Sunday, March 29, 2009

Bible Defense: Everybody Likes Pi

Today's Bible Defense article was inspired by a comment on my explanation of the birds and the bats. In the comments on that article, someone with the handle Evil Bender posted this:

Of course, one could ask why God would have the Hebrews using a word that groups animals by flight, not by relationship. Surely he could have given them a better understanding of nature?

That the Creator of the Universe would conflate bats with birds (while apparently excluding flightless birds) does not help your case for infallibility.

Nor does the fact that pi is not equal to 3, nor that the gospels disagree about the event leading up to Jesus' death.

And that's without even getting into different lineages, iron chariots, and heaps of other biblical contradictions.
First of all, I'd like to thank E.B. for making a polite, thoughtful contribution to the discussion. All too often this sort of thing turns into a flamewar, consisting of nothing more than name-calling substituting for argument. E.B. has not done that, and I certainly don't intend to either.

Before we get into the meat of this new entry, I'd like to reiterate the point I wanted to make about bats and birds: there was no need for God to explain that bats aren't birds, since the ancient Hebrew word translated as "birds", 'owph, does not mean "birds" in the modern sense. It would have been completely nonsensical for the Bible to stop at that point to explain that bats are not birds, since in the original language "birds", in the sense of the category as it now exists, was never used. If the word "birds" is a problem, then forget that it's there, and mentally insert the word 'owph at that point.

In short, "birds" is an imperfect translation of the original word, which in no way meant or implied that only feathered egg-laying animals were intended. There's no need to defend the idea that the Bible calls bats "birds", because it doesn't. It calls them 'owph, which they are, and we translated it imperfectly.

Put another way: "That the Creator of the Universe would conflate bats with birds..." He didn't. Those who don't understand that 'owph does not mean "bird" did.

I don't know how to put it any more clearly.

However, E.B. raised another point that I'd like to address: the value of pi. His other alleged discrepancies fall into the category of "stuff I haven't researched or thought about enough to discuss intelligently". Maybe some other time.

Many people over the years have argued that the Bible says that pi is equal to three, based on this passage, I Kings 7:23 (repeated in II Chron. 4:2):
He made the Sea of cast metal, circular in shape, measuring ten cubits from rim to rim and five cubits high. It took a line of thirty cubits to measure around it.
Before we get into why this passage does not say that pi is equal to three (and why some people think it does, in case you've put all that stuff from geometry class behind you), let's talk about some of what those things mean.

Ritual washing was a huge issue for the priests of ancient Israel. There are many passages, especially in Leviticus, that go into great detail explaining exactly when and how priests are to wash before carrying out their duties. Most of the explanations boil down to cleanliness being a symbol of holiness; it would be an insult to God to appear for His service looking anything less than one's best. The phrase "cleanliness is next to Godliness" does not appear in the Bible, but it's easy to see how people make that logical leap.

The principle still holds today. Nobody wants to show up for a job interview, or the first meeting with the parents of someone they're dating, with a stain on their shirt or a milk mustache. It would be embarrassing to appear before someone whose approval you seek without cleaning yourself up.

The Old Testament rules of washing served a health purpose, as well. The priests handled food that was offered as sacrifice - which was then eaten. Long before humans understood germ theory and bacteria, God was promoting safe food handling techniques.

"The Sea" was a large basin, put inside the temple for the priests to use for washing. I don't know if they actually got right into it and bathed, but it was certainly large enough for them to do so. It was pretty much a huge bowl of water.

So, how huge? Most of us don't know offhand what a "cubit" is, so that "Sea" might only be big enough to dip a Star Wars figure's head.

It turns out that a cubit is about 18 inches. We'll be coming back to that "about". So, this basin was about (there's that word again) 15 feet across, 7 and 1/2 feet high, and 30 feet around. That should explain why it got named the Sea (a term that appears several more times, capitalized as a proper noun, in the Bible).

Overall, though, you don't need to worry about what a "cubit" is. The conversion of cubits to metric or imperial measurements isn't the issue - the ratio between the distance across the Sea and the distance around it are what matter.

So, then, this passage seems to say that the Sea was 30 cubits around and 10 cubits across. In geometric terms, it had a circumference of 30 cubits, and a diameter of 10 cubits. But wait. The formula for the circumference of a circle is pi times the diameter. Pi is an irrational number (that is, it has an infinite, nonrepeating series of digits after the decimal place) a little larger than 3. It's been calculated out to thousands of places beyond the decimal, but most people are content to use the very reasonable approximation of 3.14159 in its place. Some use 3.14, but they're just lazy.

If we use the stated diameter of 10 cubits and multiply by pi the way the nuns back in parochial school taught us, we find that the circumference should be 31.4159 cubits, not 30. Conversely, if we start with the circumference of 30 cubits and divide to find the diameter, we find that it should be about 9.5493 cubits, not 10. So what's going on here?

To be fair, most people attacking the Bible over this aren't seriously suggesting that Bible believers think pi is precisely equal to 3. There's an urban myth that state legislatures have in recent years tried to pass legislation forcing pi to equal 3 on Biblical grounds, but it isn't true (which I didn't realize until researching this article).

Instead, those people are usually using this passage to "prove" that the Bible is unreliable on factual matters, usually to bolster their skepticism on other Biblical issues. See, for example, this article. The endgame argument tends to run along the lines of, "How come you understand that pi doesn't equal three even though the Bible says it does, but you still believe in the Virgin Birth just because the Bible says so?" For "Virgin Birth", feel free to substitute "global flood", "resurrection", "seven-day creation", any miracle, or anything else the Bible records that runs contrary to our everyday experience and modern, scientifically enlightened popular belief.

No matter what you substitute, the underlying claim is the same: the Bible cannot be trusted on factual, scientifically measurable matters. When the Bible and modern science conflict, the Bible is to be rejected. Refuting that argument in its entirety is well beyond the scope of this article (and probably beyond the scope of my knowledge and writing skills). However, we'll carry on with our look at pi, which may also chip away a bit at the argument outlined above.

The argument is that the Bible herein proves itself inaccurate and unreliable by stating that pi is equal to three. The implication of the argument is that the Bible is therefore untrustworthy in its entirety. I will not be addressing the implication (beyond to say that it requires a leap in logic which would bear further examination before acceptance), but I see three immediate responses to the argument about pi. Once again, in researching this article I found that others have made these same points before me. No matter.

These three offered responses are not mutually exclusive. The truth may lie in some combination of them, or indeed in some possibility I have not considered. I would only have people think before rejecting the Bible, and hopefully this helps.

First, the numbers indicated in the passage - ten cubits across, thirty cubits around - may well be approximations. This passage is a description meant to convey a visual image to the reader, not an engineer's blueprint. There is a large bookshelf a few feet to my left.If I say that it is five feet wide and six feet high, I would consider that sufficient to give you an impression of its size. I would not feel I had been proven a liar if you were to take a tape measure to it and find that it is in fact exactly 4 feet, 10 and a quarter inches wide and 6 feet, 2 inches high. This is the argument you will find in the notes of most study Bibles and commentaries - the numbers given here are rounded approximations.

A variation of this is closely enough related that I will treat it under the same heading. A good explanation of this variation can be found on this page at Purplemath, which also covers what I'll be coming up to shortly as number two.

There was no standardized definition of a "cubit". The word itself means an approximation, based on the length of a man's forearm from elbow to fingertip. As you can imagine, this isn't the same for all men. The cubits of the circumference may not have been precisely identical to the cubits of the diameter. Due to the rounding / approximation issue, this doesn't really matter, but I thought it worth noting.

Second, the measurement of 10 cubits "from rim to rim" could well be a measurement of the external diameter - that is, from the outside edge of one side of the basin to the outside edge of the other. As noted earlier, that would describe a circle with a circumference of 31.4159 cubits. (As earlier, don't get hung up on the units - the mathematical ratios are what matter.)

However, this huge bowl could not have had zero thickness, and certainly not negative thickness. Perhaps the 30 cubit measurement of the circumference was taken around the inside. Purplemath again does a terrific job with this argument, complete with diagrams, explaining that a second mold would be required for the inside of this basin, and that the 30 cubit measurement could have described that smaller mold.

A circumference of 30 cubits indicates a diameter of 9.4593 cubits. That leaves a discrepancy of .5407 cubits, or about 9.7 inches, to account for the thickness of the rim. Divide that in two for the two sides when measuring across, and you wind up with the brass walls of the Sea being 4.95 inches thick.

And, hey, what's this we read about the Sea in I Kings 7:26?
It was a handbreadth in thickness...
A "handbreadth" is another of those Biblical-era ad hoc units of measurement, and means pretty much exactly what it says: the width of a hand. The almost-five inches we calculated is a bit on the high side from what most study Bibles and commentaries say (although my own hand is considerably wider than the three inches they suggest, and I'm not a real big guy), but not unbelievably out of line. Besides, the rounding / approximation issue I described in my first response easily allows for that rim to come down (or go up...) by an inch or two. Assuming that's logistically feasible, of course. Not being an engineer, I don't know how thin those brass walls could get before giving out under the weight of all that water.

Once again, those who attack the Bible haven't read a few verses down from the verse they're basing their argument on....

On to my third possible response. To assume that a stated circumference of 30 units and a distance across of 10 units proves a mathematical contradiction is to assume that the object being measured is a perfect circle. I'll ignore the fact that physical reality contains no perfect circles, and no straight lines, for the sake of this argument. I like philosophy as much as the next guy, but I'm not going to use that kind of esoteric argument to try to get out of this. By "perfect circle", we mean one that is close enough to perfectly circular to treat it as such for all intents and purposes.

However, we have no reason to believe that the Sea was a perfect circle. "Circular", yes, meaning round, but once again we have to remember that this description was written to evoke a visual image of size (and therefore grandeur) and was not an engineering blueprint. It could just as well have been described as "immense, thirty cubits around".

I did some online research about the measurements. This reminds me why I love the Internet. Not so many years ago I would have pondered this for a few seconds, thought perhaps I should go digging through some geometry books sometime, shrugged, and forgotten all about it. Thanks to Google I was able to find some ellipse calculators and try out some numbers.

To get what I'm saying about the possible shape of the Sea, pick up a fairly rigid round plastic cup, and look at at from directly above. The mouth of the cup should look like a circle. Now, with your hands as close to the base as feasible, squeeze the cup until the mouth begins to distend slightly. The mouth will now be elliptical, but I wouldn't be shocked if someone was still willing to describe it as "circular".

That's what I'm saying about the Sea. It could have been slightly elliptical, and the 10 cubit measurement could have been taken across a wider section (in geometric terms, closer to parallel with the major focus than the minor). For that matter, the measurement across may not have been taken directly across the centre point, again affecting the results.

I found an ellipse calculator on, and plugged some numbers into Calculator Two. If you enter a major axis of 10 and a minor axis of 9.08, you'll get a perimeter of 30.035 (remember, units don't matter, only ratios). Then, you can put those same numbers into the ellipse generator at to see how close to a circle the results look. You'll find that "circular" is a fair description for purposes of the layman.

Feel free to play with those numbers - by adjusting the axes, you can get very close to a perimeter of 30 while the resulting figure looks very much like a circle. Remember too that the sheer size of the Sea would make a slight deviation from circular even less noticeable.

I wound up playing with those ellipse pages far longer than I should have. At least it wasn't as bad as that cursed online Spirograph simulator that held me in its grip many moons past. I almost wound up getting an intervention over that thing. But I digress.

While researching this article, I was pleased to see some sites where these (or similar) arguments were accepted to debunk the "the Bible says pi is three" trope. The "Atheism FAQ" at this site is a good example. Often people on one side or another of a debate, and I'm including my allies in this, are only too willing to throw any accusations they can find against the wall and see what sticks. Consider the 2008 presidential election campaign, when Democratic supporters were openly encouraging the spread of rumours that they knew to be false about Sarah Palin; as long as it made voters question her, the ends justified the means.

I don't like to see bad arguments getting used by either side of a debate, and the best way to prevent that is to police your own side. It's good to see anyone saying to their allies, "That argument has been refuted. Let's stop trying to use it and move to stronger ones."

Enough rambling. Here's a picture of my yellow Orks. I usually ran these guys as Mad Boyz.


RebelAngel said...

Differing accounts of the events leading up to Jesus' death?

Evil Bender must not work at a police station taking witness testimony.

It is when everything matches that the police actually start to think people are lying.

Anonymous said...

Most lists Biblical difficulties consist of poor translations. There are issues, but the really interesting ones are generally ignored. I expect that is because the solutions to these will give some theological insights best kept hidden. The devil doesn't want an atheist doing research. Who knows where some education could lead? Nothing dulls the mind or spirit like a little smug self-importance.

Besides, the real issue is not these apparent contradictions. The atheist doesn't care about them; they are just a means to deny the Bible. Take away the contradiction argument, and he will have plenty of other reasons to disregard the Bible. I say the real value of Biblical difficulties is to the believer. There have been plenty of times I have been faced with some issue only to find either a simple solution, as you find in the pi example here, or a profound nugget to turn over in your mind (My God, why have you forsaken me?)

If you're having problems with your Bible, just use the George Costanza Law of Hermeneutics- hold it at arm's length and say, "It's not you, it's me."