“If a ‘religion’ is defined to be a system of ideas that contains unprovable statements, then Gödel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one.” –John Barrow

God the Geometer

Image credit: Codex Vindobonensis 2554 (French, ca. 1250), in the Österreichische Nationalbibliothek.

Image is from the front cover of the most important medieval picture bible to survive. But the caption is all my fault. Anyone can fool some of the people some of the time, but to enrage all of the people all of the time, that takes talent. Don’t worry, I’ve got no future in comedy; I’ll stick to the astrophysics.

Also, for those of you who want something fun to puzzle over, try this fun math fact.

102 + 112 + 122 = 132 + 142. Is there an explanation?  Or is it just a coincidence?

Have a good weekend!


  1. #1 Sweetwater Tom
    June 2, 2012

    I found the second integer solution, but shouldn’t there be an infinitude of non-integer solutions?

  2. #2 makeinu
    June 2, 2012

    It’s not “God did it”, is it? Because that’s such a cop-out.

    *runs from the Fundies*

  3. #3 Blaise Pascal
    June 2, 2012

    I’m not sure what sort of “explanation” is needed. If one is looking for 3 consecutive squares which have the same sum as the next two consecutive squares, that boils down to a quadratic equation x^2+(x+1)^2+(x+2)^2=(x+3)^2+(x+4)^2, which when expanded, simplified, and factored, is equivalent to (x-10)(x+2)=0, implying that 10^2+11^2+12^2=13^2+14^2 and (-2)^2+(-1)^2+0^2=1^2+2^2 (this last one’s a bit trivial, though) are the only solutions.

    Is that an explanation? A coincidence? I dunno.

    Looking at this sequence more generally, you have:

    0^2 = ??? (added for completeness)
    The first number appears to be the nth triangular number where n is the number of terms on both sides of the equals sign (the 1st triangular number is 0, and there are 1 terms in 0^2=???, the 3rd triangular number is 3, and there are 3 terms in 3^2+4^2=5^2, etc).

  4. #4 ripu jain
    June 2, 2012

    reading the quote you posted by john barrow, if religion is a set of unprovable ideas, and math can ‘prove’ itself to be a religion, then by contradiction, its not a religion !

  5. #5 m
    June 2, 2012

    > if religion is a set of unprovable ideas

    It’s not though, it’s defined to *contain* unprovable ideas. The definition leaves room for provable ideas.

    A religion can claim to be a religion though, and still satisfy the definition. The definition also leaves room for incorrect ideas, so it’s possible for a religion to claim that it proves itself to be a religion, or to claim anything at all really!, and still satisfy the definition of religion.

  6. #6 WIll
    June 2, 2012

    I laughed. But that picture of Jesus intelligently designing the world creeps me out. His gaze is just a little too intense. And the inside of the sphere looks like a drug trip.

  7. #7 Bruce Crossan
    Lebanon OR
    June 2, 2012

    I prefer the Spaceman Spiff crashing planets together to get the math answer or the Dirk Derringer series, where Calvin gets beat up by goons, which leads him to the conclusion that it’s a numbers game. The only number big enough to pull it off, of course, is Mr. Billion.

    The inside of the sphere isn’t a drug trip; it’s obviously an indication of Jesus’ use of fractals, in the creation of he universe. As for the intense gaze, you would prefer or would join those that accuse God of not paying attention, when creating said universe.

    As for numerical coincidence: Numbers are what they are, no more no less; therefore, it would be hard, if not impossible, to prove that there is any coincidence to inherent properties. Though, as an astrophysicist should well know, that doesn’t mean that the universe is deterministic, by any stretch of the imagination (okay, maybe you could stretch your imagination that far). bc

  8. #8 dancor
    June 3, 2012

    for more about the numbers Blaise is talking about:

  9. #9 kale
    June 3, 2012

    Blaise Pascal – you are right 🙂

  10. #10 OKThen
    Milky Way Galaxy
    June 3, 2012

    Ethan special case equation “10^2 + 11^2 + 12^2 = 13^2 + 14^2.” got me thinking.

    It sort of looks like a special case of an expanded pythagorean theorem. hmm, yes.

    You know 3^2 +4^2 = 5^2 is a special case of the pythagorean theorem x^2 + y^2 = r^2 in two Euclidean dimensions.

    So what is Ethan’s equation a sp[ecial case of?

    Well in 3-dimensions, pythagoreans theorem is =
    x^2 + y^2 + z^2 = r^2

    But for any r^2 there are two orthogonal numbers h and g such that
    r^2 = h^2 + g^2 aah.

    So Ethan’s special equation is a special case of the general expansion of pythagorean theorem to any number of dimensions.

    x1^2 + x2^ 2 +…xn^2 = r^2 = y1^2 +y2^2 +… ym^2

    where x1, x2, x3 … xn are all orthogonal to one another
    and where ya, y2, … ym are all orthogonal to one another
    and n and m are respective numbers of euclidean dimensions.

    So what we have is a special case of pytharogean theorem comparing 3 versus 2 dimensions

    Of course, the pythagorean theorem is valid in any number of dimensaions. Fun.

  11. #11 MandoZink
    June 3, 2012

    “People are entirely too disbelieving of coincidence.” – Isaac Asimov

    “Is not all this an extraordinary concatenation of coincidence?” – Isaac Asimov, from Foundation’s Edge

  12. #12 chelle
    June 4, 2012

    That Bill Watterson from Calvin and Hobbes is the strangest character he just stopped drawing those cartoons and has disappeared as if he was sucked into a Black Hole … no information is coming out ever-since … it’s too weird 4 me.

  13. #13 Ben Vost
    June 4, 2012

    Even weirder is as an anagram:

    ELEVEN+TWO is the same as TWELVE+ONE…


  14. #14 Ian Kemmish
    June 4, 2012

    We will never know whether Fermat’s Last Theorem was a joke….

  15. #15 Neil Bates
    June 5, 2012

    Ian, as best we can tell, FLT was proven several years ago.

  16. #16 Paweł Zuzelski
    Thalwil, Switzerland
    June 17, 2012

    That’s a hoax! God on that picture uses compass to shape a Mandelbrot set, which certainly was not known in medieval times! 🙂

  17. #17 Harry
    June 18, 2012

    The irony? Atheism IS a religion,,, aka,, a “belief in things unseen” (see panel 3). To believe that the double helix (20 in the simplest life we know) magically floated together, delicately and cogently, only to destroy itself to replicate?,, aka,, ABIOGENETIC ORIGIN OF LIFE,,, is a leap of “faith”, the odds of which are almost infinite.

  18. #18 Wow
    June 19, 2012

    Nope, atheism is no more a religion than not collecting stamps is a hobby.

    “aka,, a “belief in things unseen” ”

    The belief in God is a belief in things unseen.

    “ABIOGENETIC ORIGIN OF LIFE,,, is a leap of “faith”, the odds of which are almost infinite.”

    Yet over the course of a billion years, that dice gets rolled again and again. After a while, it turns up the right number.

    Unless the odds against it ARE infinite, abiogenesis requires no faith.

  19. #19 Brain Hertz
    June 21, 2012

    “aka,, a “belief in things unseen” (see panel 3)”

    For “unseen” substitute “for which there is no evidence”. There is evidence besides being able to see. Maybe you were just being brief, but I thought I should straighten that out.

    “… aka,, ABIOGENETIC ORIGIN OF LIFE,,, is a leap of “faith”, the odds of which are almost infinite.”

    We have pretty good evidence that there was a point in time at which there was no life on Earth, and a time later than that when there was. This is evidence that abiogenesis occurred.

    That it occurred is a different question that identifying the mechanism by which it occurred.

    Given our experiences, there is no reason to specify supernatural intervention as the default answer for any phenomenon for which we have no identified mechanism, if only because there is no previous example where, after investigation, that turned out to be the case. We just don’t see magic occurring.

  20. #20 Emily Boronkay
    August 1, 2012

    Ben Vost. Love the anagram.

    Harry from Tennessee: Bravo. The math for evolution doesn’t add up. Even billions of years is not long enough to go from single cells to the incredible complexity of today’s living organisms. Where are the transitional creatures? Why aren’t we still changing, becoming more complex? God as Creator, Word of God as truth, seeing how the evidence fits those stories brilliantly: Why is that so hard? Why the knee-jerk reaction of that not being scientific thinking?

  21. #21 _
    Is there an explanation?
    January 22, 2016

    3^2+4^2=5^2 = 25
    3^3+4^3+5^3=6^3 = 216
    10^2+11^2+12^2=13^2+14^2 = 365

  22. #22 Wow
    January 22, 2016


    With all the infinity of numbers and the higher order infinity of how to combine them,you can get any pattern you wish to see by “proper” selection of the values you assert need to be looked at.

    IOW if you look for patterns until you get one this is no more than the texas sharpshooter fallacy.

  23. #23 Wow
    January 22, 2016

    “Even billions of years is not long enough to go from single cells to the incredible complexity of today’s living organisms. ”

    It’s VASTLY more time than strictly necessary.

    You can get from “patch of skin that is minimally light sensitive” to “full human eyes with humous and varifocal lens” in 30,000 generations.

    Because any useful change is kept, it’s not a random walk to “having eyes” (or “making a hippopotamus”) but a progresstion from “not having eyes” (or “being a simple RNA replicator”) to the any advanced product via incremental change without direction, but keeping those elements that are useful.

  24. #24 Wow
    January 22, 2016

    “There is evidence besides being able to see”

    A shadow from the sky much too big to be a bird
    A screaming crashing noise louder than I’ve ever heard
    It looked like two big silver trees that somehow learned to soar
    Suddenly a summer breeze and a mighty lion’s roar

    nuff said.

  25. #25 Wow
    January 22, 2016

    “God as Creator,”

    God doesn’t exist. Prove me wrong.

    “Word of God as truth,”

    cf “If you eat of the fruit of the tree of life, you will surely die”. A HUGE porkie pie there from the mystic Pinocchio. Not to mention the bats aren’t birds.

    “seeing how the evidence fits those stories brilliantly”

    If by “brilliantly” you mean “really crappily and only after the fact”. Um. No. Not even then. They don’t fit the stories. See bats’ “kind” (hint: it’s not “bird kind”).

  26. #26 Keith
    June 5, 2016

    Not “the fruit of the tree of life”, but “the fruit of the tree of .knowledge” no porkie there!

  27. #27 Michael Kelsey
    SLAC National Accelerator Laboratory
    June 5, 2016

    @Keith #26: Not “the tree of knowledge” (i.e., keeping humans in ignorance), but “the tree of knowledge of good and evil” (i.e., keeping humans innocent). See Gen 2:17.

  28. #28 Wow
    June 6, 2016

    “Not “the fruit of the tree of life”, but “the fruit of the tree of .knowledge” no porkie there!”

    nope, still huge porkie pies.

    Adam and Eve ate the fruit, didn’t die from eating it.


    PS that tree was really “knowledge you’re a slave”. Not to mention that god’s being portrayed as a huge dick there. Put the damn tree in hell or underneath a huge mountain and put a label on it “NO EATING”. Totally avoiding the need to kill himself later so he can kid on he cares for us.

  29. #29 dean
    United States
    June 6, 2016

    “Not to mention that god’s being portrayed as a huge dick there”

    No doubt. Threatening adam and eve with death when they had no concept (if you buy the mythology) is one of the largest bit of dickery.

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