SOLOMON’S SEA AND
THE GOLDEN RATIO
As noted a moment ago, critics like Sandoval ignore Old and New Testament evidences which demonstrate the basis of why there could be a hiatus between the 69th and 70th weeks of Daniel, and likewise complain of Christians who read with “micrometer” precision the numbers in the Scriptures. Thus they claim the Bible is just rounding off numbers by authors who wrote after the fact and under pseudonyms. And so these biblical authors (say skeptics) have deceived their readers through either ‘prophetic’ utterances for the purpose of rallying nationalistic feeling or, as Sandoval thinks, by offering inspirational fiction in the same vein as the Left Behind series.
In either case this matter of the Bible rounding off numbers must be addressed.
Now, of course, Christians would not say there is no rounding off of numbers in the Scriptures. For we do not suppose casualty numbers relating to Old Testament wars given in exact thousands are not always or nearly always rounded off. Likewise, in Numbers chapter 2 the count of men for each of the 12 tribes of Israel end in either a fifty or a hundred, showing an apparent rounding off to the nearest 50. We grant such examples are meant to be understood as a rounding of numbers.
But Sandoval goes too far when claiming a rounding of numbers for Solomon’s Sea.3 Here is the primary example he gives for faulting the “micrometer” reading of numbers in prophecies like Daniel 9:
Secondly, the Jews were in the habit of using round and stereotyped numbers, just as we do when we speak of a “ninety-day wonder” or a person who works a “24/7” job. To cite a parallel example, it was an acceptable round-number approximation for the biblical authors to say that the Molten Sea in Solomon’s Temple (a huge, circular bowl of water) was ten cubits in diameter and thirty cubits in outer circumference (I Ki. 7:23-24; II Chron. 4:2-3). Their measures were accurate to the nearest cubit if the diameter was actually 9.65 cubits, and the circumference was actually 30.30 cubits.
Now, when the above was quoted in an online discussion thread by someone opposing my position that
Daniel’s numbers were not rounded off, I contacted my brother David. This is because 30 years ago he had made a particular study of the biblical (sacred) cubit found in Solomon’s Sea. David had followed the 19th century work on the biblical cubit by John Taylor (member of the Royal Society of London), Piazzi Smyth (Astronomer Royal of Scotland), archaeologist William F. Albright (who established an approximate value for the royal bath, i.e., the standard liquid measurement in certain regions of the ancient world), and even the much earlier Isaac Newton, who had written an entire monograph on the subject of the biblical cubit. Taylor, Smyth, and Newton had all concluded that the sacred cubit was around 25 inches. Taylor and Smyth had found that the sacred cubit was a recurring unit of measurement in the construction of the Great Pyramid. (Newton also appealed to other evidences besides the Great Pyramid.) This included the perimeter of the four walls at their base made into a circumference of a circle, whose radius proved to be the height of the Great Pyramid, thus paralleling the circumference at the earth’s equator to the earth’s polar radius, showing the cubit to be 1/10 millionth of the polar radius of the earth.4 Albright’s work involved liquid measurements derived from comparing a broken piece of pottery marked “one royal bath” with jars that were complete, and estimated the royal bath to about 22 liters. Additional archeological findings yielded estimates for the bath at 22.7, 22.8, 22.9 and 23.3 liters.
Piazzi Smyth (1819 – 1900)
Taking this information and suspecting one royal bath might equal the biblical bath, David explored whether there might be some significance to the measurements in Solomon’s Sea. First, he assumed that the two biblical passages which give the size of Solomon’s Sea (shaped hemispherically, according to Josephus)—2,000 baths by one account, and 3,000 baths by the other—pertained to the actual fill mark of the water versus the Sea’s fullest capacity (I Ki. 7:23-26; II Chron. 4:2-5). Calculating the volumetric capacity of 3,000 baths based on the Sea’s description of 5 cubits high and 10 cubits in diameter (“brim to brim”), and assuming the biblical cubit was 25.0265 inches, based on today’s present estimates of the polar radius of the earth which are nearly exact to the Great Pyramid findings of Smyth, yielded a surprising result. The figure was 22.4149 liters, the same volumetric capacity of a molar volume of an ideal gas (the volume taken up by one mole of an ideal gas at a given temperature and pressure). Further, when one considers that Ezekiel (45:10-11) specifies the same volumetric space for one bath as also one ephah—the standard unit for dry measurement—one faces a decision. It is whether to believe that all these measurements and findings which point to a unified field of measures are mathematical coincidences, or else to believe the Bible’s statement that the craftsmen who made the First Temple objects were careful to follow the Davidic pattern set down by God, who apparently used a common unit of measurement to establish dry, liquid, and gaseous measures, i.e. all three forms of matter.
David Gracely, several years after he discovered the connection between the biblical cubit and the three forms of matter.
However, I was at first hesitant to share this information online about the biblical bath equaling a molar volume of gas because of a statement about a 30-cubit line in I Kings 7:23. This statement had puzzled my brother ever since his discovery that the volume of a biblical bath equaled a molar volume of an ideal gas. The passage runs thus:
(23)And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and its height was five cubits: and a line of thirty cubits did compass it round about. (24)And under the brim of it round about there were knops compassing it, ten in a cubit, compassing the sea round about: the knops were cast in two rows, when it was cast.
Sandoval, to his credit, actually takes a more charitable view than those skeptics who claim the Bible stupidly thinks π = 3 (30 over 10) instead of 3.14159+.
While I myself was predisposed toward granting that my brother’s discovery likely showed a divine blueprint for using the same volumetric capacity to establish liquid and gaseous units of measurements (at the time, I was ignorant of the Ezekiel passage stating that one bath equaled one ephah, or I would have added the dry measurement to my list as well), I personally felt there was a weakness in David’s theory. For when I asked him if the 30-cubit line might be the water-fill mark inside the bowl, he said, no, he had tried that long ago and found it was 30.6. “It must be a lower mark [of some kind],” he said. But I knew he could be attacked on this point by skeptics who would claim he had no right to assume π from the diameter of 10 cubits given, and that he was only assuming π for the sake of wanting data that supported his view of a divinely-instituted unified field of measures for both the biblical bath and a molar volume of gas. And, frankly, I could sympathize with this anticipated objection by skeptics, and suggested to David I delay introducing his thoughts into the discussion thread. But after some minutes of David and I discussing this problem of a lower-mark-of-30-cubits-for-some-reason, which I found unsatisfactory, I suggested he see if somehow the 30-cubit line corresponded to the golden mean. Also known as the golden ratio, this is the most discussed mathematical relationship of part-to-the-whole found in pre-modern art and architecture, especially in the Classical and Renaissance eras. It was a guess on my part, but the next morning David called excitedly to tell me that the 30-cubit line did indeed show the golden ratio if the line were placed outside the bowl, like a latitudinal line around a globe positioned about 19 degrees lower than the ‘equator’ (the bowl’s rim) of the half-ball of Solomon’s Sea.5
That is, if we could look down inside Solomon’s bowl to the bottom and saw a vertical pole reaching to the height of the brim, let us divide this pole into two line segments. The first segment (x) is the height of the 30-cubit line of circumference, the other from there to the brim (y). Then x divided by y is within 1/3400th of the Golden mean. Put another way, the Golden mean would be exact if the 30-cubit line of circumference were 1/70th of an inch longer.6 This is well within an acceptable margin of error. From there we surmised that the purpose of the 30-cubit line was to establish a line that divided above and below the two rows of gourd-shaped, brass carvings (KJV “knops”; Heb. lit. colocynth-gourds) surrounding the bowl (I Kings 7:24). Incidentally, for purposes of establishing the golden mean in Solomon’s Sea, it does not even matter what the length of the biblical cubit is, since all measurements are relative to the same unit of measure. (Note: the thickness of the bowl is stated to be one handbreadth, which by definition is 1/7 of a sacred cubit; and thus all the measurements of the Sea are defined in relation to the cubit).7 Interestingly, the sacred cubit used by Solomon was “according to the old standard” of a cubit, so stated by the writer of II Chronicles 3:3 (see NASB).
Now, the Bible records that Solomon’s Sea of cast bronze was broken up in pieces and taken to Babylon by Nebuchadnezzar upon his destruction of Jerusalem (in 586 BC), following the capture of king Zedekiah in his 11th year. It is not hard to imagine, then, that measurements could have been taken of the Sea before it was broken up (Jer. 52:17), this information taken to Babylon along with the actual fragmented artifact, to eventually find its way into the hands of contemporary Grecian mathematicians of the 6th century, such as Pythagoras, who is generally credited with the invention of the golden ratio. Or, since this written description in the Old Testament of the golden ratio predates Pythagoras by more than 300 years, the information certainly may have taken another route, especially since the Bible states that “all the kings of the earth sought the presence of Solomon, to hear his wisdom, that God had put in his heart,” which suggests retinues of persons and observers from different nations, such as the Queen of Sheba (est. 960 BC), who not only tested Solomon with hard questions but also remarked on the manner of the coming and going of his servants. But especially we are told of the Babylonian retinue that visited Hezekiah (in 711 BC). They came to congratulate Hezekiah on his restoration of health, and Hezekiah showed them all his treasures. Presumably, they may have been told in detail about temple artifacts in the Inner Court of the temple where the Bronze Sea stood. We may suppose, then, that persons among such retinues may have been interested in the architectural and artistic accomplishments constructed under Solomon. And so we ought to grant that the descriptions of the temple’s architecture and ‘furniture’ were not just exercises in mathematical draftsmanship. For elsewhere there is concern for the aesthetic—i.e., the mention of blue pomegranates as part of the temple’s decorations, a color through which pomegranates do not pass in their course (Ex. 28:33). This shows that more than bald, mathematical description was aimed for in describing temple features. And doubtless this is the purpose of the golden ratio, which brilliantly combined both concerns.
King Solomon and the Queen of Sheba, by Piero Dell Francesco, ca. 1452.
But, again, the point in all this is that either one has to attribute all these mathematical relationships to mathematical coincidences and thus conclude the Bible is “rounding off numbers” when it comes to Solomon’s Sea, and, by extended principle, the 70 weeks of Daniel’s prophecy which heralds the coming of the Messiah, or e
lse admit that the Bible often uses specificity of numbers to drive home the point of a Common Designer and Predictor of the Future. One can imagine what position our opponents would take if similarly startling evidence was discovered which supported instead an argument for the rounding off of numbers. I soon found this out when I presented this information about the golden mean on the about.com website under one of the atheist/agnostic discussion threads. The main detractor I had been engaging reproved me for (in his view) not reading the Bible accurately with its emphasis on “round… round… round,” and believed such description must mean a cylindrical object. And so I reminded him that the only extra-biblical description of the shape of Solomon’s Sea was Josephus’ statement that it was a hemisphere, while noting, too, that the roundest object with a brim is a hemisphere, not a [cylindrically shaped] soup-can shaped object, since only the former is created by a constant radius from top center to any point on the surface of the object. At this point he and others dismissed my argument based on my citation of Velikovsky’s observation of ancient cultures and their calendars of 360 days8 (one of the related discussion points). Thus they committed the common logical fallacies of ad hominem and guilt by association. Their real failure, then, was a refusal to address the voluminous attestations about a 360-day year in the records of at least nine ancient cultures spread throughout the world. It’s sad to note how often this ahistorical approach seems to convince. History is rife, I believe, with many neutral observers who briefly thought about leaving the herd for independent inquiry into religion or the Bible, only to be chased back into the fold by a simple sneer and a laugh from some skeptic with border collie-like enthusiasm. Thus our opponents ignored the math demonstrating the golden mean in Solomon’s Sea, the only historical reference (by Josephus) of its exact shape, and Velikovsky’s straight-forward research into the calendars used by ancient peoples.
In review, then, critics think: (1) the Bible is rounding off numbers, (2) extra-biblical sources cannot be trusted when the results would lead to a unexpected discovery like the golden ratio, (3) the written description of the golden ratio centuries before Pythagoras must be an accident, and (4) a crafted object divinely authorized in the Old Testament (I Chron. 28:9—29:2, esp. 28:13,19 and 29:2)—with a measurement that proves to be the common unit of measure for biblical solid, liquid, and gaseous measures—is not possible. I have to be frank here. This kind of so-called critical approach reminds me of a symposium on evolution reported in a Philadelphia newspaper many years ago, attended by both scientists and mathematicians. Not far into the seminar concerned mathematicians, though sympathetic to evolution, nevertheless candidly pointed out that the numbers simply didn’t allow for enough time to make evolution possible. To this the host of the symposium responded that nevertheless it was obvious “evolution must be true, because we’re here.” Despite such brimming confidence, the host’s tautological reasoning reveals the skeptic’s presupposition that any explanation is logical so long as it isn’t metaphysical. And so nowadays we have the idea—thanks go to Andrei Linde and Vitaly Vanchurin of Stanford University—that the number of universes is based on what the observer is able to conceive. (Apologies to those who thought the number was only in the trillions.)
Such cosmologies are the mutated species of the parent theory that has spawned them, namely, evolution, or, more specifically, what evolution has evolved into. This is why the language has become ever subtler, as evolutionary theory has devolved into epicycles of explanations to explain away anomalies. One popular case in recent decades, for example, is so-called ‘dark matter,’ with its invisible particles doing invisible things to excuse the behavior of gravity, which seems to have forgotten to lessen its effect on the ‘starfish’ arms of galaxies which trail out from galaxies’ centers and so ought to be lagging behind, but instead are keeping up their peripheral speed like the outer bands of a vinyl LP around its center label.9 Thus gravity need not be gravity when and where it conflicts with current evolutionary thought. Consequently, Christians, despite their centuries-long fight against bald materialism, wax nostalgic for the former kind of scientific method that once insisted on observation alone and of the visibly concrete. But once the visible disappointed Science in delivering a fossil record showing no trans-species evolution, theories like Niles Eldridge’s and S. J. Gould’s punctuated equilibrium showed that fossils were never important to begin with (phew!). One searches in vain for just one evolutionist willing to invoke the kind of mantra his colleagues have used to discredit creationism whenever the ubiquitous fossil record comes up, and apply it their own theory. For these have long argued that the sudden burial of masses of organisms and animals merely gives the appearance of a Great Flood. But what, then, to say? For this line of argument cannot be applied against the evolutionist, because that would require there actually be an appearance of trans- species evolution in the fossil record. But there isn’t any. This is why recent theories have been developed dismissing the fossils’ importance. And now the latest strategy—apparently to diffuse the indisputable design in DNA obvious to anyone but a bona fide ignoramus—is atheist superman Richard Dawkins telling Ben Stein in No Intelligence Allowed that it is conceivable life was brought here by alien beings, but certainly not by the kind of homophobic God depicted in the Old Testament. And so Dawkins’ final court of appeal is that Christian theology cannot be scientific because it doesn’t agree with his atheist ethics.
While visiting the American Natural History Museum, Stephen J. Gould, age 5, saw the skeleton of Tyrannosaurus Rex. He was so impressed he decided that very moment to spend his life studying fossils.
But I’m playing unfair. Atheism is not responsible for all this scientific mess per se. This is why Ravi Zacaharias freely admitted to a student inquirer that there are such things as philanthropic atheists who live comparably righteous lives. But as Zacharias also pointed out, atheism doesn’t obligate that a man should love his neighbor as himself. This is why some atheists can be philanthropists while others can be mass murderers, like Joseph Stalin. As my brother expresses it—“Atheism doesn’t condone murder, but neither does it condemn it.” And so the problem is not just atheism per se, but Individual Choice gone wrong. But thus the twist. Since atheism neither obligates nor necessitates, it is by definition purposeless. And what is purposeless is meaningless. Therefore it is not just irony but also absurdity when an atheist takes pride in his atheism, as though atheism had any significance per se. Really, there is no reason for an atheist to even mention his atheism. It cannot lead him to social lawfulness or lawlessness, or to societal good or bad, so what is the point? In fact, atheism cannot recognize that such categories even exist. Thus the dilemma in the Academy: since Science supports evolution for the purpose of dismissing God, what does that say about the significance of evolutionists taking pride in evolution? Yet the rapturous song continues. Thus Sagan in the opening of Cosmos:
The Cosmos is all that is or was or ever will be. Our feeblest contemplations of the Cosmos stir us—there is a tingling in the spine, a catch in the voice, a faint sensation, as if a distant memory, of falling from a height. We know we are approaching the greatest of mysteries.
Note the interesting comparison between Sagan’s benedictory-sounding descriptions of the Cosmos versus Jesus’ description of himself in Revelation. Whereas Sagan says
“the Cosmos is all that is or was or ever will be”
Christ said he was the Alpha and the Omega [the Beginning and the Ending]
“who is, and who was, and who is to come…” (Rev. 1:8 NIV)