Polkinghorne’s empirical evidence for god: math and a comprehensible universe

I wanted to put up a brief post to get reader reaction to two claims that are common among science-friendly theologians. They are a centerpiece, for instance, of John Polkinghorne’s arguments for God’s existence. In the evenings these days (to the detriment of my sleep), I’m reading Polkinghorne and Alvin Plantinga to learn about the brand of “sophisticated” theology that tries to reconcile faith and science.

I’ve already discussed Polkinghorne a few days ago, and the quotes I give below are from his book Science and Religion in Quest of Truth. As I noted in my earlier post, Polkinghorne, unlike many theologians, does think that pure revelation cannot suffice as evidence for God; one needs empirical observations as well.

I’ll give my brief reactions to the arguments, but, as I said, I’d like to know how readers would respond to these. I’m looking for serious responses, but feel free, as always, to be lighthearted as well.

His two arguments are these:

  • The universe can be comprehended by the rational faculties of humans, and its workings appear to adhere to laws of physics.
  • Much of our understanding of the universe is expressed through mathematics, which is “unreasonably effective” in encapsulating what we discover about nature. 

Ergo Jesus. 

Here are some supporting quotes from Polkinghorne, showing how he connects the above observations—both undoubtedly true—with God.

“. . . why is science possible at all in the deep way that has proved to be the case?” p. 71

“A distinguished nuclear physicist, Eugene Wigner, once asked, ‘Why is mathematics so unreasonably effective?’ Those seeking an understanding as complete as possible must ask what it could be that that links together the reason within (mathematical thinking) and the reason without (the structure of the physical world) in this remarkable way? The universe has not only proved to be astonishingly rationally beautiful, affording scientists the reward of wonder for all the labours of their research. Why are we so lucky?

It would surely be intolerably intellectually lazy not to seek to pursue this question.  Yet science itself will not provide its answer, for it is simply content to exploit the opportunities that these wonderful gifts afford us, without being in a position to explain their origin.  Theology, however, can step into the breach. Science has disclosed to us a world which, in its rational transparency and beauty, is shot through with signs of mind, and religious belief suggests that it is indeed the Mind of the Creator that lies behind the wonderful order of the universe. (p. 73)

I have several tentative responses, and I believe Sean Carroll has addressed some of the above, though I can’t immediately lay my hands on his essays and posts (perhaps he’ll weigh in here).

  • If the Universe didn’t obey physical laws, we wouldn’t exist, for the universe we know couldn’t have formed in the first place.  Too, we couldn’t exist as biological entities if the physiology and biochemistry of our bodies didn’t adhere to physical laws—natural selection could not create faculties and senses that behave with regularity.
  • If the Universe didn’t always obey physical laws, that, too, could be taken as evidence for God, who could intercede with alarming regularity to alter whatever laws did exist.  Heads God wins, tails physicists lose.
  • We don’t understand why there are physical laws that behave with regularity, but that lack of understanding doesn’t point to the existence of a creator—much less Polkinghorne’s Christian creator who birthed Jebus.
  • The existence of those laws must (like the existence of God itself to theologians) be left as something that does not require an answer—or the answer that “that’s just the way things are.” I think this is physicist Sean Carroll’s answer.
  • Physical laws could differ—or even be irregular—in other universes that may exist. (Remember that multiverses are not, as some theologians imply, a “desperation move” on the part of physicists to explain fine-tuning and the anthropic principle. Rather, multiverses fall out as a prediction of some theories of physics.)
  • These are god-of-the-gap arguments: science could one day explain the existence of regular physical laws, but right now we don’t understand them, or why they must take the form they do.
  • In other places Polkinghorne (along with other theologians) argue that there are many phenomena in nature that cannot be comprehended with science, much less mathematics. These supposedly include love, aesthetics, and morality.  Those phenomena, too, are given as evidence for God. In other words, Polkinghorne is trying to have it both ways: the universe’s comprehensibility via science is given as evidence for God, but aspects that supposedly aren’t scientifically comprehensible are also given as evidence for god.
  • The “God” explanation offered by Polkinghorne is not testable, that is, it can’t be disconfirmed. Even if we find out why there are laws of physics, Polkinghorne could argue that God was behind it all.

I know that there are a fair number of physics- and math-savvy readers here, and I’m particularly interested in their responses (particularly about the “unreasonable effectiveness of mathematics”), but anybody is welcome to respond.


  1. Posted February 23, 2012 at 9:13 am | Permalink

    Mathematician John Allen Paulos addresses this issue in his book Irreligion: A methemtician explains why the arguments for god just don’t add up (p. 127-132).

  2. Captain Howdy
    Posted February 23, 2012 at 9:19 am | Permalink

    A number of comments have pointed out that Polkinghorne’s is an elaborate God of the Gaps argument. (Actually it’s not that elaborate.)

    Note the number of times he asks “Why?” Polkinghorne doesn’t merely pose the inevitably unanswerable question, he insists that it is “intolerably intellectually lazy not to seek to pursue this question.”

    Of course one can ask “why” with infinite regress, and therefore one will eventually, inevitably run into a gap in our understanding. You can either continue the exploration, thereby increasing our body of knowledge about the universe, or throw your hands up and declare God dunnit.

    Who’s the intellectually lazy one here?

  3. Nicolas Perrault
    Posted February 23, 2012 at 9:32 am | Permalink

    “The unreasonable effectiveness of mathematics.”

    This argument fails to impress me. Math works for two main reasons:

    The first has to do with rigour. The axioms are carefully laid and are consistent as far as we can see. It is thus possible to spot faulty thinking even in a long chain of arguments and algebraic manipulations. If applied correctly, mathematics will not lead to contradictions or paradoxes. (In the unlikely event that this happens mathematicians won’t hesitate to change the axioms and definitions to avoid all contradictions and paradoxes. For example this was done when mathematicians were confronted with paradoxes in set theory such as Russell’s paradox).

    The second: we are free to adjust the axioms and definitions so that they very closely match whatever we observe. From the observation that candies do not spontaneously appear, disappear or merge we can account for them by using the simple rules of arithmetic. If the axioms of Euclidian geometry fail near a massive body, we’ll use non-Euclidian geometry instead.

    The simple fact that we exist is to me conclusive evidence that there is some kind of order out there. Math is now so advanced and powerful that there is usually a mathematical way to at least partially encapsulate what we observe.

    In conclusion, the unreasonable effectiveness of math is to me much less puzzling than would be its chronic ineffectiveness. To see a proof of God in the effectiveness of math is a “sophisticated” form of wishful thinking.

  4. Ian Atkinson
    Posted February 23, 2012 at 9:33 am | Permalink

    When it is known what God is made of, how he functions as an intelligent being, how he can be detected by senses or instrumentation why he is eternal and the Universe is not, God will be ‘science.’ Until then he will remain a leftover from an ancient Canaan pantheon.

    When any trace of Jesus can be found, or any record of his existence contemporary to his life, or any record before Paul of Tarsus had his vision, then Jesus will also be ‘science.’

    For millennia philosophers have been using tricks of language; metaphors, use/mention errors, swapping existence of ‘concept of object’ for existence of the ‘object,’are all mealy mouthed tricks to muddy the waters between fact and non-fact. Thank goodness we’re gradually entering an age of objectivity.

    A musky smell and rubbish scattered around a garden may or may not be proof of a fox, but it isn’t proof of anything to somebody who’s never seen or heard of a fox. Empirical Proof of God’s actual existence is needed *before* aspects of the Universe can be taken as proof of him having been there.

  5. Daniel Engblom
    Posted February 23, 2012 at 9:34 am | Permalink

    Richard Carrier has posted a collection of his refutations on these issues to these “arguments”. Anyone want to check them out? I’m not qualified, but I like Carrier already (has had many funny, clear and instructive talks over at skeptikon – here’s the youtube channel: http://www.youtube.com/user/HamboneProductions#g/u)

    Here’s the blog post:

    Opinions? Think this is enough to refute Polkinghorne’s nonsense?

    • Kevin
      Posted February 23, 2012 at 10:17 am | Permalink

      He doesn’t say it outright, but it looks like a Bayes analysis.

      But again, in my opinion he misses the mark because evidence cannot be used to justify position “A” and position “not A” at the same time.

      All of Polkinghorne’s “evidence” — whether or not we agree with his suppositions — can be used to support the following “not A” contention:

      “An all-natural universe arose from all-natural processes that continue today, and can be best understood via model-dependent realism.”

      Polkinghorne and all other apologists have to show why their “evidence” (which isn’t evidence but a series of observations) reject this “not A” hypothesis. They can’t.

      The very best they can do with this line of reasoning is a tie. Neither “A” nor “not A” are supported. And in this setting, the tie goes to the null hypothesis (ie, no god). Not to some vague deism that leads to “ergo, Jesus”. The tie goes to “all-natural processes.”

  6. Xuuths
    Posted February 23, 2012 at 9:53 am | Permalink

    Polkinghorne refuses to acknowledge and state that math has evolved.

    Imagine two early people discussing counting:

    Person A: Counting is simple. 1 apple plus 1 apple equals 2 apples.

    Person B: OK, let me try. 1 dirt pile plus 1 dirt pile equals 1 bigger dirt pile. This is complicated.

    Person A: No, you’re just stupid. Counting is simple.

    catholic Person C: 1 father plus 1 son plus 1 holy ghost equals 1 god.

    Person A: Get out of here you nut!

    Math evolved.
    What didn’t work was discarded. What turned out to be inaccurate was discarded. What was found to be needlessly complicated (a simpler solution was discovered) was discarded. What provided less accurate results was discarded.

    Of course over time math got better, more accurate, and with more elegant solutions. That would happen in any system — even intermittently random ones would eventually yield some kind of math formulas.

    Sheesh, Polkinghorne. Get a grip!

  7. Neil
    Posted February 23, 2012 at 10:00 am | Permalink

    Believers want it both ways. If the universe is comprehensible, it must be god. If the universe is incomprehensible, as in how did that electron go through both slits, it must be god.

    • Circe
      Posted February 23, 2012 at 10:14 am | Permalink

      But surely the only(TM> explanation for the electron’s behavior can be that god personally chaperoned it through both the slits? Ergo {Krishna, Shiva, Allah, Quetzalcoatl, Zeus, Thor, Ganesha, Great Juju at the Bottom of the Sea, Jesus, Jehova}!

      • Yiam Cross
        Posted February 23, 2012 at 5:14 pm | Permalink

        You miss the point. While Allah and Quetzalcoatl are chaperoning the electron through the slits, Gnaesha, Thor, Zeus and all the rest are busy keeping transatlantic flights in the air, hard disc drives functioning correctly, church spires from toppling over etc etc. No wonder we need so many gods and they really do have to be supernaturally powerful. It’s not as easy a life as you might imagine. Ask Bruce (Almighty). Or maybe Morgan Freeman.

      • sasqwatch
        Posted February 23, 2012 at 5:20 pm | Permalink

        No. Buddha.

        Because his mother had two slits, including the one he was born out of. Some guys can’t theolosophize for shit.

        • Circe
          Posted February 23, 2012 at 11:30 pm | Permalink

          Let’s leave poor Siddhartha Gautama out of this. The man was apparently fed of the ritualistic religions of the day and tried to start an agnostic religion to combat it, and even apparently had the honesty to point to his followers that he was no god, offering as proof his impending death through the usual cause of old age and disease, and what do his followers do after his death? Why, break up into two sects, with the majority sect deciding to worship the guy as a god, complete with rituals. The guy must have facepalmed if there was an afterlife.

          • sasqwatch
            Posted February 24, 2012 at 3:37 am | Permalink

            :-) A two-slit experiment gone horribly wrong.

  8. Circe
    Posted February 23, 2012 at 10:07 am | Permalink

    The universe can be comprehended by the rational faculties of humans, and its workings appear to adhere to laws of physics.

    Much of our understanding of the universe is expressed through mathematics, which is “unreasonably effective” in encapsulating what we discover about nature.

    Ergo Jesus.

    This always bothers me. Why not “Ergo {Krishna, Shiva, Allah, Quetzalcoatl, Zeus, Thor, Ganesha, Great Juju at the Bottom of the Sea}?

  9. Posted February 23, 2012 at 10:12 am | Permalink

    Humans have fallen in love with an indifferent universe after existing in it a bare fraction of a second. Except for one tiny planet, the universe appears to be an inhospitable, deadly place and certainly not evidence of a loving deity(s). Life as we know it is an accident. If a god is responsible, he is selfish, cruel, stingy, fickle, arrogant, dishonest, and an unintelligent designer.

    • Circe
      Posted February 23, 2012 at 10:16 am | Permalink

      It does not seem to be such a deadly place for stars, which suggests that if there is a god, she must be a star.

      • Kevin
        Posted February 23, 2012 at 10:20 am | Permalink

        Yes, but since fundamental process of stars is to convert H to He (and other elements), god must be inordinately angry at H.

        • Circe
          Posted February 23, 2012 at 10:33 am | Permalink

          ‘He’ is a false god, so she needn’t be anything more than bemused by “H(e)is” antics.

    • derekw
      Posted February 23, 2012 at 3:19 pm | Permalink

      So you say…while typing on your 17″ laptop sitting in a warm room on your Lay-Z-Boy sipping a hot latte while watching NCIS on your 60″ LED LCD.

  10. Posted February 23, 2012 at 10:23 am | Permalink

    I’ll say it again: the utility of mathematics makes the possibility of some “designing force” to be a conjecture with considering…nothing more than that. It has nothing to do with any deity that humans have conjured up.

    Why not some other deities conjured up by beings in another galaxy or something no being anywhere has conjured up?

    Those who claim that this is any evidence for any human god hasn’t really accepted the Copernican principle that there is nothing “special” about the earth, humans, etc.

    I think that Sean Carroll’s point of view makes far more sense.

  11. PoxyHowzes
    Posted February 23, 2012 at 10:30 am | Permalink

    I’m a true believer that “mathematics” doesn’t exist in any “real” sense.

    a) None of us will ever see a line exactly Pi units long, or 10/3 units, or SQRT(2) units. That illustrates that maths is as much a notational tool as a descriptive one. Check out Newton’s versus Leibniz’s calulus.

    b) Almost all useful “mathematical” applications these days are successive approximations built by numerical methods from engineered calculators.

    Successive approximations was the method Aristotle used to approximate Pi. Successive approximations is the foundation of “The” calculus, whether Leibniz’s or Newton’s. Millions or billions or trillions or more of successively calculated approximations, and not a whit of Newton’s formulas, got us to the moon.

    So no, Mathematics is not “unreasonably” effective at describing the real world. Mathematics is (by definition and by practice) an idealized representation of scattergrams of observations of the real world.

    • Circe
      Posted February 23, 2012 at 10:38 am | Permalink

      “None of us will ever see a line exactly Pi units long, or 10/3 units, or SQRT(2) units. That illustrates that maths is as much a notational tool as a descriptive one. Check out Newton’s versus Leibniz’s calulus.”

      Why not? just draw a line, and define its length to be units. Of course, you may never be able to draw an ideal line (papers is not really a planar, if you look close enough), but that’s beside the point.

      • Circe
        Posted February 23, 2012 at 10:40 am | Permalink

        “Successive approximations was the method Aristotle used to approximate Pi.”

        As far as I know of the history of trigonometry, the earliest estimates of the value of pi were made my Archimedes, and then improved further by Aryabhata (whose value remained the best computed for about a millennium after him), and not be Aristotle.

  12. Circe
    Posted February 23, 2012 at 10:40 am | Permalink

    “Successive approximations was the method Aristotle used to approximate Pi.”

    As far as I know of the history of trigonometry, the earliest estimates of the value of pi were made my Archimedes, and then improved further by Aryabhata (whose value remained the best computed for about a millennium after him), and not be Aristotle.

  13. abb3w
    Posted February 23, 2012 at 10:58 am | Permalink

    The reason mathematics is effective at describing the universe is because mathematics is effective at describing ANYTHING, per Gödel. (The reason mathematics seems efficient at describing parts of the universe is because the more efficiently solvable math is easier to recognize.)

    The reason human reason can handle mathematics is a result of the potential of mathematical systems to self-model, per Turing.

    (Alas, I didn’t get the chance to discuss this line of reasoning with John Lennox when he wandered through town; there weren’t enough slots in the small group discussion he had with some of the local student atheist and Christian groups.)

    I’d also respond to Jerry’s implicit question:

    We don’t understand why there are physical laws that behave with regularity

    …by suggesting again that we don’t even know that there ARE such laws. Rather, this is taken as a primary philosophical assumption, where the alternative of Refutation is fully as consistent with the evidence. In the case of the latter, any appearance of order/pattern/law is merely a local illusion, inevitable under Ramsey’s Theorem in a sufficiently large sea of chaos. This leads to no implications considered “interesting”, so the alternative of Assertion is taken… in which case, the rules themselves (or the minimal meta-rules generating the other rules) are the ultimate “uncaused cause”, and the assumption gives the mathematical potential inference as to which are more likely. And the Second Law of Thermodynamics appears uninterested in human worship.

    Or, from another angle: it’s just an assumption, without priors. Instead of saying God implies Rules, and thus in effect needing God and Rules for the philosophy, we simply assume Rules directly.

  14. Posted February 23, 2012 at 11:29 am | Permalink

    Maybe I’m missing something, but what, precisely, IS the argument? Neither statement is an argument, they are only observations. We need a testable theory, or a syllogism, to plug them in to. It’s fundamentally irrelevant whether either statement is true unless there is some persuasive context.

    Wait, let me guess…we’re just supposed to assume that if something is mysterious, therefore it is divine?

  15. Dan L.
    Posted February 23, 2012 at 11:49 am | Permalink

    The universe can be comprehended by the rational faculties of humans, and its workings appear to adhere to laws of physics.

    As others have already pointed out, what we call “laws of physics” adhere to the workings of the universe, not vice versa. There’s also a little question begging going on in the “comprehended by the rational faculties” bit. Suppose the universe such that our “rational faculties” could not comprehend it. By what lights could we insist that our faculties are really rational and it is the universe (not our faculties) being wayward?

    That is, “rational faculties” can only be defined relative to a comprehendable universe in the first place. This is ignoring the fact that there seem to be rather sharp limits to our comprehension: no one finds quantum mechanics intuitive and only a very few human beings understand general relativity and a lot of other concepts we use to understand the universe. Our best models predict only 1% or so of the energy content of the universe and also make a few other predictions that don’t seem to hold. For the most part, every time we claim to comprehend any part of the universe we’re actually pretty wrong about it.

    Much of our understanding of the universe is expressed through mathematics, which is “unreasonably effective” in encapsulating what we discover about nature.

    The only comprehensive definition of mathematics I’ve ever heard is “the study of patterns.” If you look across time and cultures at different traditions of mathematics you get different notations, different terminologies, different approaches, but all bearing on the same patterns. That is to say, as long as there is such a thing as patterns there is such a thing as mathematics. This is exactly the “laws of physics” error from above but applied to abstractions rather than the universe. It’s not that we have this thing called mathematics and for no explicable reason it seems to be really good for describing patterns. It’s that we saw patterns and developed notations and other systems to describe those patterns.

    To say that this is somehow “unreasonable” is to suggest that a universe without patterns is a more “reasonable” possibility. The onus is on Polkinghorne to explain what this even means. Is a patternless universe somehow more intuitive or obvious than a patterned one? Is it even possible? Intelligence itself seems to manifest as a capacity for recognizing patterns, what would such a faculty amount to in a patternless world?

    Other people already mentioned Douglas Adams’ intelligent puddle. They were exactly right, Polkinghorne is make the same arguments as the puddle.

  16. Bjarte Foshaug
    Posted February 23, 2012 at 11:58 am | Permalink

    What god in his right mind would make the two most important constants of mathematics (pi & e) two endless strings of random numbers, thus making calculations so much more difficult than they could have been, if they were free to vary at all? In fact, why not make it so that every natural number could be written as a fraction of two integers (as the Pythagoreans orginally believed). It would certainly make my day easier.

    • infiniteimprobabilit
      Posted February 24, 2012 at 12:52 am | Permalink

      I kinda tend to think that would be physically impossible, certainly in the kind of 3-dimensional space we inhabit.

      I’m no mathematician, but I think that if space was curved in such a way that PI=3 for example, then *we* would be physically impossible. Even for God. :)

      • Bjarte Foshaug
        Posted February 24, 2012 at 5:36 am | Permalink

        Which is why I added the qualifier “if they were free to vary at all”. If they are not, there is nothing for God to explain. ;)

  17. Joshua
    Posted February 23, 2012 at 12:05 pm | Permalink

    I realize this has already been commented on, but I’d like to add my two cents on Jerry’s comment:

    “We don’t understand why there are physical laws that behave with regularity”

    This is, of course, an assumption as mentioned earlier.

    Furthermore, the usage of the term “physical law” is not always clear. Most of us are familiar with Newton’s laws or the Laws of Thermodynamics. Outside of these rather reserved uses of the term “law”, we don’t see it that often in Physics. Examples: “Maxwell’s Equations”, “Theory of Relativity”, “Quantum Theory”, and so on. The usage seems to have fallen out of fashion since around the time of modern physics (1900 or so).

    What’s more, the term “law” is actually misused (and quite knowingly) by physicists. The examples I can think of are a bit esoteric, but none-the-less here you have them: “Ohm’s Law” in electricity, “Hooke’s Law” in elasticity theory; these are in fact not “laws” in the common sense, but we don’t change the name (out of tradition I suppose?).

    An aside: in classical mechanics there is also a term “canonical variable” which appears in regular usage. My guess is that the terms “law” and “canonical” are merely vestiges of the religious past of which physics was born.

    • Posted February 24, 2012 at 5:01 pm | Permalink

      They are vestiges, but there’s an important distinction to nevertheless make.

      All of what you gestured at are actually law *statements*. What I think really matters for the discussion are the real patterns the law statements *refer* to.

      (A theory is just a system of said statements, closed under a deduction relation.)

  18. Kevin O'Neill
    Posted February 23, 2012 at 12:39 pm | Permalink

    Polkinhorne’s argument is so evidently feeble that it does not deserve serious debate: his resembles the argument that the conditions for evolution of life are so unlikely that they could not have occurred by chance. Just applying the same flawed logic to a mathematical argument to claim that we are ‘lucky’ that the maths fits the model when of course it does: the maths comes from the model. A tired argument in a new(ish) dress!

  19. JBlilie
    Posted February 23, 2012 at 12:51 pm | Permalink

    Polkinghorne is all wet! Those points he made simply prove that Ceiling Cat exists, for Ceiling Cat’s sake! Polkinghorne: Show me where my logic is wrong on this! ;^)

    • Yiam Cross
      Posted February 23, 2012 at 4:48 pm | Permalink

      Er, we have a photo of ceiling cat. Where’s the photograph of god, jesus or even one of the many rooms in his father’s mansion.

  20. Another Matt
    Posted February 23, 2012 at 1:20 pm | Permalink

    There are also these lines of thought to consider:


  21. Posted February 23, 2012 at 2:06 pm | Permalink

    I’d say it’s ascertainment bias. He spots the neat solutions and marvels at them but seems to ignore other observations, such as the difficulty constructing a Grand Unifying Theory. Surely if the Universe was such a clean and mathematical construction of a higher power for us to discover, such a thing would just pop out? It’s the same with all the arguments from design – they focus on the designed-looking end of the spectrum and ignore the rest.

  22. MadScientist
    Posted February 23, 2012 at 2:19 pm | Permalink

    I wonder what Polkinghorne’s criteria are for unreasonable effectiveness. He sounds like a babbling moron to me.

  23. Yiam Cross
    Posted February 23, 2012 at 4:46 pm | Permalink

    Maths is unreasonably effective in describing the universe as we know it in the same way a roof is unreasonably effective at keeping the rain out. Because that’s what we built it to do.

    And if maths came from god, how come I have to fix my own roof? Jesus, bring your crawling ladders!

  24. Peter
    Posted February 23, 2012 at 6:25 pm | Permalink

    Wigner’s article is easily obtained on the internet. It is hard to detect whether even a single correspondent so far has read it. That we are able to discover physical theories with extraordinary predictive powers is even more mysterious now than when he wrote the article, with something like at least 10 digit accuracy in some cases. Wigner marvels at this (weaker then).

    But his title refers to something different, the fact that mathematical theories discovered in a purely aesthetic pursuit turn out to be a large component of these theories, particularly the application of complex separable Hilbert space.

    I agree with Shallit that this is not quite as unreasonable as Wigner thinks, but not for Jeff’s reason. It seems to me that mathematics is an extraordinarily large extension of logical methods, but still logical methods. There may be some disagreement among philosophers about the foundations of mathematics, but I don’t think my statement above, in the context of the relation to physical science, is affected much by that. And I don’t think anyone would write an article entitled “The Unreasonable Effectiveness of Logic in Physics”.

    So I think the real mystery is what is in the first paragraph above. Writings in recent decades by Putnam and Tegmark are ones of interest here. For example, the latter physicist at MIT maintains that the physical universe is not merely modelled by a mathematical structure, but actually IS such a structure.

  25. Diane G.
    Posted February 23, 2012 at 6:52 pm | Permalink

    (subscribing. Wow, when JAC asks his readers to come through for him, do they ever!)

  26. Terry
    Posted February 23, 2012 at 8:21 pm | Permalink

    It’s simpler and more elegant to see that we are children of the Big Bang; the result of uncountable molecules bouncing off each other for about 14 billion years – no soul nor gods necessary or required

    • infiniteimprobabilit
      Posted February 24, 2012 at 12:57 am | Permalink

      You realise that every one of those bounces had to be precisely calculated to the nth degree to arrive at you? That if even one of those bounces had been ‘off’ you wouldn’t be here? How astronomically improbable is that? Ergo Jesus! ;)

    • Posted February 24, 2012 at 5:05 am | Permalink

      Funny coincidence. There’s a minor skirmish on LinkedIn based on the notion of the ‘hand of god’ making the galaxies accelerate away from one another: http://lnkd.in/3JBWZQ

      Warning: the logic is so twisted it may make your head explode.

  27. Dave Ricks
    Posted February 23, 2012 at 8:51 pm | Permalink

    How would anyone judge math to be “unreasonably” effective? Judged compared to what, and judged by what criteria? I see that as an argument from incredulity, a feeling of “gee whiz” and that’s that.

    But more importantly, I can set aside what I know about math and physics to focus on history. In the video posted here a few days ago, where Neil deGrasse Tyson talked about “The Perimeter of Ignorance”, when Newton could not model the stability of orbits, Newton deferred to a god. But today, when Polkinghorne sees what we can model, he claims that as evidence for a god. This is some strange history.

    It’s simply wrong to conflate these opposite ideas about gods in sentences that use one name capitalized “God” as a proper name as if there’s only one and we know which one of these opposites we’re talking about.

  28. Bryan
    Posted February 23, 2012 at 11:11 pm | Permalink

    Polkinghorne: “The universe can be comprehended by the rational faculties of humans, and its workings appear to adhere to laws of physics.”

    Harris: “I have often wondered why walking works. Why is the world organized in such a way that we can walk upon it?”

    Harris’ essay is pure gold – it’s my favorite thing that Jerry has ever linked to:

  29. dunstar
    Posted February 23, 2012 at 11:27 pm | Permalink

    As Feynman said, at the very bottom, at the most fundamental particles of nature there are no more gears and wheels inside them to explain how they behave. It can no longer be described by a mechanistic process. It’s just the way it is! That’s where “why” questions end! At that level, “why” questions are non-sensical. lol.

    • Another Matt
      Posted February 24, 2012 at 6:31 am | Permalink

      Also, this is where any hope for Aristotelian physics has to be abandoned completely – there’s no meaningful form/content distinction at that range, and at that level it’s only possible to know particles by how they behave rather than what they’re “made of.” Or to put it even more strongly: what they are is how they behave.

  30. Posted February 24, 2012 at 3:43 am | Permalink

    It strikes me that you can’t claim that the “unreasonable effectiveness” of mathematics is evidence for God and then claim that our inability to find mathematical models for things such as love is also evidence for God.

  31. Torbjörn Larsson, OM
    Posted February 24, 2012 at 6:17 am | Permalink

    While the logic of Polkinghorne’s overall argument fails on the fallacy of a false dilemma, you can write essays on those questions.

    In fact, my comments over the years may constitute one. Here I will confine myself to narrow answers, and comment on the broader aspects afterwards:

    The universe can be comprehended by the rational faculties of humans, and its workings appear to adhere to laws of physics.

    These have straightforward answers:

    - Evolution provided those faculties against a structured enough physics.
    - A structured enough physics appears in multiverses, which is a generic physics.

    The latter fails Polkinghorne’s argument.

    Much of our understanding of the universe is expressed through mathematics, which is “unreasonably effective” in encapsulating what we discover about nature.

    This puts up two sequential blocks for Polkinghorne:

    - We can observe that empirical physics applies mathematics by empirical heuristics. (Say, when doing quantization, which can’t be axiomatized.)
    - We can observe that mathematics is quasiempirical. This is seen from the problems of axiomatizing how to do proofs, which are currently heuristics developed by breaking down the steps to mutually agreeable parts. Over how to check them for errors. To such quasiempirical mathematical objects as Chaitin’s constant.

    To overcome these blocks would take Polkinghorne to a one-one map mathematics physics, if not nature but “what we discover about nature”.

    Then he has to come up with a measure for effectiveness, and a mutual agreeable definition of “unreasonable” despite we are lacking a comparison.

    My 2p. (Some or all of these problems have been commented on already, I believe.)


    Broader aspects:

    - We don’t need multiverses. It has been long known that chaos has to encompass non-bounded sets of order, from Ramse theory. An infinite universe, which it looks to be, with chaos would hence be expected to have infinitely many ordered observable universes in it.

    - We don’t need “laws”. They are expressions of symmetry and spontaneous symmetry breaking, the latter which happens non-conserved systems are replaced with conserved systems (having energy) that then can minimize energy.

    It is a process that we can observe all the time. As Stenger notes in “God – the Failed Hypothesis” even if we have no concept of “nothing” initial chaos has a maximum amount of symmetry. Its laws look different, but it has in principle at least as many _general_ laws. (Without structure formation, there are fewer cases of, say, biological evolution. =D)

    My notion is that it has to have that, since we see more symmetry looking back, and religious insist on that we come from “nothing”.

    Notably, creationists do exactly the same mistake here as they do on information in the genome: a randomized genome has maximum information (Kolmogorov complexity); a randomized universe has maximum order (sets of symmetries).

    - Mathematicians and philosophers of mathematics would probably mostly not agree with what is observed, but hold out for Platonian ideals in the form of unobservable mathematical objects. I think that is a form of dualism.

    Tegmark makes mathematical objects = physical objects on the basic level to have a map mathematics nature. But then his multiverses looks decidedly different from randomized physics, and it is unparsimonous on physics.

    But that is philosophy of theological character which goes against observation so far. And it has nothing to do with the two blocks Polkinghorne has to overcome first.

    • Torbjörn Larsson, OM
      Posted February 24, 2012 at 6:30 am | Permalink

      I note that I use “order” in two senses. Not randomized/structured is the usual sense, “laws” is the physics (or maybe creationist) sense. Oh, well.

    • Torbjörn Larsson, OM
      Posted February 24, 2012 at 6:32 am | Permalink

      Oops. It’s _Ramsey theory_.

    • sasqwatch
      Posted February 24, 2012 at 12:26 pm | Permalink

      Really cool stuff. I’ll put in a plug for Stenger’s “The Comprehensible Cosmos” as well, for a bit more fleshing out of the concept of “symmetry-breaking” and how various symmetries lead to Laws.

      The appendices of that book are for the more adventurous, but are still accessible to the advanced/determined layperson. A very concise manual of standard model physics, IMHO.

  32. Michael
    Posted February 24, 2012 at 7:24 am | Permalink

    Two kinds of responses have come up to Polkinghorne’s argument. Jerry makes both of them, but in doing so he’s trying to have his cake and eat it too.

    First answer, exemplified by Sean Carroll: we can’t answer the question why the universe is comprehensible. The best answer to this is: it just is. (See his article “Does the Universe need God?” which he helpfully linked to above.)

    Second answer: this is a god-of-the-gaps argument and science will eventually explain why the universe is comprehensible, etc.

    Thus, heads Jerry wins and tails Polkinghorne loses: if there is no explanation we give Carroll’s response, but if there is an explanation we’re safe too.

    But you can’t have it both ways. If the correct answer is just “that’s how it is” then the correct answer can’t also be “there is an explanation but we haven’t got it yet.” And it is Carroll’s response that is the more reasonable one. Any answer along the second lines would presuppose that which it tried to explain. If it is really an explanation of the regularity and intelligibility of the universe, it will have to make use of some general principles that govern the universe and make the explanation work. And these principles will not be explained by the explanation without circularity, since the explanation requires them. (This is really just Hume’s argument about inductive reasoning, slightly modified.)

    I cannot see (can someone help me?) how a multiverse explanation of the particular laws of our universe can get off the ground without some more general laws that govern the whole multiverse — certainly not in those versions of the multiverse hypothesis where it is claimed to be a testable theory. (If it is just a mathematical formalism representing a space of all possible universes, then the claim that it is real and not merely possible is as metaphysical a posit as the posit of the theistic God.)

    • Posted February 24, 2012 at 7:50 am | Permalink

      I think the most reasonable answer is “We don’t know at the moment, and we don’t know if we can know in the future.”

      History shows that some things we thought we couldn’t figure out eventually do get figured out. Even in those cases where we still haven’t got answers, we at least understand the question better, which is usually necessary before the breakthrough that gives an answer.

    • Another Matt
      Posted February 24, 2012 at 7:55 am | Permalink

      I cannot see (can someone help me?) how a theistic explanation of the particular laws of our universe can get off the ground without some more general laws that govern the heavens.

      In any case, the place Polkinghorne’s argument gets off track is to assume that consciousness and reason are themselves things that exist somewhere or in some way separate from the universe. He might have a point if brains were not computers that operate according to the same laws of physics. Polkinghorne, if I remember correctly, claims not to be a dualist (when he dies, God will remember his neuronal pattern -> “his soul,” and will recreate it in a new body). But there’s an implicit dualism in his argument, along the lines of Feser’s common comment that evolution couldn’t have given us our powers of reason because reason is another essence separate from the base intelligence other animals have.

      It’s all similar to Plantinga’s argument that if there is no god we have no reason to have confidence in our reasoning abilities, because evolution could have delivered us brains that were great at helping us reproduce but poor at finding out what is true. I don’t think that one is even worth discussing here.

  33. Kharamatha
    Posted February 24, 2012 at 8:23 am | Permalink

    Why can’t I believe it’s not butter?

    Why is this Sparta?

    Why did the chicken cross the road?

    Ergo Jesus.

  34. DV
    Posted February 24, 2012 at 3:45 pm | Permalink

    It has been more than 150 years since Darwin’s “On The Origin Of Species…” and still we have smart people struggling with big questions as if evolution has not been discovered yet. It is amazing how much the explanatory power of evolution is overlooked. Why do we find the world intelligible? God is not the answer. Evolution is.

    • Another Matt
      Posted February 24, 2012 at 3:53 pm | Permalink


      It’s the same in principle as the question of why there’s an “unreasonable” amount of delicious and nutritious food.

  35. Posted February 24, 2012 at 4:03 pm | Permalink

    I’ll read the rest of the comments and then remark again as necessary, but the single biggest mistake in the premisses (ignoring the silly leap in the conclusion) is assuming mathematics applies to reality. It doesn’t; instead it applies at second hand, to our *ideas* about reality. It is thus no mysterious than using language. Some think the realism of everyday language is evidence for their pet superstition, which is ridiculous too, but at least then we’ve moved away from a crucial error.

    As for lawfulness, this is crucial. It is a key metaphysical finding both supported by and presupposed by scientific research. However, and most damming for the theist (including the deist) is that *lawfulness is incompatible with theism*.

  36. Leigh Jackson
    Posted February 26, 2012 at 2:18 pm | Permalink

    Mathematics applies to the thinking and non-thinking physical world. No mysticism required.

    The world is not shot through with mind because it is shot through with mathematics. Physical order does not demand an ordering mind. Perceiving order does. Evolution can produce exquisite order without need of mind.

  37. Moss McCarthy
    Posted March 23, 2012 at 10:58 pm | Permalink

    The best proof of God in my view is an argument from epistemology. In order to know anything there must be something to know (experience). But whether the experience is real or illusory depends upon an act of knowledge. Experience is undefined until after the act of knowledge. But the act (or power to obtain knowledge) itself absolutely must exist or else there can never be knowledge. The act is necessarily indefinable. Please note well the difference between undefined and indefinable. That act is the light of the world. Therefore if science exists then the reality of Christ is absolute. Better said, the act (God, Christ or the Creator) exists in a way utterly different to all other existents.

    • Posted March 24, 2012 at 5:44 am | Permalink

      Do you actually buy it yourself, though? It has the obvious problem in the claim that the only knowledge is that which can be absolutely deduced. This is simply not the case – any evolved being will gain knowledge by not being killed by its environment (and whether that knowledge is stored in the genes or brain doesn’t matter there), so practical, useful knowledge can in fact be tentative. And everything a human claims to know is in fact tentative. The probability against may be laughably negligible, but 0 and 1 aren’t probabilities.

    • gbjames
      Posted March 24, 2012 at 6:35 am | Permalink

      Come on, Moss, get real. As in “reality”. Having an delusion, is not knowledge in any meaningful sense of the word. Knowledge is measured by the relative correspondence of a mental model of things to the real universe. You’re “best proof” is no better for Jeebus than it is for Huitzilopochtli or the Flying Spaghetti Monster.

    • Steve
      Posted March 24, 2012 at 6:39 am | Permalink

      Well this “best proof of God” failed to prove such to me.Are you saying there can’t be any man-made fictions?

    • bernardhurley
      Posted March 24, 2012 at 10:03 am | Permalink

      Moss McCarthy, this lookslike incoherent garbage to me.

      In order to know anything there must be something to know (experience).

      Without the word “experience” in parentheses, this would just be an uninteresting tautology. However I wonder why you put it there. Experience is not knowledge, unless you are making a Cartesian point about knowing you have the experience. Experience is one of the ways we justify knowledge claims.

      But whether the experience is real or illusory depends upon an act of knowledge.

      The word “know” is a verb as is “eat”. But you are merely being deluded by the grammar of the language if you think there is such a thing as an act of knowledge in analogy with an act of eating. You might more plausibly speak of an act of knowing – e.g. if I am knowing something until I forget it. That would be a rather strained use of language, but it has the advantage of making sense

      All experience is real; the question is when and under what circumstances it justifies knowledge claims. For instance if I had filled myself with drugs or gone into a trance or have certain brain disorders then it may not.

      But the act (or power to obtain knowledge) itself absolutely must exist or else there can never be knowledge.

      You are conflating two things here. First an act of knowledge, which, as I have said, is merely a confused use of language and a power to obtain knowledge. Now I have a power to obtain ice cream, when I can afford it. That does not mean I will obtain ice cream. For instance the shop may have run out or the shop keeper might cheat me. It is possible, but unlikely, that I have always been cheated when I exercise my power to obtain ice cream and have never tasted ice cream in my life. The same could be said for knowledge.

      If by “there never can be knowledge”, you mean that there can never be certain knowledge then that is correct. All we can hope for is justifiable knowledge claims. In view of this, there is a moral imperative to make sure these justifications are as good as possible.

      The act is necessarily indefinable. Please note well the difference between undefined and indefinable.

      The same conflation: The act of knowledge is indeed undefinable unless you mean by it the power to obtain knowledge when it becomes quite easy to define.

      That act is the light of the world.

      Doesn’t it seem strange to you that you can kow this about something you cannot define? Or perhaps it’s just a metaphor.

      Therefore if science exists then the reality of Christ is absolute.

      Now we see the point of the metaphor. The same metaphor has been used for Christ. But you really can’t argue two things are the same because the same metaphor has been applied to them. Incidentally, schizophrenics regularly argue like this.

      Given your conflation of an act of knowledge with the power to know something, your argument seems to boil down to the following (with my comments in square parentheses):

      1. Science exists.
      2. For science to exist absolute knowledge has to exists.[untrue]

      Therefore from 1. and 2.:
      3. Absolute knowledge exists.

      4. For absolute knowledge to exists an undefinable act of knowledge must absolutely exist. [incoherent]

      Therefore from 3. and 4.:
      5. An undefinable act of knowledge must absolutely exist.

      6. This undefinable act of knowledge must be the light of the world. [metaphor]
      7. Christ is the light of the world [metaphor]

      Therefore from 5. and 6:
      8. Christ is this undefinable act of knowledge.

      Finally from 5. and 8:
      9. Christ must absolutely exist.

      Excuse me if I am not entirely convinced.

  38. manselton
    Posted March 25, 2012 at 4:48 pm | Permalink

    As a theistic evolutionist I am well aware that claiming anything is designed by God immediately precludes it from being understood by science. No one can know the mind of God and if you try to then you end up telling God what he thinks. All fundamentalists do that, sooner or later. When a religious person engages the pursuit of truth through scientific endeavour then the first thing they must do is put God aside. It must be about the science and not about God.

    Science is systematic, formal knowledge. The scientific question is, “How did this phenomenon come to be just as it is?” When that is explained science is complete. The phenomenon is a perceptual experience which forms the point of departure to engage thinking. All knowledge is a combination of perception and thought. The phenomenon lends itself as a stimulus, provided that the person who sees it feels a certain sense of dissatisfaction with the phenomenon just as it is. This makes the subjectivity of perception a necessary stage in the process of knowledge. You must go through subjectivity to achieve objectivity.

    Human beings hunger for knowledge. I believe they do so because as individuals they feel estranged from the world and scientific knowledge enhances the value of human life by re-uniting the person with the world in the most satisfying manner. In this day and age science does this far better than religion, at least in my view. In this I-World isolation my relationship to God can really only be personal to me. Thus I am not an evangelist and – you were right – I ought to keep it to myself or at least only speak of it where the company is appropriate. My apologies for being so blasé.

    • Posted March 26, 2012 at 12:55 am | Permalink

      If only everybody would admit that their faith is NOT based on evidence or reason — that it’s merely a personal conviction or personal preference, then there would be nothing (religious) to fight about any more. There would be nothing to disagree about.

      Denial is at the root of (monotheistic) apologia: denial of the fact that there is no evidence or logical basis for faith. Faith is what it is: belief without the benefit of reason.

      And denial always has a way of coming back to bite us on the butt. Anybody can confirm this fact by watching CNN at any hour of the day or night.

      The majority of the world is certain of things they can’t possibly know anything about. It’s a major problem for human progress.

      • Posted March 26, 2012 at 12:59 am | Permalink

        Oops, I meant to reply to main article, not to manselton!

    • Steve
      Posted March 26, 2012 at 6:56 am | Permalink

      Human beings hunger for knowledge. I believe they do so because as individuals they feel estranged from the world and scientific knowledge enhances the value of human life by re-uniting the person with the world in the most satisfying manner.

      …or they hunger for knowledge so that they might reap a greater amount of future happiness.

      Re-uniting? Assumes a fact not in evidence.

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