For the week ending 16 June 2018 / 3 Tammuz 5778

Circular Reasoning

From: M.S.

Dear Rabbi,

I have a question about the description of the circular brass pool in the Temple as stated in verse I Kings 7:23. The verse says that this pool was 10 cubits across and 30 cubits around. If so, then either G-d doesn’t seem to know the value of “pi”, or the pool was not exactly circular. If only approximate measurements were known to man, still G-d certainly ought to know the exact facts, and this might indicate that the Bible was written by men, not by G-d. Can you help me? Thanks.

Dear M.S.,

The verse says that Solomon constructed a circular pool that was “ten cubits from edge to edge....and 30 around.” The question is, how can this be? If it was ten across, it would be more than thirty around. (It would be closer to 31.4, a difference of 1.4 cubits, or approximately 3 feet.)

This description is independent of “knowing the value of pi.” Ascertaining the dimensions would have been as simple as circling the pool with a tape measure. Could it be that Solomon, the master builder of one of the architectural wonders of the ancient world, the Temple, couldn’t measure properly or had a tape measure that was off by three feet?

Obviously, as the commentaries explain, the verse is offering an approximation. There are many such instances where the Torah uses approximate numbers. Just one example: When the Torah tallies the members of each of the 12 tribes (Numbers 1:20-46), each tribe’s population is rounded to the nearest 50.

Why does the Torah give approximations? To offer us relevant information without burdening us with details (which, by the way, are often dealt with in the Oral Torah). In the case of “Solomon’s Pool,” the approximation teaches us that in Jewish legal matters relating to construction, we may use this 1 to 3 ratio as an approximation regarding Rabbinical law.

Additionally, even if the verse were to be more exact, this would still not solve your problem. Why not? Because, in fact, no number expresses the value of “pi”. (That’s why it’s called “pi” and not written as a number.) No matter how specific the verse would be, you could always ask, “Why wasn’t it more specific?” That is, if the verse had said the pool was 31.4 units around, you could say, “That’s wrong, it was really 31.415...” and so on. So particularly in this case, it’s counterproductive to be precise!

In conclusion, the Torah sometimes approximates, and in the case of “pi”, approximation is mandatory. Therefore this shows nothing about the Torah’s authorship, neither regarding Moses’ ability to accurately count the Tribes, nor Solomon’s ability to calculate “pi” or wield a tape measure!

A fascinating footnote for the mathematically-minded:

The Vilna Gaon illuminates the fact that the value of “pi,” 3.1415, is actually hinted at in the inner dimension of this verse. In Hebrew, each letter has a numerical value associated with it. In the above verse, the word “circumference” (kav) is written “kuf vav heh” which equals 111, despite the fact that this word is normally written “kuf vav” which equals 106. This parallels the above idea that regarding the circumference of the pool, there is a stated value and an actual value. The ratio of these two numbers times the stated value of 3 equals the actual value of “pi” to the 10,000th, i.e. (111/106) x 3 = 3.1415!

Sources:

• Rambam, Commentary on the Mishna
• Aruch HaShulchan, Orach Chaim 363:22
• See Eruvin 14a