Mathematics and Religion

Unlike physics, mathematics has managed to remain immune from efforts to promote pseudo-scientific agendas, financed with the goal of mixing up science and religion. I don’t see any reason to believe this is going to change, but I just noticed that the Templeton foundation is funding a program here in New York later this month on the topic of Mathematics and Religion.

The program will take place at the Philoctetes Center, which is run out of a townhouse on the Upper East Side and supports a variety of activities that you can read about here. The organization ran into serious trouble with its funding recently since its investments were managed by Bernard Madoff. A year before the scandal broke, Philoctetes sponsored a panel discussion (accessible here) on The Future of the Stock Market, which featured Madoff as a panelist. Because of these losses, the Center has had to look for funding elsewhere, and has found some from the Templeton Foundation.

One notable thing about the Mathematics and Religion panel is that it doesn’t include much at all in the way of mathematicians. Of the six participants, one is Max Tegmark, a physicist prominently involved in Templeton-funded multiverse studies, but the only mathematician is Edward Nelson. Nelson is quite far from the mainstream of mathematics, with a religion-infused recent paper entitled Warning signs of a possible collapse of contemporary mathematics, available here. Unlike the case of multiverse pseudo-science, which has drawn support from leading figures in the physics community, this sort of point of view about mathematics has attracted zero interest among mathematicians.

The Mathematics and Religion panel isn’t any threat to mathematics, and is part of a larger and much more worthy program about mathematics at Philoctetes funded by Templeon. In November there will be a panel discussion on Mathematics and Beauty that sounds interesting, I might even try and make it over there to see it (last year I did attend a talk at Philoctetes given by Barry Mazur). The Mathematics and Religion panel is associated with something more serious, a talk by Loren Graham on his book Naming Infinity. It’s a book I read earlier this year, but don’t think I ever got around to writing about here on the blog. I wasn’t completely convinced by some of the claims it makes about the relation between religious practices and the work of certain Russian mathematicians. The story it tells about the religious sect of “Name Worshipers” and the history it recounts of one part of the Russian mathematical community are quite fascinating.

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23 Responses to Mathematics and Religion

  1. Bee says:

    “Certainly, if one needs to believe that beyond the appearances of the world there lies a permanent and transcendent reality, there is no better choice than mathematics. No other conception of reality has led to so much success, in practical mastery of the world. And it is the only religion, so far as I know, that no one has ever killed for.”
    ~ Lee Smolin, The Life of the Cosmos

    Sorry, couldn’t resist 🙂

  2. ObsessiveMathsFreak says:

    Is this a good time to bring up the tale of Hippasus and the Pythagoreans?

  3. Chris W. says:

    From that essay of Edward Nelson:

    The most impressive feature of Cantor’s theory is that he showed that there are different sizes of infinity, by his famous diagonal argument. But Russell applied this argument to establish his paradox: the set of all sets that are not elements of themselves both is and is not an element of itself. Actually, Russell’s paradox was in response to Frege’s work, not Cantor’s. Frege gave a clear and precise account of his work, making it possible for Russell to show it was wrong, whereas Cantor’s work was in parts so vague and imprecise that, as Pauli said of another theory, it was not even wrong.

  4. Per says:

    The paper by Edward Nelson was really nice. I had never heard about it before, thanks for sharing it. It’s nice with some sort of fresh trippy take on contemporary mathematics. God knows it’s lacking in physics…

  5. inc. says:

    I had a brief interaction with E.N. some time ago; I certainly respected him on the basis of his papers. Hmm, unfortunate that he would find himself in such company.

  6. Janne says:

    The title reminded me of Gödel’s ontological proof.

  7. Aleksandar Mikovic says:

    Bee´s quote of Lee Smolin’s apology of platonism was a pleasant surprise, because very few physicists are platonists. This is contrary to mathematicians, where a lot of them are platonists, which is understandable.

    The reason why physicist are not platonist is the idea that everything can be explained from a finite set of elementary constituents (elementary particles, or strings, or something else) moving in space, subject to a finite set of laws of motion and structure. However, when analysing this framework, one has to decide whether the laws of motion are independent entities or they are simply random regularity patterns in the motion of the elementary constituents.

    If one chooses the second option, this means that our world can disappear tomorrow and that the ultimate explanation for any phenomena is that it is a random fluctuation. On the other hand, the first option leads to platonism, i.e. there exists a separate realm from spacetime, where abstract ideas like mathematical structures and laws live. Furthemore, it is then natural to identify our physical world with a mathematical structure, as Max Tegmark has proposed, which explains Wigner’s question of unreasonable effectivness of mathematics in physics.

    Now, why still many physicist do not accept a platonic metaphysics and stick to the chaotic universe metaphysics? My guess is that in a platonic metaphysics the idea of God naturally appears, and many physicist are opposed to it because it is an unscientific idea. However, it is an irony that the scientific metaphysics, i.e. a materialistic metaphysics, leads to the conclusion that the ultimate explanation for anything is that it is a random event, which is contrary to the very spirit of science.

  8. mark a. thomas says:

    It should be noted (myth?) that Hippasus was strangled or drowned by the Pythagorean order for revealing to the world the irrational construction of the dodecahedron. To keep the nature of mathematics divine they then set their sights on the continuum rather than that of the discrete whole numbers. It seems ancient maths had connections to religions or mysteries.

  9. Benni says:

    It seems that Nelson does indeed want to publish real mathematical work. Yet what he wants to write seems not to be ready.

    He has a better discussion of his program here. The content is the same, however this is aimed at mathematicians:

    http://www.math.princeton.edu/~nelson/papers/hm.pdf

    There, one can read that he wants to give a proof of something which he is still working on.

    Maybe he goes to such conferences since he is somewhat struggling with his proof.

  10. Benni says:

    Nelson writes in

    http://www.math.princeton.edu/~nelson/papers/hm.pdf :

    The goal is to produce an explicit superexponentially long recursion and prove that it does not terminate, thereby disproving Church’s Thesis from below, demonstrating that finitism is untenable,
    and proving that Peano Arithmetic is inconsistent.

    It seems that he has problems with this and then he goes to templeton conferences.

  11. Joao Leao says:

    (Aleksandar Mikovic says:
    “Now, why still many physicist do not accept a platonic metaphysics and stick to the chaotic universe metaphysics? My guess is that in a platonic metaphysics the idea of God naturally appears, and many physicist are opposed to it because it is an unscientific idea. However, it is an irony that the scientific metaphysics, i.e. a materialistic metaphysics, leads to the conclusion that the ultimate explanation for anything is that it is a random event, which is contrary to the very spirit of science.”)

    I do take issue with the notion that platonism in particular or idealism in general imply theism. Plato was quite careful in separating god from (the) good and should not be punished by what the neoplatonists and the doctors of the church made of his thought. (The same may be said of the frequent but abusive “equation” of materialism with atheism). That may explain why, even with a majority of platonists among mathematicians, Templeton has not been able to recruit any mathematicians to its campaign gatherings, as Peter noticed. God is NOT a mathematical idea!

  12. Benni says:

    By the way, I think that Nelson’s claims in http://www.math.princeton.edu/~nelson/papers/hm.pdf

    “The goal is to produce an explicit superexponentially long recursion and prove that it does not terminate, thereby disproving Church’s Thesis from below, demonstrating that finitism is untenable,
    and proving that Peano Arithmetic is inconsistent.”

    are quite ambitious. Since the link above does not contain that much fuzzy religious statements as Nelson’s other paper, can someone report what is about those claims:
    http://www.math.princeton.edu/~nelson/papers/hm.pdf

    From what I see, he is indeed using only logic. Yet I’m only a physicist.

    So: can some real mathematician report, if Nelson’s program has any chance to succeed? Or are there errors in the above pdf?

    I’m just curious. Benjamin

  13. Vidkun says:

    Now, Nelson is surely something of a philosopihcal extremist, but he is without any doubt a sound mathematician; he has many results throughout mathematics, logic and mathematical physics.

    Also the “problem of induction” in the talk linked led him to develop his Predicative Arithmetic. I don’t think many besides Nelson himself regard it as relevant to the foundations of mathematics, but his results were used when others (Sam Buss for example) began developing Bounded Arithmetic, which has strong connections to complexity theory and (variations of) the P=NP problem. Hence, the “zero interest among mathematicians” is rather unfounded (if mathematical logicians are to be included).

    I like to view Nelson as a prime example of how philosophically untenable positions could lead to valuable results. (Compare how Einstein’s and Heisenberg’s dogmatic positivism gave us Relativty and Matrix Mechanics.)

  14. Mark Stuckey says:

    “If a ‘religion’ is defined to be a system of ideas that contains unprovable statements, then Gödel has taught us that, not only is mathematics a religion, it is the only religion that can prove itself to be one.” J.D. Barrow in Between Inner Space and Outer Space, Oxford University Press, 1999, p 88.

  15. BigG says:

    Mark,

    That is not a good definition of religion because there are many counter examples that are certainly not religion. If you accept this definition than philosophy and physics would be religions which is ridiculous. The point of a definition is to show somethings’ defining characteristic; what makes it different from what is not it.

    The definition of religion is a system that contains a doctrine of liberation; i.e. a soteriology.

  16. Mark Stuckey says:

    BigG,

    I don’t know about philosophy, but here is a quote about physics:

    “Many scientists are deeply religious in one way or another, but all of them have a certain rather peculiar faith – they have a faith in the underlying simplicity of nature; a belief that nature is, after all, comprehensible and that one should strive to understand it as much as we can. Now this faith in simplicity, that there are simple rules – a few elementary particles, a few quantum rules to explain the structure of the world – is completely irrational and completely unjustifiable. It is therefore a religion.” Sheldon Glashow in The Quantum Universe, co-produced by WETA-TV and The Smithsonian Institution, 1990.

  17. BigG says:

    Mark,

    Does Sheldon Glashow of J.D. Barrow saying something make it true? I’m interested in following the idea to its conclusions. The original definition you posted said a “system of ideas that contains unprovable statements.” By your logic its hard to find a system of thought that isn’t a religion. Why? Because all systems of thought have some unjustifiable assumptions. Physics assumes the validity of the experimental method. Can physics use the experimental method to establish the experimental method? Can light illuminate itself? Can darkness obscure itself?

  18. Peter Woit says:

    Any more comments about religion will be deleted. The internet is full of other places those interested in this kind of thing can have this kind of discussion.

  19. Tony Smith says:

    Bee quoted Lee Smolin as saying that “… mathematics … is the only religion, so far as I [Lee Smolin] know, that no one has ever killed for …”.

    Whether or not math may have been involved in violent persecution of Pythagoreans, etc,
    it seems clear that Nazi Germany did severely persecute what it defined as “Jewish mathematics”. In his book “History of Mathematics: A Supplement” (Springer 2007) Craig Smorynski said:
    “… the change of mathematical direction … would reach an extreme in the 1930s with the nazi distinction between
    good German-Aryan anschauliche (intuitive) mathematics
    and
    the awful Jewish tendency toward abstraction and casuistry.

    the proponents of this distinction had to dance some fancy steps in explaining how the abstract mathematics of David Hilbert … was not the bad abstraction of the Jews. …”.

    Tony Smith


  20. The story it tells about the religious sect of “Name Worshipers” and the history it recounts of one part of the Russian mathematical community are quite fascinating.

    Uhh, no. Perhaps the story could be fascinating, but the actual book Graham produced is, let’s face it, a waste of time if you are interested in the mathematics. We learn that there are some bizarre orthodox christian practices, that some Russian mathematicians were strongly orthodox and interested in these practices, and that some of the mathematicians were gay.

    What we NEVER learn, which would have made the whole exercise worthwhile, is exactly what these Russian mathematicians did that was so spectacular compared to western mathematicians. Sure, we are told over and over again that name worshipping led to mathematics that was too “daring” for French and German and US mathematicians, but we are never told WTF that mathematics was.

    This ridiculous, to put it bluntly, c**k-teasing approach to writing history has put Graham on my list of authors to be permanently avoided. Don’t waste my time for 150 pages and then fail to deliver the only damn thing that made me interested in your book in the first place!

    (BTW do not be confused. Loren Graham is NOT Lauren Graham!)

  21. Elbadudedansky Brodudensky says:

    You can’t corrupt math, although it’s not because there aren’t mathematicians who wouldn’t corrupt it if it could be corrupted.
    Numerous mathematicians become just as illogical and biased as the pack, once they stray from math.

    What can be corrupted is the application of math, and many people confuse the application of math with math.

    Because the most useful of math is tied into the real numbers, the foundation of which is standard set theory, standard logic, and the natural numbers, then how could any corruption of note not be logically tracked down? A corrupt construct would most likely be at a higher level than the real numbers, and anything at a lower level, what would be the purpose of that? Very few people have a beef with the way we count or with the law of the excluded middle; it might be better to say that very people would even want to have the awareness that they could be aware of such things.

    Also, other than the general status of “mathematician,” there’s no glamor in math. It’s like a foreign language with thousands of dialects, where those fluent in one dialect can’t communicate in most of the other dialects.

    People will sit for hours listening to talks about physics and astronomy, because it involves the physical world, and there’s something to try and visualize. With math, there’s no pleasure in hearing someone talk in a foreign language; it’s no fun to have your eyes glaze over.

    And most people barely tolerate useful math. Why would they tolerate useless math? Especially if it tweaked the useful math in a bad way.

    But you don’t have to corrupt math to corrupt math-based science. You just have to find a set of unproved assumptions and a mathematical model that will do what you want it to do. The logic behind the math will be solid. And in fact, given your unproved assumptions, why couldn’t you get the desired conclusions? At most, you might merely need some additional unproved assumptions. With the right credentials, you’d be good to go.

  22. Elbadudedansky Brodudensky says:

    In the above, please feel free to replace “real numbers” with any other popular and useful algebraic structure.

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