Scrutinizing Stonehenge

This may be hard to explain, so please bear with me here. Having Stonehenge seemingly volunteer data on the Eclipse Year, I’m wanting to take stock of just how much planetary data we have already seen it expressing, and I’d like to see how it might express whatever is missing for that list.

One problem with this is that much of this planetary data for the visible planets is still under consideration as to which candidates might represent the “A” and “B” values that belong to the respective main calendar sets. Having to inspect Stonehenge looking for values that haven’t been clearly defined yet makes an already challenging project that much more challenging, even if in the final accounting we can hope that Stonehenge has enough to say about planetary cycles to assist us in being certain of any particular choices from the nominations.

I wouldn’t put it past the ancients to have data to offer on planets they were weren’t supposed to know about, but I don’t have any claims to make here. Rounding up any evidence related to their possibly being aware of Neptune or etc would be a massive project in itself of combing through history, and I’d rather work with the numbers, especially if I’m going to have any monopolies by default on certain perspectives relating to the numbers.

One nominee for representation of the 378.09 day Saturn Synodic Period is the 377.8020786 ft side length (unpaved) in my model of the Great Pyramid, which might then require from Stonehenge a demonstrable affinity for the “unpaved” figures for the Great Pyramid – which it may have, but it might take more than that to be more conclusive. It is an intriguing prospect, though, and a noteworthy one.

I’m also looking more at possibilities of representing multiple Lunar constants by their ratios, although it still looks pretty tangled to me. What’s interesting to me here are some recurrences in a particular range, which ideally might provide some small semblance of a frame of reference

Lunar Month ~29.53 d / Draconic Month ~27.2122 d = 1.085175032

Jupiter Synodic Period 398.88 d x 2.72 = 1.0849536

In a similar range are expressions like ~(360 / Lunar Year) x 1.067438159 or (2 / ~Phi) / 1.067438159^2. Also occurring in this range are figures such as 360 / (1 / (Perimeter Great Pyramid, paved) = 1.086519707 and, perhaps particularly interesting since I’ve given 892.9807632 as a possible max diameter on the Aubrey Circles, 892.9807632 x Remen in feet = 1.086519701.

Sadly, this doesn’t quite match some other interesting candidates such as height Great Pyramid (after pavement) 480.3471728 x (1.177245771^5) = 1.086152820 but a silver lining here may be that 480.3471728 / (1.177245771^1) = 1.5 x 2.720174976 and 480.3471728 / (1.177245771^2) = 346.59399367, making this likely Eclipse Year figure quite easily found in the Great Pyramid.

There may be some tough decisions ahead making sense of all that unless the ancients found some ingenious and inclusive strategy so that nothing important gets left out there. We do already seem to see a lot of that kind of thing where we begin to interchange the “AEMY” and “IMY” Megalithic Yards in the equations, and it may be safe to say we have already seen Stonehenge being very inclusive when it comes to relationships of the Remen and 1.067438159

Another intriguing one may be Eclipse Year 346.62 / Lunar (Synodic) Month 29.53 = 1.173789367. That might be the often mentioned figure “Alternate Pi” (Munck) 1.177245771 by some reckoning, but in case that’s too much of a stretch, I’ve been having a new look at an old number — 1.174718783.

1.174718783 seems to be a number I announced first to the world, in early October of 2004, with nothing being posted after that, to the best of my ability to determine. I supposed I’d have to guess it quickly fell through the cracks for being uncommunicative, in spite of a robust affinity for the Radian.

Normally if something talks to the Radian, we’d expect it will be happy to talk to Pi, 2 Pi, or 360, but occasionally we get exceptions, and this wouldn’t be the first time that a number has been found that may be one. It almost seems typical for such numbers that will only talk to the Radian primarily, that they tend to do so at unusually high powers of the Radian. They can be good at ignoring the standard power probes like 1.177245771 and 1.62231147, which is another thing that can make a large contribution toward a number’s obscurity.

I also find it interesting that the ratio between Eclipse Year 346.62 and Draconic Month ~2.72122 is about 4 / Pi. Not only is that a possible calibration point for some of this, but it tries to give me a mental picture of someone squaring the circle over a side view of the Cheops pyramid and then placing the moon in an “orbit” above it (I’m not sure having seen diagrams like “thousands” of times is an exaggeration), and I suppose it might only make things worse that the 120 Meg Yard outer perimeter of the sarcen circle expressed in feet / the “unpaved” perimeter of the Great Pyramid = 1080 / 10^n since many such diagrams or their accompanying text makes 1080 miles to be the moon’s radius.

Examining the relationship Venus Synodic Period ~584 d / Eclipse Year 346.62 = 1.68484219 may raise some interesting possibilities. This figure is quite close to 8 Palestine Cubits of some kind, this particular equation pointing to one at about 2.1060 rather than necessarily at my favorite of about 2.1070.

A Palestine Cubit of this sort can be obtained from the equation Radian / Megalithic Yard = 57.29577951 / 2.720174976 = 2.106326983 although its constituency according to “Remen x Royal Cubit = Palestine Cubit” may be uncertain. It may be more the stuff of “Remen x sqrt 3” instead?

Perhaps I shouldn’t go off on such a tangent just now, but more is probably due the reader regarding the sorts of “sqrt 2, 3, 5” we might see with this style of math.

Note that if we retrofit that equation with the Incidental Meg Yard of 2.719256444, we get

57.29577951 / 2.719256444 = 2.107038475, my favorite Palestine Cubit.

In spite of its incidental origin (in modern times at least), the “Incidental Megalithic Yard” is not necessarily quite so incidental mathematically.

So I’m seeing more than several equations involving one of Stonehenge’s apparent favorite subjects, 1.067438159, since seeking the ratio between the Venus Synodic Period and the Eclipse Year, but I should note that the same may also be true for another number, which is one I’d like to emphasize again – 1323.891320.

I could start out reviewing again how this number came to light. It does have priors all the way back to about August 2004, when I decided it was the perimeter of a Thom Type A flattened ring at Callanish (and a month later it came up again trying to redeem an imposter version of the Square Root of the Volume of a Sphere) but it managed to be forgotten in all the turmoil over cartography.

More recently, it secured attention when I went to experiment with circumscription and inscription of the Great Pyramid and other major Giza pyramids in vertical planes through the center of opposing sides and through their diagonal length, experiments which gave some uncanny results including showing 1.067438159 and 1323.891320.

In August 2004, I pointed out that 360 / 132.3891320 = Incidental Megalithic Yard 2.719256444, so at Callanish we seemed to have already been looking at evidence that the application of “AEMY” vs “IMY” might be selective, if it’s even that limited at other sites since it apparently isn’t at Stonehenge.

It also came to light in the here and now that 5 / 132.3891320 = a number I still hesitate to talk about because even though it seems to be important, it also seems rather strange and perhaps too easily confused with other things that perhaps it would be better to have a better grasp of before tossing the unnamed number into the mix.

Interestingly, for the second time a hint that the design of Stonehenge managed to embrace functionally one of the odd variations on the Remen generated by Stonehenge’s vast ambition to talk about the Remen and 1.067348159 in great detail. I’ve yet to see what looks like a functional role for the (1.067438159)^3 = 1.216264895, but this may be twice that there are hints of one for (1.177245771 /1.067438159)^2 = 1.216322751.

More interestingly, a first casual search for more planetary data at Stonehenge has somehow also shed more light on the candidate Draconic Month figure of 2.721223218.

In addition to the classic formula 10313.24031 / (19.46773764^2) = 2.721223218, I’m starting to see things like 132.3891320 / (1.067438159^3) = 2.721223218 / 4 (or (132.3891320 / 4) / (1.067438159^3) = 2.721223218) and (Pi^3) / (1.067438159^2) = 2.721223218.

Depending on finer details, the conjunction of Venus Synodic Period and Lunar Ratio may also establish a rare opportunity to ply 1.067438159 at unusually high powers perhaps as high as 1.607438159^6, whereas even for how much I’ve worked with 1.607438159, the previous record may be 1.067438159^3. I’m sure Stonehenge would love to do that if it can find a way somehow.

One of the troubling things in all this has been how often these ~1.0849-1.086 numbers show likely relationship to the Indus Foot without being willing to show what looks like any proper one that I’m able to recognize so far. That’s still a mystery, and makes it less certain how to proceed with evaluating what’s in this range.

I did also run into several possible nominations during the latest inquiries for the Anomalistic Month of “27.55454988 days” (Wikipedia), which turn out to be AEMY / (Pi^2) — 2.720174976 / (Pi^2) = 27.56113483 / 10^n and IMY / (Pi^2) — 2.719256444 / (Pi^2) = 27.55182815. 

I don’t know if they actually work in practice, but they have nice pedigree, perhaps particularly at Stonehenge where there’s focus on the Megalithic Yard, and with such pedigree may indeed work well there, but I haven’t actually tried them out yet and there’s still a lot to consider.

Regarding the still somewhat surprising nomination of 138.6375748 as the perimeter of the bluestone “oval with corners” (Thom, perimeter 51.06 MY x 2.72 = 138.8832000 ft, one possible vote of confidence for it may be that compared to the 120 MY = 326.4209971 ft outer sarcen circle perimeter,

326.4209971 / 138.6375748 = 2.354491541 = 1.177245771 x 2 — there’s Stonehenge still upholding a great dedication to the expression of 1.177245771.

One of the other things it could have done to make such a gesture is for the perimeter to be 138.5907605 ft rather than 138.6375748 because 1.177245771^2 = 138.5907605 / 100, which the perimeter actually is when reconsidered after swapping in IMY for AEMY.

Thanks to this versatility of the Megalithic Yard, the designers of Stonehenge seem to have very deftly managed to write 1.177245771 x 2 and 1.177245771^2 with a single brushstroke!

Is that not absolutely remarkable?

Also surprisingly, 138.6375748 responds to the square root of a false Remen constructed as (1.177245771 / 1.067438159)

138.6375748 x (1.177245771 / 1.067438159) = 152.8992544, 1/2 of the inner circumference of the sarcen circle in feet.

Probably the most dramatic support for the proposed 138.6375748 value is its interaction with (10.67438159 / 2) = 5.337190795, 53.3719095 MY also being the apparent circumference of the inner bluestone circle once its “17 MY” max diameter is recognized as 2 / 1.177245771 = 1.698880598 MY.

138.6375748 / ( 5.337190795^1) = 25.97575757

138.6375748 / ( 5.337190795^2) = 48.6634438 / 10

138.6375748 / ( 5.337190795^3) = 9.118906603

138.6375748 / ( 5.337190795^4) = 1.708559231

138.6375748 therefore belongs to a series already running through Stonehenge that includes its 25.97575757 x 2 = 51.95151515 ft outer sarcen circle radius and its 48.6634438 ft inner sarcen circle radius, making it a possible next logical step in the series or progression.

At the lower end of the series, 9.118906603 = 364.75626211 / 4, with 364.75626211 (the “B” version of the Earth year) standing in for 365 days, and 1.708559231 is something I probably shouldn’t get into, other than that historically it’s one of two candidates for the theoretical height of a certain Egyptian pyramid without its pyramidion (Teti’s), a matter I have yet to resolve because both candidates seemed to show considerable merit and pedigree.

I also hate to bring it up for fear someone may mistake it for a cubit of some kind, when we already have would-be cubits coming out our ears. I’ve yet to encounter any appreciable incentive for it to be some kind of cubit, even if it might be near to some bona fide example of a short one, such as the cubit at Karnak mentioned by Berriman.

I would have to go over my notes carefully to say much more, but I think the essence of the debate must have been something to the effect of

1.5 x 1.067438159^2 = 1.601157232 x 1.067438159 = 1.709136340

VS

(57.29577951 / 2) / 1.067438159 = 19.46773764 / (1.067438159^2) = (103.903030 x 2) / (1.067438159^3) = 1.708559217, our “mysterious” number in the Stonehenge series just shown.

In spite of such apparent successes as with that (1.067438159 / 2) series, Stonehenge still holds many mysteries. Consider the “14 Meg Yard” minor diameter of the bluestone ellipse. 14 x 2.72 = ~38.03 ft. It could easily pass for the Venus Cycle (canonically, 37.960 = (18980 x 2) / 1000), but will that work in harmony with its mathematical environment?

Hopefully we will continue to learn more about the amazing Stonehenge.

— Luke Piwalker