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by H. Peter Aleff |

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Most textbooks on the history of science assert that ancient Near Eastern mathematicans did not know how to compute the circle constant pi, and that the Bible gives the very inaccurate value of pi = 3 for this important number. They refer to the reported dimensions of the “sea of cast bronze” which king Solomon placed before the Temple he built in Jerusalem, as described in 1 Kings 7:23:
Indeed, the Rabbis who wrote the Talmud a thousand years after Solomon asserted this value based on those verses. They may not have been mathematicians, but they knew how to divide thirty by ten and get three. They affirmed as late as the middle of the first millennium CE:
Scholars of the Enlightenment era were glad to concur with that interpretation because it allowed them to wield this blatant falsehood in the Bible as an irresistible battering ram against the until then unassailable inerrancy of the religious authorities. Their Colonial era successors further embraced that poor value for Solomon’s pi to belittle the mathematical achievements and abilities of the ancient non- European civilizations, and to thereby better highlight those of their own group. The views of these scholars survive to the point that this purported lack of mathematical intelligence under the reign of a king renowned for his wisdom is still an article of faith among mainstream historians of science trained to read this obviously primitive value into the text. One of the most popular books on "A History of Pi" even offers eight translations of that biblical passage into seven different languages, presumably to drive home the point, with the common mainstream method of proof by repetition, that in every one of those translations the diameter remains ten cubit and the circumference thirty However, the disparagers of Solomon’s pi omit half the evidence. The rest of the passage they cite shows their dogma is based on a hit- and- run calculation of the type that would make any undergraduates flunk their exam. It seems that none of those who so compared the diameter and circumference of Solomon’s Sea of Bronze, as reported in 1 Kings 7:23 and 2 Chronicles 4:2, bothered to read on. Both accounts state three verses later that the rim of said vessel was
In other words, the rim was flared, and the ten- cubit diameter measured across its top from rim to rim was therefore larger than that of the vessel’s body which “took a line thirty cubits long to go around it”. The surveyors would hardly have tried to stretch their measuring rope around the proud outside of that rim where it would never stay up. The only practical way to measure such a flared vessel is to stretch the rope around the body below that rim, as suggested on the picture above. The circumference and diameter reported were thus not for the same circle, and deducing an ancient pi from these unrelated dimensions would be about as valid as trying to deduce your birth date from your phone number.
Moreover, the measuring unit conversions supplied by modern archaeology allow us to compute the inside volume of that vessel and to thereby find its shape. With the stated circumference, wall thickness, and height, only a cylinder can contain the volume of 2,000 bath given in 1 Kings 7:26. The cubit length which had been used in various Jerusalem buildings and tombs of Solomon’s time was 20.67 inches The bath was a liquid measure of “approximately 22 liters”, as Harper’s Bible Dictionary states. It was one tenth of a “kor” in the well- known dry- measuring system which is also described in Ezekiel 45:14. Its use for liquids is confirmed by eighth century BCE storage jars, found at Tell Beit Mirsim and Lachish, that were inscribed “bath” and “royal bath” As calculated and illustrated in the above diagram, the 2000 bath of water from 1 Kings 7:26 fill that cylinder close to its top, to a height of 4.511 cubit above the inside bottom. The outside height was five cubit, and the bottom was one seventh of a cubit thick, so the 2000 bath leave only a shallow rim of about 0.3461 cubit above the water level, depending on how accurate the "about 22 liter" conversion factor is.
The height and width of that rim, computed with the proper pi, produce an elegant flare that matches the biblical description. The same holds true for approximations to pi from about 3 1/8 to 3 1/6 which all produce lily- like rims and are all closer to the proper value than the alleged but unsupported pi = three. These conversions also make it clear that the copyist of the much later
Solomon’s mathematicians and surveyors, and their ancient colleagues throughout the ancient Levant, were therefore not necessarily the clumsy clods portrayed in current history books. The accuracies of transmitted lengths which Ritmeyer found in the actual dimensions those ancient builders left us in stone show that they worked with great care. It strains belief that their surveyors could have misread the rope around that vessel by almost two and a half feet in a circumference of less than 52 feet. Nor is there any rational reason to assume that the ancient number researchers were so innumerate that they could not have computed a fairly good value of pi, as close to the real one as that of Archimedes, or even closer. They had the same basic mathematical tool kit which Archimedes used many centuries after the Babylonians and Egyptians developed it. They had perhaps also more patience and motivation than Archimedes to continue with the simple but repetitive calculations required for better approximations. However, the backwardness of ancient Near Eastern mathematics has become a cornerstone of the prevailing prejudice against pre- Greek accomplishments. Examining that cornerstone exposes the scholarly bias on which it was founded. The reason for the current denial of ancient pi seems to be that the tool required for the calculation of pi is analytical thinking, the same mode of thought on which all the rest of so- called Western science is based, and which must therefore be Western. Most history books tell us that this superb achievement and gift to all humanity had to wait for the unique genius of the glorious Greeks, and that the invention of inquisitive and logical thinking was the decisive contribution from these purported founders of said science. The Greeks were, in the words of a highly respected Egyptologist born at the height of the English Empire:
Reflecting the same then typical attitude which refers to those other people as “that” instead of “who”, an equally respected historian of science quoted approvingly Plato’s partisan remark :
This cultural bias led some of those afflicted by it not only to disregard obvious facts, as in the case of Solomon’s pi, but even to fabricate evidence, as needed to support their supposed superiority. Take, for instance, the engineering achievement of king Hezekiah’s tunnel builders. This biblical king needed to prepare Jerusalem for a serious siege because he was planning to revolt against the Assyrians who had conquered the area earlier and extorted heavy tribute from it. To have a chance against this almost irresistible superpower of his day, he needed to protect the water supply of his city and so had a tunnel dug from inside the walls to the outside spring. His tunnelers started at both ends and met underground. This would have counted as a considerable achievement even if they had cut along a straight line. However, their surveying task was much harder. They took advantage of some existing fissures in the rock, and their path of least resistance to the stone cutters became an irregularly curved maximum challenge to the mathematicians who had to multiply their triangulations while keeping the accumulated errors small enough to meet the other team. They solved this complicated task with such skill that we still don’t know how they did it. Some scholars have argued that they must have followed a karstic crack underground that went all the way through. On the other hand, the Jerusalem archaeologists Ronny Reich and Eli Shukron point out that this theory is incompatible with the several “false” tunnels near the meeting point Correctly plotting such a complicated path underground implies measuring skills far better than those attributed to the people who allegedly misread so grossly the cord stretched around Solomon’s Sea. It also demonstrates a precision in their trigonometry that does not fit in at all with their supposedly crude pi. However, admitting those skills among Hezekiah’s people would have toppled the superiority of the Greeks who cut the straight and thus much easier to measure tunnel of Samos about 170 years later, and with a much greater error at the mid- tunnel meeting. So, to prove his contention that the Israelites worked “in a very primitive way”, vastly inferior to the “splendid accomplishment” of the Greeks, the above Plato- buying historian of science invented from whole cloth a series of vertical shafts he said Hezekiah’s workers had dug from the top to keep track of their confused zig- zag path This solved the problem of keeping the Greeks up on their pedestal. Except, of course, that the veteran Jerusalem archaeologist Amihai Mazar reports Hezekiah’s tunnel was cut without any such shafts Some Western scholars, from Plato on to this day, have needed such fictions to prove their and their fellow Europeans’ superiority over all the other and oh so ignorant older civilizations. The myth of Solomon’s wrong pi is therefore by now so deeply entrenched in the cultural fabric that most of those who write on this subject continue to repeat it because that is what all their reference books say. There is still no published study that explores how Hezekiah’s surveyors could have achieved their stunning success, but the Mathematical Association of America offers in its 2001 Annual Catalog a video and workbook about “The Tunnel of Samos”. These illustrate and discuss the methods its builders might have used for this “remarkable engineering work of ancient times”. This example of scholarly bias shows again how presumptuous it would be to judge the richness of the mathematics practiced in the ancient Near East from only the few surviving and so far deciphered written scraps while excluding or denying a mountain of unwritten but no less compelling evidence. Without the blinders of this academic prejudice, you can see in this book how the allegedly pi- challenged designer(s) of Solomon’s Temple incorporated in the main dimensions of their layout clear, repeated, and precise evidence that their pi was at least as good as that of Archimedes. | |||||||||

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