Monday, January 09, 2006

Pi = 3

The next “proof” that purportedly demonstrates that the Bible is scientifically unreliable comes from the description of the furnishings of Solomon’s Temple. We read:
Then he made the sea of cast metal. It was round, ten cubits from brim to brim, and five cubits high, and a line of thirty cubits measured its circumference. (1 Kings 7:23)
Aha! A circumference of thirty and a diameter of ten means pi =30/10 =3. Either Solomon’s Temple was built in Indiana or we have a serious problem.

Or do we?

(The sea, by the way, was a humongous brass basin almost certainly used by the priests for ceremonial washings.)

Notice again the same fallacy as in the “bats are birds” complaint. The underlying assumption is that the ancients were morons. (This assumption is usually reserved for ancient Hebrews alone. The Aztecs, for example, are assumed to be cultural and scientific geniuses who knew the secrets of the Super String landscape, which they enjoyed discussing over high protein meals derived from their own species.)

Any civilization building anything circular would have known that the ratio of the circumference to the diameter is slightly greater than 3. The Mesopotamians of a much earlier era used the approximate value of 25/8 = 3.125. The Egyptians may have had a much better value long before Solomon’s Temple. Here we see the assumption of stupidity: The Hebrews either didn’t know what their neighbors knew or they did know but didn’t bother to put accurate information into their sacred writings, in spite of its potential effect of weakening claims regarding the veracity of the holy words.

Not that any of that matters, because what is provided in the Bible is a description (“He made”), not a blueprint (“Makest Thou”).

There are several possible explanations—each one could stand alone but all may contribute to a certain extent.

The simplest explanation is technological. It was not possible to cast a brass object of such size in the shape of a perfect circle. So if one intended, roughly, to give its size using the (redundant) parameters of a circle—circumference and diameter, there would already be built into the description an error—given that the object was only approximately circular.

So the simplest explanation is that we are being given a rough description in terms of approximate dimensions of an imperfect shape.

However, even if we assume that the sea was a perfect circle, there is no problem. For even if it was perfectly circular, it was not infinitely thin.

The figure on the left shows a scale drawing, assuming the precise measurements as provided. To put things in everyday perspective, we have converted from cubits to feet using the relationship that 1 cubit is about 18 inches. The problem is that the given diameter of 10 cubits (or a radius L of 5 cubits) extends beyond a circle with circumference 30 cubits, which has a radius of R = 4.77 cubits, by, as shown, an amount Δ. A simple calculation shows that Δ ≈ 4.1 inches.

But what if the sea had some thickness? And what if, as in the artist’s conception shown below, it was even flared at the rim? Then the 10 cubits could refer to the “outside” distance across, giving us information on its total size, while the circumference could be the inner circumference, telling us about the sea’s capacity.

Is this plausible? Let’s continue on with the biblical passage, just after where the dimensions are provided, and look at further descriptive details:
24 Under its brim were gourds, for ten cubits, compassing the sea all around. The gourds were in two rows, cast with it when it was cast. 25 It stood on twelve oxen, three facing north, three facing west, three facing south, and three facing east. The sea was set on them, and all their rear parts were inward. 26 Its thickness was a handbreadth, and its brim was made like the brim of a cup, like the flower of a lily. It held two thousand baths. (1 Kings 7:24-26)

In verse 26 we are told that its thickness was a handbreadth, which fits nicely with the value of Δ ≈ 4.1 inches. We are also told that the brim was like the brim of a cup, which is consistent with the conceptual drawing. Either or both of these effects renders the criticism, which is based on a infinitely thin perfect circle, meaningless. The numbers given are perfectly compatible, even with a literal reading, as long as verse 26 in addition to verse 23, is taken into account.

Finally, although it need not be invoked in this case, it is also known that eastern writing of the time was numerically imprecise—we often see this in biblical writings through the use of rounded numbers—for example in discussing Job’s possessions. This potential mitigating factor, that the writers of that era (biblical or not) treated numbers differently than we do, along with the fact that they also treated quotes differently (as faithful to the content of someone’s statement but not necessarily the precise wording) are two inconvenient (for our critics) established truths that they label as copouts. As I mentioned in the previous post, other off-limits methods to counter their claims include arguing on the basis of figure of speech, hyperbole, translation error, or proper context. For their claims regarding biblical inconsistency with science to hold water they cannot relax their unspoken assumption that the ancient Hebrews were idiots and their demand that all contested passages be evaluated, not just hyper-literally, but also as if they were written using modern style and practices.

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