31. Feet, Cubits and White Rabbits: How to make sense of the Great Pyramid and other ancient places
Updated: Jun 29, 2022
What do you believe in? - In this: that the weight of all things must be determined anew.
The Gay Science, 169, Nietzsche1
When it comes to pre-historic monuments, how can we possibly know anything of the builders'intentions? There are rarely, if ever, any contemporary texts to accompany them. Whether the builders designed their pyramids using feet, metres, cubits, remen, or any other unit, there is no possible way for us today to know that for certain. The question of units of measure used is similar to the question of when they were built, in that respect: nothing can be proven for certain. All that can be done, and all that has been done, is to put forward theories. Theories can be disproved. Hence, they are changeable. This can be observed in the many construction dates put forward for the pyramids over the years, anything between the second and fifth millenium, between Greaves's and Mariette's theories. Peer review and intersubjectivity are different from truth.
Even if almost everyone interested in the question agreed that the pyramids were laid out in royal cubits, and this became the widely accepted theory, it still wouldn't become a fact, or prove the builders' intentions. They left behind no plans. Anything we say about what we think the builders did is conjecture. This applies to claims that the pyramid builders didn't use inches, feet, or metres, just as much as it does to those to claim the opposite.
It's not possible to prove or disprove that feet, metres or cubits were used deliberately. The question of measure in the pyramids is pure theory - kind of like death by spaghettification if you fall into a black hole. :) (And how long would you be then??)
You are always and everywhere limited by your ability to interpret what your measurement means and measurement technology. This is where, traditionally, science meets philosophy. We can propose models and compare them. After that the best we can do is at least be aware of our own tendency to seek out information that only serves to confirm our own biases. How do we deal with "alien paradigms”, as Karl Popper calls them? But the problem is, in this context, how to deal with unexpected things you may find which make you say "surely that cannot be a coincidence!!" To go back to Popper, he said:
"But if you are interested in the problem which I tried to solve by my tentative assertion, you may help me by criticizing it as severely as you can; and if you can design some experimental test which you think might refute my assertion, I shall gladly, and to the best of my powers, help you to refute it.”
When it comes to ancient monuments, there may be several pretty innovative and water-tight theories or models to explain them, to make sense of them. There are also lots of intriguing observations also being made. Patterns emerge. Meaningful analogies can be made. A hunch is not enough. A pre-disposition towards a certain type of theory is not enough. But also you might say that the moment of decision, or coming to a feeling of certitude about a theory, is not necessarily the outcome of the research and deliberation and discussion, but something that causes this process to begin in the first place. I'm thinking of Newton watching the apple fall from the tree.
Greta Thurnberg says 'don't listen to me, listen to the science'.
Nietzsche says 'follow your own truth, be your own truth'.
It is tempting to want to guess at intentions, in this case the intentions of the megalith and pyramid builders. The trouble is, for me, that even a theoretical system that works, has its own inner logic, complies with evidence, albeit on its own terms, is not necessarily going to be accepted by all. The experimental, mathematical, logical aspect does not necessarily persuade. In the end, for a theory to be accepted, it's still about personal hunches and pre-dispositions, the influence of those we have read, about paradigms, and accepting or rejecting widely believed theories. Perhaps that's another paradox....What kind of mechanism is there to check these theories? You can't really build a theoretical model of, say, lunar connections at Giza, and then test it on some other Great Pyramid. There's only one!
Once you start comparing your Great Pyramid findings to other pyramids, say in South America, or to megalithic structures, you have to then justify an already controversial link between all these sites. Archaeologists believe that it is a coincidence that there are large stone pyramids on several continents. Even if you disagree with that, it seems pointless to compare findings between the measures of pyramids on the African and American continents in order to impress academia.
If you were to argue in favour of the presence of moon related figures at the Great Pyramid by arguing that Jim Wakefield (a.k.a. Molder) has found lunar connections at the Rollright Stones in England, you're opening up a whole can of worms. (see Jim Wakefield's paper on the Rollright Stones). Comparing these English stones with the Great Pyramid, is both instructiove and problematic, at least in the eyes of the wider community. Many people are probably ok with comparing the two. They are also probably ok with the idea of an advanced megalithic worldwide civilisation that was behind all of sorts of structures, from the Rollrights to the pyramids of Giza, to language structures, to myths and religious motifs that have all survived, to measuring systems that link far-flung places. There are megalithic sites much like the ones in Europe over in the USA. There are pyramids all over the world. Then there are the connections between significant ancient places across the globe which suggest excellent surveying, navigational and mathematical skills from a time beyond recorded history. There is a mass of evidence pointing to a common world-wide system that preceded a long time of decline in human civilisation. Is it ok to accept connections between say the Rollrights and Giza, and say 'look! Moon here, Moon here also! Must be a thing then!'??
When faced with the dimensions of a site, or of a monument, to make sense of them, one strategy is to try and multiply and divide them by the well known numbers, such as root 2, root 3, root 5, pi, Phi, and the number of days in various cycles, from the sun, the moon, and the planets, and of course, the various values of known units of measure. Again, however, this is not going to impress those who refuse to believe the ancients knew about irrationals. One way of giving credence to a theory is the ability to predict. After a while, as a researcher, you just know that by using anyone of these numbers, you'll probably find something interesting, but it's not easy to use those little mini personal predictions as proof unless you are working constantly in a team.
Some theories that do seem to be well-received are, to my mind, based on not entirely precise connections. For example, John Legon's Giza rectangle with √2 and √3, a purely mathematical model with no astronimical cycles involved.
If you take the N-S span of the rectangle to be 35,713.2", and 29,227.1998" for the W-E span (Petrie's numbers), the 35,713.2" side then is composed of 20.619" x √3 x 1,000, and the 29,227.1998" side is 20.66675" x √2 x 1,000. You could say that the beauty of this interpretation is that it implies no cubits or any unit whatsoever, it stands on its own as a ratio of √3 and √2. But take one side of the rectangle, say 35,713.2, and divide by √3, and multiply by √2, and you get 29,159.7056". That's 67" too short. Or check the ratio the other way round, so 29,227.1998 x √3 / √2, and it's 82.7" too long. I'm not sure this really works. To keep the moon out of all this, and try Mars instead, but staying with inches, taking 686.971 for the orbital period, you get a closer fit, I think.
The W-E span could be expressed in terms of the Mars orbital period as: 686.971 x 128/3 = 29,310.7266" (83 inches too long)
The N-S span is then 52 x 686.971 = 35,722.492" (9 inches too long)
So an improvement overall but not perfect.
If you go for the moon, however, there's an improvement. The N-S distance divided by five draconic years, so 35,713.2 / (5 x 346.62) = 20.6065. The W-E distance divided by four lunar years, so 29,227.1998 / (4 x 29.53059 x 12) = 20.61929. 20.619" and 20.6065" don't necessarily match any exisiting units, but the ratios between the rectangle sides are quite good. W-E side 29,227.1998 x 5 x 346.62 / (4 x 29.53059 x 12) = 35,735.303, so that's 22"too long. In the other direction, the same ratio gives 29,209.122" for the W-E side, 18 inches difference.
There's no actual proof of a lunar connection, but it's a good fit.
As for the inch vs. the metre... personally I'm happy to just see what works. The whole starting point for me with the Giza rectangle was because of a measurement in metres and the moon. I was reading through Gary Meisner's website on the golden number (www.goldennumber.net), and I saw his diagream of the Giza rectangle. On the left, in blue, you can see the number 354.3. I couldn't believe what I was seeing. I'd never looked at Giza at all till then, I was only reading out of interest, as I'd found lots of intriguing Phi connections in megalithic northern Europe. I had read enough of Neal and Michell and Heath to know that the metre, the 'horrible French metre', was a no-no when it came to ancient metrology. And yet.. here it seemed to work. 354.367 is of course the number of days in a lunar year, or 12 lunations of 29.53059. And it's quite an important distance between the two pyramids, G1 and G2, that this number represents, as well as being one side of a golden rectangle. So I looked into a little more, and found a few more lunar connections, based initially on Glen Dash's figures.
Intriguingly the 346.62 m side is very nearly echoed, via Phi, in the N-S length of the rectangle: 346.62 x 2.618 x 10,000 / 254 = 35,726.4236, quite close to Petrie's 35,713.2" value. And what I do like about the metre is that it connects to imperial via an important lunar number: 254.
So, for me the lunar connection is a real possibility. But how to check this?
The problem the mainstream has in attributing genius to people who lived before the "Greek miracle", when Socrates and Thales and Pythagoras and Plato suddenly 'invented' all these fab new ideas and theories, is all bound up with the way modern history is taught. For example, the Copernican revolution is not generally regarded as an ancient idea that Copernicus was able to work on and prove correct. And this slight towards the ancient Greek thinkers and their predecessors verges on insulting to them, especially when it is well known that Archimedes also, in The Sand Reckoner, wrote about Aristarchus of Samos teaching that the sun stands still and the earth revolves around the sun. So really, perhaps what all heretics have in common is that they are interested in the ancient Greeks and Egyptians.
The use of the inch and foot, of the modern, imperial kind, may be controversial, but it connects significant astronomical numbers with inches and feet in other ancient sites, as well as Giza. But ultimately, the modern inch and foot are as problematic, and seemingly anachronistic as the metre, as they are really only by-products of the metre, in their present, exact form. They have been defined in relation to the metre and changed in value several times over the last couple of centuries. For me, a good explanation for the current value of the imperial inch is that it has been set to match the value of the metre in terms of 1/254, and it's not impossible that this relationship between the two is very very old. Ultimately, it all goes back to the value for the meridian circumference of the earth you go by. But who knows?
I'd also much rather be proved wrong than just not have a debate. So I'm going to go with the theory, for now, that the metre and inch are contemporary with the Great Pyramid, and looking forward to being proved wrong! :)
When the relationship between Earth and Mars is observed over a long period of time, it becomes apparent that the Fibonnaci numbers 5, 8 and 13 are involved. If we make the claim that these numbers define Earth and Venus's relationship, or 'dance', what proof do we need to back it up? It is enough to extrapolate these numbers, 5, 8 and 13, from the various cycles? Because the cycle is repeated seemingly ad infinitum, this pattern becomes a fact. Observation is enough to produce a fact.
However, when we spot Fibonacci numbers in an ancient monument, such as the Great Pyramid, is it enough to extrapolate them from the data, as we did with the planets? These numbers may appear as either ratios between entire sides, heights or lengths of the structure, or as numbers of acepted units of measure found in the structure. Is it enough to say: yes, Fibonacci numbers define this monument, as long as we don't speak of architects' intent? If not, what is missing?
If we do accept that these same Fibonacci numbers can be found in the monument, in such a way as to make them appear essential to the design, can we then go further and suggest that these numbers were deliberately placed there, by the architects? If not, why not?
What sort of proof do we require to a/ confirm that Venus and Earth have a relationship that comprises 5, 8 and 13, b/ that these same numbers can be found in a monument, and c/ that these numbers are part of the design?
(The question of whether the Venus-Earth relationship was designed is a different one!)
Is it fair to expect proof for the first two claims other than that the observation is proof enough? Even in the second case, it is enough to observe these numbers at play, and state that observation as a fact, but making no claims as to the intention of the architects or the authenticity of the units involved. But what about the third case?
It is pointless to ask for written or textual proof, if the monument in question is far far older than any surviving text which mentions it. The only real problem is the nature of the units of measure involved, and whether they fit with the construction epoch, or what we think we know of it.
Peter Strawson says: "We accept or believe the scientific theories (when we do) just because we believe they supply the best available explanations of the phenomena they deal with. That is our reason for accepting them." (Skepticism and Naturalism: Some Varieties, 1985)
The problem, of course, is the units of measure. Would it be sufficient proof to observe these same units in other ancient monuments too, and say that this Great Pyramid is by no means unique if these units are to be found there too? Or is an actual measuring rod or text necessary? Considering the great age of the great pyramid, and all megalithic structures, it is perhaps unfair of the sceptic to expect such proof. The best that can be hoped for is to observe the use of these problematic measures in other roughly contemporary strucures.
What if the great antiquity of at least one of these units of measure could be guaranteed at least? What if it could be proved that this unit was obviously derived from an accurate measurement of the planet we live on, and that such an accurate figure was only arrived at in recent centuries, long after the invention of this unit? Would this not prove that the unit, as necessarily derived from an accurate measure of the earth, must date from a time before recorded history?
Because of the great age of the Great Pyramid, the type of truth claim you can make about it cannot be backed up by any written evidence, as it is all lost. The only claims we can make are therefore of the type we make when we observe Fibonnaci numbers in Earth and Venus's relationship, purely based on observation. When we make a claim that Fibonacci numbers govern these two planets, we are not saying that Fibonnacci designed these planets, or that Fibonnacci was somehow in the deisgner's confidence. We are simply making an empirical observation.
In the light of the great antiquity of the imperial inch and foot, dating back to a lost epoch when accurate long distance surveying was possible, it is not necessarily anachronistic to speak about it in relation to the Great Pyramid. The skeptic's challenge as to the imperial inch's presence in the framwork at Giza is itself challenged. The claim that the inch is present in the Great Pyramid is based on observation, and informed (pre)historical knowledge, and so has some meaning. However, the skeptic's challenge loses meaning: both the question of the framework of measure corresponding to reality, and the question of the builders' intentions, have no verifiable answer. Therefore the challenge makes no sense.
If someone wanted to claim that the presence of the pi ratio in the Great Pyramid was invalid, this claim has no meaning either, as pi can easily be observed there, and it is impossible to prove or disprove the architects' intentions. If you wanted to suggest that this pi ratio encapsulates Mars's orbital period in Saxon feet, expressed in the height and base of the great Pyramid, the skeptic's challenge to this would be equally invalid, as long as it can be shown that the architects at Giza or contemporary architects elsewhere, on a relatively large scale, were using astronomical numbers of some sort, and that the Saxon foot is found in other contemporary structures too. In the end, what is empirically verifiable must be true, even if it's pi, Mars and Saxon feet in the Great Pyramid.
In terms of the use of a single unit of measure, it is equally hard to call. Should an interesting pattern emerge in some other contemporary unit, say pi, Mars and Saxon feet, or some cubit or other, or an imperial foot, if this can be eaily observed and fits well with the data, then what reason do we have for rejecting this observation?
So, does anything go? Can we make claims that 77 white rabbits lined up make up the length of the Great Chamber? Yes, but to quote Strawson, these rabbits do not "supply the best available explanations of the phenomena they deal with", so the value of such a claim in trying to interpret the chamber is zero. In contrast, there is value is looking for meaningful numbers in various units of measure in the Great Pyramid, especially if the units of numbers found are also present in contemporary structures. You can make any claim you like, but it might not necessarily have much meaning in the light of interpreting an ancient monument.
As for the provenance of the units in question, we can't hope to know where any cubit or foot actually originated. It is known however that many ancient units, includong some that are still in use today, are interconnected, many not merely to each other but also to pi and Phi and other constants. So it's probably more realistic to think of these units as part of a global, or at least, very widespread system of units, not as British or French or Persian or Egyptian. And on the subject of many nations at loggerheads with each other historically, it's perhaps a good time to be reminded of Edward Said's assertion that pure knowledge is impossible, and all forms of knowledge are influenced by an ideaolgical standpoint. I'm not sure that applies to the observation of 5, 8 and 13 in the Venus Earth dance. But it does of course apply to the claims involving prehistoric or modern units of measure, and also, importantly, to the skeptic's challenge itself.
We can't know the architects' intentions, therefore many explanations are possible. The imperial inch and foot, if not the modern metre, are much older than modern estimates of the earth's dimensions, but are derived from the earth's dimensions. There is no known historical period when this information would have been known. This paradox implies that therefore the imperial foot and inch must date back to before recorded history and they may be contemporaries of the Great Pyramid, or even older. This also implies that there was a time, undocumented in a conventional sense, when other precise divisions of the circumference may also have been decided upon, perhaps including the so-called ancient metre. This in turn implies that the lack of written proof of the metre before the 18th century in France is not a valid proof that the metre didn't exist prior to that time, for the inch and foot of the imperial system come from such an undocumented time also. The basis for our rejecting observations of them in the Great Pyramid, and in Giza in general, may simply be rooted in a belief that the imperial inch and foot are neither old enough nor Egyptian enough to have possibly been used there. Or it may be based on a belief that one particular type of unit alone was used at Giza, albeit in varying forms. However these beliefs are not enough to undermine the value of the observations of other units of measure there because to observe these units at play there is enough to make a meaningful claim about them, as long as architects' intent isn't invoked.
1 Translated by Josephine Nauckhoff