and numerals and their ancient religious uses in our e-book
Ancient Creation Stories told by the Numbers
by H. Peter Aleff
The mathematics of Genesis 1
in the layout of the Jerusalem Temple
We saw above that for the distance between Ark and Altar, the Temple designer had used a value of pi in the same accuracy range as that computed by the later Greek mathematician Archimedes (287 to 212 BCE). An even more accurate example of that constant turns up in another symbolically very important spot in the Temple layout, a spot that also incorporates the numbers of the heavenly bodies, or the cycles of the moon before the stars and of the sun in the solar year.
Let me explain how to arrive at that spot, beginning with the overall plan of the Temple precinct and the type of thinking that led to it. We discussed earlier the ancient practice of building temples to reflect the cosmos, as described by scholars of comparative religion such as Mircea Eliade1.
The mythical thinking behind this “as above, so below” identification often used symbols in a recursive manner on successive levels that reflected the structure of the society.
For instance, the archaeologists Philip J. King and Lawrence E. Stager argue that the ancient Israelite society perceived itself as a series of households that were nested one inside the other:
“Just as a father exerted authority over his household, so the king ruled his ‘children’, the people, -- and God was father over the ‘children of Israel’.”2
The same view of the world as a series of ever more central and ever more concentrated items, nested one inside the other like a set of Russian dolls, was reflected in this description from the Rabbinic period:
“Just as the navel is found at the center of a human being, so the land of Israel is found at the center of the world (...) and it is the foundation of the world. Jerusalem is at the center of the land of Israel, the Temple is at the center of Jerusalem, the Holy of Holies is at the center of the Temple, the Ark is at the center of the Holy of Holies, and the Foundation Stone is in front of the Ark, which spot is the foundation of the world.”3
We find a comparable recursiveness also in the literary chiasms, or nested reflections of similar story elements, that appear most prominently in the biblical story of Jacob and the ladder to heaven4.
Since the themes of successive nesting and reflecting played such a prominent role in the Hebrew traditions, particularly those connected with the ladder to heaven, it seems reasonable to investigate whether the architect of the Jerusalem Temple also incorporated these culture- reflecting concepts in the design.
The most obvious place for doing so would probably have been the spot for the ladder to heaven, the spot where David had seen the Angel of Pestilence standing between heaven and earth and that thereby reflected the function of the entire Temple project which was also meant to connect these two.
Let us therefore suppose that the square innermost Sanctum of the Temple may have been meant to reflect the entire square within the outer walls, the way God’s presence in that Sanctum reflected his presence in the nation and world at large. Continuing the metaphor, a further reflection of that precinct within the Sanctum would have produced the spot for that ladder where that Sanctum wound up in this further reflection nested within itself.
The drawings here are based on the dimensions from the Rabbinic tradition discussed on the page about Temple dimensions. The first view shows the location of the Temple and its rectangular Court within the original 500 cubit square Temple Mount. The distances from the Court to the outer walls are those the archaeologist Leen Ritmeyer cites from a 16th century commentary on the 2nd century CE Middot tractate that transmitted the other dimensions.
This source is late and therefore open to question, but its distances match those Ritmeyer scaled from his proposed ancient locations for the Holy of Holies foundation trenches to the ancient outer walls of which he located the four corners.
As to the locations on the drawing of the gates and other structures outside the outer wall, I scaled these from Ritmeyer’s ground plan of the Temple Mount during Hezekiah’s time5.
I further drew a plan view of the Holy of Holies, with the Ark oriented east- west, as proposed by Ritmeyer, and the two gold- covered cherubim stretching their wings above it, as in the biblical account. The outline of the cherubim is based on the proportions of a winged sphinx or cherub in a Phoenician ivory carving from the eighth or ninth century BCE.
Then I reduced the Temple Mount drawing so that the area inside its walls would fit inside the Holy of Holies, and I reflected it to line up the entrances into the same direction.
This required two assumptions, about the inside length of the Temple Mount and about which gate was its main entrance.
The inside dimensions of the Temple Mount square are not transmitted, but it seems likely that they were 480 x 480 cubit. The scribe of 1 Kings 6:1 clearly associated the number 480 with the nationhood of Israel when he said that Solomon began the construction of the Temple in the 480th year after the Exodus. This time span fits no archaeologically plausible chronology, but its number supplies the proper symbolic contrast when you compare it with the 500 cubit outside length.
According to an ancient Hebrew Myth,
“the earth was so large that it would take a man five hundred years to walk across from east to west, if he lived to finish it, and a walk from north to south would take him another five hundred years”6.
If the 500 cubit outside length of the Temple Mount represented those 500 years which corresponded to the entire earth, then the inside would have symbolized Israel at the center of that outside world since the Temple was its exclusive emblem. And what number could have symbolized that nation better in this context than the 480 years since its people were said to have become independent?
The association between the essence of Israel and that number survives in the Jewish folklore which counted 480 synagogues in Jerusalem7.
In the symbolic world view it did not matter whether the date or number was fictitious or not. It was more significant that 480 is 8 x 60 as well as 12 x 40, and that all these were holy and symbolically charged numbers for divinity and/or completeness that are often emphasized in the Bible. These accumulated holy numbers may here have reinforced each other’s meanings the way multiple magic spells were often deemed more potent than a single invocation.
The wall thickness that results from this postulated inside measurement is ten cubits. This is in the right range for such an outer defense, compared with a Herodian section of the Western retaining wall that Ritmeyer listed as just under nine cubit thick8.
Having thus reduced the layout of the 480x480 inside square to fit it into the 20x20 inside of the inner sanctum, I reflected that reduced projection so that its main entrance into the Temple Mount would face in the same direction as the entrance into the Holy of Holies.
This brings us to the second of the above assumptions, that about the main entrance into the Temple Mount.Fortunately, the choice which entrance was the principal one is easy. The only entrance to the Temple Mount that has in Ritmeyer’s drawing a special gate building is the “Prison Gate” to the north.
To have the main gate in the north may seem counter- intuitive since the people of Jerusalem lived south of the Temple, but the Temple precinct was the domain of God, and God was believed to dwell in the north. North was the direction from which he came in the prophet Ezekiel’s first vision (1:4) and where Psalm 48:2 located his city, so I took this architecturally emphasized gate to the north as the symbolically important entrance.
The Holy of Holies opened to the east from where God entered the Temple in Ezekiel’s second and third visions (10:4 and 43:2-5). I reflected therefore the projection of the Temple Mount across its southeast to northwest diagonal to match this orientation, as you can see in the detail view here Figure 5.
These simple mathematical transformations place the reflected image of the Altar right before the Ark of the Covenant, touching its front edge, and just over one finger’s width offset from the east- west centerline, the way the outside Altar is offset by one cubit from the north- south centerline of the Temple Mount.
This spot, right before the Throne of God, was surely also the most likely location for the Altar made of cedar wood which Solomon had placed into the Inner Sanctum (1 Kings 6:20). The excellence of the fit suggests that the proposed 480 cubit dimension on which this projection is based as well as the method and orientation of the projection were indeed part of the original plan.
The reflected center of the Holy of Holies becomes in the reduced projection a spot 4.6667 cubit south of the 20x20 square’s east- west centerline, and 2.8125 cubit east of its north- south centerline.
As suggested above, this spot must have been specially important. If the Temple complex symbolized a connection to heaven, and the actual Holy of Holies in it concentrated that connection, then the area corresponding to the reflected Holy of Holies within the actual one must have focused that contact even more intensely onto an even smaller spot.
The Jewish traditions emphasize this particular spot. According to the dimensions of the cherubim in 1 Kings 6:23-27 and 2 Chronicles 3:10-14, the reflected Holy of Holies winds up just before the front legs of the cherub to the south of the Ark. The two cherubim that flanked the Ark formed the Throne of God, and if its occupant was thought to face east towards the entrance, those front legs of the southern cherub were the right leg of the Throne.
In this privileged place stood “the celestial ladder whose first edge is on the earth and second edge on the right leg of the Throne of Glory”, as quoted here from Hekhalot Rabbati9, a set of Rabbinic texts tentatively dated from the second to the fourth century CE that guide the reader on detailed tours of the Hekhalot or “Heavenly Palace”.
To the right of God’s Throne is also where David, the king chosen by God and ancestor of the Messiah, was placed in Psalm 110:1. This tradition survives in the Christian image that David’s descendant Jesus, the embodied link between earth and heaven and thus symbolic equivalent of the ladder between these, stands at God’s right hand (Acts 7:56).
The location of the ladder foot on earth would of course have reflected that of its top in heaven, so its most likely place was before the right leg of the Throne replica on earth where the front legs of the right cherub defined the spot. This is precisely where the reflected Holy of Holies winds up. Its mathematically projected presence there makes that spot an excellent candidate for the place where the builders believed the ladder to heaven to have stood, the navel of the earth around which the world had been created.
Earlier, the Patriarch Jacob had seen this ladder at Beth- el, another “House of God” and gate to heaven. Bethel was an old holy spot where Abraham had sacrificed and where the Ark of the Covenant was kept in the days of the Judges, but the ladder had to move to Jerusalem when that royal city became the religious center of Israel and the Temple its sole official contact with heaven.
The new location of the ladder was probably the place above which David saw the Angel of Pestilence “standing between earth and heaven” (1 Chronicles 21:16). As Ritmeyer pointed out10, the place of this link to the upper realm would have belonged inside the Holy of Holies when David decreed right after his vision where to build the Altar and where the Temple.
Figure 6 and the list below give the distances of this “ladder spot” in relation to the centers of the Temple Mount and of the Altar:
Please note how well that one spot brings down pi the sun and the moon’s travel before the stars to fasten them mathemagically to the Rock, together with the biblically important period of 40 years.
The multiplier 20 for pi matches the location of that spot in the Holy of Holies which was 20 cubits long and 20 each broad and high. The 20 pi distance thus joins a circle of 20 to the square and cube of this number. This is one up on those who tried to merely square the circle -- or twenty up since the Temple designer’s solution for combining these incommensurable quantities worked, at least in symbolical terms.
That the reciprocal of 40 years was intended seems confirmed by the inclusion of the reciprocal for a single year, as if to indicate that this was the unit used for that prominently biblical group of forty. Forty years was the length for each of Moses’ three life phases, of the Israelites' stay in the wilderness after their flight from Egypt, and of both David’s and Solomon’s reigns. These may well be symbolically determined periods, just like the 12 x 40 years between the Exodus and the start of building the Temple.
The accuracy of the astronomical numbers embedded in these dimensions corresponds to the reputation of the ancient Israelites for the excellence of their calendar data. For instance, the traditional Hebrew value for the synodic lunar month was 29.530594 days, compared with the modern computation for recorded history over the last 5,000 years which yields an average month length of 29.530596 days. The difference amounts to 0.000006772%, less than one part in ten million.
A recent reviewer of a book dealing with this topic wondered:
“It has never been clear just where the extremely accurate Hebrew value came from.”11
(Just as it has never been clear how king Hezekiah’s surveyors solved their extremely tough tunnel measuring task?)
The value of pi in the north- south coordinate of the ladder spot is more than ten times closer than the much celebrated approximation of Archimedes.
This is no reflection on Archimedes who could easily have computed a much narrower range but may have had better things to do than to continue a tedious, repetitive, and to him utterly useless calculation. He may not have striven for a mention in Guinness’ Book of World Records to which he did not even subscribe.
On the other hand, if some ancient Near Eastern priests sought divine secrets or magical powers in this mysterious number so closely associated with the sun, then they and their many well- schooled assistants could easily have performed a great many such calculations instead of watching the TV programs from back then.
The closeness of this symbolically important distance in the Temple layout to the value of 20 pi suggests that the ancient Hebrews were able to compute not only astronomical periods with great precision but also mathematical constants, never mind the long- standing smear campaign against Solomon’s pi.
The precision of the matches seems to imply that the designer of the Temple plan established this ladder spot first, with relative freedom to pick its coordinates. Once it was nailed down, and the ends of the Ark- to- Altar line, their locations defined the centerlines of the Temple Mount and their grid.
The rest of the layout then followed the constraint of using whole or at best half cubits for the various dimensions. This limits, of course, the accuracy of further matches with target numbers to expressions with relatively small integers which do not always cooperate smoothly but require much computing and careful planning to be so harnessed.
The close matches which the ladder spot dimensions yield with 20 pi and with the astronomical as well as specific symbolic periods would be hard to explain as random coincidences.
Considering the constraints for arriving at this spot, you are about as likely to encounter such a constellation of mathematical and astronomical constants as you are to get hit by lightning, on a calm day, and in your basement. The Jerusalem Temple precinct was clearly laid out with superb skill around that ladder spot to produce these heavenly and holy ratios, particularly since the presence of this purported point of contact with heaven was the reason for building the Temple there to begin with.
The construction of those closely interrelated spots within the grid of the Temple Mount square also seems to imply that Solomon’s builders knew not only their pi and how to compute it, but that they used an x-y coordinate system of analytical geometry similar to our modern one which was invented by René Descartes (1596 to 1650) and Pierre de Fermat (1601 to 1665).
Many historians of science rank this invention as one of the two milestones that mark the beginning of modern mathematics12.
The numerical matches at this ladder spot also validate the authenticity of the distances from Temple Court to Temple Mount that Ritmeyer found in the 16th century commentary on the older Middot tractate. Those distances are such an integral part of the overall numerical theme that they convey two things:
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