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Ockham-Aten's Razor

 
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Khuy-n-inpw
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PostPosted: Tue Jul 22, 2008 4:22 pm    Post subject: Ockham-Aten's Razor Reply with quote

If the Akhet was the region between day and night, and the new capital of Amenhotep IV was called Akhet-Aten, could this imply a recognition that the sun was always overhead at some place on the earth, even when it appeared to set?

The Great Royal Road at Akhetaten runs North to South, with a deviation of about 10°. Could this have been an early attempt to establish a meridian?

The reason I ask these questions is because, if Akhenaten wanted to eradicate all the weird beings described in texts like the Amduat and the later Book of Gates, and replace them with one sun-disk on which everything else depended, then this would argue for a major revision and simplification of ancient Egyptian geography, particularly with reference to the so-called ‘underworld’.

I would further like to suggest that Akhenaten did not just dream all this up one day, but that these conclusions were borne home to the rulers of Egypt as a result of its increasingly international presence during the NK.

In any case, that’s the way things are, isn’t it? Even allowing for the difference in the location of the north celestial pole at that time, a star like Kochab (β Ursae Minoris) would not have set at the latitude of Thebes (some 25° 40’). If they followed its path through the heavens and compared it with that of another star, such as Merak (β Ursae Majoris) which I think would have set, briefly, they would have seen at a glance not only that the whole sky appears to wheel around, but that the phenomena of rising and setting are connected only with what we now call the declination of a celestial body.

Surely a mind like that of Akhenaten, not overly cluttered with complex superstitions, would have seen all this without difficulty.
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PostPosted: Fri Jul 25, 2008 11:54 am    Post subject: Reply with quote

Khuy-n-inpw wrote:
Even allowing for the difference in the location of the north celestial pole at that time, a star like Kochab (β Ursae Minoris) would not have set at the latitude of Thebes (some 25° 40’). If they followed its path through the heavens and compared it with that of another star, such as Merak (β Ursae Majoris) which I think would have set, briefly, they would have seen at a glance not only that the whole sky appears to wheel around, but that the phenomena of rising and setting are connected only with what we now call the declination of a celestial body.

Here are some corrections and refinements of the above.

If we assume that around 1300 BCE the North celestial pole lay at what is today a Right Ascension of about 13h 30’ and a declination of some 72°, then over a flat horizon, the star Merak (β Ursae Majoris) would not have set, as its then declination was some 67° (i.e. 90° - 23°)

A better star to consider is Taïs (δ Draconis), which at a 1300 BCE declination of about 62° (i.e. 90° - 28°) would have set at the latitude of Thebes, but would not have set at Memphis (latitude 30°N).

Thus, to an observer in Memphis, the star Taïs would have remained ‘imperishable’ and would never have disappeared below the horizon, whereas to an observer in Thebes, it would presumably have entered the Underworld with all its plethora of deities and serpents. Furthermore, Taïs is by no means unique in this way. Any star lying between the (then) declinations 60° and 64° 20’ would have exhibited the same contradictory behaviour.

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PostPosted: Fri Jul 25, 2008 2:51 pm    Post subject: Re: Ockham-Aten's Razor Reply with quote

Khuy-n-inpw wrote:
If the Akhet was the region between day and night, and the new capital of Amenhotep IV was called Akhet-Aten, could this imply a recognition that the sun was always overhead at some place on the earth, even when it appeared to set?

The Great Royal Road at Akhetaten runs North to South, with a deviation of about 10°. Could this have been an early attempt to establish a meridian?


I would think not. The layout of Akhetaten is based upon the sunrise and sunset upon the two mountains which encapsulate the city and by which the king defined the boundaries of his city with his boundary stela.

The area which was referred to in ancient times as Akhetaten represents one of the most textually described cities in Egypt, as to its religious origins, its parameters and monuments. Fourteen boundary stelae formed the boundaries of this city, each inscribed with the king’s orders on how the city was to be constructed. Yet while these stelae have been studied as to position in defining urban space, artistically and linguistically as dating tools, and textually as reflection of Akhenaten’s politico-religious position, it is also important to view how these stelae came to be placed in such a way to define the city’s limitations or use as a definition of a cosmological viewpoint of sacred and profane space.

Some definitions are in order. When I refer to the “horizon mountain,” this means the mountain which Akhenaten literally called the “Horizon of the Aten,” located on the east bank of the Nile, with the long wadi leading to the Royal Tomb. By its “orient” side, Akhenaten was referring to its east side, according to Murnane and van Siclen. When I refer to the “sunset mountain,” of Akhetaten, it is a shorthand term for the western mountain across the Nile on its west bank, opposite from the horizon niche, which appears, in later stelae proclamations to also have ritual significance as well.

The stelae which remain give us indications of how the sacred space of Akhetaten was defined. In the primary proclamations, Stelae X, K and M, Akhenaten lays out the breadth of the city along its north-south borders. He is also particular to discuss how the land to the east of the horizon niche is to be used – primarily for tombs of the Royal Family, the Mnevis bull, and the tombs of the “Greatest of Seers, God’s Fathers of the Orb (and)…tombs of the prophets (?) of the Orb be made in the orient mountain of the Horizon of the Orb…” (Murnane and van Siclen III. 1993: 41, citing Stela K:20). Location of festival offerings are also designated as being away from the northern and southern crags of the mountain range which encircle the city (Murnane and van Siclen III. 1993: 43, citing X:31 and M:32), but they are said to be placed within the deity’s “…[favourite] place [daily in the course of] every [day]…” (Murnane and Meltzer 1995: 79), which hearkens back to the initial sighting of the Aten when he “hovered” over his offerings at the noon hour as described in the earlier section of the proclamation recounted in Stela K. As such, it seems reasonable to assume that all orientation of the city will come from the god’s perspective rather than the traditional cardinal positions and the course of the sun from the east to the west will determine the definition of the sacred space, suing the more traditional means of right-hand of the god (thus, east of the Horizon niche, in magnetic north) as having status defining the sacred/prestige status areas, as defined by the king in his tombs placement plan.

This "circling" of the city can be seen below, with sunrise and sunset both touching 7-9+ of the boundary stelae at any one time:





This orientation of the city with sunrise and sunset, and particularly with the orientation of the Great and Small temples to the Aten being oriented towards these positions has been discussed in several articles on Amarna, the best being

Mallinson, M. 1989. Report on the 1987 Excavations of the Small Aten Temple. In B. J. Kemp, Ed., Amarna Reports, V: 115-142. Occasional Publications 6. A. B. Lloyd. London: Egypt Exploration Society.

__________. 1995. Excavation and Survey of the Central City, 1988-92. In B. J. Kemp, Ed., Amarna Reports, VI: 169-217. Occasional Publications 10. A. B. Lloyd. London: Egypt Exploration Society.

The location of the family palace in the north is traditional: the north wind is considered the most cooling and refreshing, and numerous texts, including a few found in Tutankhamun's tomb, discuss its bracing effect as "life-giving."

In choosing a place for his new deity to have his own estate, Akhenaten founded a city which was located in the very centre of the country, as a unifying point between Lower and Upper Egypt (Goyon 1998: 168). Placement of Stelae K and X, which formed the original north-south boundaries of the city, augments Goyon’s theory of the “centredness” as a conscious choice when one considers that centrality and symmetry of Akhetaten were defined from the outset, when the king heads down what was later to be the Royal Road toward Akhetaten, and makes his initial offering to the Aten towards the “monument he (the Aten) made for himself, his horizon, [in which his] circuit came into being…” (Murnane and Meltzer 1995: 74) which appears to have been the natural niche at the centre of the mountain range enclosing the valley. The timing and location of the offering seem recounted with clarity:

‘One rejoiced and the heart [of this god] was joyful [concerning] Akhet-Aten with exultation as he hovered over [his] place, so he could be glad concerning it and about the elevating of his beauty…’ (Murnane and Meltzer 1995: 74)

If one accepts this description as referring to the sun’s direction and timing, then the sun would have reached its zenith at approximately noon of the day (the “elevating of its beauty”) and would have been located, from its horizon niche point in the eastern mountain, to approximately the centre of the valley, or approximately at the location of the Great Altar of the eventual Small Aten Temple. This monument has been shown archaeologically to have been the earliest temple monument built at Akhetaten, likely in commemoration of this event (Mallinson 1989: 117-119). The centrality of this edifice with the mountain’s horizon “niche” was also noted by Mallinson as a significant feature of the landscape (Mallinson 1995: Fig. 5.26a).

While comparison of Akhetaten’s monument layout with Theban Karnak and its environs is instructive, the plan for this city differs from that city by reversing orientation of the necropolis from the west to east bank of the Nile and by placement of its processional way from north to south in reversal of the Theban model (Mallinson 1995: 204-205, 214). What may be of ultimate interest in considering the Theban model in discussing Akhetaten’s layout is how the Small Aten Temple maintains the same orientation position as the Theban temple of Karnak during the reign of Amenhotep III, though in a reversed realization at Akhetaten. Further, this edifice serves as the “heart” of the city’s design, even more that the Great Temple. As Mallinson notes, it is quite possible that it was Akhenaten’s intention to combine Karnak’s features (though not its orientation) as a model for Akhetaten, albeit in a compact format, and imbuing it with similar religious connotations (Mallinson 1995: 205).

Visually, this theory of "enclosure" seems borne out by the imagery on the boundary stelae and their orientation, as can be seen in Figure 1. Thus, one can see in the lunettes of the east bank stelae – X, V, K, M, J, and N – where the direction of the royal family at worship is always facing toward the eastern horizon niche (Fig. 1a) – that is, until Stela U, located at the mouth of the horizon niche on the east side of the horizon mountain.


Fig. 1a

There the royal family face left, inward towards the eastern side of the mountain, thus closing off by body imagery, the orient side of the city (Fig. 1b).


Fig. 1b

If we accept that the orientation of the city is to be seen from the deity’s perspective and utilizing O’Connor’s arguments of the north/south orientation of the Great Palace as significant indicator of its cultic use (O'Connor 1995: 288-289), then the “right-hand” of the god orients this side of the city as the sacred section, while the south defines its secular section.

Similarly do the boundary stelae on the west bank point to a “closing off” of the city’s borders towards a niche in the western side of that mountain, with Stela A, facing the river, showing the royal family worshipping towards this niche, which is “opened” by a mirror-imaged stela (Stela B) (Fig. 1c).


Fig. 1c

This stela may have had a twin (possibly a Stela C?) on the other side of the western niche, and in line with the symmetry this areas follows in a somewhat straight line from the horizon niche of the eastern mountain, through the Small Temple of the Aten, to complete the sun’s pathway into this niche on the western side (see Figure 2).



It has been noted that in the post-Amarna period, the previously north-south orientation of tombs (reflecting the sun’s nocturnal path through the underworld), is changed during the 19th and 20th dynasties to an east-west orientation, following the sun’s observable journey through the day (Wilkinson 1995: 76). While this by no means proves the above theory in full, the change in orientation may be a reflection of Amarna theology becoming incorporated into traditional religious beliefs.

Therefore, if the emphasis upon east-west movement is first started during the Amarna period, when combined with the traditional north-south orientation of the king’s buildings creates a two-fold religious statement in which the king can be said to rise from his northern location (the north Riverside Palace), and move through the sacred section of the city to “meet” the deity at his zenith at noon at the point of their first revelation to one another at the Great Altar of the Small Aten Temple, as described in Stela K:

‘After this were performed the rites of the Orb, who was [satis]fied with what was done for Him…And his [Majes]ty was in the presence of his Father THE ATEN, the rays of the Orb being upon him in life, [dominion, health and joy (?) fore]ver and ever.’ (Murnane and van Siclen III. 1993: 37)

This hypothesis of meeting the deity at noon-time for a form of “merging” with the god seems supported by not only the mirrored imagery of the stelae lunettes, but also by the complaints of the Assyrian foreign delegation who complain about the emissaries being forced to stand about in the sun at its zenith:

"If it does the king good stand in the open sun, then let the king stand there and die in the open sun. Then there will be profit for the king! But really why should they (the Assyrian messengers) die in the open sun?...They will be killed in the open sun!" (Redford 1984: 235)

So, with this double orientation in mind, it would seem that O’Connor’s suggestion that not only the buildings and monument of Akhetaten provide political propaganda to the regent in identifying with his new god, but that the orientation of the natural landscape is skewed to toward merging the two entities into one icon for the populace. As O’Connor notes, if the identification is made that the king travels from his northern point through his sacred city southward to merge with the Aten travelling from east to west from his “palace” to his other resting point in the western niche, then each will likewise partake of each other’s power as envisioned later in the Litany of Re, where Re merges with Osiris, and each become rejuvenated (O'Connor 1995: 289-290). In essence, Akhenaten imbues the Aten with royal authority, just as the Aten endows the king with divine power and authority through their merging at the meeting point of the Great Altar, in a manner Assmann has referred to as a “constellative” relationship (Assmann 1989: 68; Assmann 2001: 78-79).

Reference:

Assmann, J. 1989. State and Religion in the New Kingdom. In W. K. Simpson, Ed., Religion and Philosophy in Ancient Egypt: 55-88. Yale Egyptological Studies (YES) 3. W. K. Simpson. New Haven: Yale University Press.

_________. 2001. The Search for God in Ancient Egypt. Ithaca: Cornell University Press.

Goyon, J.-C. 1998. Rê, Maât et Pharaon, ou le destin de l'Egypte Antique. Collection Egyptologie. Lyon: Edition A. C. V.

Griffis-Greenberg, K. (forthcoming) “Aten being in festival eternally…” The definition of sacred space within Akhetaten.

Murnane, W. J. and E. S. Meltzer 1995. Texts from the Amarna Period in Egypt. Society of Biblical Literature: Writings from the Ancient World Series 5. S. B. Parker. Atlanta: Scholars Press.

Murnane, W. J. and C. C. van Siclen III. 1993. The Boundary Stelae of Akhenaten. Studies in Egyptology. A. B. Lloyd. London: Kegan Paul International.

O'Connor, D. 1995. Beloved of Maat, the Horizon of Re: The Royal Palace in New Kingdom Egypt. In D. O'Connor and D. P. Silverman, Eds., Ancient Egyptian Kingship: 263-300. Probleme der Ägyptologie Bd. 9. W. Helck. Leiden: Brill.

Redford, D. B. 1984. Akhenaten, the Heretic King. Princeton: Princeton University Press.

Wilkinson, R. H. 1995. The Motif of the Path of the Sun in Ramesside Royal Tombs: An Outline of Recent Research. JSSEA XXV: 78-83.

HTH.
_________________
Katherine Griffis-Greenberg

Doctoral Candidate
Oriental Institute
Oriental Studies
Doctoral Programme [Egyptology]
Oxford University
Oxford, United Kingdom
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PostPosted: Sat Jul 26, 2008 10:20 am    Post subject: Reply with quote

Here is some additional information which is open to further analysis:

Latitude of Akhetaten ≈ 27.73° N (I would be particularly interested in more exact data on this)

Let A = azimuth of sun at rising and setting, δ = declination of sun, φ = latitude of observer

Then cos A = sin δ . sec φ (this is a standard formula: see e.g. W. M. Smart (1965) Spherical Geometry, 5th ed.)

Summer Solstice, declination of sun = 23.5°
cos A = sin(23.5°) . {1/(cos(27.73°))} = 0.45049
cos´¹(0.45049) = 63.23º
At the summer solstice, the sun would rise at N 63.23º E and set at N 63.23º W

Winter Solstice, declination of sun = -23.5°
cosA = sin(-23.5º) . {1/(cos(27.73°))} = -0.45049
cos´¹(-0.45049) = 116.77º
116.77º-90º = 26.77º
At the winter solstice, the sun would rise at E 26.77º S and set at W 26.77º S

This is the range of bearings within which the Aten would have been seen to rise and set during the course of the year.

Using the maps of Amarna kindly provided by neseret, and centring a protractor on Akhetaten Central City, we find that the angles with the centres of the orange orbs are about E 8º S at rising and N 72º W at setting.

In order to ascertain the day or days of the year which these angles represent, we must find the sun’s declination. Thus:

sin δ = cos A / sec φ = cos A . cos φ

At rising: sin δ = cos(98º) . cos(27.73º) = -0.12319

δ = sin´¹ (-0.12319) ≈ - 7 º The sun is at this declination twice every year, on about what is for us 8th March and 8th October. As I understand it, the issue of precession would not affect this result, as the disposition of the ecliptic itself is not affected.

At setting: sin δ =cos(72º) . cos(27.73º) = 0.27353

δ = sin´¹(0.27353) ≈ 16º The sun is at this declination twice every year, on about what is for us 10th May and 10th August.

I realise that the calculations presented here are not particularly attractive for non-mathematicians, but they do not use anything more demanding than simple high-school trigonometry adapted to a set formula in spherical geometry.

The point of it all is this:

1. By the use of the standard formula, and knowing the exact latitude of Akhetaten Central City, it is possible to calculate the exact co-ordinates of the sun at rising and setting on any day of the year, and compare them with the geography of the surrounding horizon. In these calculations, ‘north’ refers to the direction of the celestial north pole, not magnetic north, so if the difference was thought to be significant, a correction would need to be made.

2. The lines shown on the maps provided by neseret (after Mallinson?) are specific for the approximate dates I have calculated, but would of course need to be re-drawn for other dates, particularly the equinoxes and solstices if these were considered important in the Atenist system. Put simply, the Aten’s position relative to ‘horizon mountain’ and ‘sunset mountain’ would vary steadily over the year. This is particularly interesting in respect of the niche point in the eastern mountain, which, if shown correctly on the first map, suggests that our 8th March and 8th October may have been significant dates at Akhetaten.

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PostPosted: Sat Jul 26, 2008 1:30 pm    Post subject: Reply with quote

Errata

Khuy-n-inpw wrote:
Smart (1965) Spherical Geometry, 5th ed.
should read:
"Smart (1965) Spherical Astronomy, 5th ed., sections 5 ( pp.6-8 ) and 31 ( pp.46-47 )"

Khuy-n-inpw wrote:
the Aten’s position relative to ‘horizon mountain’ and ‘sunset mountain’ would vary steadily over the year.
should read:
"the Aten’s position relative to ‘horizon mountain’ at sunrise and ‘sunset mountain’ at sunset would vary steadily over the year."

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PostPosted: Sat Jul 26, 2008 2:15 pm    Post subject: Reply with quote

Further Errata

Khuy-n-inpw wrote:
"Smart (1965) Spherical Astronomy, 5th ed., sections 5 ( pp.6-8 ) and 31 (pp.46-47)"
best as:
"W. M. Smart (1965) Spherical Astronomy, 5th ed., Cambridge University Press, sections 5 ( pp.6-8 ) and 31 (pp.46-47)"

Khuy-n-inpw wrote:
This is particularly interesting in respect of the niche point in the eastern mountain, which, if shown correctly on the first map, suggests that our 8th March and 8th October may have been significant dates at Akhetaten.
should read:
"This is particularly interesting in respect of the niche points in the eastern and western mountains, which, if shown correctly on the maps, suggest that our 8th March, 8th October, 10th May and 10th August may have been significant dates at Akhetaten."

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