I have no real explanation for why ancient people were such fetishists for astronomy. Were they that much believers in astrology and horoscopes? Did they have a religious belief that building numbers from calendars or decimal numbers that carry out for forever like Pi or 1.333333333… into their architecture meant they were building the imperishable cycles of the heavens or of mathematical eternity into their works?
Perhaps there was some other purpose that we have yet to understand, such as some link between calendar cycles and potentially catastrophic events such as droughts, that led such a phenomenal preoccupation with astronomy – or perhaps it’s simply as I’ve suggested before, the stars in the sky were what there was to watch at night before there were “stars” on TV.
Maybe we are still begging for explanation that we already have. In a way, there is enough of a purpose in all this just in the use of the stars or planets for purposes of navigation by night, a concern that has probably become dimmer for us now with every new streetlight and each advance in electronic navigation.
What is clear is that these concerns did not evade the concerns of metrology; quite the contrary, one major ancient unit of measure after another has been shown to have a value in Imperial measures that is quite prominent in basic calculations of multi-body calendar system, as has often been discussed in considerable detail here.
This happens with such frequency that it is less and less of a leap of logic to assume that these ancient measures began with astronomy, and even that accurate metrology was probably originally created as a way of writing down these calendar values is a universal language that can exist independently of the written word, which may help to explain the rarity with which these important operations were written down in textual form (as may the durability of the architectural medium as a vehicle for storing such data).
Because of these relationships, we can scarcely apply 1 Remen, let alone 3, without making reference to the Solar Year, or 1 Royal Cubit without making reference to the ratio Solar Year / Lunar Year, which may suggest to some that all of this was incidental if one cannot use a value of 4 Royal Cubits without making reference to the cycles of Mars or etc, yet it is much more difficult to believe there is anything incidental about these relationships in terms of their roots and origins.
To put it somewhat more casually, “Okay, so maybe they didn’t mean Mars every time something measured 4 Royal Cubits wide, but how on earth did they end up with units with values that could even have us asking this question in the first place?” – which is why I find a number of my working assumptions more or less unavoidable, no matter how we try to look at it.
The ancients very much seem to be eager to talk about astronomy, and they seem to have a great deal to say on the subject.
To put it another way – yes, they are constantly referencing astronomy with simple applications of common units and more or less unavoidably so, and if they did not wish to do so, they should and could have have simply chosen different units. They did not; instead they held onto these unit values as if they were consciously preserving what they believed to be the very oldest mathematics.
There is little saying they were not aware of this, and there is little blaming it on “coincidences” involving the Imperial Foot. Finding a unit value for reference that would give all these splendid astronomical meanings to ancient units must be harder than literally finding the proverbial needle in the proverbial haystack., the sort of “coincidence” that is engineered long before it ever happens by chance.
The much greater likelihood would seem that this most magical reference unit, the so-called Imperial Foot, has been with us since the beginning, and there are at lest three or four mathematical schemes that stand in evidence of how and why.
The “clincher”, though, would have to be the extraordinary frequency with which we find unit values in Imperial spelled out as ratios between proximal parts of ancient architecture.
I hope that by now, everyone understands what my model of the Great Pyramid actually represents. The origins of the extended model are simply that the height of the Great Pyramid as it currently stands was given by multiple sources as between about 452 and 454 feet; I originally proposed the value of 452.893421 feet purely because Carl Munck held this number in such high regard, referring to it as a “Holy of Holies” and I thought this interpretation might make him happy.
It was only some time later that I realized myself more about what I was looking at, that this gesture had created a ratio of 1.718873385 x 10 – the value of 10 Morton Royal Cubits in Imperial feet – as the ratio between the whole pyramid and the part now missing.
In other words, I’ve been seeing this “unit value in Imperial measures as ratio” phenomenon since the very beginning of my Egyptological studies, and last saw it as recently as my last Egyptological study, where we find Remen in Imperial as ratio in the data from Mariette for one of the coffers in the Saqqara Serapeum, the ratio between the coffer’s iiner and out length, or even from the raw data, 3.85 m / 2.17 m = 1.214511041 = ~1.216733603.
How do we justify this assessment of the Great Pyramid’s missing section? If we look at the Great Pyramid in its present condition, there is almost 28 feet missing at the top, and yet from bottom to top we see it stripped only of the prized casing material, implying that there was a definite cut-off point some 28 below the projected apex with the pyramid above this level made of a different and presumably prized material that supported the actual capstone. I would quite be surprised if the capstone itself exceeded 7 feet in height.
At any rate, what prompts this post is some initial reflection of the idea of astronomical values being “built into” metrological units.
Being quite surprised to find that later Egyptian dynasties in the Faiyum region seemed to be preoccupied with what is now referred to as the “Faiyum Wonder Number”, I could not come up with an explanation except the desire to emphasize the Half Venus Cycle /Calendar Round perhaps more than had been done overtly at Giza, because 3 / Palestinian Cubit = Faiyum Wonder Number / 10 and 4 / Palestinian Cubit = Calendar Round / 10^n.
What this actually distills down to is the ability to side step the calculations in designing architecture. If we know that the Palestinian Cubit is related to the Calendar Round in such a way via a whole number, if we want to write the Calendar Round architecturally, all we really need to do is select ANY valid whole number of Palestinian Cubits for a proportion, and know that someone can – and hopefully will – come along probing the unknown values with whole numbers, and they will soon find it very easily, because we know that the Calendar Round is built into the Palestinian Cubit.
Likewise, if we want to discuss the Solar Calendar Year, we can use ANY valid whole number of Remens, and the same applies, because the Calendar Year is built into the Remen, and etc.
Ideally then, if we can begin to associate unit values with their related astronomical values, then we may be able to infer the astronomical subject material in question from the unit that was used, regardless of the actual value, because if we stop to notice, the stars are often built right into the measurements themselves.
–Luke Piwalker
Luke Piwalker 