horizon-theory-Section-3

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ARCHITECTONICS

From Cosmic Theories to Urban Development

Dr. Hossam Aboulfotouh

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The Horizon Theory, Part-I: Original Concept Plan Of The Pyramids Plateau

Hossam M. K. Aboulfotouh, PhD*

* Assistant Professor, Architectonic Cosmic Theories and Development, Department of Architecture, Faculty of Fine Arts, Minia University, and Director, WPAHR-V, International Union of Architects-UIA. fotouh@mail.com

Section-3: The Scenario Of Assumptions: The Sun as a Source of Astronomical Knowledge.

To date, Egyptologists did not find any scientific papyrus8 on the ancient Egyptian astronomy. Therefore, today's scientists believe that the contributions of ancient Egyptians in this field were very limited. Although the design of the temple of Abu-Simple and the diagram of constellations (zodiac} of Denderah temple lack the astro-mathematical formulas that support their perfect designs, today's scientists consider them as products of skilled astronomers. However, some astronomer believe wrongly that the latter was designed during the Hellenistic period, On the other hand, other than the false assumption of adjusting the tilt of the great pyramid's entrance-passage to point to the North-Star, Giza pyramids in general have no other signs in relation to spherical astronomy that could be noticed by normal observation. Besides, some of the nowadays scientists do not accept the idea of using modern astronomical theories to analyze the pyramid's concept. This is because they do not believe that the architects of ancient Egypt were excellent astronomers. In addition, they can hardly follow the advances in astronomical sciences during the three millenniums before the days of Pythagoras (approximately 550BC). They were stack with the problem of defining which theory has been discovered first.

Therefore, this part of the paper is an attempt to retrieve some astronomical principles that might have been used in the design of the horizon of the three pyramids in Giza plateau. This retrieval process will be based on establishing a hierarchy of basic-assumptions that together may form a logical scenario. The validity of that scenario will be tested quantitatively, by linking its likely accumulated knowledge with the geometric survey data of the site-plan of the three pyramids in Giza plateau.

As a point of departure, assume that pyramids were the outputs of deep thoughts of architects who studied not only some sort of architectural curriculum9 but also astronomical sciences, e.g., spherical astronomy. Then, a question might be asked: how to retrieve their scenario of searching on spherical astronomy? Of course, the retrieval attempt should be supported with both the basic information and the documented history of spherical astronomy10. However, this basic information should be kept in mind to be only a scientific reference for guiding the retrieval process without affecting the logical hierarchy of the flow of knowledge to the ancient architects.

Logically, their original source of astronomical knowledge should be defined first, presuming that they were working only during the daytime11. Without doubt, in their days, the sun was the only possible source of astronomical knowledge during the daytime. Then, one more question should be asked: how they extracted information from its observed but indirect daily motion12, with the use of primitive tools? Probably, their scenario was based on recording, in each day of the year, the changes in both positions and lengths of the shadow of a vertical post that was standing on a leveled ground. It is known today that, the observed daily motion of the sun has an array of two basic quantities that were, and still are, used in the field of architecture. The first is the quantity of the daily horizontal angle of sunrise13 (or sunset) that architects have used to measure it from the east (or west) coordinate-direction of the place. The second is the quantity of the daily vertical angle of the sun, when the sun meets, or being at, the meridian of the place14. Their scenario for measuring and recording these angles, during the daytime, might was consist of four steps, presuming that they were able to put tasks in order. Firstly, marking on a leveled site15 that its perimeter was circular in shape, and that was a small horizon-model similar to the natural observed horizon, the frequent positions of the end of the shadow of a vertical-post (like an obelisk) that was standing at its center. Secondly, the identification of the two-coordinates of the place by following the method that will be mentioned in the next paragraph. Thirdly, measuring and recording the values of the horizontal-angles of sunrises and sunsets. Fourthly, measuring and recording the values of the sun's vertical angles, when the sun was meeting, or being at, the meridian of the place, as shown in figure-1 & figure-2.

Most likely, they were identifying the true geographic north16 at any place, by using the shadow of a vertical post (like obelisk). In fact, the daily process of marking the end of the shadow of the vertical post draws, an extrovert or introvert, semi-hyperbolic curve on a leveled ground; taking in consideration that each day of the year has a specific curve. The true geographic north-south axis might have been identified then as the line that divided, into equal parts, the angle between any two shadow-lines of equal length that were measured from the vertical post (obelisk) to the marked curve, as shown in figure-3.

Figure-1: The vertical angles of the Sun, when it meets or being at, the meridian of the place. The angles, from left to right: the summer solstice, the vernal equinox and the winter solstice (looking towards the west).

Figure-2: A horizon's plan shows the horizontal angles of sunrises, from top to bottom, on summer solstice and on winter solstice. Between these two extremes, the sun goes back and forth during the year, having a specific sunrise angle for each day of the year.

Fig: Identification of the true geographic north.

If they were doing the above four steps for years, they might have established an array of yearly records that could be compared in order to draw-out additional results and conclusions, presuming also that they were knew how to do comparative analysis. Then, if they were well versed, they might have recognized that those angles were changing every year. Based on the nowadays' astronomical knowledge, sunrise or sunset angles of both summer and winter solstices are decreasing, the meridian angle of winter solstice is increasing and the meridian angle of summer solstice is decreasing. However, in their days, they could have noticed the accumulated sum of yearly changes only after several decades. Concerning the meridian angle on winter solstice, at the latitude of 30°, the shadow of a 20m-height obelisk would be increased by almost one centimeter after 75 years. They might have noticed too that the sun was rising from the exact east-direction and was setting to the exact west-direction in only two days of the year, which are known today as the two days of the equinoxes.

Concerning the calculations, suppose that they were untaught about calculating the quantity of angle17. No doubt, they could have got the same results by using only the trigonometric ratio of the tangent. The array of tangent ratios would have been enough in order to get the similar hierarchy of relative quantities, as in the case of using the quantities of angles. The mathematical papyri18 of the ancient Egyptians show that, during the new kingdom, they were able to get the breakdown of any ratio, which was the base for comparing fractions of numbers, similar to the nowadays system of comparing decimal numbers. However, the architecture of that period was not as sophisticated as that of the pyramids and thus, mathematics during the old kingdom must was better or at least equivalent to that of the new kingdom.

Moreover, while they were comparing their results, they might have noticed too that, in each year, there are days that have the same values of sunrise angles. If that had happen, then it is likely that they discovered the fact that the sunrise angles of many days during winter (and spring) were equal to the sunrise angles of other days during autumn (and summer); and the order of this array of two matching days (the twins days) was not changing. Then, if they were numbering their days that might were starting from the moment of sunrise and began with the sunrise of the vernal equinox (March 21), they might have established a table of daily sunrise-orientations. The original orientation of the axis of the temple of Abu-Simple, before its relocation, proves that its architect knew that the sunrise angle of the day number 215 (October 21) was precisely matching the sunrise angle of the day number 338 (February 21). It is ridiculous that the astronomical scientists who supervised the relocation project of that marvelous temple during the sixties of the last century, were not able to conserve the prime astronomical orientation of that temple, and made unforgivable mistake by changing the dates to October 22 and February 22 with a shift of two days, i.e., October 22 is the twin of February 20, and October 20 is the twin of February 22.

Furthermore, if they were doing the same experiment at other places in the Delta and along the river Nile and were comparing the data of these places, they might have noticed two facts concerning the quantity of the meridian angle of the sun during the equinoxes. First, it was changing as they were moving along the south-north direction. Second, it was not changing as they were moving along the east-west direction. If this supposition was correct, then they might have used this fact to establish a system of east-west geographic axes or latitudes19. However, it should be taken in consideration that if they were untaught about that the earth is spherical in shape, then their east-west geographic axes might have been named after the quantities of the meridian angle of the sun on the vernal equinox. Their number for the latitude of Giza plateau might was 60°; today's astronomers are using its complementing quantity 30°.

Likewise, if they were comparing the values of the meridian angles of the sun during the summer solstice, during the winter solstice and during the vernal equinox, they might have noticed other fact. That is, the value of the meridian angle during the vernal equinox was always the median between the values of the two extremes, during winter and summer solstices. To explain this based on the nowadays' astronomical information, the meridian angle of the sun during the summer solstice is equal to its value during the vernal (or autumnal) equinox plus the value of the obliquity20 angle of the earth. Astronomers of these days said21 that "the obliquity of the earth oscillates between 24.30° & 21.91° within a period of forty thousand years; its current quantity is 23.44° approximately, in the descending path, which diminishes by 0.47 arc-second per-year. Accordingly, today, in Cairo the meridian angle of the sun during the summer solstice has a quantity of 83.44° approximately (equal to 60° plus 23.44°). On the contrary, the meridian angle of the sun on winter solstice is equal to its quantity during the vernal equinox minus the obliquity angle of the earth. Accordingly, today, in Cairo the meridian angle during the winter solstice has a quantity of 36.56° approximately (equal to 60° minus 23.44°).

Based on the results that were concluded through doing the previous experiments, they might have also known how to measure the time and define the year. Apparently, they defined their year as a cycle that contains 365 sunrises. It may was starting at the sunrise of the vernal equinox. In addition, probably, they used the quantities of the meridian angles of the sun on the summer solstices as a tool in order to record specific moment in their history.

To conclude this part, the above scenario of assumptions shows that the ancient Egyptian architects, priests and Jedars, could have been able to know the basic astronomical knowledge via recording the observed daily motion of the sun, using the primitive tools. The third part of this research is an attempt to prove that they used this knowledge as design-principles in order to formulate the contents of the first coded file in the horizon of the three pyramids in Giza plateau.

Notes:

8- Ancient Egyptians were recording their sacred sciences on papyrus that may have been used only by the scientists; perhaps, recording sacred sciences on walls or on stones for the general public was prohibited.

9- Al-Maqrizie (1364-1442 AD) the Great Egyptian historian said: "there were seven schools in ancient Egypt. Each school was for specific field and called after one of the seven moving stars: the Sun, the Moon, Mercury, Venus, Mars, Jupiter and Saturn. The study at each was lasting for seven years, and each of their graduates was called Baher (Brilliant). The scientist who graduated at the seven schools, who spent 49 years of study, was called Quater (Master); his respectable status was just below the king of Egypt." (Al-Maqrizie, Bolaque edition, 1849, Vol. I)

10- Such as: (Olaf Pedersen, 1993), (Carlo Nallino, 1993) & (A. Weigert & H. Zimmermann, 1990)

11- The same scenario could be done at nighttime, during the nights of full moon, from the moment of moonrise until the moment of moonset.

12- The earth rotates around the sun, but the observer from the earth sees the opposite of reality; he sees the sun in an indirect motion.

13- The moment at which half of the sun disk being above the tangent line of the observed horizon. It is also the moment at which the centerline of the sun being the tangent of the plane of the horizon.

14- The meridian of any place is the south to north geographic axis, or vertical plane.

15- Ancient Egyptians used side dips (canals) that were filled with water to level the pyramids sites, see the findings of M. Lehner (Mark Lehner, 1983, pp.7-25)

16- The true north is the direction of geographic north from the observer, i.e., the direction along the meridian towards the North Pole. (Jahon Whttow, 1994, p.554)

17- The ability to define the exact quantity of an angle was, and still is, based on knowing the correct quantity of Pi that should be identified first. The nowadays quantity of Pi is 3.141592654.

18- The first rule in the so-called "the Rhind mathematical papyrus" shows: how to get the breakdown of any fractional number. See for example the general explanation of this rule in the works of (G. Sarton, Arabic edition, 1957, p.102), (John McLeish, Arabic edition, 1992, pp. 72-74). However, their explanations did not include the "original rule" of the ancient Efor getting the breakdown of any fractional number.

19- The latitude of any place is equal to 90 ° minus the quantity of the meridian angle of the sun on tequinox, i.e., on March 21 or on September 23. (Carlo Nallino, second edition, 1993, p. 270 )

20- Obliquity is the tilting angel between the planof the earth's equator and orbit, having a mean quantity of 23.44 in 1960 and diminishing 0.47 second per year (Webster , 1965, p582), see also (A. Weigert & H. Zimmermann, 1990, p34, p205 & p521)

21- (A. Weigert & H. Zimmermann, 1990, p 205)

References:

- A. Weigert & H. Zimmermann, Encyclopedia of Astronomy, Arabic edition, Abdelkawy Aiad translator, The Egyptian General Organization for Book, Cairo, 1990.

- Al-Maqrizie, Al Mawaes Wal A'atebar Bezeker Al-khetat Wal Asar (Sermons and Lessons With the Discourse on Alleys and Monuments), Vol-I, Dar Al-Tahrier, Bulaque Edition, Cairo, 1849.

- Al-Masoudy, Mrog Al-Zahab Wa Ma'aten Al-Gawher (Golden Lava and Metals of Essence), Asria Library press, Saida, 1987.

- Carlo Nallino, Arabian Astronomy: its History During the Medieval Times, Oriental papers for publications, second edition in Arabic, Beirut, 1993. (first edition, 1911)

- Ernst Neufert, Architects' Data, English edition, Crosby Lockwood Staples, London, 1975.

- Gorg Serton, History of Science, Arabic edition, Ibrahim Biomy translator, Dar Al-Maaref, Cairo, 1957.

- Herodotus, History of Herodotus, Arabic edition, Abdel Elah Al-Malah translator, Al-Magma Al-Saquafie, UAE, 2, p.190.

- Jahon Whttow, Dictionary of Physical Geography, 1994.

- John McLeish, Number from Ancient Civilizations to the Computer, London, 1992.

- Mark Lehner, Some Observations on the Layout of Khufu and Khafre Pyramids, Journal of the American Research Center in Egypt, Volume XX, Egypt, 1983.

- Olaf Pedersen, Early Physics and Astronomy, a Historical Introduction, Cambridge University press, New York, 1993.

- Petrie, W.M.F., The Pyramids and Temples of Gizeh, London, 1883.

- Webster, Webster's Seventh New Collegiate Dictionary, G & C. Merriam Company, publishers, USA, 1965.

Section-1: Introduction

Section-2: Defining the core issue

Section-3: The scenario of assumptions: the sun as a source of astronomical knowledge

Section-4: Original concept plan of the pyramids plateau

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