Effectively the Same Nonsense

There is no god and that’s the simple truth. If every trace of any single religion died out and nothing were passed on, it would never be created exactly that way again. There might be some other nonsense in its place, but not that exact nonsense. If all of science were wiped out, it would still be true and someone would find a way to figure it all out again.

Penn Gillette in God No! Signs You May Already Be An Atheist via Daringfireball

Far be it from me to dismiss a pithy argument against all religions, but this is actually a very bad argument. So, since Christmas is approaching, here’s an argument showing that Religion actually represents an underlying truth just as Science does. What that truth actually is remains open to debate, of course.

Math: What Exactly Do We Mean By “Exactly The Same”?

Please note: I was a lousy student, and all of this was a long time ago, so beware!

One of the more mind-blowing Math courses I did back in college was on Universal Algebra which turns out to be, in essence, a reformulation of Category Theory, itself kind of pretty much the same thing as Topos Theory. Are you getting my drift?

Universal Algebra is mathematics applied to mathematics, all done with diagrams. (Proofs in Universal Algebra tend to consist of turning one diagram into another diagram by erasing or adding an element at a time using set rules.) But the underlying principle is that there are equivalences between mathematical concepts that are exact. For example, you can demonstrate equivalences (isomorphisms) between objects in different theoretical frameworks (e.g. a fundamental shape in Topology turns out to be equivalent to a certain kind of group in Group Theory), and once you demonstrate these kind of equivalences, other equivalences fall out. E.g. the fundamental theorem of groups (which defines every possible type of group) impacts Topology (what possible shapes might there be?).

Demonstrating these equivalences is actually not as horribly complicated as you might think; it’s a bit like Object Oriented Programming, where the complexity lives below the level of abstraction you deal with — that’s the whole point of it. It’s something that makes perfect sense to advanced undergraduate students of Math. And it is this “metamathematics” that allowed, for example, Fermat’s Last Theorem to finally be proven. You have an intractable problem, but you realize it’s similar to another more tractable problem in another field, so instead of solving the first problem, you carefully determine if the problem you think you can solve is in fact, fundamentally, the same problem. And then you solve that problem.

Now, Mathematical Principles are pretty damn immutable. In support of Penn’s statement, we have some pretty compelling real world examples of multiple researchers solving a problem independently and reaching effectively the same solution (modulo the kinds of mathematical equivalences discussed above). Newton and Leibnitz, for example, both invented (discovered?) Calculus independently using different approaches. But to accept that two theories are “exactly the same” you need to understand and accept the fairly abstruse arguments that are used to demonstrate these equivalences.

To put this a completely different way, we could rebuild math from scratch and come out with something that looks very different from what we’ve got, but which is exactly the same using these arguments. For a simple, concrete example – most of the math you know is probably built on top of counting, i.e. measuring quantity. But you can replace the axioms that give us counting numbers with different (looking) axioms that are about order or containment and end up with a functionally identical but very different looking bunch of “knowledge”. In fact the ancient Greeks built their math on top of geometry (length and area) and proved things entirely using geometry rather than algebra. We can prove their results are equivalent to results in algebra, but it’s kind of complicated. And we can prove there is some degree of infinity number of different ways we could represent the same theory, so the chances that two independent formulations of math would end up looking “exactly” the same in the naive sense is zero.

Summary: we can demonstrate, via many “natural experiments”, that science will come out “exactly” the same way, for a complicated mathematical definition of “exactly” that will make most people’s eyes glaze over. But, in common sense terms, no two scientific descriptions of the same underlying truth arrived at independently will be “exactly” the same for definitions of “exactly” that “average” people understand. (Actually, the best definition would probably be “makes exactly the same predictions”, but that’s pretty complex just on its own.)

Anthropology: The Punchline

The “founding fathers of modern Anthropology” (Claude Levi-Strauss and James George Frazer) both made their reputations in large part by finding equivalences between religions. You know, like the “guy who died and came back to life” myth. Or the “guy born of a virgin mother” myth. Or the “great flood that killed everyone except that guy” myth. Or how about the “bearded guy in the sky who throws lightning bolts” myth? Or the “dead people live forever in the sky” myth. Or the “dead people live in the underworld” myth. And the “there are spirits in the woods” myth. And on and on. In fact, there’s almost no human religious belief which, upon analysis, doesn’t turn out to be equivalent to a whole lot of other independently derived human religious beliefs. This includes the religious beliefs of previously uncontacted tribes with no written records living in the Papua New Guinea highlands — clearly a better “natural experiment” of Penn’s thesis than, say, Newton and Leibnitz.

Summary: we can demonstrate, via many — even better — “natural experiments”, that religions will come out “exactly” the same way, for a not very complicated definition of “exactly” that most people would understand. (It’s probably worth noting that many religious people are deluded into thinking their religion is unique and original, and are hostile to this line of argument. E.g. Many Christians definitely do not like to be told that the “born of a virgin” myth was all the rage in religions predating Christ’s purported birth.)

Conclusion: You Can’t Prove a Negative and Trying To is Perilous

It should not be a surprise to discover that different religious beliefs have the same kinds of equivalences as scientific theories or bodies of math. All are human behaviors, after all. It’s the underlying reasons that are in question. Are religions, like science, an approximate representation of an underlying truth, or are they, as atheists might argue, simply a reflection of human beings coming to terms with pretty much universal experiences of being human (birth, death, love, loss, hunger, uncertainty, and so on)?

But, in the end, the argument that Penn is making is actually an argument that religion points to an underlying truth. Oops.

  • We [tacitly] assume that if, starting from nothing, if a body of “knowledge” derived from world comes out “exactly” the same, it’s based on “truth”. If not, not.
  • Starting from nothing, science will come out “exactly” the same — therefore it’s true.
  • Starting from nothing, religion will come out “different” — therefore it’s not true.
  • But, arguing from natural experiment, I demonstrate that, starting from nothing, religion actually comes out “exactly” the same.
  • Ergo: religion is true.
  • And we can go further and argue that the mathematical definition of “exactly” is really weird and no-one, least of all religious people, will accept it.
  • Ergo: science is false.

Because Penn’s argument relies on the initial, unspoken, assumption, it’s a very bad argument because it actually enables the opposing argument. Luckily, I don’t accept his premise. And with that, I’ll go back to being my kind of atheist — someone who thinks of Religion and, say, Astrology, in much the same light.


  • I just discovered that, years ago, someone actually commented on this post on Hacker News. Who knew?

    “The crucial difference between math and religion is that no one discounts the previous/parallel math as being untrue. Newtonian physics still holds as valid for large distances and lower speeds even though we use Einstein-ian physics for small distances and high speeds (closer to light).

    You don’t seem to grasp that even though Christianity and Islam, for example, are extremely close a Christian discounts Islam as being absolutely UN-true. Penn’s point is that we would MAKE UP some religion, find a Bible somewhere and discount it as being complete untrue in favor of our new made up fantasy.”


    The sad thing is that this person completely missed the entire point. So I’ll make it again.

    I think Penn’s argument works fine for mathematicians, who can look at two superficially different theories that don’t even talk about the same domain of concepts and figure out that they’re consistent and possibly even exactly the same. But Penn isn’t trying to convince mathematicians — I hope.

    Ordinary people faced with two religions each having a “guy whose mom was a virgin and who died and came back to life” myth can easily see the parallels (“my goodness, there must be some underlying truth”), so the argument is useless for ordinary people (in fact counterproductive, since those same people are not going to be easily convinced that Calculus using infinitesimals and Calculus using limits are exactly the same thing. (Witness the flood of Christians trying to “prove” the parallel postulate in the 19th century when the idea of non-Euclidean geometry caused some kind of existential crisis.)

    And the example of Islam and Christianity denying each other is based on far worse comparative theology than my admittedly rusty mathematics. First, Islam does not deny Christianity — like many offshoot religions it claims that Christ was a prophet but they’ve received an updated missive from God and have a better understanding. (Incidentally, exactly the same relationship to Christianity as Christianity has to Judaism. Or various Protestant churches to Catholicism. Or Mormonism to earlier variations of Christianity. Or Quantum Mechanics has to Classical Physics — just replace “missive from God” with “data from particle accelerators”.) Physicists don’t try to burn anyone at the stake, they just block their papers from publication and ruin their careers.

    Again, I’m not saying this argument is wrong, but that it’s misguided and dangerous since it will backfire if used on its intended audience.