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
Jerusalem as "golden" city
The prominence of phi proportions in the layout of the Jerusalem Temple reflects its special status as the dwelling place of the Shekhina, or as the city where Woman Wisdom had settled to take root in Ecclesiasticus 24:8-12.
This special status of Jerusalem matches its geographical connection with the golden ratio. In the ancient number-mystic environment, this connection may well have been a key factor in king David’s decision to attack that city so he could make it his capital.
That connection was due to its latitude. The angle at which the equinox sun culminated over Jerusalem, as observable with ancient instruments and without modern corrections for refraction and the like, is very close to that of the diagonal in an upright “golden rectangle”, as shown in this illustration from the page on the construction of phi.
The tangent of this “Jerusalem equinox angle” is thus phi. Since the direction of the celestial north pole is perpendicular to the ecliptic defined by the equinoxes, except for minor differences in the respective refractions, that pole is located along the prolonged diagonal from such a rectangle laid on its long side.
Taking into account the slight differences in the distortions introduced by the bending of the light as it travels through the atmosphere at different angles, the Jerusalem Temple Mount’s differences from these observable “golden” directions were about three arc minutes for the sun, and five for the invisible and harder-to-measure north pole.
Both are closer than the error of about eight arc minutes in the celebrated measurements of the same ecliptic angle which the Greek scholar Eratosthenes of Cyrene (about 285 to 194 BCE) would perform many centuries later1.
This location of a government seat at a constant-related and therefore presumably desirable mathemagical latitude is not some isolated case or curious coincidence. To the contrary, the angle at which the average path of the sun, or ecliptic, was inclined towards a place seems to have been an important consideration for the founding and importance of many major cities in the ancient Near East.
Early evidence for the 360- degree system
In the examples below, the angles are sometimes defined by the tangens or cotangens and thus independent of the measuring system. In other cases, they appear as degrees in "our" 360-degree system, and that brings up the question whether the latitude-picking mathemagicians already knew that system.
The earliest known tablets that use the 360- degree notation date only from the last few centuries BCE2. However, in view of the haphazard survival of such documents and the very fragmentary state of our knowledge basis, this does not necessarily mean the notation began only at that late date. Much circumstantial evidence indicates it must have been much older.
At least a thousand years before those first documented 360-degree notations, the Assyrians had the habit of dividing the yearly cycle into 360 equal parts or "time degrees", as the Assyriologist Simo Parpola explains:
"A schematic year of 360 days divided into twelve months of 30 days each is encountered not only in the Assyrian cultic calendar Inbu bel arhi but also in the late second-millennium astronomical text Mul Apin; in the latter, it is correlated with a division of the solar year into four seasons of equal length, corresponding to the later division of the ecliptic into twelve zodiacal signs of 30 degrees each.
Since the correct length of the solar year (365 days) is also found in Mul Apin, the text’s insistence on the schematic year indicates a desire to state the length of the year in terms of "time degrees" derived from the circular path of the sun "round" the earth.
In other words, the author of that text associated the sun not only with the length of the year but with the circumference of the universe as well. This conclusion is confirmed by Julianus Apostata’s (361 - 363) hymn to King Helios, which, as observed by van der Waerden, is directly based on Mul Apin."3
Similarly, our 24-hour day had already in Sumerian times 12 beru of 30 gesh each (the Sumerian word for "one" and for "man"), giving a total of 360 gesh until the sun completed its daily circle.
As to the sun's yearly path, the creation epic which began with the words "Enuma elish" or "When on high" states that the Babylonian creator god Marduk "set up three constellations for each of the twelve months", bringing the total again to 36. The surviving copies of this epic date from the first millennium BCE4, but some of the information in them might be older.
The entire Mesopotamian system of weights and measures was extremely coherent in how it divided and interrelated not only lengths, areas, and volumes but also weights and time. The weight unit, for instance, was based on the weight of the water in a cube of one length unit, just like the modern kilogram, and the largest named weight, the Talent of 60 Minas, was defined as the weight of the water that flowed from a clepshydra, or water clock, in 24 hours or 360 gesh5.
Moreover, ten times 360 is 3600, the next step in the sexagesimal system, and the sign for 3600 was a circle that meant "totality, entirety".
Six times the 60-base of the system is 360, so our 360 was written as 6 such base units, and this was the number of completeness. Six, or its next-higher synonym 360, would therefore have been the most logical candidate for expressing the complete turn of a circle.
In the absence of all traces for any other graduation there can be no reasonable doubt that the imperial Assyrians and many of their predecessors used the same division into 360 parts for circles in space as for those in time.
Some modern scholars have called the 360-day year an approximation that resulted from inaccurate measurements of the actual year, but this may simply be due to their fashion of denying all non-Greek ancient achievements that are not preserved in the narrow medium of writing. They want us to believe that the ancient Mesopotamians could not keep track of solstice dates and star risings and were unable or unwilling to count accurately to and beyond 360.
Given the same Mesopotamians’ ancient reputation for their skills in both astronomical observations and mathematics, and the survival of enough cuneiform tablets to confirm that this reputation was fully justified, this "they-did- not-know-any-better" school of thought is untenable outside ivory towers.
If we grant those early astronomers the measuring and counting skills that are amply documented for their civilizations, then the 360- day cultic year appears rather as a clever and practical solution to the problem of reconciling the different lengths of the solar and lunar years because 360 is not only a round and easily divisible number, but it is also the closest whole number to the 359.8-day average between the 354.3672 days of the lunar calendar and the 365.2422 days of the solar cycle.
Latitude selections for constants
With this in mind, we can appreciate that the uncorrected latitudes of ancient sacred places or important cities often produce astronomical angles that are related to constants or other numbers with special symbolic values. For instance,
The successive capitals of the Assyrian empire are particularly telling examples of this ancient desire for numerically auspicious relationships with the path of the sun god or with the abode of the invisible world- turning power at the hub of the wheeling night sky.
Then the kings began to move further north, and their next choices confirm that the latitude of Assur had been no accident. Here is what the Cambridge Encyclopedia of Archaeology says about these moves:
“The most convenient starting point for the Neo-Assyrian empire is the reign of Assur-nasir-apli II (883 to 859 BCE). Early in his reign this king took the practical step of moving the effective capital of Assyria from its traditional home at Assur to a point nearer the geographical centre of the state. Kings had already taken to launching their campaigns from Nineveh, but Assur-nasir-apli decided to build his new capital at the ancient but by then decrepit site of Kalhu (modern Nimrud). The capital remained here, and here the kings resided until the reign of Sargon II (721 to 705 BCE); its archaeological remains are correspondingly complex and varied.
Khorsabad, on the other hand, which was founded by Sargon to the north-east of Nineveh, did not survive its founder’s death as a capital city. His son Sennacherib (704 to 681 BCE), adopted Nineveh as his capital, and it remained so until its final sack in 612 BCE.”7
These choices appear to have matched the auspiciousness of Assur in mathemagical terms:
Other people in the region appear to have shared the same concern about significant numbers for their prominent locations:
Defensible rocks and nearby water sources were and are quite common in mountainous Anatolia and are not a sufficient reason to pick this location over similar others. However, the choice of this otherwise unattractive site makes sense when you consider that the number 40 still plays a great role in Turkish folklore today. There, “once every forty years” means “once in a lifetime”, and our centipede, though thousand-pawed in French and German, needs only forty feet in Turkey to convey their multitude.
Returning to Canaan, we find that king David was by no means the first who seems to have attached importance to the "golden" latitude on which Jerusalem lies:
Seen in this context, the phi- related sun and pole angles observable from Jerusalem may well have been a major reason why David picked that city to establish his capital at this mathematically exalted location.
This favored phi angle may also have contributed to the persistent tradition that Jerusalem was the unique place where the Shekhina had made her home, the personification of Wisdom and of water and, in the proposed table of symbolic equivalences from page one, also of the golden ratio.
The equinox angle cotangens matches phi even better from Bethlehem, barely two arc minutes off. This location could well be connected to that town’s role as the reputed birthplace of king David, a Messianic figure favored by God, and then again, as prophesied a few centuries after David, of his even more exalted descendant Jesus.
Recognizing this ancient importance of the golden ratio and its connection with the Shekhina may even help to solve a modern problem: today's measuring techniques allow us to determine the exact "golden latitude" much more accurately than the ancients ever could. If the criterion for the location of the Jerusalem Temple was this connection with the number that symbolized the Shekhina, then any modern plans for rebuilding that Temple would have to reflect this improved ability to find the proper location.
If the rebuilders followed the intention of the ancients, instead of repeating their then unavoidable measuring errors, they would have to move the new Temple away from the old Temple Mount, to a location where that rebuilding might actually become feasible.
(For other proposals to change the location of that project in order to maximize the connection with the Shekhina, see this page about "Temple Rebuilding in Jerusalem" and this collection of articles about "The Third Temple")
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