Using three simple math puzzles to measure likelihood of belief in god

I had an amused reaction to this paper titled Analytic Thinking Promotes Religious Disbelief by Will M. Gervais and Ara Norenzayan (Science vol. 336, p. 493-496, 27 April 2012) based on a set of studies that looked at the correlation between analytic thinking abilities and beliefs in god. The authors use the language of System 1 and System 2 thinking to describe intuitive and analytic reasoning respectively, terms that that I have discussed in some detail earlier here and here.

The authors say that available evidence suggests a link between dependence on intuitive cognitive processes and belief in god and the supernatural. (I have omitted citations in the quotes for clarity.)

According to dual-process theories of human thinking, there are two distinct but interacting systems for information processing. One (System 1) relies upon frugal heuristics yielding intuitive responses, while the other (System 2) relies upon deliberative analytic processing. Although both systems can at times run in parallel, System 2 often overrides the input of system 1 when analytic tendencies are activated and cognitive resources are available.

Available evidence and theory suggest that a converging suite of intuitive cognitive processes facilitate and support belief in supernatural agents, which is a central aspect of religious beliefs worldwide. These processes include intuitions about teleology, mind-body dualism, psychological immortality, and mind perception. Religious belief therefore bears many hallmarks of System 1 processing.

One of the experiments they did involved asking subjects to solve three simple math puzzles:

  • A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost? ____cents
  • If it takes 5 machines 5 min to make 5 widgets, how long would it take 100 machines to make 100 widgets? _____minutes
  • In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake? _____days

Each of the puzzles suggests an immediate intuitive answer that can be seen to be wrong if people pause for a bit and use analytic thinking. They found that those who answered the questions correctly were more likely to disbelieve in god.

The overall conclusion based on the results of this and the other experiments they did was stated as follows:

[T]he hypothesis that analytic processing—which empirically underlies all experimental manipulations—promotes religious disbelief explains all of these findings in a single framework that is well supported by existing theory regarding the cognitive foundations of religious belief and disbelief.

Of course, the authors recognize that factors other than analytic thinking can also encourage disbelief, saying “Disbelief likely also emerges from selective deficits in the intuitive cognitive processes that enable the mental representation of religious concepts such as supernatural agent beliefs, from secular cultural contexts lacking cues that one should adopt specific religious beliefs, and in societies that effectively guarantee the existential security of their citizens.”

The idea that analytic thinking reduces religious belief will likely provoke a “Well, duh!” response in most of this blog’s readers. But it will be discomfiting to theologians and other sophisticated religious apologists because they pride themselves on being analytical thinkers. Studies such as this that suggest that they are more driven by intuitive System 1 thinking will no doubt be annoying to them.


  1. Chiroptera says

    But it will be discomfiting to theologians and other sophisticated religious apologists because they pride themselves on being analytical thinkers.

    Might also require a bit of Dunning-Kruger. From what I’ve read, these sophistamacated thinkers can’t seem to understand what other people are saying when they point out the flaws and errors in their “analyses”.

  2. Pierce R. Butler says

    To take the first question as an example: I think most of us would start by subtracting the given $1.00 from the given $1.10, just because the set-up encourages that.

    I did that, but then promptly realized in that case we’d have to add $0.10 to $1.10, which violates the premises of the problem. And therein, I intuit, lies the difference between the faithful credulous and the rational skeptical: not the initial thought process, but the tedious and sometimes-frustrating additional step of checking your work.

  3. Matt G says

    It takes a huge effort and a long time to get students to see that the sine of 45 is not 0.5.

  4. Mano Singham says

    Pierce @#2,

    Exactly. All of us use System 1 because it is quick and easy. It takes time and effort to use System 2 and one has to learn that it is necessary in order to check one’s results.

  5. Owlmirror says

    @Tabby Lavalamp: If you remember highschool algebra, it’s two equations with two unknowns.

    Rearrange 2nd eq:
    Substitute in 1st eq:

  6. Mano Singham says


    If algebra is not your thing, you could also try the trial-and error method. Start with $1.00 and $0.10 and you discover that the difference is only $0.90. To increase the difference, the bat has to cost more and the ball cost has to decrease by the same amount to keep the total fixed. By increasing the bat cost gradually and decreasing the ball cost by the same amount, you will arrive at $1.05 for the bat and $0.05 for the ball that gives the required difference.

  7. se habla espol says

    1. Common sense says that here’s an excess of $1.00 in the total due to the excess in the bat’s cost. Subtracting the excess from the total: the rest is equally bat and ball, 5¢ each. Putting the excess back: bat = $1.05, ball = .05. (I do speak algebra, also, but it’s not needed here.)

    2. Assuming the machines operate independently, each producing its own widgets, then each machine produces a widget in five minutes. Thus, 100 machines makes 100 widgets in 5 minutes. That’s the common-sense answer if one reads the question.

    3. That must be a really big lake, since it takes over 250 trillion (2⁴⁸) lily pads to cover it. (Yes, I spent many years working in binary, as well as other radices.) Thus, my well-trained intuition and common sense tell me that, according to the phrase “doubles in size”) that the coverage of ½ the lake was the day before day 48, or day 47.

    About sixty-some years ago, I took ‘hold of my intuition and common sense, and trained them to be analytic. Am I then System 1 or System 2, since my frugal heuristics intuitively yield analytic results?

    By the way, I’ve remained an atheist since birth.

  8. Holms says

    Well, duh! But also, it is important to put numbers and -- yes -- analytical thinking behind the obvious, to give it that old system 2 rigour.

  9. lanir says

    I bungled the first one until I started reading other comments, realized I’d made a mistake and then figured it out on my own before I read the right answer. I think the low monetary amount had me not really thinking too much about it. I don’t generally think money is all that important and I really don’t stress over a dollar or two; the margin of error on my guestimate for taxes is larger than that for most of my shopping trips (I can do math but taxes are magic numbers from nowhere).

    The second and third questions I caught no problem. This is all at stream of consciousness speed but for those two questions I started to form an initial answer, realized it didn’t feel right to me, glanced back at the problem where some detail caught my attention (the ratio of machines to output and the word “double” respectively) and caused me to jump to the right answer.

  10. KG says

    That must be a really big lake, since it takes over 250 trillion (2⁴⁸) lily pads to cover it. -- se habla espol@9

    Or really small lily pads!

  11. anat says

    For several years this type of questions appeared on Washington’s state tests. (The tests were revamped several times, and now there is a Common Core version, so I have no idea if they are still there.) Will there be a cohort of Washington kids with higher levels of atheism? Will there be a cohort of Christians who do math better? Or will it turn out that for a while kids with a skeptical upbringing have an advantage in the tests?

  12. says

    Dang it. As soon as I read Owlmirror’s explanation, I looked at the problem again and sure enough the word “more” should have jumped out at me. So of course I got stuck on thinking the bat cost $1.

    Yay! I don’t have to go to church!

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