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The Pyramids of Giza

Imperial Measures and the Pyramids

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Imperial Measurements, two words guaranteed to produce a shudder of horror in all school children. Nobody fully understands the system and it beggars belief that anyone would want to create such an unwieldy measurement system in the first place - so how has it managed to last so long?

This is actually a serious question – where and why was this peculiar and complex system of measures devised? Does anyone really know? From the British perspective, the system seemed quite natural; having 14 pounds to the stone and 12 pence to the shilling were just part of the initiation into the culture, no more peculiar than having milk delivered to the doorstep. To the rest of the world, however, it would seem that the figures of 1,760 yards to the mile and 5 1/2 yards to the rod were plucked out of thin air. For who, in their right mind, would create a system of units that used fractions? Indeed, this mismatch of odd numbered units in the Imperial System has caused many eminent heads to be scratched over the years. No less an authority than Professor R. Connor, who has been working on weight and measures for more than fifty years, says of the Imperial system of measures:

If we look again at the table of length, we might agree that the relation of inches to feet and feet to yard are not unreasonable, nor is that of the relation of rods to furlong to mile, but the entry ‘5 1/2 yards = 1 rod’ strikes a discordant note. For who in his right mind would establish a table of relationships using fractional parts? ... it can be taken for granted that the table was not set up ‘de novo’ (as new), but that two or more systems were being fused together to meet the needs of the times.

The one furlong marker at Epsom Downs race course

Fig 1.The one furlong marker at Epsom Downs race course. It says 200m below it, because one furlong is almost exactly 200 m

This is all very logical: the foot and yard were part of one measurement system and the furlong and rod were part of another; and where they met formed that uncomfortable 5 1/2 yards to the rod. But this does not exactly explain all the other odd ratios in the system, for instance, the 8 furlongs to the mile, the 320 rods to the mile and the 1,760 yards to the mile. They seem to be bizarre numbers and ratios to choose for a measurement system. There has to be a simpler and more comprehensive solution to this problem, than the fusion of two measurement systems.

That there may be a more fundamental, all-encompassing rationale to the Imperial Measurement System is borne out by some of its underlying symmetry, for even that rather odd sounding 5 1/2 yards to the rod still manages to work well throughout the system. The following are divisions of the Imperial System, expressed in yards and rods, yet both sides of the table are expressed in round and even numbers. One has to admit that the system does have an unexpected symmetry to it:

1760

yards  (1mile) 

divided by  

5.5   = 320 rods,          

220

yards  (1 furlong)

divided by  

5.5   =40 rods, 

22

yards  (1 chain)

divided by  

5.5   =4 rods,  

1

acre   = 22 x 220 yds

which is     

4 x   40 rods.

The ease with which the 5 1/2 yard rod fits into the system has also been recognised in the expert field. Professor Connor continues:

The pivot of the table of length, is the rod. It generates not only the furlong as a unit of length, but also the acre...

But this is a contradiction of the previous statement: the rod unit cannot be both the pivotal unit and also the accidental result of the fusion of two different systems. It would seem that the experts have come to no real conclusions beyond the ‘fact’ that the yard is a nice convenient household length and that a mishmash of units has grown up around it. For a long time I found this deeply unsatisfactory and I determined to find a better solution.

At last, after much patient study of the ancient texts, there does seem to be an alternative and very attractive solution to this age-old conundrum. And this is relatively simple solution which, according to the premise known as Occam’s razor, is always the test of a good theory.

Pi units

The solution is that the whole table of units was based on the mathematical constant Pi. It is this use of Pi as a base structure to the Imperial Measurement System that has determined its peculiar nature and has also determined the length of that awkward 5 1/2 yard rod. Pi is not a nice round decimal number and therefore does not lend itself easily to subdivisions. Pi is a fixed constant of nature, so there is not much that can done about that - the value of Pi cannot be changed, it just has to be circumvented. So if a designer wished to encompass the value of Pi into a building, or into a measurement system, the obvious solution would be to choose a fractional approximation of Pi that was divisible by simple, even units. The improper fraction 22:7 springs to mind as an obvious choice, as it is a very simple approximation of the precise Pi number and it also has an even numbered numerator - the number 22.

It is entirely possible that the Imperial Measurement System was designed using the 22:7 Pi ratio. The numerator in this ratio, the number 22, is fundamental to the way in which the measurement system was designed - it is the base unit. Thus we see that there are 22 yards in a chain. Multiply this number by ten and we find the 220 yard furlong. Finally, when going down the scale, if the number 22 is divided by 4 it produces that rather odd looking rod length of 5 1/2 units.

It would appear that there is a very simple solution to all the peculiarities of the Imperial Measurement System; and that awkward 5 1/2 yard rod is simply a necessary by-product of our starting point of Pi. For Pi-based measurements to work out in even units, we have to use a multiple of 5.5 somewhere in the measurement system. Therefore, the British Imperial Measurement System was not just plucked out of thin air, it was a system based on Pi. But if this is so, the implications are manifold and quite interesting, for it is indicating that the knowledge of the fractional approximation of Pi was known long ago. If this is so, the important question is: how long ago was this fraction of Pi known?  How old is the Imperial measurement System? Some further investigation may provide an answer.

Pi Mile

Having found the symmetry of the sub-units of the Imperial Measurement System, it is time to look at the mile length. When making this wonderfully new set of measurements, based on Pi, why would someone want to make them have such an awkward end-point; why derive the peculiar mile length of 1,760 yards? Where did this peculiar length come from? Well, as one might expect, this is another result of using Pi-based units; the result of using the 5.5 unit rod that is so central to this system. We can multiply the 22-yard chain by 10 to achieve the 220-yard furlong, and then by another 8 to derive the 1760-yard mile. Therefore, any of the other sub-units in the system (which are all based on the number 22) will happily divide into the mile length, including that awkward 5.5 yard rod.

The result being that there are 320 rods, or 80 chains, or 8 furlongs to the mile - a simple symmetry that works throughout the measurement system. And so the Imperial Measurement System is not the result of an awkward fusion of two measurement systems, as Professor Connor claimed. This just has to be the most logical reason yet given for the mile length in the British Imperial Measures. Someone back in the dim and distant past knew of the fractional value of Pi (22 : 7) and decided to encapsulate this into a new measurement system, one that has endured over the millennia into the present era. But the question still remains as to how and why was that done? How old is our Imperial Measurement system?

What follows may seem a little esoteric to some within the scientific community, but the artifacts are out there for anyone to witness and measure. One may disagree with the final interpretations that are made in the book Thoth, Architect of the Universe , but nevertheless facts are facts and there is a very satisfactory simplicity to the explanation that follows. Why the caution? Well, put simply, the Imperial Measurement System was created by the people who the constructed the Great Pyramid of Giza!

The Giza pyramids

Fig 2. The Giza pyramids. The Great Pyramid is in the background.

Now that may seem like a bold statement to make, but there are some good reasons for saying this. Firstly, just like the Imperial Measurements themselves, the dimensions of the Great Pyramid are based on the mathematical constant Pi. If the Great Pyramid was 7 units high, then its perimeter length would be 44 of those same units (44 : 7). And this number is simply twice the 22 : 7 ratio for the fractional equivalent of Pi. The reason for the pyramid being twice the Pi ratio, is that the formula for the circumference of a circle is 2 x Pi x r.  If we extract the number 2 from this formula, the 44 : 2 pyramid ratio will become the 7 : 22 Pi ratio. So in numerical terms, the height of the Great Pyramid is a representation of the radius of a circle, while its perimeter is a representation of the circumference.

Fig. 3. The Great Pyramid as representation of a circle. Both are formed by the Pi units 22 : 7.

So the Great Pyramid and the Imperial Measures appear to have been based on the same mathematical function - Pi. But where does the Imperial Mile measurement fit into all this? Well it is obvious that the pyramid does not really measure 44 units around the base; but if we say that it measures 921.36 meters or 3022 Imperial feet around the base, as some academic text books do, the result is totally meaningless. It is axiomatic that the Egyptians were using cubits, not feet or meters, and so it is to cubits we should look when deriving the measurements of the pyramids.

The precise unit the Egyptians used was derived by Sir Isaac Newton in the 17th century, in his small booklet entitled Dissertation upon the Sacred Cubit of the Jews and other Nations . He derived the length by noting that the King’s chamber in the Great Pyramid was constructed to have dimensions of 10 x 20 cubits, and the resulting cubit therefore has a length of 52.35 centimeters (20.6 inches). If we use this original cubit to measure the circumference of the Great Pyramid, we would discover to our amazement that it has a perimeter length of 1760 royal (or Thoth) cubits – exactly the same number of units as contained in the 1760 yard Imperial mile. So the Egyptian mile and the Imperial mile both measured 1,760 units in length. The absolute length of the cubit and the yard are different, of course, but the numerical symmetry remains the same throughout the pyramid.

Many academics may claim that this metrological equivalence is mere coincidence, and they may also claim that the Imperial Measurement System is simply a base-22 numeric system and nothing to do with Pi. I would disagree. Firstly, it has been long rumoured in mythology, that the measurements of the Great Pyramid were somehow special. That is why Sir Isaac Newton wrote his pamphlet in the first place, in which he ponders over the dimensions of the Great Pyramid at Giza and many other ancient monuments. It is a shame that the base of the pyramid was covered in rubble in the 18 th century, which resulted in Newton's measurements for the base-length being considerably short of the true value, otherwise Newton would certainly have discovered the same coincidence many centuries ago.

Secondly it is a fact that the Great Pyramid not only has a perimeter length of 1760 cubits, but also a height of 280 cubits. Thus this stupendous edifice, designed and erected some say in the early Bronze Age, is simply a megalithic representation of the circle formula:  2 x π x r.  So the dimensions chosen for the design of the Great Pyramid were simply a 40 times multiple of the fractional approximation of Pi:

                            22 x 40   =  880 cubits    (1/2 base length)         

                            7 x 40     =  280 cubits    (height)      

                            ratio        =  880 : 280

The base of the Great Pyramid Pyramid is then multiplied by two according to the formula for a circle, to achieve the true base length.  (2 x 880 = 1,760).

 Fig 5.   The Great Pyramid is a 40 times copy of Pi.
Fig 4.The King's Chamber in the Great Pyramid measures exactly 10 x 20 Royal or Thoth cubits. From this exact dimension, the length of the Thoth cubit was derived.

It is for this reason that the number 40 features in so many of the biblical stories. The kings and judges of the Old Testament invariably had a life-span or reign-length of forty years, while any deliberations or wanderings in the deserts are also said to be 40 years or days in length. These time-spans were not real, of course, but merely a sign of initiation. The number 40 demonstrated to those ‘who had ears to hear’, that the person concerned had been initiated into the mystery and mathematics of the Giza pyramids.

But does all of this in any way prove that the Imperial Measures were actually based upon the dimensions of the Great Pyramid?  Well, in the book K2, Quest of the Gods , I go on to demonstrate how most of the Imperial Measurement units are key elements of the Great Pyramid’s design, especially that peculiar 5.5-unit rod-length. It would seem unlikely that all of the ratios, units and lengths contained in the Great Pyramid just happen to be the same as are contained within the Imperial Measurement system, and so I strongly suspect that the Imperial Measures were originally Egyptian. (It is the ratios that are original, not the absolute lengths, which have been altered by the Romans and various acts of the English parliament).

Thus the Great Pyramid appears to be a mathematical and meteorological constant carved not only into the fabric of these ancient monuments, but also into the culture of the Anglo-Saxon peoples. These traditions have been propagated down though the millennia, primarily through masonic institutions where measurements and measurement systems form a fundamental component within the fraternity. It is for this reason that there is such opposition to the metric system in America. Indeed, the opposition has been so great that the essence of the measurement system that was used to construct the Great Pyramid, has now been taken into space – encapsulated within the design of the Space Shuttle. 

This article was extracted with permission from the book ‘Thoth, Architect of the Universe’ and ‘K2, Quest of the Gods’ by Ralph Ellis, available from edfu-books.com

Featured image: The Pyramids of Egypt. Source: BigStockPhoto

By Ralph Ellis

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