Pi in the Bible?

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
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One of the most famous mathematical statements in the Bible is in I Kings 7:23-26, describing a large cauldron, or "molten sea" in the Temple of Solomon:

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. Below the rim, gourds encircled it - ten to a cubit. The gourds were cast in two rows in one piece with the Sea. The Sea stood on twelve bulls, three facing north, three facing west, three facing south and three facing east. The Sea rested on top of them, and their hindquarters were toward the center. It was a handbreadth in thickness, and its rim was like the rim of a cup, like a lily blossom. It held two thousand baths. (NIV)

Now the Hebrews were not an especially technological society; when Solomon built his Temple he had to hire Phoenecian artisans for the really technical work. So the author of this passage may not have known the exact value of pi, or thought his readers might not be aware that specifying the diameter of a circle automatically specifies its circumference. In any case, the essential point was the impressive size of the cauldron, and its dimensions were only approximate, because the ratio of the circumference to the diameter is stated to be exactly three rather than the real value of pi which is 3.14159....

If the rim was made in the form of a lily blossom, we could expect it to have had decorative details with bumps and re-entrants, in which case any really exact measurement of diameter and circumference would be meaningless.

Even the comparatively innocuous idea that the writer of I Kings might have been speaking in only approximate terms is unacceptable to some people, because it implies, however slightly, that some passages in the Bible were never intended to be taken with exact literalness. There have been a lot of efforts to explain away the approximation to pi, and also some folklore about the attempts.

The most famous episode took place in the 19th century, when the legislature of Iowa supposedly considered a resolution to make pi legally equal to 3, based on the Biblical passage. Actually, the effort was the brainchild of a well-meaning but not overly mathematical legislator to make things easier for practical calculations by legislating a standard and simple value of pi. If we can define other weights and measures, why not pi? The proposal had very little to do with the Bible and died a quick death in committee.

"Fudge factors" or "finagle constants" are scientific slang for ad hoc postulates whose sole function is to get a theory out of trouble. The creationist claim that radioactive decay varies in rate is a good example; the only function of this postulate is to make it possible to deny the ages of rocks determined by radiometric dating. Another flagrant example of fudge-factoring is that of creationist author Theodore Rybka, who attempted to resolve the pi problem in an article entitled Determination of the Hebrew Value used for Pi, published in the January, 1981 issue of Acts and Facts, a bulletin of the Institute for Creation Research.

Note that the passage in I Kings explicitly gives both the diameter and the circumference. An estimate of pi is simply the ratio of the circumference to the diameter: 30/10 or exactly three. The passage in I Kings also elaborates on the depth, volume, and wall thickness of the cauldron. Rybka ignores the value given in plain words for the diameter and proceeds to develop a formula for the diameter using all the other dimensions and the totally unwarranted assumption that the cauldron was perfectly cylindrical. He converts the cubit, which was a variable unit of measure, to meters, and converts the Hebrew unit of volume, the bath, to liters. The volumes of one-bath jugs found by archaeologists give Rybka five values: 22.8, 22.9, 22.0, 22.7 and 23.3 liters. Blithely ignoring a variation of 1.3 liters or almost 6%, he averages the values to get a volume for the bath of 22.74 liters. He then puts this value into his formula and gets a value for pi of 3.143. "The calculations only warrant three-figure accuracy, however, so the final value is pi=3.14 which is identically the modern three figure value."

Now hold it a minute. First, the variation in the volume of the bath is so large that only two figure accuracy is justified, and the uncertainty is only accentuated our uncertainty as to the exact value of the cubit. Second, if the whole point of the discussion is to demonstrate the literal inerrancy of the Bible, 3.14 is just as much an approximation as 3 is. The decimal expansion of pi never ends and never repeats to infinity. (This would have been a great place to put such a statement, which would have been utterly beyond the capabilities of the ancient Hebrews, or even the translators of the King James Bible, to have known. What a stunningly convincing proof of supernatural authorship it would have been!) Finally, given a ten-cubit (about fifteen feet) diameter vessel with a circumference of fifty feet or so, anybody should be able to get at least three-figure accuracy in determining the value of pi. At the very least, anyone measuring the cauldron with even the crudest device should find a circumference of thirty-one cubits.

The clincher comes when Rybka uses his formulas to check the diameter and circumference of the cauldron. For the circumference he gets 29.97 cubits, very close to the figure of 30 given in I Kings, but he calculates the diameter to be not ten but 9.545 cubits! All Rybka has done with his elaborate manipulations is remove the approximation from the circumference to the diameter. We are told that the author of I kings did not use an approximate value for the circumference; he used an exact value but his determination of the diameter (which would by far have been the easiest dimension to get correctly) was off by about half a cubit or about nine inches!

Concludes Rybka: "Thus the Bible account is shown to be scientifically accurate."

As one visitor pointed out, there's a much less convoluted way to salvage this passage. If the inner circumference was measured, for whatever reason, then the outer diameter would have been ten cubits but the inner would have been ten cubits minus two handbreadths, or about 9.5 cubits. 30/9.5 = 3.158, a much better approximation.

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Created 3 February 1998, Last Update 02 June 2010

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