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Geographical Orientations

THE FOURTH DYNASTY - GREAT PYRAMIDS OF EGYPT
PART ONE

Copyright 2001, by Ernest P. Moyer
Revised February, 2003

In two seasons from December l880 to May 1881 and from Oct. 1881 to April, 1882 Sir Flinders Petrie (1) made accurate triangulations and measurements of the pyramids at Giza. His results showed a consistent compass misalignment west of north on all sides of the two largest pyramids. Petrie's mean value was -3' 43" for the Giza I casing (Khufu); his mean value for Giza II (Khafre) was -5' 26". In 1925 J. H. Cole (2) repeated measurements on Giza I to verify Petrie's precision and accuracy; he obtained a mean skew of -3' 06".

In 1973 G. S. Pawley of the Physics Department of Edinburgh University in Scotland and N. Abrahamsen of the Geophysics Laboratory of Aarhus University in Denmark (3) refuted several suggestions put forth to explain the misalignment. Petrie assigned the skew to shifts in the north pole position. He discussed changes in ocean currents as a probably cause (1). However the true pole position is moving at a rate of about 0.0032" annually at Cairo (Giza). Over a period of 4500 years this change would amount to no more than 0.24', far less than necessary to explain the skew. The misalignment is also not due to continental drift. South America is separating from Africa at the rate of about five centimeters per year with a continental hinge in the north Atlantic. This would cause a shift of about -0.1' over 4500 years, again far too small to produce the measured misalignment. Africa is also swinging away from Asia with a hinge near the north end of the Red Sea but this is of the wrong sign and also too small to produce the skew.

Another factor is local earthquakes. Although the pyramids show evidence of quake damage, historical and geological data show no earthquakes during the past 4500 years of sufficient magnitude to produce such dramatic results. Pawley and Abrahamsen then went on to state that the pyramid skew should be explainable in geophysical terms although no physical cause is currently known. They also remarked that no other remains in Egypt can give corroborative results; the two pyramids at Giza are unique; other pyramids are smaller and less accurate.

Examination of data from other IVth dynasty pyramids, with comparison against Giza I and Giza II, shows that the skew is due to conscious control by the builders and is suspect for evaluating past geological changes. A more comprehensive review is helpful to arrive at better estimates of builder measurement and construction control.

I compiled data from Petrie (1), Cole (2), Vyse (4), and Maragioglio (5) to obtain a more rigorous assessment of the misalignment and possible impact on our understanding. Table I is a list of base length measurements and skew available on significant Egyptian structures. This list includes the Zoser step pyramid of the IIIrd dynasty at Saqqara, the IVth dynasty pyramid at Meydum, the Bent pyramid and enclosure wall at Dahshur, the Flat pyramid at Dahshur, and the three largest pyramids of the IVth dynasty at Giza. It does not include the miniature satellite pyramids at Giza, nor the petty structures of the IIIrd and IVth dynasty, nor the many inferior pyramids of later dynasties.

Refer to list of references at end of last Paper.

Base lengths are in meters. The orientations are given in differences from the true position in minutes and seconds. Note that the individual skews are given with respect to their geographical locations. For the north and south sides this is north or south of the true west position. A negative sign indicates west of true north for the east and west sides. And so on.

TABLE I

Significant Egyptian IIIrd and IVth Dynasty Pyramids

Base Lengths and Orientations

N E S W Source
ZOSER STEP
Length
Orientation
125 E-W by 108 N-S
4 deg 35' E of N
(4)
MEYDUM
Length
Orientation
144.20
-35' 25"
144.63
-23' 36"
144.30
-20' 35"
144.15
-18' 03"
(5)*
BENT (Enclosure Wall)
Length
Orientation
298.59
-4' 34"
298.54
-16' 40"
298.63
-38' 50"***
299.03
-16' 08"
(5)*
BENT
Length
Orientation
188.60
-9' 12"
(5)**
(5)*
FLAT
Length
Orientation
219.3
---------
(4)
Giza II
Length
Orientation
215.187-5' 31 215.271-6' 13 215.314-5' 40 215.278-4' 21 (1)
Giza I SOCKETS
Length
Orientation
231.897
-3' 20"
231.923
-5' 21"
231.748
+1' 15"
231.628
-7' 33"
(1)
Giza I CORE
Length
Orientation
228.659
-4' 35"
228.585
-5' 26"
228.644
-5' 23"
228.664
-5' 39"
(1)
Giza I CASE (Petrie)
Length
Orientation
230.363
-3' 20"
230.320
-3' 57"
230.366
-3' 41"
230.343
-3' 54"
(1)
Giza I CASE (Cole)
Length
Orientation
230.253
-2' 28"
230.341
-5' 30"
230.454
-1' 57"
230.357
-2' 30"
(2)
MENKAURE
Length
Orientation
?
+16' 48
105.930
+12' 23"
105.608
+12' 57"
105.509
?
(1)
(Menkaure NW corner obscured by rubble)
*Petrie data via Maragioglio
**Mustafa data via Maragioglio
***Maragioglio questions the reported value. It is too large to be realisitic.

Figure One shows compass alignments of the respective structure sides in the sequence N-E-S-W. Each structure is shown in historical chronological order according to accepted archeological assignments except for Giza II, which I shall discuss shortly. No data exist for the Flat at Dahshur but the Bent structures fit within the sequence. I plotted the pyramids without regard for dates of construction; because of the form of the plots I intentionally avoided calendar time.

The data show that the Zoser step pyramid is badly misaligned east of north. This error is greater than one could obtain by casual eye sightings on northern stars; it was a poor attempt at north orientation. In contrast the IVth dynasty structures show refined measurement and construction. The greatest error is slightly more than one-half degree in the Meydum structure. There was continual improvement in alignment toward true north as construction approached that of the Giza I outer casing. The Menkaure pyramid then shows a relapse to greater error and of opposite sign. Following dynasties no longer held such tight control.

The data show increasing ability, not only in measurement but also in construction technique. The form of the plot suggests a learning curve, as though the builders were coming closer to the true pole position with each structure. A curve drawn through the mean values shows a monotonic decrease that is not due merely to accident of plot. Although we are missing data from the Flat pyramid the improvement is so consistent we can predict -6' or -7' for its mean orientation.

Assignment of the differences in orientation to geophysical changes during the IVth dynasty is unrealistic. The north pole position could not have moved so drastically in such a short period.

To assume that the structures were oriented around celestial objects is also unrealistic . The stars have moved with Earth precession of the equinoxes and would now be far away from a north polar position of that era. (The amount of precession is about 70 degrees since that time.) In fact, with the monotonic improvement in orientation accuracy toward the present pole position we can affirm that the earth has not moved more than the three minutes of arc shown in the data plot.

We can conclude that the builders did not use the stars to achieve their orientations. They had to have some independent means to determine true geographical north. Some have argued that they could have used a star or stars that were on the north pole position at that time. But how would they know the true north pole position to locate those stars unless they had an independent method for determining where it was?

The IVth dynasty structures were all part of a progressive improvement in great measurement and construction accuracy, with precise knowledge of the geographical north pole position devoid of any celestial reference. As I shall show, even the three minutes of arc difference was intentional. Hence, the earth pole position had not shifted significantly over the past five thousand years.

If we accept Petrie's (Pawley's and Abrahamsen's) judgment that the pole position in 2700 BC was 3' to 4' west of the current position we must explain the other structures. If Giza I was centered on the pole position why were the preceding constructions of the IVth dynasty, with their refined measurements, not all aligned randomly around that position? It seems more plausible that the builders used instruments or methods that contained bias. But even this suggestion is difficult. What instrument or technique would cause consistent bias west of north, with continual improvement, during the IVth dynasty?

The monotonic form of the curve either had a natural cause, or an artificial cause. A natural cause could be assigned to instrumentation, or to methods, and conscious awareness of increased skill with each project. On the other hand, the rate of improvement shows more than just increased skill. It shows a deliberate intelligent control of misalignment to achieve that particular form.

Another deduction seems reasonable from the graph. The progressive improvement indicates an apparent trend according to project and not according to time. Regardless of the interval between projects the improvement toward the pole position comes successively closer with each structure. If there was improvement during other unknown and intervening projects it is not immediately evident on the plot.

The builders apparently devoted their attention exclusively to the very large projects of the IVth dynasty. The geographical orientation of measurable extant structures from other dynasties do not exhibit the same control, and hence were not part of this project. But this project continued over several human generations. The data offer striking evidence that civil engineering precision or knowledge, both in measurement ability and construction, was present during this entire period. It was no longer present or exercised when the Menkaure pyramid was built. Although the proximity to the north pole position in the Menkaure pyramid suggests that some construction influence still lingered it was then not under the refined hand of the preceding structures.

Although enclosure walls were detected for both Giza I and Giza II they have long since deteriorated to the point where we cannot now reliably measure their geographical orientations. The core of Giza I has about the same control in orientation as Giza II exterior. We have no data on a possible inner core for Giza II. Therefore, we do not know how such missing data might affect our assessment, or conclusions. However, the form of the plot is so striking we have sufficient evidence to draw conclusions about the designer's intent.

As I shall show, detailed examination of the data suggests an unknown project between the Meydum pyramid and the Bent projects.

We must deal with major questions: Does the form of the data plot show a learning ability, or was it through design intent? Could the monotonic decrease be accidental? If so why would the data points not be scattered? How could the builders come so close to such a refined display merely by chance? Modern statistical studies would not assign such a neat monotonic decline to mere happenstance. Natural curiosity brings a keen interest in finding the cause. The principles of modern science should help us to determine that cause.

But if the orientations were due to intelligent control the data would demand that the designers and civil engineers intended to display such refinement to later observers. Were they merely gratifying themselves with pride about their abilities? If so, why not orient each structure to the refinement found in Giza I? It makes no sense to exercise such intelligent display unless they expected that some one could later discover it. Certainly, no observer in historic times, over the past four millennium, and especially not today, would credit such a remarkable display as under intelligent control. Our present social attitudes cannot credit the high level of intelligence, technical abilities, and social management necessary to achieve such fantastic goal.

In fact, not until modern times did we have the ability to even detect such refined control. After the Menkaure pyramid that level of technical prowess was lost to the world. Hence, the builders had to have technical capacity equal to modern abilities in order to accomplish such feat.

If the monotonic decline was through design intent, the control necessary to display it would be nearly equal throughout the entire construction period. Otherwise, the designer could not ensure that the smooth decrease would be apparent to later observers. He had to maintain intentional misplacement from the pole position at a refinement necessary to bring out the display. This fact leads to the inference that the builder was able to control misalignment from the beginning with a finesse equal to the control exhibited in Giza I.

He was not working under a learning curve. He was fashioning a project that he knew he could control from the beginning.

As I get into more details of the data we shall see how such conclusion is justified.

Importantly, the Meydum structure appears to be part of a grand design that was used to demonstrate ability to control geographical orientation. If the designer/engineer held the separate structures to intentional misalignment he was controlling how this orientation would appear to some later researcher who might assemble the data C according to the plot I have shown. Then the Meydum structure was important to this display.

We see how Giza II appears as a project that was built prior to Giza I. The plot tells us the sequence C if we are willing to accept that the orientations were under conscious control.

Insights from these graphical plots offer other thoughts. If we were to include the total spread of the data, from the Meydum pyramid to Menkaure, we could understand those two structures as showing a terminus a quo and terminus ad quem for the entire project. In other words, we might deduce that the designer consciously intended to use them to show us the range of his project. If so, he conceived the project before he started the first pyramid, and knew where it would end before he laid the first stone.

We simply do not have an explanation for the data as due to uncontrolled natural phenomenon. They require us to conclude that a conscious design intent and construction control was present throughout the entire period.

The data also require us to conclude also that if the builder could consciously control Giza I to an amazing 3' of arc west of north, he certainly could control the alignment of the other structures on exact pole position with the same precision. If he did not, he could not have offered such a vivid graphical display.

As a consequence of this deduction we can see that the Bent enclosure wall need not have been built before the Bent pyramid. That misalignment, as part of his project, could have been exercised after the pyramid was built. This thought could follow through on Giza II construction after Giza I, but this is not an inclusive deduction. Other evidence speaks against it.

 

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