Hi Mark,

Thank you for taking the time to review my paper. I post on this forum and one other in order to discuss my ideas irrespective of whether the feedback is positive or negative. I've considered some of your commentary below.

Regards,
Brendan

Mark Heaton Wrote:
-------------------------------------------------------
> You have created a theory which has powerful
> argument against it.
>
> It is essentially the same as Piazzi Smyth's
> theory for which there is no documentary evidence,
> merely a construction of numbers based on pyramid
> dimensions, which is in stark contrast to my
> theory of Khafre's pyramid which is based on its
> harmony with documentary evidence in ways which
> have been overlooked.
>
> Piazzi Smyth remains famous and it seems many
> would like to become known for a Piazzi Smyth
> style theory, but careful to point out that Piazzi
> Smyth was wrong.
>
> The essence of Smyth's theory was that the the
> primary symbolism of the Great Pyramid was a solar
> symbolism, but there are stellar aspects.
>
> You need to study 'The Pyramids of Egypt' by
> I.E.S. Edwards where the same case is made but
> based on a proper study of documentary evidence
> with no reference to Saturn.
>

This comment, in my opinion, means that I have not provided the context for "Why Saturn" to the extent necessary to support my model. In addition to the Westcar Papyrus analysis presented in my paper, there is one further avenue for the Saturn theory that I am aware of. The notion of the Pharaoh being a planet-twin is suggested by Belmonte and Shaltout (2005, pp7-8) and this notion is demonstrated in the astronomical ceiling of Senenmut, as well as the Karnak Clepsydra which is dated to the reign of Amenhotep III. I wrote to Belmonte to query whether he had undertaken any further study of this concept. His response was that in his view, the Pharaoh either male, or female was a manifestation of Horus, as were the planets. Belmonte and Shaltout present the argument that instead of a scribal error, this is the reason that Saturn was styled as "Mother of the Bull of the sky" instead oe the usual "Bull of the sky" as the reigning Pharaoh was Queen Hatshepsut and a female Horus cannot be a bull. Reviewing the photos presented in Belmonte and Shaltout's paper of Senenmut's ceiling, the Pharaoh-Planet connection seems obvious with Hatsepshut's Horus name appearing alongside both outer planets (Saturn and Jupiter). The dates at circa 1475BCE to 1450BCE would be far later than the Old Kingdom relevant for Khufu's pyramid.

I have discussed in my paper, Brugsch belief that the "Stier des Himmels" or "Bull of the sky" found in the pyramid texts of the fifth dynasty is Saturn. The context in the Pyramid Texts in which the "Bull of the Sky" is found is as follows:

Quote
James P Allen, The Pyramid Texts of Ancient Egypt, p44
Look, she is coming, the beautiful West, to meet you, to meet you with her beautiful tresses, and she is saying: “Welcome, you to whom I gave birth, with rising horn, eye-painted pillar, bull of the sky: your form is distinguished; pass in peace, for I have joined you”—so says the beautiful West about Unis.

Quote
James P Allen, The Pyramid Texts of Ancient Egypt, p45
Unis’s heart is pleasant, [TWICE]. Unis is the unique one, bull of the sky, for he has removed those who would do that against him, for he has annihilated their survivors.

Quote
James P Allen, The Pyramid Texts of Ancient Egypt, p45
Do not be ignorant of Unis, Sky Bull, since you know him and he knows you. Do not be ignorant of Unis, Sky Bull, who calls you This One Who Endures.

In these quotes, the Pharaoh Unis is being equated with the "Bull of the sky", or is expected to be familiar with, or know the Bull of the Sky. Following Brugsch suggestion that the Bull of the Sky of the Pyramid Texts is Saturn, the Pharaoh Planet connection identified by Belmonte and Shaltout would appear to have existed in the Old Kingdom. It must be noted that Brugsch who was the first to identify the individual planets identified Saturn as "Horus, Bull of the Sky" from texts from later periods and he did not elaborate on why he believes the Bull of the Sky of the Pyramid Texts to be Saturn. There is therefore some ambiguity in this result. Nonetheless, a connection between the Pharoah and the planets seems to me a valid option to explore given Senenmut's ceiling, the Karnak Clepsydra and the possible example in the Pyramid Texts.

Reference:
Juan Antonio Belmonte and Mosalam Shaltout, “The Astronomical Ceiling of Senenmut: a Dream of Mystery and Imagination”, SEAC2005 Proceedings on “Light and Shadows in Cultural Astronomy” Edited by Mauro Zedda and Juan A. Belmonte, Cagliari (2005)

Note: in order to be consistent with James P. Allen's Pyramid Texts translations, in the discussion above, I am using "Bull of the Sky" rather than the more commonly used translation of "Bull of Heaven" for Saturn.

> Piazzi Smyth proposed that the perimeter of the
> walls of the King's Chamber could be regarded as
> the circumference of a circle and the length of
> the chamber as its diameter.
>
> This proposition was accepted by Petrie, developed
> by me, as noted in this topic, and then accepted
> by Egyptologists such as Dr D.Lightbody.
>
I vaguely recall having read up on this model. Petrie also championed the idea that Khufu's pyramid embodied pi as simplified to 22/7. Corinna Rossi (2003), p87 rejects knowledge of pi and phi.

Quote
Corinna Rossi, ARCHITECTURE AND MATHEMATICS IN ANCIENT EGYPT, p87
"Their presence in the plans of ancient buildings is mainly due to our modern inter- pretation of the geometrical figures that compose the plan on paper. However, I am not arguing that mathematics was not involved in ancient Egyptian architecture, but rather that so far we have analysed cases in which the wrong mathematical system was adopted."

With respect to the limits of my exploration of this topic, I have used the accepted metrics of Cubits, Palms and Digits. However, the inference is made, since the numbers as measured in Egyptian units appear to match the algorithms developed for the synodic arc as well as the synodic timing of Saturn, that the Egyptians created, or inherited knowledge of the division of a circle into degrees. This is the big potential falsifier of my model in my opinion.

Rossi, C., ARCHITECTURE AND MATHEMATICS IN ANCIENT EGYPT, Cambridge University Press, 2003

> Smyth's connection to the size of planet Earth is,
> of course, a coincidence, just like your
> connection to another planet which Smyth might
> well have derided with glee in a ruthless way had
> you been alive 140 years ago, as was his way with
> those who chose to oppose his theories by way of
> counter theory. Don't expect Egyptologists to
> warm to your theory just because you reject
> Smyth's theory, because it does raise the profile
> of your theory as rather like Smyth's theory. So
> forget about Smyth for your academic paper, and
> save such philosophy for a forum such as this.
>
I don't really expect people to warm to the idea as it is somewhat outside the expected comfort zone of solar religion. However, lets discuss the evidence and facts.

>
> There was little wrong with Smyth's arithmetic,
> but no reason to connect the Great Pyramid to the
> size of the Earth, or to the matter you raise, the
> cycle of Saturn. You have disproved your own
> theory in your own counter argument because the
> numbers, even if a precise fit, do not pass the
> test of a reasonable historical theory..
>
> The ancient Egyptians were most interested in the
> cycles of the sun and the moon, not Saturn which
> has no effect on the cycles of the seasons. Saturn
> is not a sensible basis for a calendar to regulate
> life on earth. It was just regarded as a WANDERING
> star, with the derivation of the word PLANET from
> the Greek, so of little consequence even if the
> ancient Egyptian did track its cycle.
>
I don't make any claim that Saturn was used as a yearly calendar. It is possible that it was used as a marker for a longer time period. I have discussed the possibility that it was used to mark the timing of the Sed Festival. However, I concede this portion of my hypothesis is far from proven.

> Some years ago I spoke to an expert on Babylonian
> astronomy, Dr J. M, Steele. He is now a professor
> of Egyptology, and you may care to read his
> publications as a scientist.
I have read a number of papers by Steele on the topic of Babylonian Astronomy. However, none were relevant to the topic of my paper and as such were not cited.

>
> For a better understanding of Ancient Egyptian
> mathematics can I suggest you read the papers of
> professor T. Eric Peet? Last year an academic
> paper noted that but for his premature death Otto
> Neugebauer (who consulted Peet) might not have
> become so famous in this field. You claim that
> Otto missed what you have seen, but actually Eric
> would have cautioned both of you not to read too
> much into how ancient mathematics was understood.
>
In this context, all that needs to be established is that the basic properties of arithmetic progressions were known. The underlying method to the solutions to the Rhind Papyrus examples provides evidence for such. The Egyptians were able to divide a quantity of material goods into an unequal series in arithmetic progression. This is borne out in the examples discussed in Chace. Gillings also makes mention of the examples. Legon discusses a similar example in the Lahun papyrus fragments. Similarly, the length of the monthly scales of the Karnak Clepsydra form two arithmetic progressions - one ascending and one descending, demonstrating an example where a zig zag function is used to model a time variant process.