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Nov 21 2011

Gospel Disproof #13: Knowing Pi

The distinguishing characteristic of rationalization is that it attempts to obscure the difference between truth and falsehood so that we can no longer reliably distinguish between the two. For example, a common Christian apologetic claims that we can never know whether, say, the 9/11 terrorist attacks were inconsistent with the idea of a loving, omnipotent, and omniscient Heavenly Father. God is (supposedly) so much wiser than we are, and knows so much more than we do, that we can never question His wisdom in allowing evil things to happen. Even though it might seem obvious that a good Person would have acted to prevent it, we can never know that God was wrong/negligent to fail to intervene, because God might know something we don’t.

The argument, in other words, is that because of human limitations, we can never know what the right answer is, and therefore we can never say that anyone else’s answer is the wrong one. But that’s a false argument, as we can see by looking at the number pi.

Pi is an irrational number, which means it cannot be represented as a ratio of two integers. In decimal notation, it’s the number 3 followed by an infinite series of digits that do not repeat. We can never know the exact value of pi down to the last decimal place because pi doesn’t have a last decimal place. God Himself could not know the exact value of pi down to the last decimal place.

The fact that we cannot know the correct value of pi, however, does not mean we cannot recognize values that are incorrect. If you say that pi is 3.14…, you haven’t given the exact, correct value of pi, but at least the digits you’ve given are correct so far. Pi is not 3.19… or 3.11…, and it’s definitely not 157.27…. To the nearest 3 decimal places, pi is indeed 3.14, and is not 3.15 or -8.99. We may not know all the right digits, but we can recognize wrong ones anyway.

It’s the same with God. We may not know everything an omniscient God would know, but that doesn’t prevent us from recognizing that it’s wrong to withhold information about a terrorist plot that is going to cost thousands of innocent lives, or that it’s similarly wrong to watch people suffering from diseases that would be curable if only you would share your knowledge of the cure. We may not know the exact value of pi, but we know it’s not 77 million and something, and we can recognize an abject failure to undertake even the most minimally moral opposition to evil, even without knowing everything an omniscient God would know.

The point of the apologetic is to rationalize evil, i.e. to deprive us of the ability use real-world evidence to distinguish between truth and falsehood about God. But it’s a failed rationalization. We all know that conditions in the real world are not the conditions that would result from a real, omnipotent, loving God. It’s just that some of us try to rationalize away the problem.

30 comments

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  1. 1
    grumpyoldfart

    I really enjoy your blog. Thanks a lot.

  2. 2
    sailor1031

    Given the performance of the christian deity throughout history, it is safe to say that it wouldn’t consider allowing more than 3000 people to be killed in a horrific terrorist act to be something “bad” so why would it prevent it?

    Or maybe it wouldn’t prevent it because it doesn’t exist? or it exists but is absolutely indifferent to the point of complete non-involvement?

    See? If you abandon the single notion that your dog is always a “good” dog then the problem evaporates.

  3. 3
    Lou Doench

    Wow, not where I expected that to go at all. Glad you avoided the Pi=3 discussion, it is a little tiresome

  4. 4
    OverlappingMagisteria

    Phew… From the title I was expecting “The bible says that pi is 3!” which I always thought was a weak argument (it could’ve easily been an approximation.) I really like this pi analogy.

    Keep up these gospel disproofs. They are one of my favorite segments here on FTB!

    1. 4.1
      mikespeir

      Glad to see I’m not the only one who isn’t impressed by the pi=3 argument.

    2. 4.2
      Reginald Selkirk

      “The bible says that pi is 3!” which I always thought was a weak argument (it could’ve easily been an approximation.)

      It could have been, but the text of Teh Bible does not say that it is. Pi == 3 is an approximation is an invention of apologists, not the Word of God Almighty as laid down in His book. So by claiming that God intended it as an approximation seems to me to be blasphemy; putting the words of the apologist into God’s mouth.

      It’s not the strongest argument, but it’s not totally lame. And there are certainly bigger flaws in Teh Bible; the font of biological wisdom in Leviticus chapter 11 is a favourite of mine (bats are a type of fowl, rabbits chew their cud, insects have four legs).

      1. mikespeir

        The best defense I can think of for approximation is that 3 demonstrably wouldn’t have worked in practice. Undoubtedly, even in those primitive times there were those who would have known that. (I can only guess at how engineers pulled it off: “Make it three and a smidgen.”) That would imply that either the writer was rounding or he wasn’t closely involved in the actual process, which in turn would mean that no deity worthy of the name inspired the writing. You and I would bet on the latter, but I think it would be hard to get enough traction for an argument.

      2. Stevarious

        The best response I’ve seen to the ‘pi=3′ argument is that the thing that they were measuring had a wide lip, so when they measured the circumference they were measuring the outside edge of the thing, but when they measured the diameter they only measured the open space between the lips.
        This seems a perfectly reasonable assumption to me, so I have not brought up the pi=3 argument since.

        I’m very glad that this article is not that argument, but instead something considerably better. Just because we cannot know exactly what pi is, does indeed mean that we can say what it isn’t. Excellent.

      3. F

        Well, “engineers” weren’t doing a lot of written calculation for most of history. They did, however, use a lot of analog tools, which obviate the need for any sloppy digital approximations in building.

      4. mikespeir

        Right. Which makes the approximation thing plausible. My point is there wouldn’t have been any way for them to express 3.14… 3 might have been the best they could do.

      5. Reginald Selkirk

        I think the Egyptians were using better approximations (22/7) at an earlier date.

      6. Len

        If those engineers were anything like software engineers today, then documentation wasn’t their strongest point. The bible (being just the marketing manual) tried to make it simpler for us, rather than bore us with the facts. Except for sometimes. Like when those “facts” match people’s prejudices. Then they’re God’s own words, never to be questioned or disobeyed. Kinda.

      7. sumdum

        Wait, you have to be kidding. It claims insects have four legs ? But.. they’re right there! Any middle eastern ancient goat herder could’ve picked a mite or some insect from his goats fur and count the legs. How could they have left such an obvious mistake in there ??

      8. Reginald Selkirk

        Leviticus 11:21-23

        King James Version:

        [21] Yet these may ye eat of every flying creeping thing that goeth upon all four, which have legs above their feet, to leap withal upon the earth;
        [22] Even these of them ye may eat; the locust after his kind, and the bald locust after his kind, and the beetle after his kind, and the grasshopper after his kind.
        [23] But all other flying creeping things, which have four feet, shall be an abomination unto you.

        New International Version:

        21 There are, however, some flying insects that walk on all fours that you may eat: those that have jointed legs for hopping on the ground. 22 Of these you may eat any kind of locust, katydid, cricket or grasshopper. 23 But all other flying insects that have four legs you are to regard as unclean.

        There, two versions ought to show it is not just an artifact in one translation. (Despite its popularity with American Protestants, the King James Version is known to textual scholars to be a bad translation from poor sources.)

        The meaning seems clear: locusts, bald locusts, beetles and grasshoppers belong to the set of “flying creeping things which goeth about upon all four.”


        BTW, don’t spend too much time coming up with flying creatures which actually do go about on all four legs. There’s the flying squirrel, and um…

      9. Deacon Duncan

        There are, however, some flying insects that walk on all fours that you may eat: those that have jointed legs for hopping on the ground. Of these you may eat any kind of locust, katydid, cricket or grasshopper.

        And Renfield answered and said, “Yes, master!”

      10. mikespeir

        And the NIV is notorious for “translating” to fit the Evangelical agenda. Here, even they couldn’t bring themselves to twist the text far enough to keep it from being a joke.

  5. 5
    sew_crates

    Maybe God loves us, but he mistakenly takes us all to be masochists, and so his loving gift to us IS an overabundance of suffering. For many suffering is just hunger or uncured disease, sure, but give the Guy some credit here, he also made insoluble ethical dilemmas for humanists and irrational numbers for mathematicians.

  6. 6
    The Lorax

    I’m waiting for them to say that God allows bad things to happen for the greater good, which is the overall improvement of our species. You know, sort of like that whole “natural selection” thing, only divinely inspired.

  7. 7
    Mark

    Off the bat, I don’t think there is a god. I see no evidence or necessity for one.

    But, for the sake of argument, let’s just say that there IS a god, and that it happens to be Yahweh. Not only that, but let’s also say that every one of us recognizes this fact. If Yahweh is indeed omnipotent and omniscient, would we really be able to judge his morality?

    Part of me wants to say yes. My usual analogy is that of a 6-year-old being abused by his father, and my hope that at some point warning bells would go off in that kid’s head saying, “Wait a minute, something doesn’t add up here. Dad says he loves me, yet beats the crap out of me.”

    But the other part of me recognizes that it’s REALLY hard to judge something that’s infinite, at least in a moral sense. Another analogy I think of is a kid in a restaurant who starts choking. His dad lifts him up and starts pounding on his back. The kid may think that his dad is hitting him, when in reality the dad is just trying to save his life.

    I realize that all analogies break down. If God existed, it would be very hard for me to understand why he would just let a girl get raped. I know I would hold another human morally accountable for failing to act in that situation. But I have a hard time figuring out what kind of moral standard should be applied to being that knows everything.

    In summary, part of me thinks the character Yahweh is an evil bastard, and the other part of me wonders how to accurately judge an eternal being.

  8. 8
    Hercules Grytpype-Thynne

    I have to say I don’t find this argument at all convincing, because it assumes that the unknown digits of pi are a good analogy for what we don’t know about what God knows. But they’re clearly not. Each new digit of pi that we learn is less significant than the last, and so has an increasingly smaller effect on any calculation we do based on pi as we know it. But it’s not the case that we know so much about God’s knowledge that anything more we might learn about it pales in significance compared to what we already know.

    1. 8.1
      Hercules Grytpype-Thynne

      I should say, “it’s not self-evidently the case”. You’d have to provide an argument to demonstrate it.

    2. 8.2
      Yellow Thursday

      I think you’re missing the point, Hercules. We know pi because of what it represents, and because of that, we know when someone has the wrong value for pi. We may not know the correct value for “god”, but we can easily tell when someone has the wrong value, especially when that person tells us what “god” is suppose to represent. Someone can have the correct first digit of pi and be able to use it in an equation to get an approximate answer, but we can’t do the same thing for god, because nobody has even the correct first digit for god.

      1. Hercules Grytpype-Thynne

        In a way I hope I’ve read the argument incorrectly, because, as I said, I don’t buy it, although I buy its intention. But I think my reading of the argument is fair. The original post says:

        It’s the same with God. We may not know everything an omniscient God would know, but that doesn’t prevent us from recognizing that it’s wrong . . .

        This doesn’t sound like an argument that “nobody has even the correct first digit for god”, but rather that “we know enough about all the factors involved that nothing else we could learn would make a difference in our moral evaluations”. And the latter is what I take the analogy with pi to be asserting. We know enough about pi to know that our knowledge of it is sufficient for all practical purposes, and that anything further we could learn about it would not materially change the calculations we make based on that knowledge. Now, it may be true that this also holds for our knowledge of God’s knowledge, and it may in fact even be demonstrable. I’d love to see someone construct an argument that demonstrates it, but the analogy with pi isn’t it. It’s a petitio principii; it only works if you assume its conclusion. What if our uncertainty about God’s knowledge were at the most significant end of the decimal expansion, not the least?

      2. mikespeir

        This is the way the theist argues, of course. And I’m not saying there’s no merit to it at all. It’s just that he (the theist) uses it as an argument for the existence of God, which is all backward. It may be that we don’t have the wherewithal to accurately assess what kind of moral system God works under. In fact, I wouldn’t expect to be able to do it comprehensively, not if this being is really a fit for “god” as a description. The problem is that the theist just wants me to suspend my judgement and swallow the proposition whole, and that on the basis that maybe my judgement isn’t altogether up to the challenge. But in lieu of at least a fairly incontrovertible demonstration that this god exists, my judgement is all I have to go on. My judgement suggests to me that the God of the Bible is a moral monster. If this Great Being wants me to think otherwise, he needs to show up in real life and take a stab at explaining himself to me. No, I wouldn’t grasp the whole thing, but I’ll bet I’d pick up on enough of it to let me make a better evaluation than what “Just shut up and believe” provides me.

      3. Yellow Thursday

        Just like a theist to take a quote out of context. Your ellipsis in the quote removes the words that “it” refers to. In the quoted sentence, “it” =/= “God”; “it” == “to withhold information about a terrorist plot that is going to cost thousands of innocent lives”. As in “to withhold information about a terrorist plot that is going to cost thousands of innocent lives” is wrong. And we don’t have to know everything an omniscient God would know in order to recognize that.

      4. Deacon Duncan

        What if our uncertainty about God’s knowledge were at the most significant end of the decimal expansion, not the least?

        That’s certainly an intriguing possibility. What if everything Christianity teaches about God actually falls at the least significant end, such that the truly significant factors governing His behavior are something entirely foreign to anything known about Him by His believers. Suppose, for example, that the most significant thing about God is that He is a psychovore—a devourer of souls. All we know about Him is that He desires for us to be good, but the really significant thing—that by “good” He means that He intends for us to TASTE good—is something that lies outside of human knowledge. The most we can know about God are trivial and insignificant things with a negligible influence on His actual behavior.

        That would indeed explain the sharp disparity between the goodness we would expect and the evil we actually observe, and it’s also an even more devastating take-down of Christianity than the pi argument. The point of the pi argument is merely that lack of knowledge about one thing doesn’t mean you can’t see the error in something else, but reversing the significance, wow. That puts Christians in the position of knowing nothing significant about God, and if they end up digesting for all eternity in the acids and bile of a divine stomach, their only consolation will be the knowledge that God indeed found them “good.”

        Kudos.

  9. 9
    rork

    Not a bad point but as a nerd I didn’t like the pi analogy. Hercules made the point well. I think Job is still worth reading, even by atheists like me, the point being that you have to think for your self, or that if something like God exists, we know very little about it, and it doesn’t seem loving – it’s not there for your happiness. (oh, please ignore the little preamble and ending of the book.)

  10. 10
    rork

    Reason #2 for not liking pi-is-irrational analogy:
    Please take a minute and try to convince yourself it is true. Hi Ho!
    (Hint: use square root of 2 next time – it’s easier.)

    1. 10.1
      mikespeir

      I’ve always thought that calling pi and similar numbers “irrational” was an insult to the numbers, one we make because of our own limitations. The number itself has a precise value. We just don’t know how to express it precisely.

  11. 11
    Janney

    It’s a petitio principii; it only works if you assume its conclusion. What if our uncertainty about God’s knowledge were at the most significant end of the decimal expansion, not the least?

    Perfect is the enemy of pretty good. Christians (for example) have plenty to say about God. Based on what they say, we can draw some pretty solid conclusions about Him. Our knowledge is less than perfect, of course, but it works well enough. Sounds just like pi to me, except for the vast army of people unwilling to accept the straightforward implications of their premises.

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