23 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[o] to measure around it. 24 Below the rim, gourds encircled it—ten to a cubit. The gourds were cast in two rows in one piece with the Sea. – 1 Kings 7:23-24
I’m not sure what a “Sea” is, but it’s circular (sounds like a cylinder), has a diameter of 10 cubits, and it takes 30 cubits to go around it – the circumference. But we know now that Pi * D = Circumference, and therefore the only value for Pi that would work here is exactly 3. So is this pointing out how the bible is garbage?
First, lets find out what a cubit is. I’ll use wikipedia:
The cubit is a traditional unit of length, based on the length of the forearm. Cubits of various lengths were employed in many parts of the world in Antiquity, in the Middle Ages and into Early Modern Times…The Egyptian cubit was subdivided into 7 palms of 4 digits each; surviving cubit rods are between 52.3 and 52.9 cm (20.6 to 20.8 inches) in length. (link)
Wait a minute…surviving cubit rods are of different lengths? So they couldn’t even agree? Yes and no. We are talking about 52.3 cm and 52.9 cm, a difference of 6 mm. So really what this tells us is that there is a maximum error built in. If everyone and their dog needed a cubit stick to conduct business, certainly error would creep in. No one cared too much to make them all EXACTLY the same length, but certainly, they better be close enough – they better be a cubit! If they were off too much, certainly someone would care, and fight it. If I’m buying a cubit of cloth from a merchant and I disagree with their cubit length, I either (a) wouldn’t buy it there, (b) claim they were thieves and have them investigated somehow, or (c) I can probably get someone else to measure it for me. Situation (b) actually happened often in the ancient world. How do I know? The bible speaks clearly AGAINST using dishonest weights and measures (see for instance Deut 25:15, Proverbs 20:10, Amos 8:5) …and why would it speak against something if it never happened? Note:
So using these measures, how far across could the diameter actually be? Ten cubits is the between 523 cm and 529 cm. The circumference is the between 1569 cm and 1587 cm. Using all of these values, pi would still be between 2.965973535 and 3.034416826, which it’s not, so we still have a problem.
So, lets do some graphing. Here are the two circles in question: one with radius 5, and one with circumference 30:
Wow those are close. For reference, the equation of the larger one is (x/5)^2 + (y/5)^2 = 1 (radius 5 circle), and the other has a circumference of 30 cubits, and the formula is similar, but instead of a 5, we have 30/(2 pi) on the bottom of each fraction, resulting in a formula of: (x/4.77464829275686)^2 + (y/4.77464829275686)^2 = 1 (a circle with radius 4.77464829275686 = 30/(2 pi) cubits). Now approx 4.77 * 2 = 9.55 cubits is pretty different than the 10 in the scripture (about 23.707 cm difference), and the larger one has a circumference of approx 31.415 cubits, which is pretty different than 30 (about 74.4777 cm difference, or 3/4 of a meter), so while we are close, such a measurement cannot be just given up to error…but what if it’s not a circle?The scripture says “He made the Sea of cast metal, circular in shape“. Lets assume both measurements were right: 10 cubits from end to end (at one point), and a circumference of 30 cubits. What ellipse would have this property? Experiementing a bit, assuming that the x-factor was 5 (resulting in a diameter of 10 on the x-axis), I checked different values for the y-factor until I got a circumference that was within 1/1000000 cubits of 30. The formula was (x/5)^2 + (y/4.5438452484)^2 = 1, and here’s the graph:
Exactly 30 units in circumference, exactly 10 units across (parallel to the x axis). Is anyone going to suggest this doesn’t fit the criteria of “circular in shape”? If you look at the Hebrew word that was used for “circular”, it is “agol”, and if you look up the details of it here (or here), it says “circular” and “round”, but doesn’t say “perfect circle”. So it appears to me that God didn’t even ask for a circle. He asked for an ellipse…he just didn’t call it that.By the way, I used the approximation for circumference of an ellipse given on wikipedia as:
I don’t see any problem here. I don’t think I am being unreasonable, or trying to just justify my position of being a Christian. I think this is very reasonable. It might be interesting to consider next how the metal smith was to make this. How were things made with metal back then? What kind of tools did he have at his disposal? Perhaps the reason the particular information was given was that these were what was needed to build it. I don’t know. If anyone has some insights on this, please let me know!
Thanks for reading!
Rob
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