During the 4th dynasty of ancient Egypt, a vast monumental project culminated with the appearance of a pyramid at Gizeh on the west bank of the river Nile. This, the erection of the now well known ‘Great Pyramid’ otherwise known as Cheops, was to be the first such pyramid of an eventual main group of three.
The ‘Great Pyramid’, according to the early historian Herodotus, was completed in a period lasting 20 years utilising a labour force of some 100,000 men. Its erection was to be to later generations a seemingly endless source of wonder, and to the exponents of ‘Pyramidology’ a suitable vehicle into which could be crystallized their numerous concepts. It is therefore no wonder to those of us today when on reflection do we remember our instruction of pre-history, and our being informed that the pyramid in question was one of the wonders of the ancient world.
As to the purpose of this remarkable monument, then our reference sources soon extend beyond those classified as exoteric, i.e. archaeological/scientific modes of thought, for an abundance of esoteric literature exists. Perhaps at this point it would be a good idea to define these two conceptual approaches to the pyramid.
The term exoteric is used in the context whereby an evolving system of thought is established, which when subject to independent analysis a common result is arrived at. Here the intellect reigns. Hence the concepts eventually expounded are made intelligible to the layman as it were.
By esoteric, first of all to take a dictionary definition we are informed that it relates to ‘philosophical doctrines etc. meant solely for the initiated’ . Basically this means that within a circle of individuals a tradition (or school of thought) is expounded, that with its understanding are principles of evolution comprehended, that in the general race consciousness are embryonic. Within this approach will be found to a greater or lesser extent the employment of symbols. Symbols apart from their usual graphic representation provide metaphorical keys to the innermost domains of the mind. This realisation can be seen in the numerous documents of religious import, though to one not versed in such matters it has a tendency to be lost in an over-literal interpretation. Hence existent esoteric concepts may appear to be intelligible to one of pure exoteric leanings, but this in no way denies their validity. However, before too great an entry in made into this particular aspect, let us see the manner in which the pyramid has revealed its many faces.
The 19th Century saw the remarkable growth of a particular pyramid study known as ‘Pyramidology’. Its perpetrator was a certain Victorian publisher by the name of John Taylor. Taylor formally revealed that the outer dimensions of the ‘Great Pyramid’ indicated the usage of the mathematical ‘pi’. It was found that taking the height of the pyramid as a circle radius, then the perimeter measure of its base was approximately equal to the circumference of said circle. The Professor Piazzi Smyth, one time Astronomer Royal of Scotland, found Taylor’s work stimulating for he was to later further the study of this pyramid which he eventually published as a book – Our inheritance in the Great Pyramid. This together with Life and Work at the Great Pyramid captivated the minds of many people of that era. Smyth carried [out] an exhaustive analysis of the dimensions and geometry of the outer and inner structure of the pyramid. The result indicated the usage of several systems of metrology or rather revealed a Canon of measures which were used in later cultures. Unfortunately the numerous figures as proposed by Smyth were, with independent analysis, found to possess inaccuracies. The followers of Smyth had, without realising it, limited their vision in a too rigid adherence to certain number sequences. It was therefore seen in exponents of exoteric leanings that in viewing such material a cautious approach was needed.
The discoveries continued however. Again with the Numerological approach the art known as Gematria established itself. Gematria is a system of relating to certain sacred names or phrases in root texts the corresponding numerical values. Therefore to understand how this approach can be employed in pyramid research, one studies known pyramid dimensions and compares them to a list of significant Gematric-derived numbers. By this approach one gains an insight into the nature of the pyramid having established a religious or occult function through the literary definition. The argument against the validity of the numerical approach comes from a field encountered in mathematics known as ‘chance’. The exponents of ‘chance’ tell us that if one takes a set of random tables, then certain number sequences will eventually arise that to the operator appear to be significant. That the mind has a natural selective function is an established fact in psychological circles, so it is important that this critical attitude is seen in correct perspective by the numerologists. By this I maintain that a degree of openmindedness from both parties is essential for mutual understanding, for all too often closed minds give way to open conflict. This will unfortunately only lead to a greater degree of separateness.
Continuing with the geometry of the pyramid, it appears that the ‘pi’ property as established by Taylor was seen as the only mathematical ratio established by the outer dimensions. Later, as we were to find, the ratio known as ‘phi’ could also be related to the pyramid’s outer measures. ‘Phi’, a letter taken from the Greek alphabet and written thus φ, is often employed in the mathematics of plane geometry This irrational number can be arrived at from the following equation:—
φ = (√5 + 1)/2 = 1.618033…
φ also appears in Nature, in the design element of the logarithmic spirals of certain sea shells; the pentagonal arrangement of flower petals and in the number sequences favoured by the florets of a sunflower. In the latter case, the sunflower, here we see a definite use of a series of numbers known as the Fibonacci series. This particular sequence of numbers are evolved from the adding of two consecutive numbers which generates the next ad infinitum. φ appears in the ratio between these numbers, the higher the Fibonacci numbers the closer one gets to φ. The number sequence evolves in the following manner:—
1 1 2 3 5 8 13 21 34 55 89 144 …
In relation to the Great Pyramid an alternative design element to ‘pi’ in the outer measures is obtained. (Fig. 1).
The natural evolvement of φ to generate the pyramid elevation is of course to geometrically produce an approximation to the ‘Circle Squared’. The solving of the synthesis of Circle with Square is a problem that has taxed numerous minds. Documentary evidence can be followed back to the Egyptian civilisation. It was deemed that to solve this problem was to achieve a rare insight into the nature of the Universe, but I must hasten to add, though conclusive evidence survives to the mathematical approach, the answer to the problem lies in a philosophical understanding. From the mathematical research into the solution of this problem, the work of Lindemann amply illustrates the impossibility of its solution. However, the paradox is that an answer does exist but not in its mathematical exteriorization! The mathematical/geometrical expression of the synthesis of opposite elements was employed in order that some vehicle was provided in the transmission of the concept. Hence it is a logical conclusion to say that if one solely tries to solve the problem through a rigid adherence to mathematics, then no solution will truly arise. Though it could be said that through probable confusion, illumination may shine forth.
It is interesting to note in connection with the ‘Squaring of the Circle’ and the use of φ in a geometric approximation, the similarity to the groundplan of the ‘New Jerusalem’ as formally interpreted by the writer John Michell. In his book City of Revelation can be seen a similarity of groundplans of Stonehenge and Glastonbury with the ‘Holy City’ as described by St. John the Divine in Revelation. The use of φ to generate a ‘New Jerusalem’ scheme provides an alternative approach other than the original method of construction. (Fig. 2).
So far certain facets of the pyramid have been expounded. By now it should be relatively clear in the reader’s mind that the pyramid does have a stimulating quality in the mind of man.
Very often when a degree of correlation is attempted between the esoteric and exoteric, difficulty is encountered. The reason basically revolves around a lack of communication in that to the parties concerned, terms of reference vary. When an attempt to illustrate the mechanics of a function in man related to his religious expression appears, very often an interesting reaction is encountered.
Each person has a particular approach to the Universe, though generally we can relegate people into well defined groups. The approach is dependent on many factors but through experience we manage to obtain an insight into the principles that are expressed through numerous aspects of creation. Man is indeed a complex being. Biological functions can be examined through experimentation in that certain anatomical parts can be isolated. However, to understand the workings of the mind, no amount of surgery will provide us with a ‘mind on a slide’. The approach to the understanding of this function in man has therefore to be conducted in different fashion. The method of analysis is therefore based on ascribing certain functions to it on noting how it expresses itself through the physical shell it adopts.
One of the strongest functions encountered in man is the ‘religious function’. With the advent of the detached manner of the scientific mind, through the field known as psychology, a framework is afforded us whereby we have a suitable descriptive language to express certain concepts. Unfortunately when attempting to explain the religious instinct in man a certain reluctance to participate appears in many people. It is [as] though a fear is triggered off in that with the analysis an atheistic concept will be formulated. I mention this as with the divergent natures of the eventual contributors to this folio, it is likely that a person on perceiving a ‘spiritual message’ in the pyramid, will probably feel alarm in the materialistic manner in which his subject is defined. This is a facet of the particular period in which we live and a certain degree of acceptance is needed. However, the following is an attempt, from an esoteric viewpoint, to explain why the pyramid is to man, stimulating, and to help exponents of the exoteric is approach to understand the reason why a ‘spiritual significance’ is encountered.
Man, insofar as his mental makeup is concerned, possesses a waking conscious function, an unconscious function and a synthesis of both elements that can be expressed as the self. The self therefore is seen as the centre of our beingness. The concept of the Self as a totality of our existence and its realisation is to be found expressed in numerous traditions. In Christianity we find it in man knowing the inner Christ; in Alchemy as the attainment of the lapis or the ‘treasure hard to attain’; and in Buddhism a key to the ‘Jewel in the Lotus’. In each case this realisation seems to have a common foundation in the ‘sacrifice’ of the ego to a unity with the Self that by its nature is at one with the Universal Self, or God to use a more familiar term.
The stimulating effect of the pyramid on the consciousness of man seems to indicate the activation of a linking process whereby through the unconsciousness an aspect of the Self is realised. Here I relegate this function to those individuals in which the pyramid is found to have an esoteric significance. So the pyramid in this light can be taken as a symbol which is the manner in which a flow is created between the conscious and unconscious elements of the mind. Symbols are representations of principles that are embryonic in our conscious realisation. Hence they are naturally used by the unconscious, for within our experience there are no other relevant terms of reference by which an understanding can be achieved. In the past the use of symbols was delegated to the holders of numerous traditions of esoteric thought. It was deemed necessary that for the safety of the layman from the unbalance that can arise when the gates to the unconscious are opened, the transmission of certain concepts of the mind were clothed in ‘obscurities’. However, man is now at period whereby an understanding of the esoteric is necessary in order to maintain a degree of psychic equilibrium. Therefore it is beneficial that certain of these concepts be expressed.
The early stage of human evolution seems to indicate that man was primarily an unconscious motivated creature. With the development of the consciousness the at one time ‘feelings’ were eventually understood in an analytic sense. Today while a growth can be seen in the use of the intellect, it is apparent that the intuitional function is seen by many as a subsidiary sense. This unfortunately has led to a failure for many people to see the similarity of religious realisations irrespective of what school of thought they belong to. However, this must be accepted as an evolutionary cycle working itself out; meanwhile we shall have to resort to known exoteric concepts in psychology in order that a degree of understanding takes place.
The pyramid and its adoption as a vehicle by esoteric-minded individuals is an interesting study. Man it seems in order to consciously understand a purpose of life is unconsciously directed to situations in his environment whereby through experience a pattern is gradually established. This process can be seen in the attraction that the pyramid has for many individuals. In the case of a person ascribing religious significance to the monument, here we see the symbol being exteriorized into the physical world. This process happens with those individuals who for some reason or another have a difficulty in using the symbol as a wholly mental image. In the Orient the inner use of symbolism is apparent, while in the more materialistic West we find the symbol finding animation with suitable physical objects. It is just a case of differences in racial psychology.
The correlation of an esoteric concept with a physical vehicle sees certain interesting factors arising. First of all the selective function of the mind, which was mentioned in the ‘chance’ aspect of mathematics, arises. When through a physical object is a linking established through the unconscious to the Self, the mind tends to discard the irrelevant aspects of the physical object vehicle. This takes place for the simple reason that too much detail hampers the realisation process of wholeness. Hence when the pure exoteric-minded individual examines the ‘spiritually significant’ object, through the inaccuracies etc. a rejection takes place. The irony of this situation is that both parties have valid contributions to make and each has perceived what is deemed as truth from their observations. The thing about truth is that our understanding of it evolves. It is rather like a circle of people around a fixed object, each seeing an aspect of the whole and arguing that each has the ‘answer’. Of course we can say that were they to change their viewpoints a better understanding of the whole would take place; however, when one’s mind is channelled into one direction this realisation can be difficult. Hence the gift of an open mind!
It was because of the manner in which the pyramid led me into a mystical insight of the value of its symbology, that this article took its present format. The ‘Squaring of the Circle’ to which the pyramid relates is perhaps of greater import to this author, but nevertheless the pyramid as an actual object of permanence has been of immense value. Could it be that with the increasing evidence of psychic disorder and the remnants of at one time traditions for psychic growth, the integration of Jungian psychology, the unconscious in its projection to material objects indicates an inner struggle for equilibrium? In this light it is understandable that those who ascribe ‘spiritual significance’ to the pyramid will become disturbed in the analytic methods of scientific minds ‘nibbling away’ what has been a last resort to establish a foundation for psychic equilibrium. And so on this note I shall bring this article to a close, hoping that in some way it has created an understanding between the exoteric with the esoteric.
The View over Atlantis by John Michell.
City of Revelation by John Michell.
Pears Cyclopedia (Ideas and Beliefs section) 84th edition.
The Sphinx and the Megaliths by John Ivimy.
An Introduction to Jung’s Psychology by Frieda Fordham.
Psychology and Alchemy by C. J. Jung.
Acknowledgement is given to Robert Forrest for the time spent in the analysis of the elements of the ‘New Jerusalem’ scheme as outlined in Figs. 1 and 2.
David Randell. October 1976.
cos x = 1/φ = φ−1 = 0.618033…
x = 51° 50′
Triangle αβγ = half cross section of Cheops or ‘Great Pyramid’
The ‘New Jerusalem’ scheme evolved from the ‘Great Pyramid’ as outlined in Fig. 1. This proposed scheme is fully constructible using ruler and compasses.
Note by Michael Behrend, May 2014
The photocopy of the original Fig. 2 has deteriorated and is now too faint to read in full. Fig. 2 above is a partial replacement. David Randell’s idea is possibly as follows:
Starting with the “pyramid triangle” shown in Fig. 1 (red in Fig. 2), draw the square and circles as shown. Draw a regular hexagon inside the inner circle, as shown (green); each side, such as HK, has length 1. Draw a circular arc with centre δ and passing through α, cutting the side HK at M. Then M is very nearly at the midpoint of HK. More precisely, it can be shown that HM ≈ 0.501159.