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Thursday, April 14, 2011

Debunking the fallacy of Solomon's Sea and other good stuff - Pi served up ala carte


There are many commenters who blithely dismiss the Bible because of the verse in I Kings 7:23 & 24 that states the following:

"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."

Now there are portions of the Old Testment in which God gave the people a plan to carry out, such as when He told Noah to build the Ark.  The general sizes given in Genesis produce a massive ship that is built to specifications that modern shipbuilders use today for large ocean-going vessels.   How could Noah have known what design could withstand a world-wide flood?  But God knew.   We do not get the blueprint that Noah received in whatever form from God, but we know it worked and we know the general descriptive dimensions of the Ark are perfect for the job.

Later in the Pentateuch we see God giving Moses specific instructions concerning the construction of the Ark of the Covenant and all aspects of the Tabernacle, beginning in Exodus 25.   Instructions from God are PRESCRIPTIVE in nature.  They are telling the receiver precisely what to do.  Whatever God ordered, they matched it exactly as they could.

Once we get to I Kings, the scripture is DESCRIPTIVE in nature.   The entire passage is describing the Temple and portions thereof.   As I have mentioned previously, we do not know what effect the rim of the sea has on the dimensions and, as the sea was not a cylinder, the measurements would vary depending upon where they were made.   We cannot be sure exactly which "cubit" was being used or which "bath" describing volume is in use here  (but I include an article farther down that speculates intelligently upon that).  Both terms have long fallen from use and both terms had slightly differing measurements depending on several factors.  Unlike today, measurements were often standardized according to individual builder or individual culture and time.   If you think that is being evasive, well, consider the English language.   Daniel Webster undertook the job of making a dictionary in part to standardize meanings of words but especially to standardize spelling.   People used to spell words as they saw fit and that did not work well in a world in which being precise was becoming more important.  The common man had become literate due to the widespread printing and reading of the Bible and so Webster saw the need to define words and spellings to aid in the process of communication in the "modern" age.

As a carpenter stick-building houses, I commonly worked from a blueprint and even in our modern world I found that some directions and requirements were precise and others not so precise.   For instance, if we were to build a room with inside dimensions of 9 feet by 14 feet according to the blueprint, we would carefully measure and erect walls that fit that requirement and seek to be precise within reason.  If we were one-sixteenth off the world would not end.   But once the drywall was erected the thickness of the drywall would slightly decrease that 9 by 14 measurement and also the trim along the bottom would come into play.   So we could get three measurements from the same room - as a stickbuilt frame, with the drywall added and also from the bottom we'd have to also add the width of the trim.   Furthermore, we would have instructions to use, for instance, two-by-fours or two-by-sixes in erecting the home.   Did you know that a two-by-four is common usage and perfectly acceptable in the building trade but in fact they usually measured 1 and 5/8 by 3 and 5/8 when I was a carpenter and now apparently 1 and 1/2 by 3 and 1/2 are accepted. 

Go ahead and find the blueprint for your home, which should be among the mortgage paperwork (If you own your own home) and see what dimensions are listed for the individual rooms.  Then go measure them for yourself.   Some homes are built with room sizes that account for drywall and some are not.  So after you do that, remind yourself that you have just proved that modern man doesn't understand how to read a tape measure...or have you?  No, you have just realized that a descriptive of a building or other items does not have to be and probably will not be precise.   Not unless there is a very good reason for precision.   The exact size of pistons within an engine must be checked to very rigid standards or either the engine will overheat or not get a good seal and lose compression and blow out oil and gas with the exhaust.  But your outdoor patio dimensions are not critical, so that a 20 by 16 porch could well be 19 and 1/4 by 15 and 1/2 and up to this moment you may not even have noticed!

Below is one look at the so-called problem...

Does the Bible Contain a Mathematically Incorrect Value for "Pi"?

Does the Bible contain errors in math? If it does, this calls into question its moral and spiritual authority. Much is at stake. Let's carefully examine one of the most frequent charges of error.
When describing Solomon's Temple and its fixtures, Scripture tells of a great basin cast of molten brass "ten cubits from the one brim to the other: it was round all about, . . . and a line of thirty cubits did compass it round about" (I Kings 7:23).

The circumference, c, of a circle is related to its diameter, d, by the ratio "pi" or "P" according to the equation c = Pd. Mathematical derivatives have calculated the precise value of P to many decimal places, but for most applications the approximation 3.14 is sufficient.

Inserting the value of circumference and diameter given by Scripture into the equation yields a value of P to be 3, and it is this apparent error which gives Bible detractors such glee.

Construction techniques in those days were surprisingly advanced. We can assume that their mathematics was precise and measurements handled with care. Notice that the basin "was an hand breadth thick, and the brim thereof was wrought like the brim of a cup, with flowers of lilies" (v.26). A "hand breadth" is an inexact distance of about four inches, but sufficient for this general description. The whole basin flared out at the top, much like a lily. So, exactly what do the dimensions given really represent?

The diameter of the basin would be the inside diameter, measured from side to side. But the circumference would be measured by placing a cord around the outside, then measuring the length of the cord. Furthermore, at what elevation along the tapered basin was the measurement taken? Obviously, these are not intended to be precise, but to give the overall impression of great size and beauty.

Engineers have adopted a technique to insure that reported measurements are properly understood. To do this they use the convention called "significant figures." The number 10 is quite different from the number 10.0 or 10.00 in the precision it implies. To an engineer the number 10 can actually mean anything between 9.5 and 10.5. Likewise, the number 30 can actually mean anything between 29.5 and 30.5.

While the number P is accurate to many decimal places, the other two numbers do not have this precision. When one precise number is multiplied by an imprecise number, the product should be reported with no more precision than the least precise factor. Multiplying the diameter, 10 (i.e., 9.5 to 10.5) by P, is properly understood as implying a circumference somewhere between 29.8 and 33.0.

When constructing an object for which extremely high precision is needed (e.g., the space shuttle), numbers are designed, reported, and fabricated to several decimal places, but to expect such precision in a lay description of this huge basin cast from molten brass is not only improper, it shows lack of understanding of basic engineering concepts. Properly understood, the Bible is not only correct, it foreshadows modern engineering truth.


When I worked in the automotive industry, we had differing requirements for various parts depending upon their purpose.   Some measurements were critical and some were not.  We had variations built in to the requirements for padding and sound deadening parts that allowed for a good bit of variation, as they were not critical parts of the automobile.   But some parts had to be made exactly right, enough so that they would fit precisely on a "buck" and their dimensions and the spacing of punched holes or added pieces of metal all hit the exact mark.   The same was true in the steel industry.   There were many items that had to be measured by a caliper to fit within a very narrow band of acceptable readings.   In all of these scenarios, I was part of the production team and was following specific instructions.

In I Kings, however, the Temple is being described.   Therefore I can assert that no matter how they described the measurements of the sea, it does not tell us precisely how, where, and with what requirements such measurement were made.   Since it is descriptive of a building and features, precision would hardly be expected.   The scribes would not write that the sea was 9.82 cubits across, for instance.   In fact, in descriptive mode it would be highly unlikely that a general description of such an object would be particularly precise.   So those who claim that the Bible is wrong here are over-reaching terribly.   Now, if God had instructed someone to make a precise sea of thirty whatevers around and ten whatevers across and demanded precision, then the builders would have had a problem.  But this is not a blueprint, it is a kind of feature story of the unveiling of the new temple.

Nevertheless, there is an article, below, which gives us a logical explanation for the measurements.   I agree with the author in that it was an Oriental/Middle Eastern culture that first came up with the Pythagorean Theory, it was that culture that adopted the modern numerical system that is far superior to the awkward Greco-Roman system, it was the Jewish peoples who first had a system of writing (actually no doubt carried on from the pre-Flood culture) found by archaeologists.   If you know the Bible you have to know that writing and using numbers predates anything we have recovered from the past.

I suggest that you go to the site and read the article there to get the links and other information but I am presenting it in plain text here.

The political value of Solomon's Pi

Most current textbooks on the history of science assert that ancient Near Eastern mathematics were too primitive for its practitioners to compute an accurate value for the circle circumference-to-diameter ratio pi. They even claim that the Bible gives the rather inaccurate value of pi = 3 for this important mathematical constant.

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:

“It was round in shape, the diameter from rim to rim being ten cubits; it stood five cubits high, and it took a line thirty cubits long to go around it.”

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. Accordingly, they affirmed as late as the middle of the first millennium CE:

“that which in circumference is three hands broad is one hand broad”.

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, in turn, 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 modern Western group.

This parochial attitude received a major blow when the Columbia University professor of Comparative Literature Edward Said published in 1978 his book "Orientalism" in which he exposed the colonial roots of the then still common Western disdain for the abilities of "Orientals". His influential comments changed the way some open-minded literary scholars regarded this biased legacy, but it seems that many mathematicians and historians of mathematics never got the memo.

In their domain, the biased views of those colonialist writers 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 typical mainstream method of proof by repetition, that in every one of those translations the diameter remains ten cubit and the circumference thirty.

However, all these 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, ever bothered to read on. Both accounts state just three verses later that the rim of said vessel was

“made like a cup, shaped like the calyx of a lily”.

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 narrow 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.

The volume and shape of Solomon's Sea

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, according to the archaeologist Leen Ritmeyer who investigated the standards used in those structures. Like the ancient Egyptian royal cubit of typically similar length, it was divided into seven hand breadths of four fingers each.

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 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”. A liter is 61.0237 cubic inch, so 2000 bath equal 304.04 cubic cubit.

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.

SolomonsPirimdetailgif.gif (6344 bytes)

The rim flare inscribed into the computed rectangle looks indeed like that of a cup, or like the calyx of a lily.

The height and width of that rim, computed with the actual value of 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 parallel history in 2 Chronicles 4:6 misread that volume when he gave it as 3,000 bath. No matter how much you fudge the math or try to squeeze the incompressible water, this volume does not fit into a vessel with those dimensions.

Mainstream bias against non-Western minds

Solomon’s mathematicians and surveyors, as well as their ancient teachers and 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 credulity 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 which Archimedes (about 287 to 212 BCE) obtained later, or even closer. They could wield the same mathematical tool, the theorem about the squares over the sides of a right-angled triangle which is now named after the sixth-century-BCE Greek Pythagoras and which Archimedes used many centuries after its real ancient Babylonian and/or Egyptian authors had discovered it. They also had perhaps more patience and motivation than Archimedes to continue with the simple but repetitive calculations required for pointlessly closer approximations.

However, the backwardness of ancient Near Eastern mathematics has become a cornerstone of the prevailing prejudice against all 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 calculation of pi requires analytical thinking, the same exalted mode of thought on which all the rest of so- called Western science is said to be 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:

“... a race of men more hungry for knowledge than any people that had till then inhabited the earth” .

Reflecting the same then typical attitude which referred to those other people as “that” instead of “who”, another equally respected historian of science quoted approvingly Plato’s partisan remark :

“... whatever Greeks acquire from foreigners is finally turned by them into something nobler”.

The dismissal of Hezekiah's tunnel

This cultural bias led some of the "scholars" afflicted by it not only to disregard obvious facts, as in the case of Solomon’s pi, but even to fabricate the evidence they 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 dangerous siege because he expected a new invasion by the Assyrians who had conquered the area earlier and extorted from it a heavy tribute which Hezekiah planned to stop paying. To have any chance at all 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.

Because this life-or-death project was so urgent, the tunnelers started at both ends of that path to then meet about halfway underground. This unprecedented mid-way meeting in a more than 1,700-foot-long tunnel would have counted as a considerable achievement even if their tunnel had followed a straight line. However, their surveying task was much harder.

At the spring end, the stone cutters started at an almost right angle with the shortest path to their goal and took instead the shortest path towards the city wall. Maybe they wanted to bring this most vulnerable part of their dig as quickly as possible under the protection of that wall and of the high overburden in that area, and maybe they also wanted to take advantage of a few existing fissures in the rock that happened to run there for short stretches along their general direction. Then they veered back outside the wall under shallower terrain where no enemy risked to find the tunnel but where a postulated surface team hammering on the rock above would be easier to hear for confirmation that the diggers were not straying too far.

However helpful and encouraging these presumed signals from the surface team may have been to the diggers below, they would have been too diffuse to determine precise locations. The path of presumably greatest convenience for the stone cutters became therefore an irregularly curved maximum challenge to the surveyors who had to multiply their triangulations while keeping the accumulated errors small enough to not miss the other team by too far in these two stabs into the three-dimensional dark.

These ancient Hebrew surveyors 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. However, the Jerusalem archaeologists Ronny Reich and Eli Shukron pointed out that the theory of simply following a pre-existing fissure is incompatible with the several “false” tunnels near the meeting point. These indicate some uncertainty about the path to follow until the teams actually met, and they are more compatible with the accumulated errors in a small spread of measuring results.

Moreover, a recent close examination of the tunnel walls shows that there was no such continuous fissure. To the contrary, over long stretches most of the cracks in the rock ran rather at right or almost right angles to the path of the tunnel.

That theory about the continuous crack also ignores the famous inscription about how elated the cutters were when they at long last heard the voices of the other group just before they broke through, “axe against axe”. The joy and relief expressed in that short text would be hard to explain if the two underground teams had known beforehand that they were just following a pre-existing path.

Even the authors of the most recent survey of this tunnel, the ones who proposed the stone cutters might have been guided by the sounds of hammer tapping on the bedrock above the tunnel, do not think those signals were precise enough to pinpoint the exact locations underground. One of them admits

"Yet, all things considered, it is quite incredible how the two teams managed to meet almost head-on, at virtually identical elevations as evidenced in the very small difference in ceiling elevation at the meeting point."

Correctly plotting such a complicated path underground implies measuring skills far better than those attributed to the people whose predecessors from just two and a half centuries earlier had 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 tradition's supposedly so crude pi.

On the other hand, admitting those skills among Hezekiah’s people would have toppled the superiority of the Greeks who cut the mostly straight and longer tunnel of Samos about 170 years later. This tunnel was much easier to measure but displays much more zig-zagging in the northern leg before 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 and meandering 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 intermediate shafts. The one and only shaft that is open to the surface near the southern end of the tunnel is a pre-existing natural feature and not man-made.

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” which the Greeks dug about a century later, also simultaneously from both ends. These discuss the methods the Greek tunnel builders might have used for “one of the most remarkable engineering works of ancient times”. And an even more recent article on this Greek tunnel still relies on the long debunked ad-hoc assertion about the continuous carstic crack the ancient Hebrew stone cutters allegedly followed to belittle their even more remarkable achievement:

"The tunnel of Hezekiah required no mathematics at all (it probably followed the route of an underground watercourse)."

Such examples of Orientalism-inspired scholarly bias show 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.

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 Western cultural fabric that most of those who write on this subject continue to repeat it uncritically because that is what all their reference books say, no matter how obviously wrong these are.

Without the blinders of this academic prejudice, you will 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, and that they as well as the ancient Egyptian inventors of their mathematical methods had also computed several other important mathematical constants with remarkable precision.

All not otherwise credited material on this site is
©1982 to 2009 H. Peter Aleff. All rights reserved.

From Greatest Mathematicians

Apastambha (ca 630-560 BC) India
The Dharmasutra composed by Apastambha contains mensuration techniques, novel geometric construction techniques, a method of elementary algebra, and what may be the first known proof of the Pythagorean Theorem. Apastambha's work uses the excellent (continued fraction) approximation √2 ≈ 577/408, a result probably derived with a geometric argument.

Apastambha built on the work of earlier Vedic scholars, especially Baudhayana, as well as Harappan and (probably) Mesopotamian mathematicians. His notation and proofs were primitive, and there is little certainty about his life. However similar comments apply to Thales of Miletus, so it seems fair to mention Apastambha (who was perhaps the most creative Vedic mathematician before Panini) along with Thales as one of the earliest mathematicians whose name is known.


Pythagoras assembled a team of great thinkers, but to be sure the Egyptians and Mesopotamians understood the concept and practical application of the Pythagorean theorem long before Pythagoras existed.  Part of the fallacy of Darwinism is the failure to understand that man's history begins with people who were able to accomplish great feats, some of which we cannot copy today!   The Flood wiped out civilization, so even though Noah and his family had great knowledge and experience, all of their "toys' were gone and man had to "start from scratch."   This explains how Neanderthals were able to make detailed paintings deep within caves with no smoke traces - therefore, they had artificial lighting!   This explains how mankind could so accurately cut stone and design massive temples and buildings and pyramids...we didn't evolve from pond scum, we were created with a fully-functional brain.

Imagine if EMPs were exploded all over the Earth?  The electric grid?  Gone.  No machines work that are powered or managed by electric devices.  Computers would all be fried.   We don't have chimneys in most homes and, with no furnace or stove, we'd be figuring out ways to cook whatever we could hunt down on a grill and hand-making fireplaces and chimneys using mud bricks.   Suddenly horses would have value again!   

Noah, Ham, Shem and Japheth and their wives came out to a world that was much more primitive than that...there was NOTHING handmade at all.   No wonder they used caves when caves were available.   The infrastructure of civilization was completely gone and had to be built back up again and specialized knowledge from the past went unused and therefore was lost.   We had to rebuild from mud on up.   But by the time of the building of Solomon's Temple, the arts of crafting wood, metal and stone were well developed.   The description of the sea in Solomon's Temple doesn't reflect ignorance of science by either God or man at that time any more than a modern weatherman stating times for "sunrise" and "sunset" does.   We know that the Sun doesn't rise and God knows the sky is not a tent.  He made it and He is the only one that could.  He also made all living things and again no one else is capable.   

Men cannot make material from nothing nor can they produce life.   At some point Darwinists need to face reality and quit playing these little games.  The fact that there is no natural source for life or information alone should be enough for scientists to drop Darwin like a hot potato and come on over to common sense.  Obviously God is a logical First Cause and the myriad design features of organisms complete with the signature of God (DNA) on each and every one of them should be enough. 

To summarize, those who think God is not able to comprehend the concept of Pi are simply taking the scrutiny away from the prime issues that Darwinism miserably fails to address.   Darwinists lie and cover up and fake evidence as we know from a long history of such things.   So I will now dismiss any further discussion of Solomon's Sea by those who have any cranial capacity worth noting by this post.