Seahenge

A thread on the Megalithic Portal started some 4 or 5 years ago by Geoff Bath was recently booted to the top of the board, and it managed to spark my curiosity. For some reason, I haven’t been terribly interested in Seahenge or Woodhenge – although Thom provided data on the later, I’ve generally found it somewhat unfathomable and I remain suspicious of his nice round numbers of Megalithic Yards for Woodhenge – but I can’t help but be something of a fan of Geoff’s work since to the best of my knowledge, more than one of the most important innovations in understanding ancient monuments that I’ve witnessed in the past year are to his credit.

These are innovations that have helped greatly to advance my own understanding.

In the opening post, Bath remarks “I believe that a coppiced pole of 839mm found between timbers 32 and 33 may well be the megalithic yard of 16 meg-x used at this site, and that the diameter of the originating circle would be seven such yards (5.9m).”

These specifications indicate a length of 839 mm = 2.752624672 ft. Jim (“molder”) Wakefield at GHMB, a noble champion of the Indus Foot, has suggested a Megalithic Yard of 2.5 Indus, and although I use a slightly different Indus Foot value (mainly 1.100874628), I would probably agree with Jim’s general mathematical assessment here even though I’m still likely to think that a measure of ~2.75 feet is exactly that, 2.5 Indus and not a kind of Megalithic Yard, although matters like this may ultimately hinge on mere semantics.

This Indus Foot unit appears to be one of the unit of Silbury Hill’s base proportions (diameter 500 Indus Feet), and also appears to be applicable to Mycerinus’ pyramid, albeit not in the usual “Inductive Metrology” or “whole number of units” sense.

According to Geoff’s specifications 2.752624672 / 16 = “Meg X” = 1.720390420 ft. This may correspond to the long version of the Royal Cubit 1.718873385 x 1.000723277 = 1.720116607, which is eventually a metrological fact of life; however, it’s rarely seen and rarely mentioned, and probably for good reason, and would be more inherent to architecture or geometry involving squares or rectangles.

I would tend to see such a situation as the one in actually in question here as “standard Royal Cubit x (16 x 1.000723277) = 2.5 standard (‘long’) Indus Feet”.

I will refer the reader to the diagrams on page 1 and page 2 of the Megalithic Portal thread, especially page 2 where Richard (Orpbit) Bartosz weighs in with metrological projections. While I’m not entirely certain of the data’s provenance (we will keep that in mind as we explore the data to see what we might learn), it seems to behave like good data, and the implied design logic is probably rather clever. There’s also apparently an interesting contrast to Callinish that’s most likely worth talking about.

For the circles relating to Seahenge’s arrangement, Bartosz projects 4.1292 m for the outer circle, 3.4301 m for the middle circle, and 1.2863 for the inner circle.

I have replied to the thread there to suggest that these may be intended to mean 13.49024283 ft, 11.24186904 ft, and 4.212653970 ft respectively, or about 4.111826 m, 3.426521 m, and 1.284017 m.

To offer more background on these selections, why they were selected, and what they may represent:

13.49024283 — this figure is in inverse Hashimi Cubits, or in Petrie Stonehenge Units (PSU) (they’re the same thing, the difference is really just semantics). It’s 72/10^n PSU or 144 Inverse Hashimi Cubits.

This figure may not have been intended to work with the standard linear “AE” Megalithic Yard, but rather with the inverse form of the unit. It also responds favorably to the ordinary “forwards” form of the Squared Munck Megalithic Yard.

The associated perimeter would be diameter 13.49024283 x Pi = circumference 42.38084777 ft = 360 x 1.177245771 — rather the “opposite” of Stonehenge, where 360 / 1.177245771 describes the inner circumference of the sarsen circle. This perimeter projection also works quite harmoniously with the Squared Munck Megalithic Yard (SMMY).

11.24186904 — this is of course 1/20th of the value of the Petrie Stonehenge Unit in inches, or 6 PSU in feet / 10, with the PSU working exponentially here to secure additional data, which includes the “short form” of the Palestinian Cubit, which is rather timely and beneficial, since it will probably help us along to know what it is, because the third projected figure appears to be twice this value.

4.212653970 ft — this is equal to 2 “short” Palestinian Cubits. We have recently seen where the architects of Callanish would have to accept this relatively rare Palestinian Cubit value in order to make several of their equations balance out, although at both Callanish and Seahenge, they may have chosen it deliberately simply because of the data it contains and the way that it fits together with the other pieces of the puzzle.

Whereas the standard Palestinian Cubit embodies the A version of the Half Venus Cycle (HVC), the “short” version embodies the C version of the HVC. As with the Petrie Stonehenge Unit and others, simply using these units in the first place expresses astronomical data, at least as long as we have the so-called modern foot to use for reference.

Let’s look at some basic formulas here

Radian 57.29577951 / IMY 2.719256444 / 10 = Palestian Cubit 2.107038475 = 4 / (HVC A 18983.99126 / 10^n)

Radian 57.29577951 / AEMY 2.720174976 / 10 = Palestinian Cubit 2.106326983 = 4 / (HVC C 18990.40383 / 10^n)

We of course look to ratios between components of a design for guidance as to original intent, and that consideration has been used to help arrive at the figures suggested, although products of parts (including area figures) have yet to be considered.

For the original data projections from Orpbit, “4.1292 m for the outer circle, 3.4301 m for the middle circle, and 1.2863 for the inner circle.” The raw ratios between the values of these parts are

4.1292 m / 3.4301 m = 1.203813300
4.1292 m / 1.2863 m = 3.210137604
3.4301 m / 1.2863 m = 2.666640753

The refined figures (values given in feet rather than meters here) look like this:

13.49024283 / 11.24186904 = 1.200000000
13.49024283 / 4.212653970 = 3.202314485 = 1.067438159 x 3
11.24186904 / 4.212653970 = 2.668595398 = 10.67438159 / 4

The projected circumference values are

13.49024283 x Pi = 42.380847768 = 36 Megalithic Feet
11.24186904 x Pi = 35.317373187 = 30 Megalithic feet as Bartosz noted
4.212653970 x Pi = 13.234442763

That’s where they really managed to surprise me, and that’s where we find the interesting contrast to Callanish.

At Callanish, we have been discussing the important “Callanish Number” which is 360 / IMY 2.71925644 = 132.3891319, whereas at Seahenge, it looks as if they went for the other major option, which is 360 / AEMY 2.720174976 = 132.3444275.

Why do we see some of these gestures? Well, we can see what they’re making ratios out here, the PSU and simple Hashimi Cubit fractions and multiples, so this altered value for the Palestinian Cubit sort of comes with the territory, for one thing.

However, lately I’ve been reflecting on the merits of the “short” Palestinian Cubit since it seemed to making an appearance at Callanish sites, and was reminded that it is a number of merit that is worthy of “advertisement”, and one reason for that is its responsiveness to the Megalithic Foot value I use.

What is the value of this “Seahenge Number” that is analogous to the “Callanish Number”, when expressed in Megalithic Feet?

132.3444275 / 1.177245771 = 112.4186901 = VOP A 224.8373808 / 2 — 10 times the same number in Megalithic Feet as the suggested diameter of the middle circle in “modern” feet.

I’m rather glad to see these developments since I’ve known for a very long time now that we should be expecting these variations, and have been somewhat troubled by the apparent absence of some of them.

Some of the diversity and versatility we see here of course arises from the fact that the ideal squared form of the Megalithic Yard is Munck’s (which is actually an expression in inverse Egyptian Remens). The Squared Munck Megalithic Yard (SMMY) is the only known form of the Megalithic Yard that dependably displays exponential value, and ironically given its origins in the Remen, exponential value that often seems to exceed that of the Remen itself, just as the exponential value of 2 / (Assyrian Cubit in feet) seems to far exceed the normal exponential value of the Assyrian Cubit itself.

Yet because the SMMY’s own square root is an invalid number, to construct the SMMY from Megalithic Yards, we are required to use false square root pairs like AEMY and IMY, or DMY (Draconic Megalithic Yard) and the unnamed Megalithic Yard constructed from 32 / Megalithic Foot, as multipliers.

Perhaps we could call this unnamed unit the Megalithic Foot Megalithic Meg Yard (MFMY), as long as it doesn’t promote confusion. It would actually be a timely thing to do to review interactions between the Megalithic Foot and the various forms of the Megalithic Foot, wherein a spotlight on “MY/MF” would be in order.

This is because Callanish seems geared somewhat toward the IMY as a potential primary unit (thus far Stonehenge appears to readily accommodate the IMY and other variants while seemingly reserving primacy for the AEMY). Callanish has the capacity to remind us that while the interactions between AEMY and Megalithic Foot can generate expressions of the best Eclipse Year, interactions between the IMY and Megalithic Foot can generate expression of the likeliest candidate for the primary Jupiter Orbital Period value, which we have seemingly just seen at both Callanish I and Callanish X.

We can take that quite literally, in fact – IMY 2.719256444 / MF 1.177245771 = 2.309846008, which is the reciprocal of none other than 1 / 2.309846008 = 4329.292929 / 10^n, 4329.292929 being the current A value for the Jupiter Orbital Period.

These formulas may help further explain the multiplicity of Megalithic Yard values since it seems to be taking more than one MY value to properly honor both Jupiter and the Moon thusly, even while they are paying so much homage to Venus herein that you might think the architects were Mayan.

I should hope this also helps to emphasize the role of metrological unit values in “modern” feet as “building blocks” that we can use to construct approximations of important numbers from.

Again, I haven’t looked at products of parts or area figures here – but that isn’t always conducive, either, because such numbers can often be a bit strange, and take considerable time to understand. Sometimes such figures have waited years for someone to stumble over clues to their nature.

We can try to have a quick look though. Radius squared x Pi = area, so

Outer circle area = (13.49024283/ 2)^2 x Pi = 142.9319819 square feet. That may look very odd unless we can take it apart and find out it has some familiar content, such as 142.9319819 / 360 / 360 = 1.177245771 / 1.067438159.

I find it most interesting that if we convert this figure into Megalithic Feet

142.9319819 sqrt ft / (1.177245771^2) = 103.1324032 sqrt MF

That’s the generic area of a circle there! (Radius = Radian)^2 x Pi = Area 10313.24031.

Middle circle area = (11.24186904 / 2)^2 x Pi = 99.25832106 = 142.9319819 / (144 / 100). As a measurement in feet, 99.25832106 = 270 Inverse AE Meg Yards. I have a small neglected dossier on this number that I started the better part of 20 years ago, but we don’t hear from it that much because of its tendency to get overshadowed by numbers like 99.29184894 (enthusiasts of Munck’s work will hopefully recognize that number right away).

Note that for both of these area figures, if we keep applying the Megalithic Foot past the area conversion value of MF^2, we continue to obtain important data, some of it being rather reminiscent of Stonehenge data.

That once again is the story of my relationship with the number I am taking to be the Megalithic Foot in my own lexicon – I knew it as a mathematical constant with exponential value long before I knew it as a metrological unit, which we might not ordinarily think of having exponential value.

When introduced to the work of Harris and Stockdale by DavidK, I was initially skeptical that there was such a unit of measure – it seemed like a massive downgrade somehow – and had to stumble around for a way to convince myself of its metrological legitimacy.

That’s perhaps enough said for one post – this is running long although I’ve already omitted a number of extended mathematical displays – but I would still like to touch base with some of the rationale for the “short” Palestianian Cubit showing up, in the context of the Megalithic Foot

Radian 57.29577951 / AEMY 2.720174976 / 10 = “short” Palestinian Cubit 2.106326983

2.106326983 / 1.177245771 = 1.789199023 – recognize it? In my book, that’s the main thing Stonehenge means by “56”, written backwards.

2.106326983 / (1.177245771^2) = 1.519817753 = 15 / Pi^2

2.106326983 / (1.177245771^3) = 1.290994447 — now there’s some buried treasure, the most powerful data retrieval tool known, the reciprocal of sqrt 60 – or the inverse Thom Mid Clyth Quantum if you prefer.

2.106326983 / (1.177245771^4) = 10.96622710 = (1 / 9) x Pi^2)

2.106326983 / (1.177245771^5) = 9.315155226

Finally, for those with a disposition toward geodesy,

2.106326983 / (1.177245771^6) = Polar Radius in Miles / 10^n

Thus, seeing 2.106326983 in place of the usual Palestinian Cubit in the Megalithic landscape does not seem to mean that it’s what they got stuck with because of the numbers they chose to group together, but rather this variation on the Palestian Cubit seems to have its own important reasons for being. We had reason to be expecting it encounter it at any moment.

–Luke Piwalker