The Current State of Ancient Metrology
Several more probable ancient units of length measure, thought to have been used to express astronomical / calendar related values, have been discovered since last posting.
At present, the all-inclusive series (which seems to find the proposed Egyptian Sacred Cubit in the middle) looks like this, after the realization that both the “Best Eclipse Year” and “Best Anomalistic Month” values must represent values with their own novel metrological unit.
Have we finally found the end of the metrological unit series based on the Sacred Cubit and (2 Pi)^n with the “Anomalistic Month Unit”?
At least two more possible members of the other vital metrological series, based on a whole number and 2 Pi, have now been identified. The series has been extended by as many as three possible units and may run to at least (Pi^8). The series based on a whole number and 2 Pi.
The metrological unit series based on a valid whole number and Pi (or 2 Pi).
On an explanatory note, these equations don’t necessarily generate the familiar unit value per se, but what they will generate with certainty is at least a simple fraction or simple multiple of the familiar unit. At least one of these units values – such as the Outer Sarsen Circle Unit – may still be an unidentified quantity; at this point I still know only that we can construct the Stonehenge Outer Sarsen Circle radius and diameter, and the height of the Great Pyramid, from this unit, whatever the preferred form of the unit may be.
At this hour, a predicted unit based on a valid whole number and Pi^7 remains completely unidentified, although it is now thought to exist because the unit of the Venus Orbital Period C value lies beyond it in the same series at Pi^8.
I have been working with the concepts seen here
What we are seeing in these series tables is indicated at upper left, as the ability of Pi or 2 Pi to connect metrological unit series exactly.
The realization that there was more to the whole number based series than the units using Pi^1 (the Egyptian Royal Cubit) through Pi^5 (the “Alternate e’ Megalithic Yard” or AEMY of 2.720174976, still apparently the primary Megalithic Yard value) came about when I was working on a very first draft of a table illustrating some of what is indicated at upper right in the chart, of how unit values can be generated by multiplication and division of other units.
This again hopefully goes to underscore somewhat the amazing collection of ancient units we are dealing with, that they can be connected in such ways, and especially simultaneously.
The first rough draft of a metrological relationships table (incomplete) showing the ability of ancient units of measure to transform each other into other ancient units through multiplication (x) and division (/).
As I pointed out in a recent post to the Megalithic Portal forum, having displays like this may help us to simplify things and to think more like the designers of ancient architecture may have been able to think of their designs. We can look at this and rather than using trial and error and countless calculations, we can see at a glace that if we want to write the Draconic Year = Draconic Megalithic Yard, we can for example write it quite simply as the product of length x width of a room measured out in Short Remens and Royal Cubits.
During the course of preparing it, it was discovered that the Egyptian Mystery Unit of 1.676727943 ft and a Megalithic Foot of 1.177245771 interact to create a unit based on (Pi^6). The value in question has long been known as one of the original “Tikal Wonder Numbers” but it was not realized that the resulting value might belong to a whole metrological series that includes the Royal Cubit and primary Megalithic Yard values.
That is, 1.676727943 / 1.177245771 = 1.424280286, which I have written about in some detail at least as far back as this post. This “Mayan” number was subsequently found in the architecture of both Giza and of Stonehenge.
As these proceedings represent something of an experiment in progress, I have not yet managed to explore the metrological makeup of every important number that is known to us, so there continue to be such occasional surprises.
Regarding the number that has found its way into the Pi^8 column of the smaller table, the Venus Orbital Period C value seemed to be strongly indicated by Stonehenge upon closer inspection, and it wasn’t long before the corresponding Calendar Round C (HVC C) value was found in the Great Pyramid with ease. (It had previously been thought to be “noise” rather than “signal”).
One reason the VOP C value became recognized is because it is the product of the standard Palestinian Cubit x the Hashimi Cubit, both prominent units of measure that seem to be used in the Stonehenge design
Palestinian Cubit 2.107038476 (ft) x Hashimi Cubit 1.067438159 (ft) = Venus Orbital Period C 224.9133272 / 100.
It was then discovered that there is probably sufficient reason for being recognized as a valid representation in its own right, in addition to it or its corresponding Calendar Round value ((VOP x (1 / (12 x (Pi^2))) = Calendar Round (Half Venus Cycle), the customary relationship between VOP and HVC seen and used in the Planetary Cycle Tables) being retrievable from various notable ancient monuments or artifacts.
Some General Comments on Mayan Matters
I should mention that numerous sources will inform us that I have the wrong answer to the question “Is it Maya or Mayan?” in using “Mayan” as I do. I continue to do so probably because of being a creature of habit; I am using “Mayan” to indicate “of the Maya people” just as we would use “Egyptian” as if a possessive to indicate “of the people of Egypt”. At least we know enough not to refer them as “The Mayans”.
I have been looking for any materials that might help promote a better understanding of how planetary activities are described in ancient American myths, with emphasis on the possibility that the frequently associated “captive” motif may be a significator of planetary activities associated with retrogrades that may coincide with the close of a calendar period, following up (or attempting to) Susan Milbrath’s suggestions regarding Jupiter and Saturn.
It’s very slow going and rather time consuming, and yet a better understanding of the translation of astronomy into art and stories still seems urgently needed; without it, we may risk falling into the trap of what may be doing little more than still repeating the same Conquistador propaganda that was used to justify the conquering and pillaging of the Americas.
What has been encouraging is that although the archaeological orthodoxy are still good for going endlessly on about “ritual sacrifice” and indeed, trying to make some superstitious “ritual” out of virtually any and every aspect of ancient American life, they may nonetheless be an important source of materials that contraindicate barbaric, superstitious ritual cultures.
In fact, even though there are limits to even my own generous view of cultural diffusion, in which ancient transoceanic voyages were probably somewhat commonplace and may account for a striking number of uncanny cultural parallels between “Old” and “New” worlds, I wouldn’t want to miss the possibility that as with “creation myths”, the parallels between Old World and New World “astrological” concerns may run deep.
The latest remark I have committed to notes asks the question, “What if Mars was the “war god” or “war planet” for ancient Americans just as it is said to have been for ancient Greeks and Romans, and what if the very mention of the theme of war refers to the planet Mars?
Something that I would hate very much to lose sight of here is that the science of astronomy reveals that the planets behave according to what are ultimately the rather predictable routines of inanimate objects in their orbits, an observation that by rights should quickly raise questions about notions that planets are the unpredictable, erratic, sentient gods that historians so often insist that ancient people thought of them as – quite possibly due to misunderstanding how ancient mythical iconography works.
I’m reminded of some of Bill Saturno’s comments about the “end of the Mayan Calendar”:
“The ancient Maya predicted the world would continue, that 7,000 years from now, things would be exactly like this,” he said. “We keep looking for endings. The Maya were looking for a guarantee that nothing would change. It’s an entirely different mindset.”
How do we reconcile this sense of keen awareness of the regularity and dependability of the Solar System cycles with the idea of endless offerings made to placate unpredictable and easily angered “gods”?
Maybe the truth is that we can’t, and that it’s time to accept that, and to accept what it means, even if all the talk about blood, guts and gore is more titillating than simply thinking of ancient people as harmless Carl Sagan types.
Further Perspectives on Calendar Mathematics, and Is There a Truncated Calendar Round?
At any rate, I also continue to seek progress in understanding the mathematics involved here, in spite of a great many discoveries already made about how ordinary crude ancient calendar numbers can be more effectively represented through close approximations, such as using 365.0200808 instead of 365 for the Solar Year or 353.9334578 instead of 354 for the Lunar Year, and etc.
While the best ways to reconcile diversity in ancient calendar systems are still under investigation in this work – after all, we have it that our system can successfully represent Solar Year values of 360 days, 365 days, 364 days, 365.25 days or 366 days for a Leap Year, which makes it no simple thing overall – some new observations continue to come to light.
The classic canonical Calendar Round (half Venus Cycle) is 52 years = 365 x 52 = 18980 days; what is the best way to use a 364 day year with this?
One way of looking at it may be two multiply 52 years by 364 days, believe it or not.
364 x 52 = 18928 days.
I have no idea where this figure would be located in academic materials, or what it would be called, but there may be possibilities that it is a viable figure. For reasons unknown, a figure like this had begun to appear in some of my calculations, and I tried to ignore it until I looked at the equation above.
In my notes on the possible figures for Altar 11 at Oxpemul, we find
“The thickness of Oxpemul Altar 11 may be another instance of 1.834791047, only this time in the thickness of the artifact rather than in the radius, diameter, or circumference.
This would give us
5.156620150 / 1.834791047 = 2.810467250
5.156620150 * 1.834791047 = 9.4613204839
The ratio is obviously coherent, it’s 1/8 of the Venus Orbital Period / 10^n and it may not be the only instance of that in this list; the resultant product I’m not so certain about and would like to see some stronger showing of its reason for being there. To be honest, it does wax very close to the Calendar Round without actually getting there, and contains a “mystery number” in that 9.4613204839 x 2 = 18922.64097, rather than something closer to the Calendar Round range of ~18980 +/- 18, which might be more sensible for it to be at least as far as the diameter x thickness product goes.”
To see if the numbers currently in use can actually facilitate such an expression, I’ll use the very popular 52 approximation from Stonehenge, the outer Sarsen Circle radius of 51.95151515 ft
18922.64097 / 51.95151515 = 364.2365562 — and I believe that actually could be the current top candidate for use in approximation or representation of “364“.
So, it may be possible that we also have a “truncated Calendar Round” loose in the works along with the standard “A, B, and C” figures.
I was looking again at some of Bill Saturno’s work and comments; having achieved what I think is some success in understanding and adapting some of the variant figures in the Dresden Codex – i.e., 117 instead of 116 days for the Mercury Synodic Period and 585 instead of 584 days for the Venus Synodic Period – I was interested to see if there might be something in the calendar related discoveries at Xultun or San Bartolo that we might be missing out on.
In doing so I was reminded of something I’ve known about for a long time but have never quite understood, which is the use of the raw numbers 177 and 178 as pertaining to Lunar Cycles.
Quoting Bill Saturno again
“The span between the final two columns is a lunar “semester” of 178 days. Subtracting either 177 or 178 from the penultimate number (4606), we arrive at 4429 (12.5.9) or 4428 (12.5.8) days, both of which fit with what remains of the third-from-last column. In this light, it is reasonable to suggest that the Xultun number array represents a running sequence of consecutive multiples of 177 or 178 with only the last three totals well preserved. The numbers 177 and 178 are important in ancient Maya astronomy. The eclipse tables on pages 51 to 58 of the Dresden Codex are based on these same intervals. The Dresden tables use this basic unit, along with an interspersed correction span of 148 days, or five lunations, to represent patterns in both lunar and solar eclipses (8, 11). The 4784-day Xultun array represents 162 cumulative 6-month lunations (162 × 29.530589 = 4783.9554), or twice that of the Palenque lunar reckoning system (8)”
“For the record”, if we combine the two numbers, we get 177 + 178 = 355 rather than 354, or effectively, a Lunar Leap Year rather than a standard Lunar Year.
What I am surprised to discover is the possible amenability of a Lunar Leap Year to some of the possible calculations.
364 / 355 = 1.025352113, which might be several things but at first sight it very much resembles the “Tikal Wonder Number” 1.025135530. It may not be what it looks like at first sight, and yet it at very least may belong filed under “justification” because it is a very close approximation that is derived from canonical calendar numbers.
It’s difficult to quality because the complete spectrum of what might have been done to accommodate a 364 day year still isn’t well known.
(By the way, in my notes there is a quip about “Amazing how they can understand that (162 × 29.530589 = 4783.9554) when they ‘shun fractions and don’t know decimal’…”)
On the subject of justification, which is the term I use for when one of my outlandishly inaccurate approximations turns out to be amazingly close to an actual number that can be generated from classic canonical calendar numbers, my notes on Saturno’s text include
“Incidentally, Saturno’s description of ~4428 is a better match for my version than for the quasi-canonical if it is based on the Synodic Month
1500 x 29.53 = 4429.5
1500 x 29.52 = 4428″
So yet again – “justification” – maybe some of my outlandish numbers aren’t quite so outlandish after all, once we see how they are like numbers that ancients working with calendars would have encountered in real life.
What I work with as the “Best Lunar Month Value” is 29.52390320 days, rather than something more like the “textbook” value for the Lunar Synodic Month of 29.53058798. It’s a minuscule different, but it can matter to the calculations.
The other day on GHMB, I demonstrated this series of equations that I’m still a bit proud of myself for discovering, that is only part of a bigger picture concerning the “Best Lunar Month” and the standard Lunar Year:
29.52390320 / (224.8373808^1) = 1.313122530 / 10^n = (3.282806350 x 4) / 10^n
29.52390320 / (224.8373808^2) = 584.0321270 standard (“short”) Venus Synodic Period / 10^n
584.0321270 / (224.8373808^3) = 259.7575745 / 10 = probably the most useful value for the 260 day (see Tzolkin) period
584.0321270 / (224.8373808^4) = 1.155313114 = Best Eclipse Year / 3 / 10^n
This also informs us of more ways we can find the “Best Lunar Month”, the standard Lunar Year, and the “Best Eclipse Year” at Stonehenge, even though it originates with a study of numbers from Tikal (in Guatemala) and Chichen Itza (in Mexico).
For whatever it’s worth and wherever it may lead, I have started experimenting again a little bit with the possibility of 177 and 178 being best represented as “Square Root of the Volume of a Sphere (SRVS) x 2, divided by 10^n” – that is, (SRVS 887.6223994 x 2) / 10 = 177.5244799 – and “400 / Venus Orbital Period A 224.8373080, times 100” – that is, (400 / 224.8373808) x 100 = 177.9063600.
There isn’t as much call these days to refer to it as the “Square Root of the (generic) Volume of a Sphere,” but it continues in its own way to be an important number – and after all, it’s the same number as 120 Squared Munck Megalithic Yards (SMMY). We could even obtain it from Stonehenge very easily through inference because of that, knowing the value of the Squared Munck Megalithic Yard value there, if it doesn’t prove to be woven into the intended proportions of the Aubrey Circle as well.
More recently we know that “SRVS” has considerable value as Pi / standard Lunar Year.
Pi / SRVS 887.6223994 = (standard Lunar Year 353.9334582) / 10^n.
There is more to be said, but I will leave it at that for now. That’s already a good number of things to be considered for a single post.
–Luke Piwalker
Luke Piwalker 