Short Reports 7

Greetings all!

Having a number of bits and pieces on my mind, another Short Reports article might be a good way to address them.

We Salute Mercurial Pathways

Mercurial Pathways is a remarkable blog that I haven’t been able to view in about as long as I’ve had troubles posting to my own blog here. The proprietor, Mercurial, is a regular contributor on the GHMB Mysteries Forum where I am no longer participating as a regular contributor (although it is still always good for some very interesting and thought-provoking reading) and has contributed a great many interesting ideas. I may not always be on the same exact wavelength (which is probably to be expected just because I tend to look for signs of more holisitic systems), but many times the findings of one researcher are translatable into the terms of another researcher (that is where we can often obtain some very important consensus), and more importantly I still believe personally that no one labors sincerely at the ancient Mysteries long without uncovering real treasures.

So… I have a lot of excellent reading to catch up on! Many thanks, Mercurial, and keep up the great work!

Back to the Flattened Drawing Board?

I was going over some figures I posted to the Megalithic Portal concerning projected diagonals for the platform that the Great Pyramid rests on. It may or may not be news now, but quite some time ago I’d worked out a figure for the platform width based on data from Glen Dash. What I apparently didn’t realize is that Dash published several works which were similar in nature, and I mistakenly remembered matters as having read both of them. A while back, I finally really read the other one and was able to make further data projections for the platform, and was able to clarify that the original width figure I gave (equal to 300 “Palestianian” Cubits of 2.107038476 ft each) would likely be the width at the top, while the width at the bottom of the pedestal would likely be about .4 Royal Cubits wider on each side.

The Great Pyramid’s platform: The original rough projections based on a combination of data from Dash and very crude pixel measures of materials from Dash. (The incomplete present pavement seen here is not the theoretical missing pavement layer of highly prized and easily accessible material that may have resulted in its complete removal even before the pyramids themselves began to be plundered for building material for later projects at nearby locations).

.4 Royal Cubits or just a little over 2/3 foot – about .6875 ft – is also the final projected thickness of the missing layer of pavement that would reconcile Carl Munck’s model of the Great Pyramid with one based on John Michell’s conception of a base of 1111.111111 Megalithic Yards – not Cubits! (For a Giza Pyramid based on Royal Cubits we want to look at our available models of Chephren’s pyramid rather than Cheops’).

While I believe I successfully projected all of minimum, mean, and maximum width for the Great Pyramid platform in one or more posts to the Megalithic Portal, and may have successfully worked out reasonable proposals for the mean and maximum diagonals of the platform, it looks like I must have mistyped a number into the calculator, and need to go back to the drawing board and start over concerning the likely minimum diagonal of the Great Pyramid platform…

That would also mean that any inferences as to the function or theme of the pedestal’s diagonal values should probably go out the window with the erroneous figure.

This is something I wish hadn’t happened, because the projection for the platform’s minimum diagonal comes to about

Minimum platform width 300 Palestinian Cubits = 300 x 2.107038476 = 758.5338514 ft, and the raw diagonal for a basic square-based design therefore projects as 758.5338514 x sqrt 2 = 1072.72886 ft…

Which may be just into range that is dark, mysterious, and increasingly contentious after my having observed the number 107.0581434 as a raw projection of the minor diameter of the modified Type A Thom Flattened Circle design, which Thom also referred to as the Type D Flattened Ring.

I have been struggling with what that is doing there, and have some unconfirmed notes that there are significant internal solar system ratios that look like this, which may inspire a sense of caution. The data projections I have thus far for the Flattened Rings suggest there is a good deal of solar system data that appears in their deceptively very simple designs (including recurrence of what is apparently lunar data).

It would be simply enough to try to qualify the Flattened Ring projection as meaning 107.3519415. In feet, this would be – like the Great Pyramid baseline in Munck’s model, whether Munck knew it or not – measured out in “Egyptian Mystery Units” (that which used to be called the “LSR” or “Le Serpent Rouge” unit and I’ve told the story here before of how all that came about and how the unit was discovered). 107.3519415 was identified in height data from Maler for the El Castillo Pyramid at Chichen Itza, and can be found in Petrie’s data for the still unsolved Bent Pyramid of Egypt…

Thom’s Flattened Circle Types: For Type D, if major diameter MN = 2 Radians = 57.29577951 x 2, minor diameter AB has a raw data value of 107.0581434.

This figure x 10 also easily qualifies as the mean diagonal of the Great Pyramid’s platform, but that brings us to the problem that it can’t be the minimum diagonal if it’s already the mean diagonal value.

So, I may have more to say about numbers in this range soon, and perhaps should, since the issue also came up here recently… As hinted at in the preceding post, numbers in this range also appear while looking at the square root figures for the Double Radian. 2 x 57.29577951 = 114.5915590, which is the square of 10.70474470. That square root value isn’t likely to be valid, but there may be two numbers very similar that would serve in its place (something we have seen with other important numbers, although I do not like to often mention the “false square root pair” concept for fear of confusing people about something that already outwardly seems rather complicated).

The Two Latest Wonder Numbers

One of them we already knew about from Stonehenge and working on the bluestone “Oval with Corners”, as Alexander Thom described it. It belongs to a rather rare variable equation, which seems to become permissible because a number of situations at Stonehenge appear as they were deliberately chosen because, at least in part, they readily accommodate all three versions of the Megalithic Yard that would be attested to and legitimized by the mathematical organizing schemes themselves which can be projected for ancient units of measure.

So far, in my experience, it’s been rare to find accommodation of all three Megalithic Yard values in ancient designs, let alone single equations which accommodate all three – that in itself may very much speak of conscious, intelligent design at work in this respect.

Without further ado, the first number is 1.451809286, and it has very recently been discovered that one of things it is apparently doing in the Stonehenge design is that not only may it be capable of helping us to find the Eclipse Year value, but when we subject it as a measure to metrological analysis, we find its metrological unit would be the Anomalist Month Unit of about 27.55 ft (27.551828115, which is actually made from 100 of the Megalithic Yard values / (Pi^2). That’s one of the things the planetary and lunar tables I’ve been building have provided us with, that with (Pi^2) we can transform Draconic Month Units (i.e., Megalithic Yards) into Anomalistic Month Units.

1 / (1.451809286 / 4) = 27.55182818 / 10^n.

While I was experimenting with it recently, I realized that 1.451809286, even though it is somewhat “secular” or limited in its response to classic data probes, still responds enough to meet several classic criteria associated with giving out the title “Wonder Number”, one of them being the prodigious stream of data that issues forth when exposed to the right common data probe.

Here are the notes I was taking at the very moment of discovering this, giving you a ringside view of metrological history in the making 🙂

Okay… What was I REALLY doing? lol

1.451809286…

Is it Pi-friendly? Well it’s good for DIVISION by Pi by up to at least the Fourth Power… the series provides us with Meg Yard/Meg Foot, 1 / IMY, and what I believe is the approximated Dresden Codex VSP, 585.2884657, since the Dresden modifies the 584 day Venus Synodic Period to 585 for various purposes.

I’m not sure the status of discoveries there. I think scholars have beaten me to the 585 d Dresden VSP being half of 10 Dresden Mercury Synodic Periods (MeSP) = 10 x 117 d, as if it were to synchronize Mercury and Venus Calendars better, but I don’t know about my observation that this odd gesture perhaps seems better explained if we include that Venus ORBITAL period 225 x Tzolkin 260 = 58500.

Synchronize Venus and Mercury calendars indeed???

Not a bad Pi / 3 series… has Eclipse Year, Callanish Number, Egyptian Royal Foot, Indus Foot, 1.003877282 and others.

1.451809286 IS more than halfway to Wonder Number, at very least, I think…

1.451809286 seems fairly Remen-resistant until we apply the Remen in its most powerful known permutation, the backhanded 2/ 1.622311470, when it spawns a series bookended by false Megalithic Feet and a strange doppleganger of the target number… wait, NOT bookended. It continues…

IT’S A FRAKKIN’ WONDER NUMBER.

Not more than several hours later, the number was discovered at Giza

…somehow 1.451809286 converts the height of the Great Pyramid (Munck) into the perimeter of the Great Pyramid (Michell), so odd gesture though it may be, but I guess we can therefore say we have just found the Stonehenge number 1.451809286 in the Great Pyramid now…

Extra! Extra! Read all about it, etc…

The other Wonder Number I wanted to introduce is… (let me see, there are a great many interesting tangents in my notes at about this point, including no less than an attempt at a finished set of projections for the Mycerinus pyramid, and what amounts to roughly a DOUBLING of the number of known sightings of what I am often calling the “Valley of Kings Number” for lack of a better idea)…

It concerns that there is already a Wonder Number near to the range of these 107-like figures we are seeing here. It’s part of one of the most classic Tikal exponential series that launched the very idea of Wonder Number in the first place (that is part of their character, generally making excellent “fodder” for exponential data recovery, they “conceal” many important pieces of data “within” them if we can find the right tool or tools to recover it.

It’s convenient to begin the series at 1/2 of the standard Venus Orbital Period, and begin dividing consecutively by (Pi / 3)…

(224.8373808 / 2) / (Pi^3) = 107.3519416 – see El Castillo Pyramid and the Bent Pyramid further back in this post – and then the series passes through more of the Tikal Wonder Number or their reciprocals, and then at (224.8373808 / 2) / ((Pi^3)^4), we find 106.9734371…

So if someone builds 106.9734371 into a scheme, they are really building in the whole series, and this qualifies 106.9734371 itself as a Wonder Number…

So if we apply this to the observation that 107 is about ten times the square root of 2 Radians,

(57.29577951 x 2) / 1.069734371 = 107.1215080, and THAT turns out to be a Wonder Number too, even if no one’s ever heard of it before.

Here is the bulk of the original notes from at the moment of this discovery

Here’s another for the “may be something, may be nothing” file.

The natural square root of 2 Radians is 10.70474470, very like some of the mysterious numbers we see with Thom Flattened Circles and some of the Planetary & Lunar Cycle ratios.

If we give a “false square root function” to our nominee 106.9734371, we get

(57.29577951 x 2) / 106.9734371 = 107.1215080 / 10^n

Having that “pedigree” may designate this as an important number

IT IS ALREADY A BONA-FIDE WONDER NUMBER. It forms an adequately powerful series with Pi / 3 as does 106.9734371 to qualify for this description.

That is all I know about it so far. It has never gotten on the radar before that I know of.

Offhand it is seemingly another “secular number” with a limited spectrum of powerful data probes it responds to and DOESN’T care for the Radian or 360… It DOES also respond well to the Megalithic Foot, which probably makes it a little less secular than the last designated Wonder Number.

Did we do this one? It’s TRYING to make me think it’s Eclipse Year / Apsidal Cycle (346.62 / 3233 = 107.2131140)

It is in Anomalistic Month Units at 38880 AMU = 107.1215080 x 10^n; 38880 = 108 x 360

So there is another new Wonder Number to learn more about, and it COULD be not only the intended value from the Thom Type D Flattened Ring, but also the intended minimum diagonal of the Great Pyramid’s platform… MAYBE…

A Long Standing Stonehenge Mystery Solved?

This particular discovery is not all of 24 hours old as I am writing this.

For some time there has been an unsolved mystery at Stonehenge, which is the “Lintel Circle Circumference Remainder”.

It isn’t the sort of place I normally look for data in ancient architecture, but some time ago it came as rather encouraging that for the SARCEN circle at Stonehenge, if we go to compare the inner and outer circumference by subtraction, we get a figure that is very convincingly in Egyptian Royal Cubits, and I believe I was impressed enough with that fact to include it in a very informal paper I’d written in Thom’s defense, which largely concerned the presence of ancient Egyptian units in the Megalithic Landscape, since Euan MacKie, John Michell, and others offered that the Megalithic Yard was related to common ancient Egyptian units of measure through the simple geometry of squares, rectangles or right triangles.

For the sarsen circle, it looks like this: We take Petrie’s 100 Roman Ft. inner diameter for the Stonehenge (I prefer 80 Remens because that’s probably older and more rightfully the identity of the value, 80 x 1.216733603 = 97.33868824 ft), and multiplied by Pi to get the circumference gives us 97.33868824 x Pi = 305.7987059 ft, just as Carl Munck called it so long ago. For the outer perimeter, we indulge Thom’s 120 Megalithic Yards, using a refined Megalithic Yard of 2.720174976 ft in place of “2.72” ft = 120 x 2.720174976 = 326.4209972 ft, and so the difference between outer and inner circumference is

326.4209972 – 305.7987059 = 20.62229122, whereas 12 of Morton’s Royal Cubit is 12 x 1.718873385 = 20.62648062.

For the LINTEL circle projections that would be

327.0127142 – 305.1421040 = 2.187061018.. and what on earth is THAT?

We fire mathematical probes at it but it keeps wanting to come back as 2.188537567 (which may be valid as an ancient Middle Eastern metrological unit in Imperial Feet) or maybe 2.185419355 ft, but they can’t seem to pass a standard of accuracy.

2.187061018 / 2.188537567 = .999325326

2.185419355 / 2.188537567 = .999249347

Both BELOW the minimum standard of accuracy of .9995 we are still aiming for with ancient architecture.

I’ve written about this in previous blog posts, but if memory serves, I’ve probably never really touched on the original logic at work here; I think it might be THIS: What happens if we divide 12^2 x 10^n by the Best Value for the Saros Cycle?

14400 / 6584.4495242 = 2.186955791

2.186955791 / 2.187061018 = .999951872, which DOES pass the accuracy of approximation test with a score greater than .9995.

Also, if we divide 218.6955791 by 8, we get

218.6955791 / 8 = 27.33826310, which MAY yet turn out to be a valid approximation of the Tropical Month, and

2.186955791 / 1152 = 18983.99124 / 10^n, 18983.99124 being the best approximation of the 18980 day Half Venus Cycle or Mayan Calendar Round.

By now we might have guessed from all that, that as a unit of length measure, 21.86955791 is a whole number of the so-called “Palestinian” Cubit (might as well continue to call it Palestinian Cubit but the ancient Egyptians were rather obviously quite aware of it, and used it often as well).

So there for now are a few things that might be new and hopefully interesting in the world of what ancient mathematics might have been like after hundreds of thousands of years of preoccupation with astronomy and the complex task of synchronization of diverse calendars.

It’s good to be back.

–Luke Piwalker