I came across a book with the lofty title Disinformation Guide to Ancient Aliens, Lost Civilisations, Astonishing Archaeology & Hidden History, a series of essays edited by Preston Peet. Within this tome was a essay by Crichton E M Miller called The Constantine Conspiracy which fairly set my teeth on edge. Never have I read such a shoddy piece of prose espousing such preposterous claims.
Intrigued by Miller's outrageousness I went online and searched for more. In a similar article he expounded further and introduced an equation which he claimed the ancient Egyptians had used to create a measuring device with which to build the pyramids. As a sometime mathematician myself I decided to check it out. The article below discusses my findings.
Miller claims ([1] & [2]) to have rediscovered an ancient measuring instrument that he calls the Cross Staff & Plumb Line (also referred to in some of his other works as the Egyptian Staff or Egyptian Cross) that was used by the Egyptians in the construction of the Great Pyramid of Khufu. Miller makes further claims as to the accuracy and uses of this instrument in [2].
Specifically, Miller claims:
- He discovered the remnants of the so-called Egyptian Cross and from these proposed the actual staff construction
- The Egyptians were able to construct such a staff accurate to 3 arc minutes of inclination
- It was used by the Egyptians to design the Great Pyramid of Khufu
- The Egyptian Cross had been hidden from the public until he rediscovered it
We also review some of the details of the UK Patent for the Egyptian Cross.
The objective here is simply to refute these claims and to suggest a possible reason why Miller would have published these claims.
Let us first consider whether such an instrument could have been constructed, in particular with the accuracy claimed by Miller.
In [2], page 211, Miller states: "The author has discovered the remnants of a cross that was hidden by the House of Amen, in the Great Pyramid of Khufu." The remnants he refers to (a 130cm piece of wood, a round ball of granite and a small brass hook) are shown below in Fig. 1 and were discovered by Waynman Dixon in 1872. Due to an oversight at the British Museum they lay dormant until rediscovered in 1993, not by Miller, but hidden in the British Museum.
Figure 1
Miller used these remnants as the starting point for his creation of the Egyptian Cross, as shown in his own drawing below (Fig. 2). Note that the brass hook is conveniently used to anchor the plumb line.
Figure 2
It should be noted that no such instrument has ever been found and is entirely speculative on Millers part. Indeed, how such an instrument could be deduced from the three given artifacts is quite remarkable. Unless, perhaps, he got some help?
The triquetrum or Ptolemys Rules (Fig. 3) was the medieval name for an ancient astronomical instrument invented and used by Ptolemy in the first century AD. It was still in use by the time of Copernicus, and clearly regarded as state of the art. Millers Egyptian Cross is clearly based on the same principles as the triquetrum (basically an isosceles triangle) and used for the same purpose, viz., measuring angles of inclination of distant objects, such as the moon in Ptolemys case.
Figure 3
One has to ask: if Miller's Egyptian Cross had already been in existence for over 2500 years, why did Ptolemy, who worked in Alexandria (a metaphorical stone's throw from the Great Pyramid), not know about it? Why did such a seemingly powerful instrument have to be reinvented by Ptolemy?
One instrument that the ancient Egyptians were definitely known to use was the A-Frame shown below in Fig. 4, also referred to as the plumb line, level and set square.
Figure 4
If one inclines the Egyptian Cross in Fig. 2 over by 45 degrees to the left one would get precisely the same shape as the A-frame, including the position of the plumb line. Hence, if one combined the principle of the triquetrum together with the physical shape of the A-frame one would basically have the Egyptian Cross. Is this how Miller "discovered" the Egyptian Cross?
Let us now investigate whether the instrument shown in Fig. 2 could have been constructed by the ancient Egyptians with the tools available in 2580 BC when construction of the Great Pyramid began.
With regard to its working, the observer sights along the top bar (initially horizontal in Fig. 2) at a distant object and in doing so the central staff will incline so that the plumb line crosses the graduated measuring rod from which the angle of inclination of the viewed object can be read. [We refer to the graduated rule in Fig. 2 as the measuring rod.]
The accuracy of the instrument is chiefly dependent on the accuracy with which the measuring rod is graduated. Starting from the top left corner in Fig. 2, the measuring rod is graduated in degrees from 0 to 90, with each degree being measured by the offset A from the top left given by:
A = (2 B sinα) ∕ √2 (Eq.1)
where B is length of the left side of the top bar and 0 <= α <= 90 is the angle of inclination to be measured. Note that the offset A is a function of sinα and is obviously non-linear.
The graph of the Eq. 1 is given below in Fig. 5 showing offset A against the angle α. The calculations [4] agree with Millers (as shown in Fig. 7 of [1]).
In this graph, the X-axis measures the degree of inclination from 0 to 90 degrees and the Y-axis measures the offset A as given by the Eq. 1 above. For these calculations we chose a staff side length of B = 20 units, giving a hypotenuse (i.e., measuring rod) of length 28.28 units (Y-axis).
The curve X (red line) indicates the linear form of the equation in which A does not depend on sinα, and is included to show by how much the curve of A is non-linear. The graphs of tanα and sinα have been included to emphasise the non-linearity of the offset A.
Since the offset A is non-linear every degree mark made on the measuring rod must be individually measured from the origin. It also implies that whoever is doing the measuring and marking must be able to calculate sinα.
Figure 5
Let us assume a real cross staff having a measuring rod length of 900mm, as suggested by Miller in [1]. Then the mean length available for each degree on the measuring rod is:
Mean length = 900mm/90deg = 10mm/deg
= (10/60)mm/minute = 0.166mm/minute (Eq. 2)
Firstly, Miller claims that the instrument was accurate to within 3 minutes of arc, equivalent to 0.498mm on the measuring rod. This would require individually measuring and marking 90x20 = 1800 distinct marks on the measuring rod. It would seem reasonable to assume that without fine-grained marking equipment and optical magnification it would be impossible to manually mark off intervals of 0.498mm using ink on a measuring rod made of wood.
Indeed, did the Egyptians have a ruler even capable of measurement to within 0.5mm? See [3] for further comment on this point.
Consider also the plumbline which crosses the measuring rod to give us the degree of inclination. If the thickness of the plumbline was more than about 0.5mm it would cover more than one mark on the rod and thus lead to inaccurate readings of the degrees.
In view of the above it is our contention that the ancient Egyptians could not have constructed such an instrument with an accuracy of 3 minutes of arc.
In view of Section 2.2, obviously not, since according to our research no such instrument ever existed. However, there is even more damning evidence of this.
The ancient Egyptians at the time of the major pyramid constructions did not yet have the concept of angles, never mind the trigonometric sine of angles. Thus, Eq. 1 in Section 2.2 could not have been computed, and hence the measuring rod could not have been graduated in degrees.
In ancient Egypt, slopes and inclinations, especially in construction, were measured using the seked, shown in Fig. 6 below.
Figure 6
The seked is now accepted as the method by which the Great Pyramid of Giza was measured. An inclination of 5 palms and two digits is equivalent to 51.84 degrees, the slope of the Great Pyramid sides. Note that there is no need to actually know the angle: the horizontal and vertical measurements suffice to define the inclination.
Notwithstanding this, Miller makes the claim [1] that the Egyptian Cross was used to measure the slope of pyramids, as shown in Fig. 7.
Figure 7
This diagram is completely misleading and a misrepresentation of the supposed purpose of the instrument. Because of its construction as a cross it is specifically intended for sighting objects, not aligning itself parallel to existing slopes. Even if the observer was both below and beneath the pyramid (as suggested in Fig. 7), which object on the pyramid would the observer sight along the crossbar?
Alternately, suppose the observer positioned himself someway to the side of the pyramid and aligned the crossbar parallel to the pyramid slope (as we view it on this page). He may then be able to tell the slope of a small section of the pyramid in front of himself (say the first 2m of height), but how would he confirm that the slope of the entire pyramid was accurate?
Clearly, the Egyptian Cross would have been of no use in the construction of any pyramid.
Miller received a patent for the Egyptian Cross that was titled "Survey and Navigation Device" [9]. The patent ceased in December 2009 through non-payment of renewal fee.
Why would someone need to patent an archaic instrument that was clearly only of historical interest? Clearly, to establish credibility for the idea, and also to serve as a substitute for his much sought after peer review. Here is a quote from Millers Facebook page, dated 10 November 2015:
"The Patents Office duly did their research and eventually granted me two patents on the instrument design and function, proving the model works. Gaining a patent on this instrument is more challenging to achieve than peer group reviewed academic approval. The Patent Office operates the toughest of commercial tests and is often relied on by Universities to help with funding."
Let us review the degree of rigour with which the Patent Office reviewed this application. In the section Statement of Invention Miller makes the following statements:
- A one centimetre sub-division of such a scale [90cm] is equivalent to one degree of arc, in angular determination-and which, in longitude, subtends some 60 nautical miles at the earth's surface.
- Thus, 1 millimetre is equivalent to 1 minute of arc - which in longitude represents some 6 nautical miles.
- This in turn allows an accuracy to some one minute of a degree-being equivalent, in navigational terms, to 6 nautical miles of longitude.
Statements 1 and 2 are incorrect: 1mm is equivalent to 6 minutes of arc, which represents some 6 nautical miles. Hence, the instrument is accurate to 6 minutes of arc. See Eq. (2) in Section 2.2 above.
So much for the rigorous checking by the Patent Office.
In a further quote from a separate source [6] Miller states:
"Despite intensive research by The Patent Office prior to publication, no instrument with its complete attributes has been discovered and its application was not found to be obvious."
It is not known whether these words came directly from the Patent Office or were yet another fabrication by Miller. Nevertheless, the quote could be viewed as a double-edged sword, a confirmation by no lesser source than the Patent Office that such an instrument never existed before. Talk about shooting yourself in the foot.
As an aside, in reference [6], referred to above, Miller states that he had been asked to submit "an academic 20,000-word paper in the November 2000 issue of Fortean Studies". Apart from the fact that Fortean Studies is not by any stretch of the imagination an academic journal, no reference to such a paper exists today.
Returning to the patent application, on the subject of the artifacts shown in Fig. 1, Miller states:
"Fragmentary archeological finds have supported the present Applicant's hypothesis that plumb lines and weights were used in early surveying".
In the patent application he doesnt show what these finds are or how they contribute to his hypothesis. How interesting that he uses the word "hypothesis".
Notwithstanding that the title of his essay is "The Constantine Conspiracy" Miller discusses Constantine's supposed hijacking of the Celtic Cross and Egyptian Cross in only the briefest and vaguest manner. He also drags the Knights Templar into the argument that over the centuries a great deal of effort has been expended in keeping the Egyptian Cross hidden from the public.
If Constantine did suppress knowledge of the Egyptian Cross why did he not also suppress the triquetrum (Fig. 3), which had been around since Ptolemy's time and was used for the same purpose? What was so special about the Egyptian Cross when the Romans already had excellent measuring tools such as the groma, chorobates, and dioptra?
Miller's work is a good example of poorly presented and sloppy writing. Ref. [2] is a mumbo-jumbo of unrelated and ill-structured facts, for which no concrete references are given. Regarding the latter, consider in particular references 18 and 19 in Ref [2]: 18. Miller 19. Ibid. Not very helpful.
Miller's writing, particularly in Ref [2], is often obtuse. For example he states, as a single paragraph: "You will notice that the wheel cross is always associated with the highest form of geometry and mathematics, the measurement of the stars". There is no reference as why this should be so or for that matter what relevance it has to the ongoing discourse. Also, since geometry is a subset of mathematics, why mention both?
Another perplexing statement: "The early [Paleolithic] hunter-gatherer mariners had developed a form of geometry and mathematics that was linked to astronomy and astrology to move around in their environment". But since Paleolithic hunter-gatherers were largely restricted to the use of stone tools, how did they construct ocean-going boats and become mariners? How did a stone-age people invent mathematics? Since they left no written records what did they write their mathematics on? Indeed, where is the proof of any of this?
The so-called Egyptian Cross does work as far as roughly measuring the inclination of objects, but is obviously of no practical value today. There is also no firm evidence whatsoever that it existed in ancient times. This is in contrast to the triquetrum that has been well documented and works on identical principles, but has only been known since the time of Ptolemy (c 90 - 168 AD).
So perhaps Miller copied the ideas of the triquetrum and A-frame and placed this "new" instrument in the pyramid of Khefu on the extremely flimsy evidence of three fragmentary archeological finds?
But his claim that the Egyptian Cross can "find the elliptic pole as well as the north and south poles, make maps and charts, design pyramids and henges, ... and predict the cycles of Nature and Time" is plainly preposterous.
Miller and his ilk are keen to get the approval of mainstream academia for their ideas, to be peer reviewed, but get extremely upset when their ideas are castigated (see, for example Ref [7]). The problem is that mainstream academia are not their peers.
It can only be assumed that Miller and the rest of his colleagues are either profoundly deluded or are attempting to hoist a silly hoax on society, probably a bit of both judging by the number of people who subscribe to this nonsense. Fortunately, the general consensus within academic circles is that this is all hogwash.
[1] Crichton E M Miller, Cross Staff and Plumbline and the Great Pyramid, www.touregypt.net/egypt-info/magazine-mag03012001-magf7.htm
[2] Crichton E M Miller, The Constantine Conspiracy. Published in The Disinformation Guide to Ancient Aliens, etc, Disinformation Books, 2005.
[3] E.M. Antoniadi. L'Astronomie Egyptienne, 1934. Antoniadi expressed the opinion that the Egyptian cubit was divided into hundredths with very fine subdivisions, comparable to our millimeter.
[4] The detailed calculations and graphs are by the author.
[5] Sticks, Stones and the Zodiac, from The Celtic Guide, March 2012.
www.thecelticguide.com/uploads/1/5/1/5/15152728/mar12.pdf
[6] "The Cross and the Plumbline" can be viewed here: old.world-mysteries.com/sar_5.htm
[7] Will Hart, Archaeological Cover-ups: A Plot To Control History? Published in The Disinformation Guide to Ancient Aliens, etc, Disinformation Books, 2005.
[8] For a brief discussion of the triquetrum see: www.setterfield.org/Dodwell/Dodwell_Manuscript_2.html#return_triquetrum
[9] The patent application can be found here: worldwide.espacenet.com/publicationDetails/description?CC=GB&NR=2344654A&KC=A&FT=D&ND=&date=20000614&DB=&locale=en_EP
We acknowledge that Figures 1, 2 and 7 were taken from various online documents written by Crichton E M Miller.