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Full text of "The Lunar Context of the Hekat Fractions"

A REMARKABLE DISCOVERY affords conclusive evidence 
that the ancient Egyptian god Horus was not in fact the 
sun-god history contends, but rather a lunar theophany of 
the waxing crescent (in a schematized lunation). The other 
gods of the Egyptian pantheon prove, in turn, to represent 
the successive lunar phases. 

Myths of the various conflicts between Horus and Set 
involve destruction of the Eye of Horus (wadjet). In one 
myth Set tore the eye into six pieces which he scattered to 
the wind. The Ennead or Council of Deities directed Thoth 
to recover the parts and restore the eye. 

As Horus represents waxing crescent (which emerges on 
day 3 of the lunation), Thoth embodies waxing half-moon 
(occurring on day 9 in the cycle) - consecutive focal phases 
of the rising arc of the lunation, separated by six nights. 
The eye of Horus, in this respect, reflects the first visible 
phase of the new lunation - the first two nights of the cycle 
remaining dark without any moon in the sky - while the six 
pieces of the eye represent the six spectres of the concave 
quarter of the rising arc which fuse to form the half-moon 
(completing the reign of the concave spectres, before the 
throne of heaven is relinquished to the gods of the convex 
spectres of the gibbous quarter of the waxing arc). 

The six portions of the figurative eye were subsequently 
adapted as measures by Egyptian mathematicians - each 
part designating a signal fraction employed in the measure 
of volume (the hekat fractions). The portion of the cornea 
nearest the nose represented Vi and was associated with the 
sense of smell. The pupil signifying V4 represented sight. 
The eyebrow added Vs, inclined to thought. 

The outer portion of the cornea comprising V16, appears 
drawn to the sense of hearing. The falcon flange beneath 
the eye (toward the ear) designated V'32, directing attention 
to the sense of taste. While the figurative leg depending 
from the eye (toward the nose) comprised the fraction V64, 
partial to the sense of touch — as in 'touching down'. 



Addition of the hekat fractions, liowever, presented an 
inexplicable discrepancy: restoration of the Eye of Horus 
from the recovery of all the parts leaves y64 unaccounted 
for [Vi + V4 + V8 + V16 + V32 + V64 = ^3/64]. In the myth, 
the missing portion was ultimately supplied by Thoth, the 
god of just measure. 

There is something more to this equation, it turns out, 
than meets the eye of scholarly consensus. When applied to 
the length of the Egyptian month (30 days) the product of 
the assembled fractions relinquishes the length of the mean 
lunation, to within a minute [^V64 x 30 = 29.53125]. The 
length of the average lunation is currently calculated at 
29.530588 days; the difference between the modern and the 
putative Egyptian measures amounting to 57.1968 seconds. 

Somehow the Egyptians appear to have recognized that 
the difference between the calendrical expedient of their 
30-day month, and the actual length of the mean lunation, 
comprised a 64th of the month! 

The Eye of Horus, in other words, embodied two distinct 
lunar measures: the Egyptian month of 30 days (discrete); 
and the mean lunation (anatomized), which the Egyptians 
apparently calculated to extend 29 days 12 hours 45 minutes 
(our contemporary calculation 29 days 12 hours 44 minutes 
3 seconds). 

The leg symbol for the fraction V64, moreover, denoted 
'rest' and 'healing'. 'Rest', it now becomes clear, because the 
terminal fraction of the lunar equation required doubling 
- or 'resting at that point in the equation', to count it again - 
in order to complete the month and 'heal' the shattered Eye 
of Horus fully. 

It bears further notice that the terminal phase of the 
schematized lunation - waning crescent, represented by 
the Egyptian god Osiris - embodied a duplex count when 
two successive lunations were configured alternately as male 
(29-day) and female (30-day) months: the terminal phase 
counting as day 29 in the first and day 30 in the second. 



The waning crescent of the 30-day month, therefore, was 
to be equated with the missing 64th in the hekat equation, 
supplied by Thoth - a categorically underworld completion 
(in that it embodied an interval which could not claim to 
reside in the lunation, the actual source of time: because 
^3/64 of the 30-day month exhausted the lunation). An echo 
from the catacombs of the underworld goddess, Hecate... 

The equation of the hekat fractions - with denominators 
doubling - also prefigures the celebrated Paradox of Zeno 
(Zeno of Elea,/!. ca 460 bc): a sequence of successive half- 
measures extending to infinity without ever reaching their 
terminus (unity). 

The eyes of Horus have long been thought to figure the 
sun and moon, yet my research challenges the established 
reading. As the figure below illustrates, the Eye of Horus 
mirroring a second Eye of Ra, accords perfectly with twin 
full moons presiding over their respective arcs of lunation: 
Horus as waxing crescent representing the first visible phase 
of the waxing arc (which culminates with first full moon); 
and Ra as second full moon, the first phase of the waning 
half of the lunation. 

In the composition, Set figures as the first waning phase 
(mirroring Horus as his waxing counterpart) because the 
Eyes surveying their respective arcs embody the two full 
moons. Hathor between them - with two opposing horns 
to reflect the mirror-images of the opposing crescents - 
represents the two dark nights between crescents when the 
moon 'remains' in the underworld realm of the goddess. 
The winged disk above her configures a complete lunation. 

Thus the composition of Horus confronting Set may be 
reviewed as a depiction of 'first waxing spectre' figuratively 
complementing 'first waning spectre' - with opposing Eyes 
of Horus and Ra surveying their respective arcs of lunation 
from the pinnacle of the cycle: that of Horus oriented as 
'rising to its brightest light' (first full moon) and that of Ra 
'descending from its brightest point' (second full moon). 



OPPOSING ARCS OF LUNATION 



WANING OR SECOND FULL MOON 
EYE OF RA 



WAXING OR FIRST FULI 
EYF. OF HORUS 



WANING 
CRESCENT 




WAXING 
CRESCENT 



Few scholars realize that there are two apparent full moons 
every lunation or that the cycle begins with two dark nights 
without any moon in the sky. Thus the lunar key to ancient 
myth has remained obscure. Neither have they recognized 
that the seven focal gods represent the seven focal phases; 
nor that the alphabet is a serial mnemonic of lunar cycle. 

DAY LUNAR PHASE 

1 no moon 

2 no moon 

3 waxing crescent 
9 waxing half 

15 first full moon 

16 second full moon 

17 first waning 
23 waning half h 

29/30 crescent hae 

The figure of Horus and Set is a depiction of lunar cycle 
employing traditional iconography - feline trunks drawing 
on the lion as the symbol of half-lunation (as at Mycenee); 
& elaboration - papyrus crown {djet) conjuring half-moon, 
the phase ruled by Thoth {Djehuti). nick drumbolis 



OLYMPIAN 


EGYPTIAN 


LETTER 


ARTEMIS 


ISIS 


> 


1 




NEPHTHYS 


B 


2 


ARES 


HORUS 


C 


3 


HERMES 


THOTH 


G 


8 


APOLLO 


AMON 





15 


ZEUS 


RA 


n 


16 


POSEIDON 


SET 


Q 


17 


EPHvESTUS 


PTAH 


X 


22 


>ES/PLUTO 


OSIRIS 


double 



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