In his Encyclopeadia Britannica article on weights and measures (1), Sir William Matthew Flinders Petrie describes the "circuit of the city wall of Khorsabad" as 24 740 U feet, with the size of the U as 10.806 inches (0.2744724 metres). This gives a total of 267 340.44 inches (6 790.44718 metres) for the city wall. Petrie tells us the circuit is stated as 24 740 U on a tablet, and that the size of the U has been derived from the circuit, presumably from Petrie's own measurements. 108 was an important number in the ancient world, so it makes sense to find it in the dimensions of the U, but 24 740 is more unusual. Another number associated with the city wall perimeter is 16 283 cubits, presented by Sargon II in several inscriptions, who also connects this number to the value of the letters of his own name, through ancient Assyrian gematria, a system that assigns numerical values to words.

The measurements of the ancient city wall of Khorsabad, built by Sargon II, may encode more than mere structural dimensions. Petrie quotes the number **24 740** in relation to the U feet in the wall perimeter, and elsewhere Sargon uses a different number, **16 283**, in relation to the number of cubits associated with the circumference of the wall. What is the significance of these numbers?

### Ancient Khorsabad

Khorsabad is now a village in northern Iraq, but it was once, for a short time, the Assyrian capital. The city was planned and built by Sargon II, in the decade preceding 706 BC, but was only used as a capital during Sargon II's reign. After his death, Sargon's son and successor Sennacherib moved the capital to Ninevah, and Sargon's city was abandoned forever. Sennacherib was very upset by the fact that his father's body was not recovered from the battlefield, and interpreted this as a sign from above that Sargon had done something wrong and upset the gods. So, as was reasonably common in the ancient world, the capital was moved elsewhere when Sennacherib became king. In fact, Sargon II had had successive capitals in Assur, Calah and Ninevah, so the move back to Ninevah made sense in a way. Perhaps the son had forgotten about the part of Sargon's inscription in Khorsabad, in which he threatened destruction by the gods of anyone who should destroy his city or his statue.

(11)

With Ninevah near the Tigris, it might seem odd that the capital of Assyria was ever moved away from it at all. However, the spot was carefully chosen by Sargon II, who put alot of thought into the process of placing and designing his perfect capital. Many texts have survived, which recount, in Sargon II's own words, the story of his conquests, campaigns, and how his new city, "at the foot of Mount Musri, above Nineveh" was built. Sargon II reveals how he planned the city, saying that "day and night he planned how to build that city", and that he chose the site because it was at the foot of a mountain above fertile ground and watercourses. There was a town there called Magganubba already. He describes the site as "like a pillar", which is strangely reminiscent of L'Enfant's description of the hill on which he planned to place the Capitol, in what is now Washington DC (in 1791 L'Enfant wrote to Washington: “I could not discover one in all respects so advantageous . . . for erecting the Federal Hse. [as] the western end of Jenkin’s Heights [which] stands really as a pedestal waiting for a superstructure.”) Sargon II describes how, though his wisdom, understanding and craftiness, given to him by the gods, "and by the fertile planning of my brain, which thinking had been made to surpass that of the Kings, my fathers, by Nin-men-anna, ("Lady of the Heavenly Disk"), mother (creatress) of the gods, planned day and night to settle that town, to raise aloft a noble shrine, a dwelling of the great gods, and palaces for my royal abode.I gave the order and I commanded that it be built." (12)

### Sargon's account of how he came to build Khorsabad

Below are some excerpts.

There are many other shorter accounts of how the city was built, such as this one:

Here we learn that the gates, eight in all, and all had names, as did the wall itself: "Urta Establishes Foundation Platform of the House for All Time to Come". In the text below, the dwelling of the god Assur is described as "the model of dwellings". Assur is thanked "for the restoration of the temple structure" and "the complete revival of the cultus".

Most of the texts written by Sargon to describe his reign read like a long list of cities conquered and destroyed, people and treasure taken, enemies defeated. Below is a typical passage, which features destruction, and death, but also the sense of order being restored.

Yet, Sargon's victories are nothing like as gruesome in nature as the accounts of Sennacherib, his son, which are quite different, enough to make many of the power hungry leaders of the world today look meek. Below is an example.

Though there are inscriptions which show Sennacherib built city walls too, they do not offer measurements, which implies that the measurements, and by extension, the mathematical principles of the world, were not taken as seriously as Sargon II had done.

All of these clues point to a Sargon II who, though a self-appointed king of the universe, as he refers to himself in these inscriptions, was a thoughtful man, intrigued by ancient customs, wanting to create a better world, albeit one forged by his own hand, and one in which the old philosophy of everything being ruled by number should prevail. By contrast his son was really just about power, violence and destruction.

### Measurements overview and cosmological significance

The archaeological remains that survived until about a decade ago (until they were tragically targeted for destruction) were Sargon II's work. It follows that the dimensions cited on the tablet must correspond to the walls that survived and were measured. It is difficult to know whether the dimensions given on the tablet referred to the interior, exterior or mean of the perimeter wall. With walls that are ancient, and with no clear direction on the tablet (to my knowledge) about whether to measure the interior or exterior circuit, and with gates and a palace built into the wall, it's hard to be certain of what the measure given by Sargon refers to exactly.

What could be the significance of the dimensions of a wall which measures 24 740 U feet? There must surely be some significance, because this length is recorded in a tablet. The wall was not just about keeping the enemies out. It had an important symbolic role too. Sargon II is quoted as saying:

"I made the circumference (lit., measure) of its (the city's) wall 16,283 cubits, (corresponding to) my name (Nibīt Šumīya), and established the foundation platform upon the bedrock of the high mountain."(2)

The reference is to gematria, whereby a letter represents a number. The quotation comes from a cylinder inscription. Sargon, who's name was most commonly written *Šarru-kīn*, or *Šarru-ukīn*, doesn't say whether he received that name at birth, or whether it is a name that came with his position. It is likely he gave it to himself when he became king, aligning himself with a previous king Sargon, a thousand years before him. He claimed his name came from "the great gods" (3). His very name encodes the dimensions of his city wall. The importance of the wall is underlined by the fact that the city is actually named "Wall of Sargon", Dūr-Šarru-ukīn. (4) This suggests that there was a numerological method for calculating the value of names or words, but the details of how these numbers were derived or the specific system of gematria used are still enigmatic.

Greek and Hebrew gematria are well understood and systematically decoded. Both use a system where each letter corresponds to a numerical value, allowing words and names to be analysed in terms of their numeric significance. These systems are used for mystical, religious, and linguistic purposes. Assyrian gematria, however, is less well-documented and not as systematically decoded as Greek or Hebrew gematria. The Assyrians, like other Mesopotamian cultures, had systems of numerology and symbolic mathematics that were complex and often connected to cuneiform script. The precise way in which numerical values were assigned to letters or words is less clearly understood than in Greek or Hebrew gematria.

** **

There are two competing values associated with the wall perimeter: 16 283 and 24 740. Both these numbers are somewhat surprising, not being multiples of 6 or 12, as one might expect, in a culture that used a sexagesimal counting system, nor are they obviously connected to an astronomical cycle. 16 283 is 19 x 857, two primes. 24 740 has more factors: 1, 2, 4, 5, 10, 20, 1 237, 2 474, 4 948, 6 185, 12 370, and itself, and 1 237 is a prime number.

Petrie, in his article on weights and measures, notes that a tablet describes the circuit of the city wall of Khorsabad as 24 740 U feet. With his estimate for the U as **10.806** inches (or 0.2744724 metres), the perimeter will be of 267 340.44 inches or 6 790.44718 metres. 108 is an important ancient number, so it is almost reassuring to find it here.

** **Wikipedia lists the city wall dimensions as a rectangle of 1 758.6 meters by 1 635 meters, with a total perimeter of 6 787.2 meters, which divided by 24 740 U, yields a U foot of approximately 10.8008 inches, which closely matches Petrie's value. If we take the number 10.8 to be a factor instead of a measure, and divide the wall perimeter by π and 10.806, the result is very close to 7 875 inches, which is approximately 2 meters (or 63 000 ÷ 8 inches).

Petrie's value for the perimeter: 267 340.44 inches.

Divided by pi and 10.8: 267 340.44 / (10.8 x π) = 7 874.9866.

24 740 U feet of 10.8 inches are equivalent to 2160 x 39.375 π inches. 2160 x 39.375 inches are 480 x 6 x 29.53125 inches.

The number of cubits in the width of the Giza rectangle (connecting the outer north-east corner of the Great Pyramid and the outer south-west corner of the third pyramid) is 2 160 x 39.375 / 60 = 36 x 39.375 = 1 417.5.

This is similar to squaring the circle except here we have a circle and a rectangle. We can call it rectangling the circle. It is something that we can find at Giza too (see image in the Appendix, showing the links between circles and the rectangle that connect the outer corners of the Great Pyramid and the third pyramid, and how the King's Chamber, laid out as a double square, has a perimeter of close to 10π). The circle on the outline of the city wall below seems to go through the extremities of the corner features.

The sides of the rectangle according to Wikipedia are 1 758.6 and 1 635 metres, the length is close to 12⁴ / 10 x 0.27π metres. In fact, if we take the wall as 12⁴ / 10 x 0.27π metres of 39.375 inches, and convert from 39.375 inch metres to 39.3700787 metres, i.e. to modern metres, the result is even closer: 12⁴ / 10 x 0.27π x 39.3700787 / 39.375 = 1 758.6699.

The Egyptian foot being 0.27 metres (C. Mauss)(4), the length can also be though of as 12⁴ / 10π Egyptian feet.

What about the other divisor, give by Sargon II himself, 16 283? Converting the wall length to cubits with 16 283 as the divisor gives a nameless cubit of **16.4184** inches (or 0.417 metres).** **

** **King Sargon II had written, on a cylinder, that the city wall’s circumference was 16 283 cubits, a number which, he claims, “corresponds to my name (Nibīt Šumīya)”.(5)

The city’s name, Dūr-Šarru-ukīn, means "Wall of Sargon," underscoring the importance of this wall to its builder’s legacy. This implies that the length of the wall, and possibly other aspects of it, is encoded statement about Sargon’s divine connection and authority. What is the significance of 16 283, the number of cubits in the wall length according to Sargon?

Dividing 16,283 by 2π yields approximately 2,591.52. This is remarkably close to 2,592, which is significant in ancient cosmology as the number of years in a precessional cycle divided by ten, and 2 592 also represents the Persian royal cubit in inches (25.92) multiplied by 100. If this connection is one that was intended, then the number of cubits in the wall perimeter implies a circle, with a diameter of 2 592 cubits. This suggests the number may have been chosen to echo celestial cycles, connecting the city wall to the cosmos. If 16,283 represents the circumference of a circle, then the radius of 2 592 (using π as approximately 3.141), would make reference to precession. The city wall then becomes connected symbolically to the heavens.

A possible ratio between the numbers 24 740 and 16 283 could be 160 / (9 x 27), close to the value in metres of the Persian royal cubit, 0.6582857 m (25.92 inches). If we use the value of the Persian royal cubit in metres, 0.6582857 m, and multiply this by 24 740, we get 16 285.988, which is close to 16 283. However, if we divide the perimeter into 16 283 units, the resulting unit is 16.4184 inches, or 0.4170268 m. Another interesting possible connection is with the square root of three and the number 235 which is the number of synodic months in a Metonic period of 19 years. 235 x 40 x √3 = 16 281.2776, a number which is close to 16 283, if not an exact match. 16 283 lunations are therefore the approximate duration of 40 Metonic periods divided by √3.

Wikipedia gives the dimensions as a rectangle with sides of 1 758.6 x 1 635 metres, so that the perimeter is 6 787.2 metres (267 212.5984 inches), which, divided by 24 740, gives a U of 0.27434115 metres, or 10.800833 inches. French-German Assyriologist Jules Oppert gives 1750 x 1645 metres approximately (5). Oppert quotes Flandin's measures: 6 791.13 metres for the perimeter, with the sides as 1 647 x 1 748.565 m. The ratio between length and width could be 14 / 13 or 968 / 900, but Oppert's 6 000 x 6 370 is a very good fit, and 6 000 x 2 + 6 370 x 2 = 24 740.

The diagonal of the city wall is of interest. With the perimeter of the wall 24 740 cubits of 10.803 inches: 267 266.22 inches / 6 788.56199 m, and the sides 6 000 and 6 370 cubits of 10.803 inches: 1 646.3772 m and 1 747.9038 m, the diagonal is 8 750.8228 cubits of 10.803 inches: 94 535.1389 inches / 2 401.1925 m. This is a curious number of metres, as 19 x 28 x 8 / √π = 2 401.19087, or 19 x 28 x 8 / π x √π = 2 401.19087.

A circle with a radius of 1 has an area of π. A square with an area of π will have sides of √π.

The diagonal of the rectangle which surrounds the city is approximately equal in length to the diameter of a circle with a circumference of 19 x 28 x 8 x √π, which itself is equal to the side of a square with an area of (19 x 28 x 8)² π. This square is equal in area to a circle with a radius of 19 x 28 x 8.

19 x 28 x 8 as a number of years is combination of three time cycles. The Metonic cycle is 19 years, after which lunar phases will occur on the same calendar dates. After 28 years, the same day of the week falls on the same calendar date. Every 8 years, the same phases of the Moon occur on roughly the same dates (octaëteris). It seems that here these cycles are combined and expressed in metres, first as the radius of a circle: 19 x 28 x 8 metres. This circle is then squared: a square of the same area is produced. The side of this square measures 19 x 28 x 8 x √π. A circle is drawn with a circumference equal to the side of this square. The diameter of this circle is equal to 19 x 28 x 8 x √π / π, which is the diagonal of the city rectangle of Khorsabad in metres.

As seen above, the wall perimeter itself being equal to the circumference of a circle with a diameter of 2 160 metres, the squaring of a circle procedure is repeated with the diagonal, linking it, through a quite complicated process, to a circle of radius 19 x 28 x 8 m, which is a way of representing time in a linear way.

A similar idea might be present in Egypt, though in inches. The base perimeter of the second biggest pyramid at Giza is 8 x 19 x 223 inches (8 x 19 x 223 = 33 896, Petrie’s measure is 33 899.6 inches). In this case the 8 and 19 years cycles are combined with the Saros cycle of 223 lunations.

Did Sargon II, self-styled king of the universe, believe that in the design of his capital city, he was not only representing aspects of the mysterious world, through astronomy, geometry, number and measure, but also that he was part of the lineup of gods, an active participant in the cosmic cycles?

### Jules Oppert, the Phoenix, and 653

The number of U feet in the wall perimeter, according to the tablet quoted by Petrie, is 24 740. This number can be understood as 20 x 653 + 40 x 292, or 20 x 653 + 40 x 653 / √5.

The number 653 appears as a mystery number, and another prime. Jules Oppert, in a 1902 article, writes about the number 653 in relation to the Khorsabad walls, and to inscriptions on a tablet from an archaeological dig at Sippara. Oppert describes the document as "une œuvre mystique", a mystical work, linked to "cyclical numbers used by Chaldeans and other nations of the ancient orient, and then by other peoples."(6) In particular, the number 653 is important, because it is connected to astronomical cycles. Oppert explains:

The prime number 653 is a cyclical number: 653

lustri of 5 years give 3 265 years, called the period of the

Phoenix, and composed of the Sothic period of 292

lustri or 1 460 years, and the lunar period of 361 lustri or

1 805 years, after which the eclipses return in the

same order.

Five lustri are 3 265 years: 653 x 5 = 3 265

A Saros cycle is in fact 18.02 years.

(There may be an error on Oppert's part, when he says the Sothic period is 1460 years when it is in fact 1460 days, and 653 lustri of five years are in fact 3 265 days)

There is a cycle of 1803 years, found by Irv Bromberg, of the University of Toronto, an expert on the Hebrew calendar. This is close to the 1805 years mentioned by Oppert.

An alternative accurate leap cycle with a superb fixed lunar cycle has 1803 years and 22300 lunar months, including 664 leap months. Its mean year is only about one second too long, its mean month is less than 1/2 second too short". (9)

This is a great match between lunar and solar years, especially as it also incorporates the Saros eclipse cycle, that other way that the sun and moon have of meeting, at least as seen from earth. The 223 lunar months of the saros cycle are very close to 18.0300129 years. Multiply this by 100, and there is an excellent match, 22300 lunar months for approximately 1803 years. This find marries the solar and lunar cycles as well as the saros cycle. Irv Bromberg also mentions a 353 year period, which contains almost exactly 4366 lunar months (4365.997979).

Oppert is referring to an ancient cycle, called the period of the Phoenix, which had various periods of time attributed to it by different authors. According to Pliny the Elder, it was 540 years. Tacitus said the cycle was either 500 years or 1461 years. This is the Egyptian Sothic cycle: 1 461 days of 4 x 365 days are equivalent to 1460 days of 4 x 365.25 days, so it combines two different ways of calculating a year, both of which have advantages in calendars.

There are other Phoenix traditions also. Because of a possible confusion between years and days, Oppert's supercycle of 3265 years, equivalent to 5 Phoenix cycles, doesn't really work in the way he puts it forward: as a combination of Sothic and Saros cycles. However, 3 265 days are roughly equivalent to 120 draconic months (120 x 27.2122 = 3 265.464), and 2 Sothic cycles of 1 460 days are 2920 days, which divided by Phi is 1 804.6476 (2 x 1 460 / 1.61803 = 1 804.6476). The period of 3265 days could be interpreted as a draconic year plus 8 vague years (345.62 + 8 x 365 = 3 265.62). 3 265 x 2 / 10 = 653. So we can think of 653 as 24 draconic months expressed in days: 24 x 27.2122 = 653.0928.

Curiously, though, a Sothic cycle, as 1 460 days, can be approximately calculated as 653, the mystery number, multiplied by the square root of five (1 460 / √5 = 652.932, very nearly 653). One might imagine a double square to express this.

So √5 x 653 is approximately a Sothic period, rather than 5 x 653 being approximately a super cycle of 1 Sothic cycle + 100 Saros cycle, as Oppert suggested.

According to Oppert, the Suda gives 654 vague years (of 365 days), which are roughly 653 tropical years, plus 163 days, for the period after which the phoenix reappears.

27.2122 x 24 x 365.242199 + 163 = 238 700.0504.

In fact, the Suda only seems to give 654 years. The online Suda the entry for "phoenix" is as follows:

[Meaning] the tree [of that name].[1]

And the bird [of that name]. In the time of Emperor Claudius[2] they say that this appeared to the Egyptians after654years.[3]

Also [sc. attested is] phoenix meaning foinikou=s ["crimson, dark-red"].[4] Homer [says]: "[one] that was blood-bay for all the rest".[5] In reference to a horse.

So concerning the bird it is on record[6] that when it reaches the [time] alloted by destiny it comes into Egypt, from somewhere unknown to men; and it makes a pyre for itself out of cassia and myrrh and it dies. And when the pyre has burnt out, after a while they say that a worm is born from the ashes; this is transformed and becomes again a phoenix and it flies away from Egypt to the place where[7] the other phoenix before him came from.(7)

In any case, the numbers 654 and 653 are very close, and the difference may be due to a copyist error at some point in time, or to the difference between tropical and vague years, though vague years are not mentioned. The Suda probably got the number of months in a Saros cycle wrong (giving 222 instead of 223) so an error here is not inconceivable.

If the correct value is supposed to be in fact 654 instead of 653, 654 is not a prime but 654 = 6 × 109, and 109 is a prime.

Oppert also remarks that in *Genesis*, 653 years pass between the deluge and the end of *Genesis*, the death of Joseph. Also, this period of 653 years is divided into a period of 292 years, from the deluge to Abraham's birth, and 361 years, from the birth of Abraham to the death of Jacob's son. 292 years are approximately 73 Sothic cycles of 1461 days and 361 years are 19 Metonic cycles of 19 years. According to Oppert, the Phoenix cycle connects further with the Saros cycle, comprised of 223 synodic months (18 years, 11 days), leading to a combined "super cycle" of 3 265 years (5 x 653). This combination of 653 with major celestial cycles suggests it held a symbolic, cosmological meaning across cultures. The theme of prime numbers lingers, or at least the lack of multiples of 6 or 12, as 292 = 4 x 73 and 361 = 19 x 19.

There may be an additional geometric connection, with the square root of five: 653 / 292 is almost exactly √5. This means that 653² / 292 = 1 460.3045, or just over 1 460, a Sothic period in days. Also, 653² / 361 = 40 x 29.52971, which is very close to 40 synodic months, expressed in days. A lunar connection through 40 cycles strengthens the city’s possible symbolic link with other heavenly cycles.

Oppert suggests that there is a cycle of 1 460 years plus 1 805 years, a total of 3 265 years. A 1803 yer cycle is a definite possibility, as Irv Bromberg demonstrates, as it is a natural cycle in which solar and lunar cycles resolve almost exactly. But it is difficult to see the purpose of a cycle of 1 460 or 1805 years, as 1461 or 1460 makes sense as a cycle in days, not years, and 1 805 is two years off 1 803 years. Curiously though, 3265 is close to a hundred megalithic yards expressed in inches.

### Connecting the number 653 to astronomical cycles

The number 653 connects to the fraction π / √3, which is arguably a central part of the Giza design plan. Aspects of the pyramids encode pi and the square root of three, for example the height and base of the Great Pyramid. The fraction π / √3 links various astronomical cycles to each other, and to geometry. A civil year multiplied by a draconic year, divided by a lunar year and a lunation, all expressed in days, are very close to π / √3 x 20 / 3. And the mean number of lunations in a year is close to π / √3 x 300 / 44.

Pi, the square root of three, and the number 360 come together to express the number 653, approximately: π / √3 x 360 = 652.9678 ≈ 653.

As a consequence we can express the mean number of days in a year using the number 653:

653 x 300 / (360 x 44) = 12.3674 (the actual mean number of lunations is 365.242199 / 29.53059 = 12.368266). This can be simplified to 653 x 5 / 264 = 12.36742. It's worth noting that the number 264 is central to ancient Indian, Babylonian and Sumerian metrology, and to the old Saxon measures found in the UK: 20 x 264 feet make a mile of 5 280 feet. 2 Saxon feet of 13.2 inches are 26.4 inches, which in turn are 40 shusi or angula of 0.66 inches. So it's interesting to see this number 264 combined with 653 to produce the mean number of lunations per year. Furthermore, a megalithic yard can be interpreted as 264 x 12.368266 / 100 = 32.652222 inches, with 12.368266 the mean number of lunations per year, and 2.64 inches being 10 Indus inches of 0.264 (English) inches.

It's also possible to express the astronomical relations expressed earlier in terms of 653 directly: A civil year multiplied by a draconic year, divided by a lunar year and a lunation is close to 653 / 54. Again here, we find a key number in metrology, 54. there are 54 digits of 0.72916666 inches in a metre of 39.375 inches, for example, and 54 is half of the key ancient number 108.

653 / 54 = 12.092592

π / √3 x 20 / 3 = 12.091996

These numbers are part of the Giza pyramid design, expressed in proportions, but also in inches. It's possible to interpret various aspects of the Giza design in terms of the number 653, such as the base side (or perimeter) of the Great Pyramid, the side of the third pyramid, and therefore connect the design to the Khorsabad design.

Alternatively, 653 can be understood as:

270 000 / (14 x 29.53059) = 653.0758, with 29.53059 the number of days in a lunation.

### Symbolism of 653 and Sargon’s Walls

In this context, Oppert cites a measurement from Flandin for the Khorsabad walls at 24,740 palms, equivalent to 123,700 digits. Flandin gives a perimeter of 6 791.13 metres. Oppert interprets the dimensions as two sides of 6000 palms of 0.2745 m (1 647 metres per side) and two sides of 6370 palms of 0.2745 metres (1 748.565 m per side). This gives a total of 24 740 palms, and 24 740 is the number given by Petrie in his Encyclopedia article. Oppert proposes this reflects cycles associated with Sargon’s name, Sar-kin, with “sar” denoting 20 and “kin” signifying Ea, the god associated with the number 40. According to Oppert, these measurements could symbolically represent:

20 Phoenix cycles of 653 years = 13 060 years (8)

40 periods of 292 years = 11 680 years, which is also 32 vague years of 365 days.

Totalling 24 740, symbolising the number of palms in the city walls.

Babylonian and Assyrian cosmology placed high significance on numbers tied to celestial cycles, often linking architectural proportions to these. By adding 20 x 653 x 5 years to 40 x 292 x 5 years, the total is 123 700. The 292 year period is the same as in Genesis, the number of years from the deluge to Abraham's birth. Or by adding 20 x 653 lustri to 40 x 292 lustri, the total is 24 740, the number mentioned by Petrie.

Oppert analyses the dimensions of a series of courtyards within Khorsabad, and find that the total area is equal to the square of 653 units, even though the courtyards are in fact a series of squares and rectangles. The image below shows a diagram from Oppert's article:

Indeed, if we add up the areas of the parts in the diagram, 390² + 864 x 114 + 122² + 30.5² + 400², the total is 653², which would be the area of a square with sides of 653 units. While the rectangular shape of the city is based on a circle, here the various elements of the courtyard are based on a simple square. These are the numbers from the tablet Oppert mentions in the beginning of his article:

### Reflections on the U Foot, Persian Cubit, and Cosmological Meaning

The number 24 740 U feet (measured at 10.806 inches per U foot) is unusual, as it is not divisible by commonly significant numbers like 6, 7, or 12. However, if we take 24 740 as a circumference in inches, dividing by π produces 7 875 inches—again close to 63 000 ÷ 8, indicating this number may relate to the lunar or seasonal cycles encoded in other ancient cultures.

Taking 24 740 as a circumference in U feet measured at 10.806 inches per U foot, this can also be interpreted as 216 000 ÷ π metres. This figure reflects cosmological multiples, like 216, which is tied to 12 zodiac signs (12 x 6 x 3), potentially symbolising unity between the city’s form and celestial cycles.

And taking 24 740 as the circumference of a circle, the diameter would also be 7 874.9866, very nearly 7 875, equivalent to 63 000 / 8, or 800 x 29.53125 / 3. Alternatively we could multiply 24 740 by 55 / 21, an approximation for Phi squared, and 4 / 10, to obtain 25 918.0953, very nearly 25 920, the precessional number.

As 7 875 inches are close to 2 metres, Petrie's wall perimeter value of 267 340.44 inches (6 790.44718 metres) is close in value to 20 π x 108 metres (267 159.06 inches), a difference of 15.115 feet from Petrie's value if we use the calculator value for pi, or 6.154 feet if we use 22/7. The number 24 740 can therefore be interpreted as 63 000 / 8 x π. But what is the significance of 63 / 8? One possible explanation is that 63 000 / 8 inches are 200 metres of 39.375 inches. So that 24 740 x 10.803 inches, the perimeter according to Petrie, is equivalent to 216 x 1 000 000 / 254 x 7 / 22 inches, which can be interpreted as 216 000 / π metres or 63 000 / 16 x π cubits of 21.6 inches.

The perimeter of 267 340.44 inches, Petrie's estimate, can be interpreted also as 43 x 21 / 55 x 16 283 inches, or 330 000 Persian digits of 0.81 inches, or 19 x 2 5920 x 300 units of 16 283 inches (with 19 being the number of years in a Metonic cycle).

### Why so many prime numbers?

An intriguing aspect of all these numbers is the repeated presence of prime numbers. The first thing Sargon II says about his city is that the perimeter was 16 283 cubits, which is an odd number of cubits to brag about (literally). 16 283 = 19 x 857, and 19 and 857 are both prime numbers. There must be a significance to this number.

A prime number cannot be the product of two other natural numbers, except for 1 and itself. For example 7 = 1 x 7 but has no other natural number divisors. The number 4, by contrast, is not a prime, because it is a product of other natural numbers, 1 x 4, or 2 x 2. Numbers such as 4, 6, 8, 9 are composite numbers, and a composite number of dots can be arranged into a rectangle, whereas a prime number of dots (1, 3, 5, 7, 11 etc) cannot.

Yet, Sargon II chose a prime number to actually define a rectangle, the symbolically important perimeter of his capital’s wall. Why?

It may be impossible to generate a prime number by multiplying together other natural numbers, except for 1 and itself, but it’s possible to cheat, using a combination of natural numbers, irrational numbers (such as pi, √3), and astronomical values, to *approximate* a prime number.

857 = 4 π x 354.36708 / (3 x √3)

so 16 283 = 19 x 4 π x 354.36708 / (3 x √3)

π = pi

354.36708 = days in a lunar year

19 = number of years in Metonic cycle, and a prime number

16 283 x 3 x √3 / (4 π x 354.36708) = 18.9999768 ≈ 19

Other combinations of irrational numbers and astronomical values to loosely approximate 16 283 could be: 6⁴ x 4 π = 16 286.0163, or 235 x 40 x √3, with 235 being the number of lunations in a Metonic cycle.

Did Sargon II think of creating a rectangle out of a prime as one might think of squaring a circle, that is, as a mathematical tour de force? If precise values are used, a circle cannot be squared because the full value of pi is unknowable, but it can be done in an applied sense, by approximating pi, so that, seemingly, the rules of maths are overcome. In the case of this city wall, a rectangle is defined as the product of two prime numbers (19 x 857), which should not be possible. The number in question, 16 283, is arrived at through approximations of geometric constants (√3 and π), and numbers derived from astronomy (the lunar month, lunar year, and the Metonic cycle).

### Conclusion

The dimensions of the Khorsabad wall, whether measured in cubits, U feet, or other units, reflect ancient cosmological symbolism, encoding numerical values that resonate with celestial cycles and cosmic principles. 16 283 cubits, in particular, stand as a mathematical reflection of Sargon II’s name and divine mandate, encoding both his authority and an attempt to mirror the heavens on Earth. Calculations connecting 16 283 to 2π and 2 592 suggest that the number was carefully chosen to align with precessional cycles and the Persian royal cubit, thereby embedding the city within a divine, ordered cosmos.

The dimensions of the Khorsabad wall, whether measured in cubits, U feet, or other units, reveal a sophisticated layer of cosmological symbolism, encoding numbers that resonate with celestial cycles and cosmic principles. The wall’s 16 283 cubits especially stand as a mathematical reflection of Sargon II’s name and divine mandate, encoding both his earthly authority and an alignment with the heavens. Calculations connecting 16 283 to 2π and 2 592 suggest that this number may have been deliberately chosen to mirror precessional cycles, alongside the Persian royal cubit, thereby embedding Sargon’s city within a divinely ordered cosmos.

This same attention to cosmic alignment appears in the 24 740 U feet perimeter of the wall, according to Petrie. This measurement is curious because it is not a multiple of commonly significant ancient numbers like 6, 7, 8, or 12, yet it reveals hidden symbolic connections when interpreted in relation to π. Dividing this value in inches by π (using 10.806 inches per U foot), we arrive at approximately 7 875 inches, which aligns closely with 63 000 ÷ 8. This suggests that 24 740 may relate to lunar or seasonal cycles, reflecting ancient symbolic ratios.

** **653, 361 and 292 are not common numbers in most ancient texts on cosmology, which typically include figures like 4 320 (common in Babylonian calculations) or 25 920 (the precessional cycle). Oppert’s discovery seems unusual but might reflect a unique Assyrian approach to incorporating mystically resonant numbers into civic structures. If these figures are indeed encoded in Khorsabad’s layout, they could suggest a distinct Mesopotamian numerological system, with 653, 292, and their related cycles possibly serving as keys for interpreting other Assyrian or Chaldean structures.

In this way, the Khorsabad wall transcends its function as a mere physical boundary; it becomes an architectural expression of Sargon II’s divine kingship and Assyrian cosmology. Through these encoded measurements, Sargon’s identity is fused with the geometry of Earth and the stars, embodying his reign within the order of the cosmos and the divine.

Towards the end of his article on the number 653, Oppert wrote:

In the present case, our surprise is surpassed by our admiration. We are not surprised to find in this people, from the most remote times, an almost stupefying arithmetic science which did not shy away from calculations with six or seven digits. We may bow with respect in front of this nation which, seven thousand years before our time, handled sexagesimal calculations, applying it to daily uses, introducing the division of the day into 24 house or 60 minutes of 60 seconds, the division of the circle into 6 parts of 60 degrees, and as many sexagesimal subdivisions, the week of seven days and and their denominations, preserved religiously since these remote times, and which are the only institutions which the French Revolution couldn't touch.

The sophistication of ancient Babylonian and Chaldean thinking serves as a reminder that there have been other intelligent civilisations before our own.

### Appendix

A few screenshots from texts on Khorsabad, and some images documenting circles and rectangles at Giza.

Here are just a few examples of circle equivalences at Giza. The first one links the Great Giza Rectangle, i.e. the perimeter of the outer north-east corner of the Great Pyramid and the south-west corner of the third pyramid, to the side of the third pyramid. This side can also be approximately linked to the equatorial circumference of the earth in fact. If we take √(20 000 000 π) x π = 24 902.3198 as the length in miles of the equatorial circumference, one side of the third pyramid, given by Petrie as 4 153.3 inches, can be interpreted as approximately √(20 000 000 π) x π / 6 = 4 150.38664 inches.

There are many instances of circles being implied, if not explicitly drawn out, such as with the dimensions of the King's Chamber.

In the diagram below, the large red square and the large black circle share a perimeter, instead of an area, and the square corresponds to the base of the Great Pyramid, while the radius of the black circle corresponds to the height of the Great Pyramid. The smaller green circle has a circumference equal to one side of the Great Pyramid. The circles and the square are drawn around an equilateral triangle with sides of 10 000 inches.

In this example, a square and a circle are compared one to the other, but not in terms of area, in perimeter instead. The perimeters of the red square and the black circle are of equal length.

### Notes

1911

*Encyclopædia Britannica*, Volume 28, Weights and Measures by William Matthew Flinders Petrie and Henry James Chaney__https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Weights_and_Measures__From a cylinder inscription from Khorsabad, written in 713, quoted in "44) Observations on the Name and Age of Sargon II and on Some Patterns of Assyrian Royal Onomastics*", by Eckart FRAHM (15-07-2005), in N.A.B.U. Nouvelles Assyriologiques Brèves et Utilitaires 2005 N°2 (juin) – 25 – NOTES BRÈVES,

__https://web.archive.org/web/20160510232206/http://sepoa.fr/wp/wp-content/uploads/2012/06/2005-2.pdf__Ibid. See also Luckenbill, Daniel David (1927).

*Ancient Records of Assyria and Babylonia Volume 2: Historical Records of Assyria From Sargon to the End*. Chicago: University of Chicago Press. p1C. Mauss

Oppert, Jules, 1902, "Six cent cinquante-trois. Les carrés mystiques chaldéens", Comptes rendus des séances de l'Académie des Inscriptions et Belles-Lettres Année 1902 pp. 457-468

__https://www.persee.fr/doc/crai_0065-0536_1902_num_46_4_17246__Ibid.

Suda On Line

__https://www.cs.uky.edu/~raphael/sol/sol-cgi-bin/search.cgi__13 060 / pi = 4 157.127, and this is very close to the measure of a side of the third pyramid of Giza (4 153.3 inches according to Petrie). Does this number have significance as a cosmological number?

Irv Bromberg, "The Seasonal Drift of the Traditional (Fixed Arithmetic) Hebrew Calendar (הלוח העברי הקבוע)", Seasonal Drift of the Traditional Hebrew Calendar (utoronto.ca)

quoted in The Mysterious Mr. Jenkins of Jenkins Hill: The Early History of the Capitol Site JOHN MICHAEL VLACH

Luckenbill, Daniel David (1927).

*Ancient Records of Assyria and Babylonia Volume 2: Historical Records of Assyria From Sargon to the End*. Chicago: University of Chicago Press.__https://isac.uchicago.edu/sites/default/files/uploads/shared/docs/ancient_records_assyria2.pdf__

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