Math is the product of pure abstract reasoning. First order predicate logic will always work in exactly the same way in a universe created by a benificent deity, a universe created by a malevolent deity, a universe created by a gaggle of insane elves, or a universe created by absolutely no one.
    Nonsense! Pure abstract reasoning is only in your HEAD. Your head is BIOCHEMICAL PROCESSES. These processes are governed by the laws of THIS universe.

    Reply

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