Herodotus, the great 5th century BC historian, mentions that the key south-facing "datum" edge of the Great Pyramid was 800 feet long whilst in English feet, the best survey found it was 756 feet long. Dividing 800 by 756 gives a foot length of 0.945 feet (fractionally 189/200 ft). John Neal has called this foot the Samian foot, since Herodotus lived as a young body on the island of Samos, as did Pythagoras. Neal found another historical reference to the same ("Samian") module in the pre-metrification city standards of at least seven German cities; in Danzig the variation was the Root value for the module (33/35 ft), in Bremen the Root Canonical (x 176/175), in three others the Standard microvariation (i.e. x 441/440) and two more the Root (33/35).
The Samian module is therefore quite well attested by Neal as a historical measure, but my own work finds a new significance in it. Neal's Standard Canonical is a foot 0.945 feet long, where 1000 such feet are 945 English feet which, divided by 32, equals 29.53125 feet, the number of days in a lunar month. At Le Manio Quadrilateral, the 32nd stone from the "sun gate" origin of day-inch counting appears to signify 945 day-inches from which I discovered this relationship between 32 lunar months and 945 days of day counting, in any unit. Could the Samian foot (then using feet to count days) have used one thousand such feet to conveniently arrive at 32 lunar months? I will return to this, but also need to point to the apparent coding of 27 feet to represent months at the Crucuno complex. This led to finding that this same 27 regular feet is 29.53125 Iberian feet (each 32/35 feet), allowing days to be counted within a lunar month counted in units of 27 feet! One must also recognise that 27 feet is ten steps (viz. megalithic yards) of the Druzian foot from which the astronomical megalithic yard is derived as 176/175 of 2.7 feet.
This reveals some relationship between Iberian (32/35), Samian (0.945) and English feet (as 1 in metrology) which allows the lunar month being realised as a length 945/32 (29.53125) days long in feet. And one can see that the Samian foot of Neal (Root 33/35 feet) quoted as 800 feet (of 0.945) feet by Herodotus, in the Great Pyramid's southern edge, indicates that length is 4/5 of 1000 such feet (945 English feet^{VV},see below), a ratio which is the major third in musical tuning. Ancient Metrology has an interesting relationship to tuning theory since it too seeks to constrain measurement units to the lowest possible integer factors, tuning using fractions only using the prime numbers 2, 3 and 5 whilst metrology uses 2, 3, 5, 7 and 11 in its foot ratios, the extra 7 and 11 being included largely, it would seem, to model pi in its approximation as 22/7, this used throughout the ancient world.
The Samian Root Foot and its True Module
The root value used by Neal is 33/35 feet (0.9428571), which contains those higher primes 7 & 11 in its formula of (3 x 11) / (5 x 7). This would normally indicate that it is the larger Root Canonical Samian foot (176/175) of a root involving only the harmonic primes 2, 3 and 5. Sure enough, Neal's "reciprocal" (page 34 Volume 2 of Ancient Metrology) is the ratio 15/16 feet, the descending just semitone and one of the most significant modal measures of tuning theory. This indicates to me that 15/16 (0.9375) feet is the Root of the Samian module and indeed, none of the German city standards for this unit exceed the Canonical column in Neal's table so that they are probably, in fact, Geographical variants of the Samian module.
feet | Canonical | Geographic | |
Root |
15/16 |
33/35 0.9428571 |
5808/6125 |
Standard |
189/200 |
594/625 0.9504 |
Figure of Sabian modules
^^
If 1000 ft of 0.945 equal the 945 days in which 32 lunar months pass, then the standard mile would be 5000 feet, that is the time for 160 lunar months, which is 10/9 (another musical ratiom the just whole tone) of 144 lunar months, or twelve lunar months. Another interesting fact about 945 days or multiples thereof is that its formula is 27 x 5 x 7 so that in time it equates to 135 weeks whilst as a length is a perfect radius (when using pi of 22/7). Both these properties are due to the presence of seven.
The Unexpected Numeracy between Celestial Bodies
As a time period, 945 days is particularly interesting because, as is clear in my books, the root Samian foot should be 15/16 feet long whilst the lunar year's relationship to the Saturn synod of 378 days is the descending semitone of 15/16. The Standard Canonical of a unit is defined as the root foot multiplied by 126/125 (or 1.008), and 15/16 times 126/125 is 0.945 feet. This gives purchase on how this 32 lunar month time period emerges from the semitone relation between the Moon and Saturn, as numerically inevitable. One can substitute the time periods of Saturn synod and lunar year into the 15/16 ratio to see this inevitability:
- LY/Saturn x 126/125 = 0.945 so that LY/Saturn = 0.945 x 126/125 = 15/16
- but also LY/12 = 945/32 = LM so that LY = (945 x 12) / 32 = 354.374 days compared the actual lunar year of 354.367 days
- Therefore (945 x 12) / 32 x 1/Saturn =15/16 so that Saturn synod = (945 x 12) /32 times 16/15 = 378 (exact), compared to the Saturn synod of 378.09 days
The Standard Canonical of 126/125 transforms the 15/16 ratio, between Saturn and the lunar year, into a ratio 0.945 through the artifice of the denominators 16 x 125 give, times 8, which equals 1000. The numerators 15 x 126 (where 126 = 18 x 7) arrive at the number 2 x 945 and the two cancels reduces 16 to 8 in the denominator. 945/1000 = 0.945, the Standard Canonical Samian foot.
The Week as a Natural Time Period
I have been rattling on about the seven day week for nearly 20 years, having found that Saturn provides the most compelling origin for it, also being traditionally associated with the number seven. The Saturn synod is 54 weeks long whilst the 364 day year (called Saturnian, 365 days being "a year and a day") is exactly 52 weeks and 13 months of 28 days. Defining the original jubilee calendar of the Jews, the 364 day year preserves rituals as always on the same day of the week. The Jupiter synod of 398.88 days is 57 weeks whilst also 13.5 lunar months, a ratio of 9/8 the lunar year. In 945 days there are 135 (27 x 5) weeks, and so the harmonic relationships of these two outer planets is feeding back, through the numbers, into a calendar based upon weeks. One can even define the week as,
- 7 days = (Saturn(378) x 32 x 15) / (135 x 12 x 16 ) = Saturn(378) / 54
Conclusions
This brings me to some vital conclusions, relevant to all my work and that of others interested in the origins of esoteric number symbolism.
- The time periods surrounding Earth are remarkably numerically coherent with the implication that number must have been a causative in the arising of the synodic periods seen from Earth and their relationship to the Moon.
- That the time periods were coherent numerically is the likely reason the megalithic astronomers were able to achieve so much by using integer number methods, including triangular geometries, without modern mathematics or instrumentation
- That the numbers above then entered history via the ancient Near East to become the bedrock of their number symbolism in which the celestial bodies were considered gods, that is as the foundations of religious thought.
- Such apparently primitive ideas, based upon facts, have been dismissed by modern scientific thinking as arbitary or superstitious in origin.