Isopsephia
 

During the first half of the 1st millennium BC in the Eastern Mediterranean region there appeared a mode of writing in which the letters of the Greek alphabet served as numerals. Genuine attempts to exemplify the system (Greek Isopsephia or its Hebrew counterpart Gematria) have only been partially successful for the precise rules of play are still unknown. The origin of the curious numerical scripts like the alphabets they applied to are not easily traced for each in its own way appears to be an experiment with something that preceded it. The Greeks believed the alphabet to be an Egyptian invention and while it might now be disputed in favour of the Canaanites the quest for origin is far from over. It is clear however that within Isopsephia and its concealed teaching lies a considerable body of mathematical knowledge.


Aa Bb Gg Dd Ee * Zz Hh Jj
1 2 3 4 5 6 7 8 9
Ii Kk Ll Mm Nn Xx Oo Pp *
10 20 30 40 50 60 70 80 90
Rr SsV Tt Uu Ff Cc Yy Ww *
100 200 300 400 500 600 700 800 900

There was once a sixth letter to the alphabet, the digamma or double gamma of value 6 (F sound = w) but it fell out of use as did the letters with the values 90 and 900.   The value 6 remains however where the letters s and t occur together.   An example might be stauroV (a cross) which would thus either have the value 777 or 1271.

It is through Isopsephia that we can confirm the Egyptian use of certain key geodetic numbers. The Egyptian geodetic code revolved around the four numbers 1080, 666, 1665 and 2220 and in the following illustrations it will be shown how they were used. They will appear highlighted as above. The Greeks inherited these numbers together with the Egyptian hand dimension theme and glorified them with Isopsephia.
It was said for example that Abraxas headed the Gnostic sciences. Of the many words and phrases attributed to him through Isopsephia none reflect the Egyptian geodetic numbers better than the following:

    The hand of Abraxas


T o c e r i t o u A b r a x a V = 2220
300 70 600 5 100 10 300 70 400 1 2 100 1 60 1 200
370 715 770 365

Where 1080 = (hand) + (Abraxas)
Where 666 : 1080 is as 37 : 60 whilst 37 x 60 = the sum of the phrase 2220.


One of the more obvious occurrences in Isopsephia is the continual appearance of words and phrases the numerical sums of which are always the multiples of 37 or 74, the above phrase being no exception. The Egyptian circumference number 1665 can be easily demonstrated in the above as part of the celebrated Pythagorean proportion 3:4:5 or 1665 : 2220 : 2775 where 2775 is the sum of all the numbers 1 - 74. There is beauty of number and proportion here, the architecture of which was well known to the Greeks.
The question must therefore be asked : Did the hand of Abraxas fit the metrological mould, and was this the key to his position of success ?

the egyptian geodetic code according to Isopsephia
1080
The holy spirit
1080 x 666 x 88
handlengths
7912.08 miles
Diam of Earth
666 Biblical
the number of Man
1080 x 666 x 300
handspans
24859.1445 miles
Circ of Earth
1665
Spirit of the Earth
360 x 60 x 60 x 1665
digits
24859.1445 miles
Circ of Earth

Note : 88 handlengths of 7.92 = 10 armspans of 69.696 ... thus Earth's diam = 10800 x 666 armspans


= 300 + 70 + 1 + 3 + 10 + 70 + 50 + 80 + 50 + 5 + 400 + 40 + 1 = 1080


= 300 + 70 + 80 + 50 + 5 + 400 + 40 +1 + 300 + 8 + 200 + 3 + 8 + 200 = 1665

Recent research, in particular that of John Michell, confirms that the numbers 1080 and 666 were by far the two most important of Greek Isopsephia. In the above where there is emphasis on the measure of man we also have the original biblical reference to fall back on. The numbers 1665 and 2220 although less common are easily found in Isopsephia.   All four numbers are geodetic and all four are Egyptian.  When combined as they are above to express Earth measure using the ancient anthropometric theme of hand magnitudes the results are truly surprising. As a direct comparison the modern middle degree is used. Did their astronomical observations allow them to take into consideration an irregular sphere ?

greek architecture
The architects of the Piesistratid period appear to have been partly familiar with an Egyptian metrological code because in Athens the temple foundations of both the Parthenon and the Olympieion temple of Zeus are laid in accordance with the geodetic digit. Not only was the digit employed but it was also used in conjunction with the number code which originally supported it, a code that through the numerical language Isopsephia is now understood to apply to Earth measure.

Parthenon (stylobate dimensions) 30.86 x 69.51 * metres (1665 x 3750 digits)     ratio 111:250

1665 digits = 1215.33582 inches = 30.869 metres
3750 digits = 2737.24313 inches = 69.525 metres

It is understood that at least one of the architects of the Parthenon was also responsible for the mysterious temple of Apollo high up in the Arcadian mountains at Bassai. Here the temple proportions reflect similar ideas:

Temple of Apollo : 13.7 x 34.7 * metres. (1665 x .444 digits) x (1665/.888 digits)

739.26 digits = 13.706 metres
1875 digits = 34.762 metres

While in the foundations of the Olympieion there is knowledge of the ’Golden section’ or the irrational number (Phi )

Olympieion : 41.10 x 107.75 * metres (2220 x 5812.035 digits)

2220 digits = 41.159 metres
5812.035 digits = 107.756 metres       ratio 1 :

* Quoted measures ... R.E. Wycherley. "The Stones of Athens" (Princeton UP 1978)

Confirmation of an Athenian digit does not necessarily defame the foot for it appears that the latter being typically Greek was chosen to replace it. The geodetic digit and its supporting code were probably the exclusive property of the Athenian architects and as such were not meant for the common man. The foot of approximately 12.15 inches which equaled 16.65 digits or 1/100th sec of latitude was meaningful enough to the Greek except when it came to understanding the digit's odd value or its role within the geodetic code. By all accounts Herodotus didn't receive any instruction as to the foot's origin, nor it seems to its correct value, although in fairness to Plutach who later referred to the Parthenon as 'Hekatompodon' or 100 foot, it is reasonably clear that some linear clarity eventually prevailed.
100 Greek feet = 1665 digits = 30.869 metres = 1 sec of latitude.

alignments
In the Greek examples given there is a definite Egyptian influence because the digit multiples 1665 and 2220 are geodetic and memories of their much earlier use survived in the libraries of Alexandria.

The first estimates of the Earth’s circumference were made by Eratosthenes (275-194 BC) and as head librarian to Alexandria there is every possibility that he had access to the ancient records. Eratosthenes’ simplified procedure required no special equipment but it did rely on a few elementary considerations including the fact that light rays from a great distance appear to hit the Earth in parallel. Calculations were made on simultaneous events that occurred at Alexandria and Syene (Aswan) some 500 miles to the South, at Syene when the sun was vertical to the horizon at noon, directly overhead, and at Alexandria when the sun over an obelisk caste a shadow of about 7º 12’. Eratosthenes simply divided the shadow angle into the degrees of a circle and multiplied by the distance separating the two events.

The knowledge that Eratosthenes relied upon was probably extremely old because archaeology now tells us that Syene on the first cataract was Egypt’s most southerly Early dynastic boundary. The site around Aswan or Elephantine was a cult centre, one of the few in Egypt which can be traced on the ground back into the 4th millennium BC. It would also have been the perfect site for the ancient astronomers to record the limits of Atum’s influence on Egypt, or as we understand it the sun’s furthest journey North on the tropic of cancer (then much closer to the 24th parallel). Today’s tropic of 23º 27’ North has been slowly shifting South away from the 24th parallel at an ever increasing rate. Based on today‘s rate of change 48 seconds of arc per century, the tropic would have probably been recorded near the first cataract in about 3000 BC.

But if the astronomers were Heliopolitan intent on laying down the ancient boundaries of Egypt in relation to some prime position associated with Atum and the river, would they not have tried to include in their calculations the locality of their own sanctuary at Heliopolis where the river first divides to enter the Delta.

There are definite grounds to consider a Heliopolitan alignment, especially when some 568 miles due South on the second cataract lies another Predynastic settlement, the Old Kingdom boundary of Buhen. The two sites are uniquely aligned for at the river crossing at el-Badari (latitude 26° 59' 30" N) the distance between them is divided into its mean and extreme ratio. The coincidence is not an isolated one for if the same idea is applied to an alignment between the two (3rd dynasty ?) pyramid type structures at Tukh near Nubt and the ancient Naqada cemeteries, and el-Kula near ancient Nekhen, a tropic is located which just happens to align with the Heliopolis - Buhen river division at el-Badari and the only other 3rd dynasty pyramid type structure within the vicinity which is at Zawyet el Amwat near el-Minya. How this might have come about without the prior mapping of the entire river system between the Delta and the 2nd cataract is difficult to imagine, and it suggests that the Heliopolis - Buhen alignment was juggled into place according to some pre - determined mensuration that first occurred at the cataract near Aswan, Syene or Elaphantine.

As the geometry illustrates Tukh and el-Kula pinpoint the viewing area from which the tropic was measured. The tropic was originally located at about 24° 02' N (just after 3000 BC) where the geometry crosses the Nile at Syene, which fixes the viewing area at approximately 23° 47' some 15' South , the reasoning being as follows : To observe the least shadow at the summer solstice the recording apparatus must be positioned under the outer edge or the upper limb of the sun disk, not its centre, and as the sun has an apparent diameter of about 30', an adjustment of 15' or half the diameter must be made to locate the tropic. The recording apparatus would therefore have been set up either 15’ North of the tropic or 15' South (23° 47'). This particular geometric interpretation based on the ruins of four Early dynastic settlements and three of its remaining monuments produces some fairly impressive results (see last link above). It remains to be seen if the distances have any significance metrologically.

Heliopolis approximately 30 º 08' North
Buhen approximately 21 º 55' North
difference 8 º 13' (567.4 miles)

2220 x 2220 x 10 digits = 8 º 13' 20 "
= 567.77058 miles
=Circ x 37
27 x 60

And by conversion where the coincidence 1665/27 digits approximates 45.012 inches :
8 º 13' 20 " = 1665 x 310 armspans.

1665/27 digits (.729931503... inches) = 45.01244272 ... (45.012 inches or 124 post divisions) which is a coincidence better than 1 in 100,000.   This is one of the few instances we know of where the irrational digit (of circumference) can be successfully converted into the cubit rod language of diameter.

View the 2 x 1 rectangle illustration where the 1665/27 digit conversion occurs.

Incidentally if you wish to check the co-ordinates and distances between the key positions mentioned here in this section then the Baines and Malek Atlas of Ancient Egypt is a fairly good starting point.
For instance you can start by locating the two pyramids called 'tukh' and 'el-Kula' which are about 50 minutes of arc apart,
Better still is a 1 : 950000 map of Egypt, especially if the ancient towns are marked.

Apart from el-Kula which has been read with precision this year, the coordinates given here are not necessarily 100% accurate for most have been taken from older sources which usually round off the positions to the nearest minute.
When archaeologists want exact coordinates in Egypt they go out and take readings for themselves, rarely do they rely on those taken from books and charts. Only the exact coordinates will either prove or disprove the theory.

  . .. el-Kula at el-Mamariya

el-Kula in more detail .
el-Kula closeup.
Tukh reconstructed 3D model.
Tukh yet another 3D model courtesy of the Digital Egypt site.