Thursday, September 27, 2007

Pi Eyed

Does the Bible claim that pi is 3?

I Kings 7:23 states the following:

"The sea was then cast; it was made with a circular rim, and measured ten cubits across, five in height, and thirty in circumference."

Apparently, critics of the Bible and any claims to its infallibility love using this passage. They point out that these proportions imply pi equals 3, when its value (according to Wikipedia) is really closer to 3.14159. That is, if the width were really ten cubits, the circumference should be, not thirty cubits. but closer to 31.4159 cubits.

None of these critics are more gleeful than Jason, the proprietor of Follow the link for his detailed analysis, but here's what caught my eye:

"Now, as it happens I don't think it is unreasonable to conclude that the writers were simply giving round, ballpark numbers. But I'm not the one claiming that every word in the Bible is divinely inspired and infallible. Please don't tell me that on the one hand the Bible is reliable in everything it says, but on the other I have to first learn math and science from some independent source before I can know how to interpret it properly.

"There is no reason, outside independent knowledge that pi, in fact, is not three, to interpret those measurements as approximations. And even if you do interpret them as approximations, you're still left with the fact that the plain meaning of the Biblical text can lead you astray on matters of math and science."

This breathless passage sent me back to check the words of the passage again. Here's what I don't see:

"The sea was then cast; it was made with a very precisely circular rim, and measured 10.00 cubits across, 5.00 in height, and 30.00 in circumference."

If this were how the passage was presented in the Bible, I think Jason might have had a point. However, the Biblical passage does not seem to be pretending to a high degree of precision -- ten, five, and thirty seem like nice round numbers. Nor do we know how perfectly circular the "circular rim" was. We often describe the earth as a sphere, but in fact it is an oblate spheroid -- does that mean that if you use the term sphere, you're being fallible?

No, you're being imprecise. It seems clear that Jason is conflating imprecision with fallibility.

  • Pi does equal 3, if you're rounding to the nearest integer.
  • Pi equals 3.1, if you're rounding to the nearest tenth.
  • Pi equals 3.14, if you're rounding to the nearest hundredth.

And so on. You can carry this out to as many decimal places as you like, but there is some specification at which pi will always be an approximation. Wikipedia carries it out to five decimal places, and still characterizes that as an "approximation". Pi generally equals 3.14 in grade school math, but NASA would probably require a little more precision. A shepherd culture, circa 800 B.C., might be forgiven a little imprecision.

Postscript: There is an excellent discussion from a physics web page of the concept of significant digits. The basic rule is that no calculation can be considered as more precise than the least precise number used to calculate it. The numbers given in I Kings 7:23 -- "five", "ten", "thirty" -- each contain only one significant digit. Therefore, even if we were to assume pi = 3.14, then (3.14)(10) = 30, because the operand 10 has only one significant digit.

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