It may be time for a break from Stonehenge, I’ve done a lot with it recently and it’s assisted us in having what look to be like the right formulas for Anomalistic Month and Eclipse Year, and it’s even helped us to understand a “C” set of calendar values and the correct placement of the Venus Synodic Period within its respective calendar set, for the first time since this inquiry into the possibility of ancient calendrical architecture began three years ago.
As I said, I really wouldn’t mind getting back to Mayan studies, and the first place my mind tries to wander back to is still Rio Bec. I’m still in awe of the architect that designed at least one of the main structures partly described by Andrews, who seemed to have an unusual gift for making use of neglected numbers.
Something else that presumably the same architect achieved was making rooms into mathematical formulas on multiple levels. It’s still too soon for me to declare that since I can’t offer all the data involved and indeed cannot count the structure in question as being successfully solved, but I invite the reader to consider this carefully for a moment.
What we are talking about here is most likely not only rooms designed as self-referential geometric formulas, but at the same time the usual type of data display is likely riding “piggy-back” on top of that.
Imagine for just a moment just how mathematically demanding a mandate like that has to be. As I said, I am literally in awe of whoever designed that. It seems to make a relatively small and modest Mayan building into something to in ways rival the Great Pyramid, and we barely have any data on Rio Bec to speak of yet can still point this out.
Anyway, I thought it might make for a good occasion to go over some of the basic premises I work with. I expect every room I encounter in ancient architecture to have carefully chosen length, width, and height that assemble into meaningful mathematical formulas, and years of working with the data have taught me that I should expect that, even if I still haven’t solved half of what I’m looking at.
The premise here is that “sacred” mathematics must have been the domain of both astronomers and architects, with who knows how much overlap between the two in any given instance.
Ancient architecture was used as if “paper”, and ancient architects used it to try to immortalize it to “write down” important formulas that they knew (particular those concerning astronomy, is what it looks like), and important building commissions may not come along every day, so the “paper” they used was still in limited supply, so they let nothing go to waste.
They used stone as “paper” to the best of their ability with no feature being simply by chance, with every measurable quantity having a deliberate and well-chosen meaning.
The idea of nothing being by chance and nothing going to waste here is premise you will encounter as far back in this work as Carl Munck’s own efforts and writings.
Beyond this, the durability of the medium – the permanence of stone compared to that of paper – and the advantages of using a more durable medium to “write on”, are hopefully self-explanatory.
I recently raised the possibility with a skeptic who asks for written proof of this ancient mathematics – show us a papyrus where it’s written down that the ancient Egyptians could conceive of a decimal point or long division – that maybe ancient people simply weren’t in the custom of writing it down because once you start committing these equations to papyrus you’re at risk of depleting the national supply of the stuff.
I’ve filled whole shelves with my limited calculations, and Carl Munck is said to have filled whole rooms with his, the sheer volume of his notes being owed in part to many of them having been taken prior to the general availability of pocket calculators, and we are still barely scratching the surface of ancient mathematics.
I want to tell the reader the point of all this, why all this is so important to consider, and I’ve probably never been good at articulating it. For my own participation in it, I’ve felt like it was important to prove that ancient people were capable of understanding highly sophisticated mathematics, as if it would actually prove that ancient customs were something that should matter to highly sophisticated people and not a bunch of superstitious rot.
The most common thread running through any account of why this matters is something of an object lesson in prejudice – sometimes I think I’d like to approach any member of the 22/7 squad who thinks that 22/7 was the best ancient people could do for Pi as to grip them by the lapels and say, “Look, would it kill you to try to give them the benefit of a doubt that they were smart enough to have figured out decimal points and long division long before a fragmented and devastated historical record gives them credit for?”
What I am saying in my work is what the ancient Egyptians commemorated as metrological units are some of the oldest numbers and math to mankind that demonstrably, easily derive from trying to work out the very first calendars, and that the AEs as we call them, had worked that notion out for themselves, with their architects and mathematics taking it into consideration in their choice of metric units.
That would have given mankind hundreds or more likely thousands of years to perfect mathematics.
What on earth is so implausible or unthinkable about that unless one actually relishes the idea that they are so much smarter than their ancestors?
If I could find my copy of John Michell’s Secret of the Stones, I’d quote the passages on urdummheit, the theory of “original stupidity”, that the early back you go in time, the dumber people were, until finally way back there, they were too stupid to come in out of the cold and became extinct before they could give rise to the likes of us.
What’s wrong with that picture? Often plenty, obviously.
I’ve no wish to become an example of Godwin’s Law here, and that certainly isn’t the point or intention, but there is a reason after all that a German word is being used for the phenomenon of urdummheit, and much more innocently many of have simply spent a lifetime having it drummed into our heads by advertising that what we have is bigger, better, faster, stronger and smarter than anyone has ever had before and that anything that came before it including last year’s model is junk.
Better yet, I could recommend some of U. Utah Phillips’ astute comments on how this is done with with own contemporary culture, the dismissive bundling of popular music or culture by decade – “Oh, that’s that fifties stuff” or “sixties stuff” or what have you.
By this time, having urdummheit creep its way into our view of ancient history risks going so far as coloring what we are able to even perceive about our own past as humans. Remarks may arise like “the ancients couldn’t possibly have known something like that” – because? Because they were ancient? As if a single individual cannot acquire remarkable skill at something with a lifetime of practice, no matter what century it may be?
I am not even going to bother asking what could happen next if prejudice gets a foot in the door, but that isn’t the point. I’m sure it’s how much that decent conscientious people still outnumber raging bigots that keeps us safe before it’s knowing that many ancient mathematicians, like many of us in our vocations, were awesome at what they did.
The ancients, unlike us, may have a very different mindset than the “bigger, better, faster, stronger and smarter” that we’ve become so accustomed to ourselves, and instead honored and upheld traditional ideas and standards to the point that we may look back and mistake that for cultural stagnation.
The tragic part of this is that if we rest a little more faith in them, and their skills and their abilities, the ancients may still have something to offer us, if only reassurance, even if we haven’t really any use for all this fancy math I try to demonstrate that ancient people were doing.
Imagine someone being convinced that the Y2K Bug was going to set civilization back a thousand years, but not looking to people a thousand years ago and their writings for tips and advice on how to live at that level of civilization.
Those people wrote the book on how to survive without the last 1000 years of technology, and they may have some helpful hints because of it, and a phenomenal wealth of ideas may survive as folklore and mythology if we sometimes dig just a little deeper than face value.
That’s really what we’re talking about here, is the possibility of cheating ourselves out of seeing something truly amazing (or even something useful) by reflexively looking down our noses at our ancestors, that’s all.
In case that sounds a little preachy in parts, if I’m preaching it might only be the choir, but I already know I’m not entitled to a soapbox anyway if the sermon is still as much for my own benefit as anyone else’s.
My recent work with Stonehenge has probably taught me already that even the likes o’ me still has at least a nagging touch of urdummheit myself. If I’m not actually a little surprised they were even capable of what I see, I’m still a little too surprised that they summoned the skill to actually pull it off.
I’m rightfully in awe of what I see, but I shouldn’t be surprised by it.
The best part of it is perhaps that with Stonehenge, I have a sense of my own ancestry being involved that I’m not going to get from studying ancient architecture in Egypt or the Americas, and the level of skill I’m seeing in it lately makes me pretty proud to think that this is what I come from, as opposed to thinking they were primitive, superstitious idiots.
As far as I can see, the view seems to be worth the climb.
So, this post being about what mathematicians wrote on back in those days, and how paper was precious, I think it might be safe to say that at Stonehenge, they were definitely not wasting paper.
–Luke Piwalker
Luke Piwalker 