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The Great Pyramid
I was checking my records to see if we had anything in the past about this proposed Venus figure, although technically as the reciprocal of 1/2 of SRVS 887.6223994, it's probably seen plenty of action...

I found more on the history of "herpetometric". (Not entirely sure what I meant about the Assyrian Foot or the Egyptian Finger here, I will have to get back to those sometime).

Grid Point post #1141
Note on coined phrase...
Wed Jan 22 20:48:20 2003
"Herpetometic (Adj): metrological units of linear measure related to matematical values associated with reptilian-themed monuments.
The "LSC" constant, 2.794546571 is "herpetometric" because it is associated with the "Le Serpent Rouge" Grid Point. Note that without intent or premeditation, this constant appears in the proceedings (27.94546571 replacing "28" fingers as given by Berriman, and one of the original components of "LCS" representing "S", 1.08154098, appears with a formulaic divergence of the Assyrian foot from 1.08 feet to 1.08154098 ft:

Assyrian Foot, Divergence B: 1.08154098 Ft
Again, there seems to be a simple visual reason the part of (part of, I emphasize that) the symbolic meaning of serpent effigies denotes linear measure owing to a fanciful resemblance between a measuring tape (especially when coiled) and a serpent; this connection seems to appear in mythology, as noted here previously"

Or when a museum or an archaeologist wraps a tape measure around an ancient calendar stone, they are doing what is ideographically instructed, or making an ouroboros, or however one wishes to think of it (I like to think of it as not having to measure the circumference of something large and circular with an inflexible yardstick).

I'm not sure where the other post went now, but I found another that reveals the origins of "LCS":

"Grid Point" of "Le Serpent Rouge" 1.676727943 
"Grid Point" of the "Circle of Churches" (Morton?) 1.5410111111
"Grid Point" of Scottish Stone Serpent 1.081540979 (rescinded)

1.676727943 x 1.54101111111 x 1.081540979 = 1.676727943 x 1.666666666 = "LCS" 2.794546571

And of course 1.541011111 = 1 / (19.46773764 x 33.33333333)

Grid Point post #207
Wed Nov 28 10:40:59 2001
"8111.557354 / 360 = 22.53210376
365.020081 / 22.53210376 = 1.62" 

So we know that "Alternate Phi" 1.62231147 / 2 = .8111557354, and so 

2.920160646 / 360 =  8.111557354 / 10^n
2.920160646 / (360^2) = 225.3210376 / 10^2

Another possible Venus figure directly connected to an Earth circumference figure (in the case the very prominent cube root of the estimated 24901.19742 (mile) equatorial circumference / 10^n = 2.920160646

But I also found where this probably underappreciated newly-proposed Venus Orbital Period figure belongs to an impressive chain of figures that's rather reminiscent of the things we've seemed to finding at Tikal (particularly because of 1/3 Pi and sqrt 1.666666666 = 1.290994448, preceded in the same post by a set of equations starting with another combination of 33.33333333 and 19.46773764, namely the so-called "Masonic Cubit" of 33.33333333 / 19.46773764 = 1.712234567), so
we know now that it can proceed directly from applying the components that Tikal has already provided, even as largely unexplored as Tikal actually is mathematically.

The second series also highlights a close relationship of 225.3210376 to the Radian, and even links in the classic "Alternate Area of Vesica Piscis Ratio"

Grid Point post #2472
Tue Jun 24 05:15:26 2003
And last but not least, as far as more everyday stuff goes, the highest figure in this particular chain "just so happens to be", speaking of tetrahedra and their precursors, 33.33333333 / 19.4677376..."

In stead of just saying so, why don't I go ahead and show some of this here? Or, first of all 1 / 1.290994449 = 7.74596669 / 10, and 7.74596669 = (sqrt 60); 1.290994449 = (sqrt 1.666666666), and 3.33333333 / 2 = 1.666666666....

3333.333333 / 19.4677376 = 171.2234649
171.2234649 / (1.290994449^1) = dh 1.326291257 = dh (1 / 240 ) / Pi
171.2234649 / (1.290994449^2) = dh 1.02734079 "3 Giza Pyramids" Grid Point Ratio  1 / Inner Sarcen Circle Diameter Stonehenge
171.2234649 / (1.290994449^3) = dh 7.95773754 = dh 25 / Pi = dh Orion Belt Stars Composite
171.2234649 / (1.290994449^4) = dh 6.164044744 = (1 / Alternate Phi 1.62231147) / 10
171.2234649 / (1.290994449^5) = 47.74648293 = 150 / Pi
171.2234649 / (1.290994449^6) = dh 3.698426665 = 1/2 (Squared Munck Yoda Meg Yard^2)
171.2234649 / (1.290994449^7) = 28.64788977 = (Radian 57.29577951 / 2)
171.2234649 / (1.290994449^8) = 22.19055999 = Grid Longitude Stonehenge / 100
171.2234649 / (1.290994449^9) = 17.18873386 = Michael L. Morton Royal Cubit, in feet x 10
171.2234649 / (1.290994449^10) = 13.314336 = 26.62867199 / 2
171.2234649 / (1.290994449^11) = 10.31324031 = (Generic) Area of A Circle / 100
171.2234649 / (1.290994449^12) = 7.9886016
171.2234649 / (1.290994449^13) = 6.18794419 = dh 108 Radians
171.2234649 / (1.290994449^14) = 4.79316096 
171.2234649 / (1.290994449^15) = 3.71276651 = dh Volume of a Torus
171.2234649 / (1.290994449^16) = 2.87589659
171.2234649 / (1.290994449^17) = 2.22765991 = 1.11382995 x 2
171.2234649 / (1.290994449^18) = 1.33659594 = dh 1.181810286 x 360 x Pi
808.0227996 / (1.290994449^1) = 625.8917693
808.0227996 / (1.290994449^2) = 484.8136799 = dh Pi / 648
808.0227996 / (1.290994449^3) = 375.5350618
808.0227996 / (1.290994449^4) = 290.8882081 = dh G.P. Rosslyn Chapel & Stonehenge Mound
808.0227996 / (1.290994449^5) = 225.3210371
808.0227996 / (1.290994449^6) = 174.5329249 = dh 1 / Radian 57.29577951
808.0227996 / (1.290994449^7) = 135.1926223 = dh Grid Point Silbury WGS 84 1 / Squared Yoda Meg Yard x 10^n
808.0227996 / (1.290994449^8) = 104.719755 = dh (Pi / 3)
808.0227996 / (1.290994449^9) = 81.1155734 = (Alternate Phi 1.62231147 / 2) x 100
808.0227996 / (1.290994449^10) = 62.831853012 = 2 Pi x 10
808.0227996 / (1.290994449^11) = 48.66934408 = (Inner Sarcen Circle) Radius Stonehenge in feet
808.0227996 / (1.290994449^12) = 37.69911183 = 12 Pi
808.0227996 / (1.290994449^13) = 29.20160646 = Grid Point Stonehenge x 10 cube root Earth Circumference in Miles
808.0227996 / (1.290994449^14) = 22.6194671 = ht Mycerinus Pyramid / 10
808.0227996 / (1.290994449^15) = 17.52096388 = dh Grid Values of Pyramid of Magician & Woodhenge, WGS 84
808.0227996 / (1.290994449^16) = 13.57168027 = dh Grid Lat. Chephren Pyramid x 2
808.0227996 / (1.290994449^17) = 10.512578333 = 5.256289167 x 2
808.0227996 / (1.290994449^18) = 8.143008164 = 1 / "Alt Area Vesica Piscis Ratio"
808.0227996 / (1.290994449^19) = 6.307547003 
808.0227996 / (1.290994449^20) = 4.885804901 = (.7776 x Pi) x 2

& etc... at least to the 20th power..."

So that is part of why I am beginning to take this 225.3210371 figure more seriously, even when we already have a perfectly impressive figure 224.8373803 to signify Venus' Orbital Period, not to mention a frequently useful second figure of 225.0000000.

225.3210371 is also linked to 1.290994449 by The Radian 57.29577951 (arc-degrees, aka The Giza Constant, also the other proposed dimension of the Tikal masonry block, along with 1.290994449, ignoring decimal placement) in another interesting, albeit shorter, chain

(5 / 1.271425432*) x 57.29577951 = 225.3210371
225.3210371 x 57.29577951 = 1.290994449 x 10^n
1.290994449 x 57.29577951 = 7.396853331 Squared Yoda Megalithic Yard x 10^n
7.396853331 x 57.29577951 = 423.8084775 = "True Outer Sarcen Circle Area of Stonehenge"** / 2 = (Generic Area of A Circle 10313.24031 / Remen 1.216733603) / 2

*The interesting and seemingly important figure 1.271425433 = (108 x Alternate Pi 1.177245771) / 100 = MLM Royal Cubit in inches = 2.062648062 / "Alternate Phi" 1.62331147 and etc etc.

**Obtained by substituting the Unsquared Yoda Meg Yard 2.719715671 for the "Alternate e' Meg Yard" 2.720174976 in calculation of the area enclosed by the outer circumference of the Sarcen Circle, inner sarcen circle area = 48.66934411^2 x Pi = 7441.506403 sq feet (Yoda).

It also reminds me to go back and double check on exactly what they may be using to represent "13" where in the Tikal temples. So far we only have The Amazing 1.290994449 probably expressed by a masonry block that divides one of the temple staircases from the top platform to the temple door, but further displays of this number's great usefulness imply it may be expected that it will be found there with some frequency. It has the makings of an ancient favorite, and is of course the reciprocal of the square root of 60, which Pi Jedi have traditionally thought to be on blatant display at Stonehenge along with the square root of 15, courtesy of separate major arrays of 60 and 15 stones respectively in an unusual presentation.

And yeah, there's some old data peeking out of the strikethroughs of "Grid Coordinates" (= Map Crap) that's historically interesting. How did Yoda and I both get taken in by the Map Crap game? Well, using the Stonehenge coordinates "as is" from British maps, he got the Double Remen as the "Grid Point" of Stonehenge, and when I attempted to correct the coordinates to the WGS 84 Datum I got 2.920160646 for the "Grid Point" of Stonehenge. What could possibly be more deceptive? If we were complete boneheads, at least we were commendably picky about being complete boneheads, I'll say that for us.

I tried working on Rio Bec again but got very confused once more, it's really looking like the sort of thing where we'd find that the length of structure A at the top of the outer walls would be slightly different than the length at the top of the walls in order to catch a number of "near-miss" equations, and the same might go for the interior rooms.

That may be what is meant by "feathered serpent," that equations concerning the mythological mathematical serpent begin to "feather" around the edges, or what I call "fraying" - when the ancients ambitiously tried to link up certain numbers that didn't quite match up perfectly, so that numerous possible equations and probably many with equal validity, begin to pour forth from the proceedings.

(No idea what the Xibalba the "underworld" is mathematically - the closer of two geodetic figures in a literal representation of the larger "over" the smaller? (i.e., the difference between 2.920160646^3 x 10^n and "a zillion Cholulas" 1.315947254 x 10^n ?? - or the difference between a circumference figure and a mean circumference figure?? "A zillion Cholulas" does look a lot like a mean Earth circumference figure if you take it more literally. However, the concept of "the underworld" also seems to be linked to ancient water sources, so it might be possible that mathematics was employed to provide these water sources with some sort of coordinates, although I have no idea how that might work. Some of the literature suggests that these may have been strategic and/or protected resources, and the frequent association of pyramids or other ancient monuments with underground water is also duly noted. Perhaps the theme of water is being used in context to refer to both the local water source(s) and geodetically to the distance "across the water"?)

I really don't have the data to do that sort of detailed work with Rio Bec or a lot of other places, though - only single measures for the length or width of rooms and doors generally. It's still a lot like Lehner giving us single figures for the dimensions of the Great Pyramid chambers rather than the more detailed and more interesting measures provided by Petrie. I can see in many photographs how many ancient Mesoamerican doorways look deliberately irregular so that they may have valid measures at top, bottom, and probably mid, but I have yet to find any data that detailed. Again, in many cases no one seems to have even taken measures of the door heights, let alone providing us three different figures for width, and same with what are probably deliberate irregularities in calendar stones. (Likewise, George Andrews, bless him, frequently gave us complete measures for first chamber inside the temple door so that someday we might see a few complete interpretations of such things, but rarely complete data for temple chambers after that). 

I'd like to get back to the Tizoc stone, I think it's part of the workings that they managed to incorporate an interesting pair of important numbers

MLM Royal Cubit 1.718873385 x sqrt 240 = 2662.867198 / 10 = Squared Yoda Meg Yard x 360, etc
(6 x (Pi^3)) x sqrt 240 = 2882.083037 = height Great Pyramid (paved) x 60, etc

Although the loudest proof that I need to revisit it is that offhand, I can't remember exactly how they did that... I'd be mighty proud of myself though I could design a monument that deftly incorporated both of these numbers (in addition to all the calendar-related demands being put on the associated equations) but I think the Aztecs might have managed?

Been looking for more data on calendar stones - if I had two more as eloquent as the infamous and often misnomered Aztec Calendar Stone (aka "Mayan Calendar"), I'd probably consider e-mailing real archaeologists and begging them to stop throwing away priceless examples of ancient mathematics. I suppose the last thing they'd want to believe without further stunning examples is that ancient Mesoamericans seem to have constructed these elaborate mathematical formulas in modern feet, as strongly evidenced by the "Sun Stone".

However, the data I have so far on calendar stones makes it look like they come in a variety of sizes, whereas repeating the same formula as the "Sun Stone" would of course require the same measurements (a 1:10 scale model seems uncharacteristically puny), so if they repeated the exact formula with different proportions, I'm not sure yet what creative manouvers they might have used to accomplish that - possibly by using a second metrological unit, or halfing, or using reciprocals, but I've no idea which offhand. It's a subject in itself really.

Just a piece of trivia, I suppose, but going through photos I was intrigued with Nakum since it's near to Tikal and probably displays some parallels in design. There is a temple where there are what appear to be two circular recesses about the size of calendar stones in the exterior wall with small holes in them that might have facilitated mounting of a circular object. I can't think of any other time I have seen that. I have virtually no data yet about the matter, but if someone came up with a couple of calendar stones so good they were worth hanging up on a temple exterior, I'd dearly love to know more.

[Image: Nakum-7.jpg]
Temple A, Nakum (Peten, Guatemala)
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
I think I will just take the opportunity to put some of this onto the table - explaining it better may have to come later (as often happens with numbers we are all still learning about) with possible revisions of some of these not being out of the question. Everything to do with the "Pyramid Pi System" is still sort of a work in progress really, not just this. Still a bit premature, but does seem rather timely as I've been seeing a fair amount of 573.7753105 (see below) in interesting equations lately, it looks like something I had underestimated...

(My proposals for additional intended Great Pyramid data, anyway)

Attribute: Edge length (with paving)  
Formula used: sqrt (1067.063129 / 2)^2 + 480.3471728^2
Calculated value: 717.9062172 ft
Intended value: probably 717.7378860 ft?
Accuracy: .9997655248

Attribute: Edge length (without paving) 
Formula used: sqrt (1068.585650 / 2)^2 + 481.0325481^2
Calculated value: 718.9305496 ft
Intended value: 718.9741438 (untruncated apothem length with paving of 194.4 Pi ft x Alternate Pi 1.177245771)
Accuracy: .9999393661

Attribute: Apothem length (without pyramidion and without pavement) 
Formula used: 611.6589930 - 35.53417641
Calculated value: 576.1248165 ft
Intended value: 576.0000000 ft (240^2 / 100)
Accuracy: .9997833516
(for hypothetical untruncated pyramid)

Attribute: Truncated apothem length (without paving or pyramidion)
Formula used: 609.2348397 - 35.39334578
Calculated value: 573.841493 ft
Intended value: 573.7753105
Accuracy: .9998846661

Attribute: Edge length of proposed pyramidion
Formula used: sqrt (ht 27.95783074^2 + diag (62.07921643 / 2)^2
Calculated value: via paved / unpaved scaling ratio = 41.75629759 ft
Intended value: 41.75629759 ft
Accuracy: 100% via scaling ratio formula
Honorable mention: 41.77436507, 41.79798863, 41.82822012

Attribute: Edge length (with paving but without pyramidion)
Formula used: 717.9062172 - 41.77436507
Calculated value:  676.1318521 ft
Intended value: 675.9731125 ft (dh 5 / Squared Yoda Meg Yard; dh 2 / proposed Lunar Synodic Period value 29.58741332)
Accuracy: .999765209

Attribute: Edge length (without paving or pyramidion) 
Formula used: 718.9305496 - 41.77436507
Calculated value: 677.1561845 ft
Intended value: probably 677.1274165 ft?
Accuracy: .9999568797

BTW, I am probably not proposing that the Great Pyramid was equipped with a pyramidion fashioned from a single block of stone almost 28 feet high (27.94546577) and almost 44 feet wide (43.89663498). Maybe, but perhaps more likely it was constructed from consistently sized blocks of the same material used for the casing. Ultimately there may have been a smaller pyramidion at the very top consisting of a single piece, although I have absolutely no guesses on this unless they stuck to a rigid scaling ratio between the Cheops and Mycerinus pyramids for this attribute too, in which case the values may yet be extrapolated from data for the Mycerinus pyramidion.

Also BTW, I spent some time at the Megalithic Portal yesterday, seeing if I could verify for two or three several randomly-chosen stone circles whether we could corroborate that the main geometry points to the next circle yonder, as suggested at one of the sources I gave for material on Thom's circle types. On the one hand, the Megalithic Portal has data on nearby monuments for sites and the azimuths in their direction, but on the other hand there are often numerous nearby sites, and the distance between sites is rounded at the nearest .1 mile or about 382 feet, so it can end up looking pretty messy plus there is no way using data with that level of inaccuracy to see if the distance in the indicated direction to the indicated moment might be clearly encoded in the monument pointing toward it.

Additionally the British Ordnance Survey now wants a small sum for access to online mapping, but don't seem to have made it clear if I can expect the same service we used to be able to expect with their free "Get-A-Map" service. I could expect the data to be helpful but probably not decisive, so I'll probably pass for now on the whole prospect and move on to other questions. Besides, even after all this time away from the OS, I'm still ready to lob smart remarks about how the Ordnance Survey first invented a Grid System to geographically disorient the Germans, then decided it would somehow make it easier to navigate the UK if they inflicted it on the rest of the world. I didn't actually need to be told it was invented in order to confuse someone, I could tell.

I wish I were enough of a historian to have a clue what became of this ancient mathematical system, it's still only speculation that it survived among architects and was later incorporated into churches or whatever. I suppose it could be a reason that some historians prefer isolationism, there are probably some messy questions concerning exactly how many people knew "The Americas" were there apparently without feeling the urge to turn Conquistador, seeing as the circumference of the Earth is plastered virtually everywhere as if every monument might be aspiring to be "the Navel of the World" (or a model of the world - same thing conceptually?) or whatever mathematically. Navigation or geographic coordinate systems retain some sensitivity even now, said one of the guys who had to sit around waiting for certain nations to stop scrambling GPS signals in a probably misguided attempt to reduce the accuracy of encroaching projectiles.

I can easily enough picture the locals suddenly turning stupid and forgetting what the ancient stones were for when invaded by ambitious types like Romans or Spaniards, but really it would be easy enough to tell there was a whole other side to the world from formulas attributed to the ancient Greeks and probably expedited by inheritance of surprisingly accurate metrological units from the ancient Egyptians.

That's my impression of the stone circles, anyway, that they were all kinds of community resources all in one - direction finders, distance finders, star finders, water finders (geometrically indicated azimuths on first two test circles ostensibly seemed to match azimuths toward Holy Wells), libraries, meeting places. I wish I knew quite how to do a better job proving half of that.
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
573.7753105... What is that besides something rather annoying on account how of easily it might be mistaken for The Radian if one is not aware of it?

Let's see... 573.7753105 x or / 10^n 

= Radian 57.29577951 x Great Pyramid paved/unpaved scaling ratio 1.001426834 (of course)
= (ht Great Pyramid (paved) / 2 Pi) / 365.0200808 
= (Cholula squared 1.315947254^2 = 1.73171717174) / Perimeter Great Pyramid (paved)
= "Alternate Phi" 1.622311470 / (900 Pi aka Perimeter Chephren Pyramid in feet accd. Yoda) 
= 4 / sqrt 4860 (found in Thom Type A Flattened Ring as approximation of angle?)
= 8 / sqrt 194.4
= 11154.19204 / 194.4 
= 64000 / 111.5419204
= 1(.032795559 / 18) x 10^n
= "Fourth Meter" (?) 3.287490369 ft (= 4 / Remen 1.216733603 ft) / Radian 57.29577951

It's probably accumulated some other aliases (although not in my log book which still awaits its first update in 10 years), including a few more interesting ones, if I had them actually rounded up, even though it generally seems a poor responder (and being sort of a mutated form of the Radian, it quickly generates mutated forms of Pi in numerous equations, making it something of in invitation to consider whether some numbers near to Pi may be valid at Giza, as in Vianova's excellent models). The same is true of our new friend 1.271425433 for being a sort of mutated form of 4 / Pi, yet Yoda Himself might not mind this desecration of sacred geometric constants as much as one might think, since his "Grid Latitute" for the Giza Sphinx came to 63571.27163 = 127142.5433 / 2.

I'm usually in the process of giving up on 573.7753105 and its "decimal harmonics" when it turns up again in something I'm working on. Case in point, it's become of interest again of late because, besides its appearance in the Great Pyramid equations, 

573.7753105 x Venus Orbital Period as 225 (days) = 129.0994449

And because 

(1 / (Pi / 3)) x 573.7753105 = 5479.150661 

Which is sort of a point of contention even for one person, since it's as legitimate as

2 / 365.0200808 = 5.479150611 / 10^n

Yet 5.479150661 may be at much more risk of being mistaken for the Squared Yoda Squared Meg Yard 7.396853331^2 = 5.471343920, than 57.37753105 is at risk for being mistaken for The Radian 57.29577951.

Both 5.479150611 and 5.471343920 could have both been hugely popular with the seemingly very calendar-conscious ancient Mesoamericans but a relative newbie such as me could mistake one for the other easily enough.

It also comes up again here involving the calendar and geodesy

57.37753105 x 73.00401620 = (131.5947254 / Pi)
57.37753105 x 73.00401620^2 = 305.7985081 Inner Sarcen Circle Circumference of Stonehenge
57.37753105 x 73.00401620^3 = 72 Pi^3 x 10^n (a designator of Regulus in Michael Morton's "ASM" cosmology, this noble numbers seems to still await discovery of its appearance in a fixed location such as a circle circumference or pyramid perimeter)
1.271425432 x  57.37753105 = 72.95125222

73.00401620 and 72.95125222 both being likely approximations of "73" in scenarios of the ancient Mesoamericans using the Pyramid Pi System for time keeping purposes.
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Ancient stone monuments may have been used for mysterious moonlit ceremonies, say archaeologists 

[Image: TELEMMGLPICT000132535682-large_trans_NvB...pCom4.jpeg]
The Summer Solstice at Stonehenge CREDIT: WENN

7 JULY 2017 • 10:00PM

Ancient stone monuments may have been used for mysterious night-time ceremonies, archaeologists believe, after finding that some rock carvings only appear in moonlight.
Traditionally Neolithic structures were believed to align with the movements of the Sun, with  the huge Wiltshire circle of Stonehenge lining up perfectly with the summer solstice.
But a new investigation of the stone age engraved panel Hendraburnick Quoit in Cornwall by Dr Andy Jones, found nearly 10 times the number of markings when viewed in moonlight or very low sunlight from the south east.

They also discovered that pieces of quartz had been deliberately smashed up around the site which would have glowed in the dark under moonlight, or firelight, creating a gentle luminescence.

[Image: Hendraburnick_Quoit-geograph-org-uk-7332...pQBfEs.jpg][img=620x0][/img]
 Hendraburnick Quoit

Dr Jones, of the Cornwall Archaeological Unit said: “I think the new marks show that this site was used at night and it is likely that other megalithic sites were as well.
“We were aware there were some cup and ring marks on the rocks but we were there on a sunny afternoon and noticed it was casting shadows on others which nobody had seen before.
“When we went out to some imaging at night, when the camera flashed we suddenly saw more and more art, which suggested that it was meant to be seen at night and in the moonlight.
“Then when you think about the quartz smashed around, which would have caused flashes and luminescence, suddenly you see that these images would have emerged out of the dark.
“Stonehenge does have markings, and I think that many more would be found at sites across the country if people were to look at them in different light.”

[Image: rock1-large_trans_NvBQzQNjv4BqrpfQw2hJyG...TInME.jpeg][img=620x0][/img]
Marks on the rock came into view under a camera flash and would have lit up in moonlight, say experts  CREDIT: DR ANDY JONES 

Hendraburnick Quoit is a large propped ‘axe-shaped’ stone that was set upon a low platform of slates on Hendraburnick Down, near Davidstow.  Dr Jones believes it was dragged up from the valley below to act as a ritual marker for a sacred site in the Late Neolithicor Early Bronze Age, around 2,500BC.
Previous studies had recorded 13 cup marks on the rocks but Dr Jones and colleague Thomas Goskar found 105 engravings when he started to look under new light, making it the most highly decorated and complex example of rock art in southern England.
Writing in the archaeology journal Time and Mine, and Dr Jones and Mr Goskar conlcude: “As in many cultures where darkness is associated with the supernatural and the heightening of senses , it is possible that some activities at Hendraburnick Quoit may have been undertaken at night.
“Quartz has luminescent properties and reflects both moonlight and firelight
“Given that human eye perceives colour and shade quite differently at night than by daylight and the art would have been visible in moonlit conditions, the smashed quartz at Hendraburnick could have been used as part of night time activity on the site in order to ‘release’ the luminescent properties of the quartz around the monument and ‘reveal’ the art in a particular way.
“After the ritual, the broken pieces, once they had fallen on the ground, could have effectively formed a wider platform or arc which would have continued to glisten around it in the moonlight, and thereby added to the ‘aura’ of the site.”

[Image: cupandringmarks-large_trans_NvBQzQNjv4Bq...lEOVI.jpeg][img=620x0][/img]
More than 100 marks were eventually found on the rock  CREDIT: THOMAS GOSKAR

Smashed up quartz pieces discovered at the Early Bronze Age cairn at Olcote near Calanais, on the Isles of Lewis are thought to be linked with funerary and lunar rites.
The new research was published in the archaeology journal Time and Mind.

Along the vines of the Vineyard.
With a forked tongue the snake singsss...
What happened with the discovered hidden chambers on the Great pyramid?
Seek and ye shall find. JESUS
I am a recovering vegetarian   Hi
Speaking of voids discovered in a pyramid by remote sensing Mayito ...

Quote:The tunnel is long, extending from the central square known as the Plaza de la Luna to the nearby pyramid. It is about 33 feet (10 meters) deep, and is similar to other tunnels that have been discovered recently, like the tunnel that was found under the Temple of the Plumed Serpent.

While no one has been able to go inside the tunnel yet, the discovery was made through a method known as electrical resistivity tomography, which creates subterranean images.

New Tunnel Discovered Under Ancient Pyramid

Archaeologists think the tunnel under the Pyramid of the Moon in Mexico's Teotihuacán may represent the underworld as part of an ancient belief system.

[Image: pyramid_of_moon_NationalGeographic_17822....590.1.jpg]
The tunnel was found under the Pyramid of the Moon and the Plaza de la Luna, the adjacent square.

By Heather Brady

Archaeologists have discovered a secret tunnel under a famous and massive pyramid in the ancient city of Teotihuacán, northeast of Mexico City.

The tunnel was found under the Pyramid of the Moon, the second-largest structure in the ancient city (the largest is the Pyramid of the Sun), according to the International Business Times. The archaeologists who discovered it believe that it mirrors the Teotihuacans’ great monuments and may represent the underworld in the belief system of the pre-Colombian, 2,000-year-old civilization that built it (a civilization thought to pre-date the Aztecs, who later occupied the site).
The tunnel is long, extending from the central square known as the Plaza de la Luna to the nearby pyramid. It is about 33 feet (10 meters) deep, and is similar to other tunnels that have been discovered recently, like the tunnel that was found under the Temple of the Plumed Serpent.

While no one has been able to go inside the tunnel yet, the discovery was made through a method known as electrical resistivity tomography, which creates subterranean images. A team of archaeologists from Mexico's National Institute of Anthropology and History was using the technique as part of their conservation efforts for the central square when they stumbled upon the tunnel.

The Pyramid of the Moon was likely used for human sacrifice and other rituals, based on studies of human remains found at burial sites. It is unclear what the tunnel may have been used for, and archaeologists plan to do more research to determine its purpose and whether or not it contains more artefacts.
Teotihuacán was long a major city and had a complex history, much of which has yet to be unwound. It was one of the largest in the Americas in the pre-Columbian era, having been home to at least 125,000 people.
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Was the metre invented by the Ancient Egyptians 4500 years ago?
Posted on 2013-06-07 by admin
One of our readers, John Frewen-Lord, speculates that the metre may be the modern version of a measure that was familiar to the Pharaohs.
While we think of today’s metric system (SI) as mostly a modern invention (1960), we have been led to believe for many years now that its most fundamental base unit, the metre, originated in France in 1793, and represented one ten-millionth of the earth’s quadrant (the distance from the earth’s equator to the North Pole, as measured at sea level) . Yet just a few years ago, the late Pat Naughtin discovered that the proposal for a universal standard of length very close to the metre may in fact have originated much earlier, via Bishop John Wilkins, an English cleric and philosopher, and a member of the Royal Society, in the mid-1600s. Recent comments on Metric Views now bring even that assertion into doubt, with the discovery of a measuring device called the wand having been around much longer still.
It is known that the wand, divided into ten segments, was almost exactly, to within a few millimetres, the same length as today’s metre, and that it was used as long as 1000 years ago. But what if all these versions of the metre were simply the rediscovery (or the handing down over time) of a standard measure, equating to the metre, that was invented in Egypt over 4500 years ago?
When we think of units of measure used in Biblical times, the cubit usually springs to mind. In fact, opponents of metric conversion have often referred to the cubit, in jest at least, as having as much validity as the metre. Such people should be careful for what they wish for, for, as we shall see, the cubit and the metre may in fact be directly related – and remarkably both are directly traceable to the Great Pyramid at Giza.
At first sight, such direct relationship may not be immediately apparent. There are a number of variations of the cubit, each different in length, but it is accepted that the Egyptian royal cubit is the definitive cubit, of which a physical example is on display in the Liverpool museum. Used to set out the Great Pyramid, its length measures 524 mm, or 0.524 m. For anyone hoping to see a nice round relationship between the cubit and the metre, I’m afraid the story is much more complicated than that! But keep in mind that number of 0.524 – for it will crop up again.
Let us look briefly at some of the mathematical properties of the Great Pyramid. Apart from the fact that it is just 3/60ths of a degree off an orientation of true north (the Prime Meridian through Greenwich is 9/60ths of a degree out of such an alignment), the Great Pyramid contains some quite stunning dimensional relationships between the numerical constants of pi (?), phi (?) and Phi (?) – and those relationships involve a dimension that is exactly equal to today’s metre. Let us explore this a bit further.
We all know what pi is. It is the ratio of a circle’s circumference to its diameter, and is approximately equal to 3.1416 (another number to keep in mind). We are probably less familiar with Phi and phi. One is the reciprocal of the other, with values of 1.618 and 0.618 respectively. The value of 1.618 is known as Phi with a capital P (?), while the reciprocal 0.618 value is represented by the lower case phi (?), and the two collectively are known by many names, such as the Golden Ratio, the Golden Mean, the Golden Number, and others, but they are values that exist throughout nature. Their discovery is attributed to mathematician Fibonacci in the 13th century.
Fibonacci noted that much of nature – and indeed much of Roman architecture – encompassed relationships of 1.618 and 0.618 for various aspects of design, and that these relationships relate to what is known as the Fibonacci sequence, consisting of 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on, where each number is the sum of the previous two numbers. What is not always realised is that if you take any two adjacent numbers, say 55 and 89, you can obtain two ratios – 1.618 if you divide the second by the first, and 0.618 if you divide the first by the second (the minor variations in the decimal places get smaller as the numbers get bigger, coinciding at infinity). The Golden Ratio has a few unique properties – in fact these equations work only with the Golden Ratio and nothing else:
? = 1 + ? (i.e. 1.618 = 1 + 0.618);
? = 1/? (i.e. 1.618 = 1 ÷ 0.618);
? + 1 = ?² (i.e. 1.618 + 1 = 1.618² = 2.618);
? – 1 = 1/? (i.e. 1.618 – 1 = 1 ÷ 1.618 =0.618).
If we skip alternate numbers in the Fibonacci sequence, we end up with the same result as either ?² or adding 1 to ? – e.g. 144 ÷ 55 = 2.618 = 1.618 + 1 = 1.618² (keep in mind also the number of 2.618). Now you may be saying that this is all very interesting, but what has it got to do with the Great Pyramid at Giza, let alone the origins of the metre? All will become clear!
It is well known and accepted that the Great Pyramid incorporates the value of ? in its geometry – this was discovered by Englishman John Taylor in 1859, when he found that if you divide half the length of the Pyramid’s base perimeter by its height, you end up with ?. The base length of one side is 230.3 m, while its original height is 146.6 m. Therefore (230.3 x 2) ÷ 146.6 = 3.1418 – not precisely ?, but then the height of 146.6 m is at best an estimate of just how high the Pyramid was 4500 years ago (the very top is now missing, as is part of its external cladding, and ground level has likely changed). Likewise, take a circle with the same circumference as the perimeter of the base of the Great Pyramid. Calculate the radius of this circle. It will be found to be exactly equal to the Great Pyramid’s height (230.3 x 4 = 921.2. 921.2 ÷ (2 x 3.1416) = 146.6).
We must note that these relationships, along with many other relationships embodied in the Great Pyramid, can be made using any measurement units – they are not exclusive to the metre.
The Golden Ratio ? is there as well. If we take the surface area of the four sides, and divide that by the area of the base, we come to the value of ? (4 x 0.5 x 230.3 x 186.4 ÷ 230.3² = 1.618). Again, that is purely a ratio, and is not dependent upon any particular unit of measure. But now let us do some more calculations involving the Great Pyramid’s geometry that are dependent upon the metre – and only the metre.
  • If we add two of the sides of the Pyramid’s base together, then subtract the height, we end up with a rounded value of 100 x ? (230.3 x 2 – 146.6 = 314.0).
  • The King’s Chamber measures 5.24 m x 10.47 m. The Chamber’s perimeter = 10 x ? (31.42 m). There are also many measurements in the King’s Chamber that relate to even multiples of ?, but only using metres.
  • If we draw two circles, one circumscribing the Pyramid’s base (i.e. intersecting the four corners) and one inside (i.e. touching the mid-point of each side), then subtract, in metres, the circumference of the inner circle from that of the outer circle, you end up with a figure of 299.71. This is almost exactly one millionth of the speed of light in metres per second (299 792 458 m/s – the slight discrepancy is due to rounding at various points along the way).
Hold on – the ancient Egyptians may have known about the metre, but surely they didn’t know about the second? Perhaps they did. The length of two sides of the base of the Great Pyramid is the distance a point on the equator moves through space in exactly one second.
I’m sure if you tried hard enough, the Great Pyramid may be found to contain some mathematics that support imperial measures, even though things like the foot and inch were not anywhere near close to existence 4500 years ago, and anyway are promoted as being based on human properties, not mathematical ones. But there is one thing that really does indicate that the ancient Egyptians were very familiar with the metre. I mentioned early on in this article that the cubit, which was used to build the Great Pyramid (each side has a length of 440 cubits), was 0.524 m long, an apparently odd relationship to the metre. Let us however look at three equations:[/size]
  • One sixth of ? is 0.5236 – to all intents and purposes exactly the length of the cubit in metres (to within 0.4 mm of the known physical example, and even that assumes that this example’s stated length has not been rounded to three decimal places); quite why one sixth is not clear, but the Great Pyramid is located exactly 30° above the equator – i.e. one sixth of the distance between the two poles.
  • One fifth of ?² (2.618) = 0.5236 – again, exactly the length of the cubit in metres. There are five increments of 72° in a circle of 360°. It is known that the earth wobbles slightly on its axis, at the rate of 1° every 72 years.
  • ? – ?² (3.1416 – 2.618) = 0.5236 – another relationship that yields the length of the cubit in metres, and ties together, by means of the cubit (and hence the metre), the two constants that are embedded in the Great Pyramid’s mathematical properties.
These equations cannot be pure chance or coincidence, but must have been created by a society that knew all about the metre 4500 years ago, and from which they derived the cubit. One thing is certain – no measurement unit can be more natural than the metre, based as it is on nature’s constants of ? and ? (not to mention the circumference of the earth). Clever people, those ancient Egyptians.
[Note: I claim little original material in this article, but have made extensive use of sources from Wikipedia, YouTube and others, all of which must be treated with the usual caution as to their absolute accuracy. J F-L][/size]

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Use cylindrical coordinates for the Galactic plane to define the Sun’s motion w.r.t the Local Standard of Rest
The Sun (and most stars) are on slightly perturbed orbits that resemble rosettes making it difficult to measure relative motions of stars around the Sun.
Establish a reference frame that is a perfect circular orbit about the Galactic Center.
Local Standard of Rest - reference frame for measuring velocities in the Galaxy.
Position of the Sun if its motion were completely governed by circular motion around the Galaxy.
Local Standard of Rest

Slide 17
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To determine the Suns motion wrt to LSR, we observe the average motions of all stars in the Sun’s vicinity and measure the following:

Π - Πo = U (speed away from GC) = -10.4 km/s [7.5 +/-1 km/s]

Z - Zo = W (speed towards NGP) = 7.3 km/s [6.8 (+/- 0.1) km/s]

Θ - Θo = V (speed in direction of motion) = V = 14.8 km/s [13.5 (+/- 3) km/s]

The Sun is moving toward the Galactic center, faster than the LSR, and northward toward the NGP. Net motion is 19.5 km/s in the direction of constellation Hercules



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Nothing is standing or stationary. As you are reading this, the Earth spins around its own axis; it revolves around the sun, the sun is moving through space at a stunning 792,000 km/h around the gigantic center, and our universe is moving at a mind-boggling 2.1 million kilometers per hour.

You may contemplate that as you are reading this, your body in a stationary position. But, everything inside the universe travels, from our planet (Earth) –which revolves on its axis at a speed of approximately 1700 km/h— to the solar system and even the Milky Way Galaxy.

All the planets in the solar system and their personal moons also travel through space. Actually, in order to retain a stable orbit, it is essential for Earth to move around 30 km/s. The innermost planets in our system, Mercury and Venus travel faster while planet Mars and the external planets of our solar system fly through space at a sluggish pace.

But think superior and bigger. Even yet the Sun is at the heart of our solar system, it is also traveling at an unbelievable speed through space. If we consider even bigger, we will understand that even our gigantic Milky Way galaxy is in motion, and all continuing things that make up the universe such as stars, gas clouds, planets, black holes and even the mighty dark matter travel within the universe.

Just as Earth revolve around the Sun and our Sun revolves the galactic center –which from our vantage point is situated around 2500 light-years away— in an elliptic trajectory. It finishes a revolution every 225 million years roughly. This is known as a Galactic year.

It is predicted that since the Sun and Earth came into being, 20 galactic years have passed, which means that we ended 20 successful revolutions orbiting the galactic center. However, if we relate detailed human history to our movement through the universe, we would understand we hardly moved in our galactic path.

But what about the Speed? In order to finish a successful revolution around the galactic center, the Star (Sun) has to travel at a stunning speed of 792,000 km/h. Including Earth and all other objects in our complete solar system follow the sun at this obsessive speed.

In comparison, light-travels at a mesmerizing speed of 1.09 BILLION km/h.
Though, not only do moons, planets, and in this particular case, our sun travels through space, the galaxy also moves through space, pushed by the gravitation of other enormous objects in the universe.

As it turns out, our Galaxy is now being thrown, by other huge galaxies and clusters in the surrounding area — near a certain point in the universe.

But wait a minute, related to WHAT is we actually calculating the movement through the universe? Well, when arguing our speed around the Milky Way Galaxy, researchers are capable to measure it relative to the HEART of the Milky Way Galaxy.
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However, the Milky Way Galaxy isn’t motionless or stationary, and it also moves through the universe. So is there anything to which its motion can be compared?

For a long period time, astronomers and scientists were not able to answer any questions like this. We can compare our galaxy’s speed with other galaxies, but all the other galaxies travel through the universe just as the Milky Way Galaxy does.
In order to answer this mystery, astronomers and scientists point towards the CBR (Cosmic Background Radiation) and the Big Bang.

As stated by NASAThe Big Bang theory guesses that the early universe was an extremely hot place and that as it grows; the gas within it gets cooler. Therefore the universe should be packed with radiation that is exactly the remnant heat left from the Big Bang, called the “Cosmic Microwave Background,” or CMB. The Cosmic Microwave Background (CMB) radiation was produced 13.7 billion years ago.
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Theoretically speaking, the CBR suggests experts with a frame of reference for the entire universe, compared to which we can determine and calculate our motion.
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This means that the Milky Way Galaxy is travelling through space at an amazing speed of 2.1 million km/h, in the direction of the constellations of Virgo and Leo; exactly where the so-called Great Attractor is situated.

Maybe they did use an ancient form of the METER???

The Ancients have shown precision we only thought was possible in modern times.
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
There have been several things I thought were compelling arguments for an ancient meter (or ultimately, a few very similar ancient meters) - one is that on top of Yoda's rendering of the Cuicuilco pyramid as a treatise on circular and spherical math (something that may survive even when the maps are thrown out the window), Dimitios Dendrino's rendering of the largest circular pyramid at the Guachimonte's site includes some passages that comment on how close it is to being something of that very nature, and the thing that makes both Dendrinos' proposal and my tentative values for the structure to be correct, is to acknowledge a possible meter of 3.289868134 ft (aka the "Third Meter" or .33333333333 Pi^2 ft) being involved in the design. 

"It turns out that not much is available in terms of concrete and detailed measurements, and what’s available is not exact (i.e., at an accuracy of centimeters) but approximate (i.e., in meters). Basically, two measurements have been published regarding CS-2: the length of its circular base (given as about 360 meters), and the geometrically linked diameter of that circle (given as about 115 meters), [1] [3]. We shall use these base measurements, plus an estimated measurement (the cone’s radius r at the top surface of the main frustum cone component of the monument) obtained by observations from numerous photos available, so as to derive the complete mathematical (geometric) specifications of the CS-2 structure. 

A note is in order at the outset. If one accepts the 115 meter diameter as a closer approximation, then the corresponding perimeter length should be 361.28 meters. If one accepts the 360 meters measurement as more accurate, then the diameter should be 114.59 meters. This study is carried out based on the 115 meters diameter length (corresponding to 361 meters perimeter, given the value of Pi=3.14159….). It could be carried out based on the 360-meter perimeter approximation, although the results would be sufficiently close to validate the findings presented here. This is left as an exercise for the interested reader. 

Obviously, the builders of the structure did not use the current metric system. However, it turns out that they employed a modulus for the monument, and that modulus has a unit length which turns out to be quite close to the contemporary “meter” – a major finding of this study"

I found that more compelling than any proposal so far involving a possible ancient meter posted at Tikal as the still unsolved recurring "6.56 feet" (~2 meters) figure of the Tikal temple platforms as obtained from Teobert Maler's data.

What's most compelling to me, though, is the ability of some of my proposed meter values to reduce the proposed values for the earth's circumference down to round figures of 4 x 10^n - little if anything may be quite as universal in ancient symbolism as taking a circle and dividing it into four segments. The equatorial circumference reckoned as "One Zillion Cholulas" or 131594725.4 ft,

131594725.4 ft as equatorial circumference / 3.289868134 ft as meter = 4 x 10^n "meters". 

It's a somewhat symbolic value in that context for being somewhat lacking in accuracy - I think it manages to undershoot textbook figures for equatorial circumference by about 22 miles? - but this proposed meter that measures it out that roundly may have often enjoyed more accurate applications measuring much smaller things like monuments and sizable artifacts.

(And yes, because technically this circumference would occur "just under" the surface of the earth, or "just under" a more accurate circumference in simplified geometric models, I'm seriously wondering just how often the ancients might have referred to this as "the underworld").

This same ("Third") meters gives useful responses when used to measure the Great Pyramid as I've traditionally regarded it

Ht Great Pyramid in feet (with paving) 480.3471728 ft / 3.289868134 ft as meter = 146.0080323 "meters"

146.0080323 x 2 = 292.0160647, or 1/10 of the cube root of the Earth's circumference in miles

29.20160647^3 = 24901.19742

So that is sort of a convergence of several geodetic functions when this proposed meter is applied to the traditional GP model.

I don't know what happened to the secret Pyramid chambers. The technology they were using sounded admittedly new and their first outing might have given misleading first results? - but some of the articles I read didn't help much for making it out to be "x rays done with cosmic rays" - I thought that the Great Pyramid already had something of a robust history of giving strange cosmic ray readings?

Personally, I don't quite know why anyone would go to the trouble and then only put one doorway or one passage system in the thing. Maybe someone should go to the same place as the entrance, only on a different side, and try knocking? If that doesn't work, maybe I could try mulling over again what sort of mathematical formulas might have informed "the initiated" where the doors were located?
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Just some stuff I've been up to, recovering from another bout of anthropologitis from watching documentaries on ancient Mesoamericans - there's something about hearing "ritual human sacrifice" over and over out of a guy whose voice compression is turned up so high you think his balls are about to pop, that makes the morbidity of Mayanists like Mary Miller seem to almost pale in comparison. I have about as much interest in measuring monuments accomplished through tyranny as I do in measuring some millionaire's gold toilet seat (i.e., none whatsoever).

Thankfully, it's a little therapeutic when suffering from anthropologitis to cling desperately onto several core principles - namely, that the clockwork of the heavens is not quite so divine, given all the splices and patches that arithmeticians have to use to milk more of a semblance of order out of it, that it should inspire ritual sacrifice. It's also actually hard to imagine the priests keeping this secret from the masses when it's blatantly obvious after five days have to be artificially dropped off the calendar to achieve the divine harmony of a 360 day year that divides into 13 periods of 20 days that a number of ancient people supposedly used. Likewise, it's hard to imagine some secret monopolistic order using secret astronomical cycles to subjugate the common folk when they're actually making the astronomical alignments obvious to virtually everyone by marking them with huge objects like temples and pyramids.

(And dammit, sometimes it even helps to remember what an admirably staunch defender of ancient intellect that Yoda has been, despite his own occasional bouts with Von Daniken Syndrome).

I was going to have another go at the terribly novel Monte Alban Structure J mentioned previously, an intriguingly complicated structural design that is claimed by some sources to be lacking right angles... (Urcid and Joyce's article was a flop, it shows three different fascinating stages of design for Structure J, but not a measurement to be found, sadly).

Finally found a copy of the diagram from Caso that I can almost read half of (the diagram based on this one appearing in Marquinas' Architectura Prehispanica omits the data)...

A lot of Google searches like "Monte Alban Structure J Measurements" keep turning up a paper on remeasuring of Structure J's astronomical alignments rather than the building itself, apparently.

I haven't actually seen this paper 

"Building J at Monte Alban: A Correction and Reassessment of the Astronomical Hypothesis"
Damon E. Peeler and Marcus Winter
Latin American Antiquity
Vol. 6, No. 4 (Dec., 1995), pp. 362-369

But as described by several sources it includes the remarkable concession that the distance from Structure J to other structures at Monte Alban might encode the important calendar ratio 365/260, although I can't find any evidence of anyone inquiring whether similar data could be encoded internally within Structure J. 

So I finally also tracked down my copy of Aveni's "Skywatchers..." to double check if it offered any help (it didn't) and was inspired to look more at his body of work, when I came across an interesting example of possible calendars that I haven't thought about in a good long while, the pecked cross.

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Several examples of pecked crosses from Anthony Aveni via Science Frontiers

It's curious that I can't seem to find where anyone has ever catalogued these (even though some archaeologists have it that mighty Teotihuacan was oriented in accordance with a pair of them) any more than anyone has actually catalogued the solar discs or circular altar stones (can I assume from the apparent absence of such references that a proper comparative study of either may have yet to take place?) so I've spent way too much time trolling Pinterest lately looking for more of both.

The example provided by Aveni in his paper on possible ancient calendar reform (from the floor of structure A-V at Uaxactun) may be sufficiently intact enough to extract some interesting calendar formulas.

Anyway, the tentative conclusion from some preliminary poking around suggests that perhaps pecked crosses, as humble as they may look, should perhaps not be underestimated, and even that perhaps the ancients were surprisingly adept at working with coarse fractions. (This includes a case in point of possibly signalling for (Pi / 3) via 45/43, accuracy .99934!)

Also in one of his works, Aveni ponders the possible synonymy of the 260-day cycle and the human gestation period. I have to applaud him for that, since it could yet explain everything from numerous fertility goddesses to Sheila-na-gig figures, although I'm still suspicious personally that fertility references might actually signal an average 280 days (Wikipedia) with 260 being a different thing.

Also in the area of iconography and symbolism, I think I've posited some of this previously, but I've come up with two reasons for all the skulls in ancient iconography - first is that it facilitates display of the teeth, totaling 52 (Wikipedia) which in all likelihood represent the weeks of the year, and secondly, combined with 2 eyes, 2 nostrils and 1 mouth (2 + 2 + 1 = 5), skulls (like five-fingered hands) are eligible to also signal Venus via being a numerical analog of the 5-pointed star pattern Venus traces in the heavens, but additionally 52 x 5 = 260, so that skulls are further eligible to also singlehandedly symbolize the 260-day Tzolkin period. Perhaps not quite the death cults that some archaeologists insist on, as opposed to having some killer incentives to practice poor taste, precisely as moderns do for Halloween?

Also after looking at some Northern Native American artifacts, particularly from the Moundville site in Alabama, I've begun to wonder how many ancient peoples might have used the human eye to symbolize the world, with the radial striations symbolizing the radial division of the world into bands of longitude. (If the Eye of the Illuminati were telling us that a pyramid represents the world, we kinda sorta already knew that).

[Image: hands20_93.gif]
"Rattlesnake Disc" from Moundville Site in Alabama: "It's All (Hopelessly?) Tied Together" - ??
Accurate iconographic description of the tangled and twisted messes that are my Geodetic Metrology tables
and corroborating the interconnectedness of ancient geodetic and astronomical arithmetic?
(If the 17 notches in the periphery of the disc don't correspond to any known calendar periods, 
they may nonetheless belong to some ancient calendar formulas? This possibly includes at Tikal, 
where we may yet confirm a doorway diagonal length of  what may be a representative
20 / 1.177245771 = 16.98880598 ft)

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Five and a spiral, emblems of Venus? (Olmec)

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Swapping eyes for spirals: more variations on the same theme? (Maya, l - Olmec, r)

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Spiral = Spiral?
An Anasazi petroglyph that reminds people that the (double headed) serpent and the maze 
may be synonymous when used in the context of "The Ancient Mysteries"?

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Spiral dualism and Venus unassumingly referenced in an early spiral motif? (Valdivia Culture, Chile, 3500-1800 BC)

I had the good fortune to find a source for Tiwanaku, although the story is a bit alarming. I have two papers by Protzen and Nair that seem to almost gloat about the authors being in possession of voluminous accurate measurements which in both cases they do not share with the reader, but homogenize and pre-digest in some arcane manner to give us a pair of ratios which I would toss right out except they're a little curious

Figures 14 and 15 of the second paper are captioned with the speculatively significant ratios of 1.0399 and 1.4499. "1.0399" does bears suspicious resemblance to the calendrical figure 52 x 2 = 104, divided by 10^2, so perhaps they actually are onto something, although I'm skeptical we should find only two such significant ratios there and they still might have done some damage to the trickle of actual data with their homogenization.

This one actually is a gem, and the source offers a larger sized download big enough to actually read the notation on the diagrams

"Die Ruinenstätte von Tiahuanaco im Hochlande des alten Peru (The Ruins of Tiahuanaco in the Highlands of Ancient Peru)"
(1892 book about Tiwanaku written by two German discoverers and engineers, Alphons Stübel and Max Uhle)

Which has enough fine details it ought to keep me busy through Christmas, except it remains to be seen whether there's enough data to extrapolate some of the door heights, since apparently in spite of all the lavish detail it was still against the religion of either author to clearly annotate the height of a thing? Such is life for the aspiring Pi Jedi...

Also on the subject of Tiwanaku, I might add that I was impressed with J.M. Allen's proposal of how some of the stones of Tiwanaku work in regards to alignments (provided things actually do work that way in real life) and how this is written on one of the gates themselves, but I did find another occasion to do U-Word-Patrol. This guy does some great metrological work and a lot is probably impeccably reasoned, but while one could do worse than trying to find the Royal Cubit everywhere, I wonder if his eagerness to do so has kept him from overlooking what may be the occurance of Phi or a representative thereof in modern "British" feet, just as Harleston's enthusiasm for making everything into rational numbers of "hunabs" might have kept him from noticing his beloved 19.47 written at Teotihuacan in a rather obvious place in modern feet, if I am not terribly mistaken.

"The overall length of the pillars is 49.300 metres (161.74 ft) and the distance from centre to centre of the end pillars is 48.4575 metres (158.98 ft) so the row of pillars is virtually 160 feet long if we were using English feet."

Is the Golden Ratio or thereabouts trying to bite the poor guy on the proverbial nose? 

I could also throw in that on either side of the gate which probably contains the instructions for using the stone sightings for calendar keeping there are groups of 15 squares, as Allen notes.

15 squared = 225, approximating Venus' orbital period - which of course means that when we find the square root of 15 presented in a monument, it may sometimes have the task of signalling concerning Venus, since (sqrt 15)^4 = 225.

Sqrt 15 may also have other roles to play in some astronomical or calendar calculations, including that my call on "158.98" ft would probably have to be 159.1549431 ft - that's a reciprocal of the mighty Giza constant 2 Pi, and I'm not entirely sure it was intentional, but

2 Pi / (sqrt 15) = 1.622311470, any Pi Jedi's most useful approximation of Phi.

I don't know why we don't seem to have surviving evidence of the foot as a universal ancient standard of measurement, but then again I can name lots of things we don't seem to have evidence of either, including blueprints of some of these intricately designed ancient moments. According to the available evidence, these ancient types just started randomly slinging stones around and totally improvised their exquisite pyramids and temples - but I highly doubt that such a thing would be actually be safe to assume.

I have by the way given up on Teotihuacan for the moment in spite of the fact that Harleston's materials may still be useful. When I got out of my copy of one his books, I noticed the dotted line on his diagram showing where he is merely speculating on the pyramid measures after a reconstruction effort by Bartres and I would need to try to sort all that out somehow. This is where I have to give a really big hand to Graham Hancock, I am so pleased that someone with such a high profile "gets" this:

"Graham Hancock has called Bartres's restoration of the Pyramid of the Sun at Teotihuacan "grotesque vandalism", citing the removal and selling of a layer of sheet mica between two of the upper levels—mined from 2,000 miles away and used for unknown purpose—removing the outer layer to a depth of more than 20 feet, and adding a fifth stage. Hancock argues that because scientific data might have been incorporated into many of the key dimensions, drastically distorting the original shape and size of the pyramid had possibly deprived posterity of some of the most important lessons Teotihuacan had to teach.[3]"
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
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Perhaps the meter was discovered audibly??? 

[Image: sh.jpg]
Sammy Snake & Harry Hat Man

Sammy Snake loves to hiss,
so he hisses a lot,
hisses a lot, hisses a lot.
Sammy Snake loves to hiss,
so he hisses a lot.
There aren't many hisses he misses.

But the Hat Man hates noise
and hushes him up.
The Hat Man hates noise
and hushes him up.
The Hat Man says 'sh'
as he hushes.
'Sh, sh, sh!'.

The Ether Model & The Hand of God - Page 51 - Google Books Result

Now, the speed of light is 300,000,000 meters per second (in vacuo)—huge in comparison with thespeed of sound (in air) at 333 meters per second.

I-physics Iv Tm' 2006 Ed. - Page 110 - Google Books Result

The speed of sound is equivalent to twice your distance from the wall divided by ... to this measurement is: 1000 meters = 333 1/3 meters per second 3 seconds.

Wireless telegraphy and wireless telephony an elementary treatise
A.E. Kennelly - History
Spireri of Electromagnetic W acres The speed of sound waves in air we have seen to be in the neighborhood of 333 meters per second, (1090 feet per second or ...

Would you take note if eye snap my finger but you saw it first there [Image: sheep.gif] heard it second later here?

~333 meters per second because Many cultures seemed to know what a "Second" of time is.

Have you heard the word @ ~333???

Two ducks with one ashalar


A set of possibilities on Naked-eye accurate astronomy and how the Constellations were envisioned!!!

However, one of the most beautiful galaxies we can see with the naked eye isvisible in the night sky all this month (November). The nearby Andromeda Galaxy, also called M31, is bright enough to be seen by the naked eye on dark, moonless nights.

Can you see other galaxies without a telescope? - NASA

[Image: m31.gif] 
You Spiral /Eye Spy Role  chiral and polar-eyes'd
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Exposure to a common visual illusion may enhance your ability to read fine print
July 12, 2017

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Our ability to discriminate fine detail isn’t solely governed by the optics of our eyes. Credit: Dr Rob Jenkins
Exposure to a common visual illusion may enhance your ability to read fine print, according to new research from psychologists at the Universities of York and Glasgow.

Synapses in the brain mirror the structure of the visual world
July 12, 2017

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Our brain is especially good at perceiving lines and contours even if they do not actually exist, such as the blue triangle in the foreground of this optical illusion. The pattern of neuronal connections in the brain supports this ability. Credit: University of Basel, Biozentrum
The research team of Prof. Sonja Hofer at the Biozentrum, University of Basel, has discovered why our brain might be so good at perceiving edges and contours. Neurons that respond to different parts of elongated edges are connected and thus exchange information. This can make it easier for the brain to identify contours of objects. The results of the study are now published in the journal Nature.

plural noun: constellations

  1. a group of stars forming a recognizable pattern that is traditionally named after its apparent form or identified with a mythological figure. Modern astronomers divide the sky into eighty-eight constellations with defined boundaries.
    • a group or cluster of related things.
      "no two patients ever show exactly the same constellation of symptoms"

Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Well, shoot... His Divine Holiness Swami Iforgethisnamebutitwasreallylong should have told me that staring at mandalas all day might help my astigmatism. Here I though he just wanted to get me in a trance so he could go through my pockets.

I wonder if The Ancients referred to the world as "the Eye of God" as euphemistically as their referring to geodetic monuments as "the Navel of the World"?

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[Image: the_eye_of_god_by_jarff.jpg]

It would be something of a misnomer since geodesy immediately informs us that The World is not in the shape of a divinely perfect sphere, with this imperfection mandating voluminous amounts of number-crunching, sprawling tables of metrological equivalencies, separate metrologies for polar and equatorial circumference, and mile values that seem to have little intrinsic value except as means to an end - but who am I to argue with tradition, especially if it's conceptually correct? 

I suppose it will make interesting fuel for philosophy how ancient Americans "failed to invent the wheel" when their entire concept of reality is a great big freaking wheel...

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Examples of this ancient American application of The Wheel are found from Mexico to Peru.

Do you know, I think the point of the famous Aztec Calendar Stone might have gone over my head slightly? It may not just incorporate a very clever mathematical formula, but possibly a very specific one.

[Image: 1416.jpg?v=1485680501]

When we go about deciding how we will divide the 365 day year into months (in a rather Julian manner, no less)...

365 days in a year / 30 days in a month = 12.16666666
365 days in a year / 31 days in a month = 11.77419355

Remind us of anything? Say, a 1.216733603-foot remen, and this insane contraption 1.177245771, Yoda's "Alternate Pi"?

We have only to "fine tune" these to 

365.0200808 / 30 = 12.16733603
365.0200808 / 31.00627668 (Pi^3 as 31) = 11.77245771

And that is what they become, precisely. Rather than originating with geometry, perhaps they (and geometry itself?) originated with the observation of the calendar?

Not that us "bean-counters" didn't earn that name for a reason, or that the Mayan vigesimal system isn't well suited for creatures with 10 fingers and 10 toes, but more possibilities of ancient American pocket calculators might end up including Patolli boards, since they seem to keep turning up in discussions of pecked cross petroglyphs?

Then there are some rumors and rumblings about the abacus... 

Almost makes you wonder if ancient peoples managed to "migrate across the Bering Strait" without a little culture trying to tag along?

I managed to find a copy of Caso's book with the diagram of Monte Alban Structure J for thirty bucks. Scant as the data is, it might turn out to be the most useful book I've bought this year. A little trouble with the offset on the red and black plates so that there's a thick black line through one set of measurements printed in red, but generally much easier to read than anything I've found so far.

Mostly at present I'm just wresting with more numbers that are new to me - there are opportunities at Chichen Itza, Tiwanaku, and Monte Alban to assign rational number values of feet for certain measurements, and it's very tempting to have examples where we might say, "Aha, this might be proof that ancient Americans used the same foot we use now" because that is what's typically accepted as validation of a metrology is to find its application in rational, whole-numbered units, even though that is not what we actually find, and even though many important constants worth encoding (such as Pi, Phi, or the Radian) are not rational numbers. Rational numbers numbers by comparison may be generally less exciting than irrational ones, and may often be included structurally rather than metrologically - for example, expressing the number six via six steps on a pyramid, rather than a pyramid step precisely measuring a very boring six feet in width. Why not make it 6.283185307 (2 Pi) feet wide since as everyone knows, 2 Pi is the greatest invention since bread (provided of course that 2 Pi isn't even older than bread).

If these measures that look like whole number values were not intended to be interpreted as whole numbers, the next most likely thing might be that we're seeing rational numbers "shaved" slightly using well-known fine ratios - so where, for example 15^2 = 225, representing Venus' orbital period, as is seemingly achieved by 15 recurring designs on the Tiwanku gates, in measured feet we might get something like 15 / 1.000723277 = 14.98915869 and 14.98915869^2 = 224.6748781, as if the semi-standard 225 / 1.000723277 = 224.8373803 value for Venus' orbital period weren't already sufficiently useful as a representation of the "224.701" day cycle.

The unanswered question, I guess, is just how many of these funky variations was it really worth putting up with? Does their utility sufficiently compensate for the ensuing complexity and confusion?

For what it's worth, it's not something I should say without evidence at the ready, but I've poked around the Tiwanaku data enough that it really does look like the masonry there is going to turn out to be from the "Pi Jedi" school - not that I think the ancient Egyptians came over and designed Tikwanaku. Quite the contrary, the origins of mathematics (how many logs and berries must we gather to live through the winter? - that's math, and it's math that requires a calendar even if it's just scratches on tree bark) and the corresponding mythological symbols seem so ancient and universal that visitors or immigrants to ancient America from Egypt, Africa, Asia, India, Indonesia, the Middle East, and possibly Europe and Alpha Centauri, weren't really in a position to "bring" culture to the indigenous people, because culture was most likely already here when they arrived.
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Well, let's see here... I think I'm managed to nearly convince myself, in spite of appearances and in spite of propaganda, that the only reason we find skulls morbidly plastered all over the world of the Maya is in fact NOT death worship, but a mathematical rationale wherein a skull represents a number, as previously detailed here.

(2 eyes + 2 nostrils + 1 mouth) = 5; 5 x (52 Teeth) = 260, the number of days in the sacred "Tzolkin" calendar.

Next is why we would find an entire human skeleton in Maya art if they were not in fact insufferably morbid and superstitious. (Fine way to talk about people who aren't even here to speak up for their reputations). Can we find a mathematical reason for this, too?

Wikipedia figures differ (well make up your effing mind, Wikipedia), but this entry states

"The human skeleton is the internal framework of the body. It is composed of around 305 bones at birth – this total decreases to around 206 bones by adulthood after some bones have fused together.[1] The bone mass in the skeleton reaches maximum density around age 21"

Let's hope they're not just talking shite at me, because

~305/~206 = ~1.480582524 = ~1.216791899^2 = ~1.216733603^2 = ~((365.020081 / 30) / 10)^2) = ~((sqrt 225) x Pi^2)/10)

Fancy meeting that again, ALREADY...

Question, is this all a complex coincidence, or were the ancient Maya even capable of making anything that wasn't some kind of number puzzle involving calendar math?

Because life might be wasting its time trying to hand us blessings, if we don't know when it's time to receive them?

"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
I found in the conventional archaeological literature where the passage of Venus into the Underworld is described simply as Venus passing below the horizon, which I think is consistent with the iconography I'm inferring. Another thought I might as well share although it's very incomplete, since I've never really figured out what else to do with it, is "What if" there was a tendency to decorate or associate people's resting places with both irrational numbers (which at least for intents and purposes "go on forever" after the decimal place), and astronomy as perpetual cycles of the heavens, as at least sentimentally wishing such perpetuity upon the departed? That's a very different thing than thinking the cycles of the heavens have to be wound up like a wrist watch with sacrifice...

In case it merits pointing out, I'm also inclined toward the opinion that part of the rationale for an ancient American "obsession" with calendar numbers is that, as pointed out here, they may be hopelessly entangled with geodetic figures. Even if you aren't a sailor or a navigator, remembering the circumference of the Earth is obviously a way of remembering that it isn't actually flat and that there is another side to it, but also remembering ones' roots if that other side is where ones' ancestors originated.

(Also, I think I could philosophize over this a bit from an artistic point of view - if all of these ancient artworks and monuments and ancient myths are really sort of all about the same thing, where's the freedom of expression? Then again, there may be a certain creative joy to succeeding in a restricted context, where even after a minimum of 10,000 years of all kinds of people coming up with ways to express the same limited central themes, it's still possible to find new and creative ways to express the same core truth. Sort of like writing a song - a new song might be about the last thing the world really needs, but it can be extremely rewarding to write one when even after all the countless songs that have written, one can still theoretically somehow manage to write one that still hasn't been written yet).

I've returned to this subject for a minute, for possible comparison to Monte Alban "Structure J," and done a tiny bit more work... 

Caballito Blanco, "Mound O"

[Image: caballitoblanco05.jpg]

It's risky, but I tried doing some pixel measures after having derived a meters-per-pixel ratio from examining the side opposite the point, so that I could try to fill in a few missing measurements. Even at a reduced scale, this method gave me 3.199 meters for the 3.20 meter figure given on the side in the image, so unless it's beginner's luck, I found that encouraging...

The structure as depicted doesn't seem to be evenly divided. Based on the pixel measures and a central axis defined by the point, the estimated length opposite (and furthest from) the point broke down into estimates of 12.1555 feet and 13.5367 ft... What I'm guessing they did here was to go Pi Jedi To The Max and cleverly add ten remens to 100 of the (true) Reciprocal of the Squared Yoda Megalithic Yard (RSYMY)... What a fine pair of big players!!

12.16733603 ft + 13.51926225 ft = 25.6865828 ft, probably meaning 25.68351851 feet (accuracy 0.99988!)

Which is a number we can also construct from two calendrical numbers, Venus Orbital Period as 225 days / Primary Figure for Number of Hours in a Calendar Year 8760.481938 (365.020081 x 24 = 8760.481938)...

225 / 8760.4819 = 25.68351851 / 10^n

(It's still somewhat unconfirmed but representing the calendar year by the number of hours in it may well have been done with the Aztec "Tizoc Stone" as hinted at previously).

Daniel Schavelzon's text describes "Mound O" as a structure that was built then expanded upon at a later date (as also appears to have happened with "Structure J" at Monte Alban), which I find hugely fascinating. Expanding pyramids in one layer being built over another is certainly a potential act of multiplicity, resulting in multiple pyramids in one, but the pyramids that have been built over seem to generally be poorly accessible for study or comparison. Things may be different at Caballito Blanco "Mound O".

As of this hour, our top scientists are working round-the-clock in an attempt to confirm these incredible findings, and we'll have more late-breaking developments as they happen, but what I think may have happened, is that "Mound O" at Caballito Blanco may have been an extremely well-designed structure mathematically speaking, but...

The architects of the revision may have decided to "go for the gusto" and rebuild it as a structure whose new length and width multiply to give the Long Count in days / 10^n? That in addition to any number of other spiffy incentives for reinventing what was likely a very clever work of arithmetic, astronomy, and architecture already.
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
I was looking for data on the remarkable Quiahuitzlan site, which has quite a number of fascinating miniature "temples" or "tombs"...

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Some of the diminutive monuments at Quiahuiztlan in Veracruz

The search for data brought me to Cuaderno de Arquitectura Mesoamericana Issue Number 8

(31 issues of CAM. Not sure what all is in them yet but Issue Number 3 has an article on pecked crosses with Aveni,
and there are also articles by Daniel Schavelzon and George Andrews in the series)

Which also contains some base measurements of the Pyramid of the Niches at El Tajin, which look like they might just have been carefully taken. 

I still have plenty of work left to do with the data from Palenque, Tikal, Tiwanaku, Chichen Itza, and Monte Alban, but I think the El Tajin data, even for what little there really is of it, may further bear out a number of things I've been saying - including that it's probably a pretty good example of deliberately uneven measurements being used purposefully, and probably more evidence that the ancients really were thinking about temple and pyramid diagonal measurements although being inherently loose around the edges like that, it's harder to get a good grasp of. It also looks a bit tricky because they may well have intended to represent a selection of important numbers from roughly 57.0 to perhaps as high as roughly 57.64 (with the Radian 57.29577951 probably being among them) through the variations in the value of the half-base length resulting from the slight irregularity.

[Image: Nichos_flying.JPG]
Pyramid of the Niches at El Tajin (Veracruz)

If I did the math right, however, we may be seeing max width values of 100 Alternate Pi (1.177245771 x 100) = 117.245771 ft and 12 x (Pi^2) x 10 = 118.4352528 (calculated from the data as 117.8805774 and 118.5867454 feet, respectively), and diagonals of (depending on which adjacent sides they are calculated from) both 162.231147 ft (calculated from the data as 162.2110909) and 161.882914 ft (calculated from the data as 161.8598464). There is probably more rather adept use of simple fractions also on display in the Pyramid of the Niches, and at a casual glace, after representing the solar year though the number of niches, its designers may have proceeded to represent the 225 day cycle by placing 15 niches (the square root of 225) into the staircase? (This would probably lend credence to an earlier proposal that the same thing was done using the number of glyphs on one the gates at Tiwanaku).

There's also a possible value of 115-something feet for one of the possible simultaneously-valid length measurements of the Pyramid of the Niches. I'm not sure yet how exactly it would work out, but the ratio between two major calendrical numbers, the "Tzolkin" of 260 days and ~225 days of the Venus Synodic Period is 260 / 225 = 1.155555..., hence a possible width measurement at El Tajin representing this as about 1.155555 x 100 feet. The possibly that a similar ratio between major calendrical numbers may be reflected in distances between monuments at Monte Alban has already become part of actual academic discussion, as previously noted.

If someone could make a sufficiently strong showing for an example from each the additional sites named, adding two or three particularly noteworth altars to the collection I think there may actually be enough for this have the potential to become a bona fide academic topic (regardless of the obligatory rending of garments and gnashing of teeth on the part of skeptical academicians) instead of the much disrespected "pseudoscience" - even in spite of how much rests on the "absurd" premise that all of these monuments were measured out primarily using the very same foot we use today. 

That's a very happy thought for me since it's those guys and gals out there in the field with the tape measures who most need to be taking this stuff more seriously.
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
I'm trying to table up more of the data from George Andrews - as scarce as any reliable measurements seem to be, the wealth of data the available papers by Andrews is simply too valuable to pass up - but it's literally weeks worth of clerical work trying to condense all those 40 page reports into one page data tables.

Meanwhile, I've run into several points that still sort of confuse me, which is another incentive to try to get an even broader overview of ancient American arithmetic... I think I've made numerous arguments in favor of ancient Mesoamericans having been rather fond of Yoda's "Alternate Pi" 1.177245771 in addition to the Pi ratio itself, as well has having possibly given examples of how the ancients liked to "mix-and-match" creatively, so we might want to expect numbers that can be made using Pi with Alternate Pi, not the least of which is the primary figure for the calendar year itself

1.177245771 x Pi = 3.698426663 = 1/2 Squared Yoda Megalithic Yard = 7.396853327 / 2
1.177245771 x (Pi^2) = 11.61895004 (sqrt of 135, which may have been important just for being part of this series)
1.177245771 x (Pi^3) = 365.020081 / 10

Likewise, we can divide Alternate Pi by Pi

1.177245771 / Pi = 3.747289674 = (4 / 1.067438159) x 10^n = (1.040913798 x 360) / 10^n = 14.989158700 / 4

So we are already back to my proposal that we might see some of these "shaved" numbers in practice, such as 14.989158700 instead of 15, in some metrological applications like this (and half of this figure, 14.989158700 / 2 = 7.494579343, is at this hour still trying to get itself declared to be a number intentionally built into Tikal's temples)

1.177245771 / (Pi^2) = 1.1927993500 / 10^n

And that's one of the things that still confuses me - it still seems hard sometimes to tell in a given instance whether they meant this, or perhaps 1.184352528 = (12 x (Pi^2)) / 10, which has managed to make something of a name for itself in these procedings, or perhaps something else. (At a tolerance of about 2/100 of a foot, sometimes the intended figure in the target range could even be 1.177245771 itself).

Next question, did the ancients find a lot of usefulness in dividing Alternate Pi by another power of Pi, or have we about run out of good combinations of Pi and Alternate Pi here?

1.177245771 / (Pi^3) = 3.796798252 and THAT, is the primary figure suggested here to represent the Venus Cycle, divided by 10^n

37967.98252 / 2 = 18983.99126 representing 18980 (days)

So 1.1927993500 may indeed fall within the spectrum of useful items, we might expect to see a certain amount of it accordingly, (the bulk of the equations in this post thus far appear to be written into the Aztec Sun Stone when measured in modern feet) and we may have increased or at least better organized our insights into any ancient fondness for Alternate Pi 1.177245771 given some of the things can be built of just it and the Pi ratio.

Not sure what it means yet but I've seen a number of occasions when trying to figure out what the ancients might use to represent the number 19, which does not itself actually belong to this system of numbers, where the equation comes out suggesting that 18.98399126 could have been used to represent 19.

Another curio turns up often enough in the proceedings, and there's a small amount of backstory I might add. A curious notation, "Stone Pi" often turns up in my notes. This started back when I thought that 2.920160646 might be the "Grid Point" of Stonehenge - a proposal that's now gone into the waste basket, but the numbers remain. So, "Stone Pi" is shorthand for

(Formerly Stonehenge "Grid Point") 2.920160646 x Pi = 9.173955233

And at this point, the history of the number 9.173955233 might include that after undoubtedly testing more equations than I even care to think about, Yoda decided that 917.3955239 was the "Grid Latitude" of the Kulkulan Pyramid at Chichen Itza. As often, Yoda may be making these numbers out of numbers found in real life at the respective sites rather than just making them up out of map data, so they continue to promise to mean something independently of concerns about global "Grid" positioning.

2.920160646 x (Pi^2) = 28.82083036, which may have been already found in the Tizoc Stone

2.920160646 / (Pi^2) = 29.58741331 (360 / 1.216733603), which may be the primary ancient figure for representing the Lunar Synodic Period.

9.173955233 x 2 = 18.34791047

And that's one that I think I seem to see a lot in working with ancient American monument data (I've forgotten all the details but I know in the past I had some discussion with Michael L. Morton about the possible usefulness of the square of this number)

18.34791047^2 = 336.6458185

These days we are aware of the possibility that 259.7575763 may have been a highly favored way for the ancients to express the very sacred calendrical number, 260 - so it probably catches our attention with sufficient ease that

(1 / (1.177245771^2)) x 10) = 7.215488230 (as proposed to occur at Rio Bec), and 

7.215488230 x 360 = 259.7575763
259.7575763 x 360^2 = 33664.58188 / 10^n

So 336.6458185 could have been valuable to the ancients, just for having been made out of some rather obvious ingredients, if it will better prove its usefulness in practice.

But obviously in an arithmetic system that, at least at Giza, seems to have elementary circular geometry as its lowest level (i.e., 360 / Radian 57.29577951 = 2 Pi), 

18.23781305 = Radian 57.29577951 / Pi 

Is both obviously very important, but is also easily confused with 18.34791047, and similar confusion (at least for me) still exists surrounding any given example whether what LOOKS like the Double Radian 57.29577951 x 2 = 114.5915590 could turn out to mean 114.8380617, which is a reciprocal of the door height at Tikal Temple II (1 / 8.707914303 = 114.8380617 / 10^n), or even some other third possibility. Some instances of values in this range could turn out to be 1.141489711 or even 11.4148971 feet without exceeding a reasonable tolerance for error (1 / 1.141489711 = primary figure for Hours in a Year / 10^n = 365.020081 x 24) / 10^n).

There are more that may call for some careful thought - I see a good number of things that look like (72 Pi) / 100 = 2.261946711, and we may have reason to believe that 72 was an important symbol of Venus and its path through the heavens, but 225 / Pi^2 = 2.279726632 or 224.88373803 / (Pi^2) = 2.27807985 are also ways of mixing numerical Venus symbols with the Pi ratio in simple combinations. It's really up to whether a particular number makes good sense in a particular application, and whether or not we actually have the data needed to clarify some of these situations (worse, I've gathered enough photographs to know how often the top and bottom widths of ancient "temple" doors seem to be two different figures where I only have a single width figure in the data). 

I have an awful lot of data on ancient American door widths where unlike with Tikal, all I can do is suggest a few possibilities because I just don't have the data on their heights to be more certain. On the other hand, I should have enough data that I'd better be able to make something out of it.

(BTW, here is my link for Andrews' data if anyone else is interested in archiving it or working with it).
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
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Structure 39 at Yaxchilan

Re: George F. Andrews, Architectural Survey Yaxchilan and Bonampak, Chiapas, Mexico (txu-aaa-gfa00350.pdf), Structure 39 at Yaxchilan, text page 72 and plan showing altar, page 74

Other: Round stone altar, 1.14 m. in diameter, in front of central recess in back wall. (See Maler, 1903 and Morley, 1937-38 for details).

I need to do some more research on this (I was apparently not aware of these Yaxchilan altars from previous researches into ancient altars), but the text of Carolyn Elaine Tate, Yaxchilan: The Design of a Maya Ceremonial City, pages 231-233, makes it sound like this might be Altar 4 from Structure 39?

Diameter 1.14 meters = 3.74015748 ft
3.74015748 ft x Pi = Circumference = 11.75005126 ft

Remind anyone of anything? Hopefully, the quoted Diameter of the Aztec Sun Stone at about 11.75-something feet.

Proposed Circumference of Yaxchilan Altar 11.77245771 ft = Diameter of 3.747289674 ft =  Diameter of 1.142173893 m

Given these possible applications of Alternate Pi 1.177245771 to circular mathematics (Circumference / Pi = Diameter)
these two altars may represent the two first and most obvious combinations of Alternate Pi and Pi:

Sun Stone: Alternate Pi x Pi (x 10) = 36.98426666 ft (Circumference)
Yaxchilan Altar: Alternate Pi / Pi) (x 10) = 3.747289674 ft (Diameter)

I'm not sure what it might mean yet but Tate quotes the height (thickness) of the altar as .33 m = 1.082677165 ft, possibly meaning 1.082323234 feet. I'm not sure how easy it will turn out to be to tell what they intended, as there may well be another instance of the dreaded Ancient Mayan Fake Square Root Trick involved - i.e., 1.082323234 is somewhat near to the square root of 1.177245771: 1.082323234^2 = 1.171423583 and they could have been making an observance of that (see also proposed function of numerical "Hero Twins" previous).

On the other hand, it might turn out to be 1.096622711 ft (.334250602 m) or something...

Bit less of a no-brainer than the Sun Stone but I hope the total package turns out to be half as interesting as that Aztec monument that's famous for all the wrong reasons.
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
I think it's safe to say that from the data I've scrounged up so far, it may not be uncommon to find cases where the radius of this calendar stone here is the diameter or the circumference of that calendar stone there. There definitely appear to be a number of cases like that already even in the data presently at hand. (One of these apparently recurring numbers is a strange one that I still can't figure out, and might think was a mistake if this figure didn't already appear to recur even in what relatively little data I have).

I might also point out that in Teobert Maler's Explorations in the Department of the Peten, Guatemala, Tikal* (page 86 pdf pagination, page 71 original pagination) Maler reports a circular altar of diameter 118 cm:

"North Side (Plate 16, Fig. 1). The carving of glyphs on this side is adapted to the considerable unevenness of the stone. The photograph held in the right position and compared with my sketch,1 will give a correct idea of the glyphs. At the top is the large initial glyph, below it are two glyphs, and then (counting the horizontal rows) four sets of three glyphs : — Thus 14-2 + 3 + 3 + 3 + 3 = 15 glyphs. Before this shattered stela stood a circular altar (No. I in my enumeration) 118 centimetres in diameter and of considerable thickness (or height). This stone was not deeply buried and it seemed to me to have on its upper surface remnants of sculpture very much worn away. Badly weathered glyphs on the cylindrical side were more plainly recognizable."

*can be downloaded as a free Google pdf here - Download PDF option in Tools menu

In this case (as in possibly some others), inexactitude of measurement might have managed to balance out impact from erosion to show us what may have been the original specifications:

Diameter 118 cm = Diameter 3.871391076 feet = ~3.872983346 (sqrt 15) ft
Radius = Diameter / 2 = 3.872983346 / 2 = 1.936491673 (sqrt 3.75)
Circumference = Radius x 2 Pi = 1.936491673 x 2 Pi = 12.16733603 (ten Remens or 365.020081 / 30)

(No data on the thickness to try to see if this is part of another stunning calendar formula)

I'm even less certain of this one, but in the same text (page 96 pdf pagination, page 81 original pagination) describes as altar paired with Stela 11

"In front of Stela 11, on the general level of the cement pavement, stands a circular altar 170 cm. in diameter. It is sharply and smoothly dressed and is the largest in Tikal, which proves that its stela must have been of a certain importance in sacrificial ceremonies."

Diameter 170 cm = Diameter 5.577427882 ft = ~5.577096019 ("Giza Vector" / 1000) ft
Radius = Diameter / 2 = 5.577096019 = 2.788548009
Circumferene = Radius x 2 Pi = 1.752096388 (8.760481940 x 2; 3.504192776 / 2)

8760.481944 being a probably standard figure for hours in a year as previously suggested (365.0200808 days x 24 hours) = 8760.481944, and 350.4192776 (360 / .027340740) having also appeared previously in work on Thom's flattened circle types; 17520.96388 and its "decimal harmonics" can probably be considered to be a "tried and true" number for Yoda having assigned it as a Grid Coordinate of the Pyramid of the Magicians at Uxmal, original Grid Coordinates 17520.96388 / 129600 (360^2) = 7.396853329 (the Squared Yoda Meg Yard).

Regarding the Tizoc Stone, that work has gone up "in the air" (as did work on Teotihuacan) since I actually have two sets of data for the Tizoc Stone and I'm not entirely sure if I should believe either one, but the quotes for diameter are 2.60 m and 2.67 m...

Diameter 2.67 m = Diameter 8.759842520 ft = ~8.760481944 ft

(The original circumference by design would be exactly 1/10 of what is proposed to be the radius of Silbury Hill by original design).

Diameter x Pi = Circumference = 8.760481944 x Pi = 27.52186570 ft

And then at Yaxchilan, Structure 40, Altar 13 (Tate, Yaxchilan..., Google Books preview)

Diameter .84 meters = 2.755905512 ft = ~2.752186570 ft

Which may (or may not) be a repetition of same, divided by 10.

Also, I get at least one instance of Diameter .97 m from Maler (via Tikal Reports No.33 in Google Book preview) for Tikal

Diameter .97 m = Diameter 3.182414698 feet, which is suspiciously close to the reciprocal of Pi, times 10

(1 / Pi) x 10 = 3.183098862 

Not sure of that, that would make the Circumference to be 3.183098862 x Pi = 10.0000000 feet, but unless they were that intent on an homage to Pi, it could still be something like 10.00723277 (or some other fine ratio) according to original design? (This same question still confounds the quest for the true and intended original diagonal length of the Chephren pyramid, which is about 100 times either one of those).

Likewise, I have two figures from Maler for an Altar 3 at Tikal, both 1.01 m (Tikal Reports 33) and 1.00 m (Maler, Explorations...) which could make for another fairly blatant advertisement for basic circular math, with Circumference possibly being 10.31324031 ft (generic area of a circle = 57.29577951^2 x Pi = 10313.24031 square arc-degrees) - but that extra centimeter can make a difference.

Other than to go over a few of the other numbers that seem to repeat in the data, I think that's about all I have on the metrology of calendar stones at the minute that might offer further insight? I'd probably rather work on temple and palace rooms and doorways, both for them hopefully having seen less erosion, and for them hopefully having more "checks and balances" built in to help guide the proceedings, which may be a big part of the point of all the vaulted ceilings in the architecture of the ancient Maya.

Not feeling all that swell at the minute and just thought I'd throw this stuff out here half-baked before my doctor finally does me in...

"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Oh, another thing for posterity's sake... For some time now, I've been nursing the idea of cup-and-ring marks not only providing possible direction to the weary traveler, but possibly also a wee drink. Somewhere I have a short magazine article on what was supposed to be a Russian pyramid of considerable antiquity, made by piling rough stones, that was supposed to act as a air well, gathering water from the air via condensation. 

I went on to speculate that the Greek hermax might be similar in value (say an occasional pile of stones by the wayside and maybe a cup underneath to collect condensation) and found that there was some preposterous legend about some diseased individual who was stoned to death - apparently in preposterous excess, because they had to dig this person out from under a huge pile of stones afterwards, only to discover this person had turned into a dog. It may essentially have been a reminder not to let rabid dogs drink from what may have been something on the order of an ancient public drinking fountain, because it otherwise seems like a really sad excuse for a story, or for history. (Really a long time ago now but I think Apollonius of Tyanna might have been involved somehow??)

Thus I ask the esteemed reader, could these be examples of ancient stones caught doing what they were once meant to do?

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I don't know who might have come along and corrupted that into some kind of blood cult - again, how exactly do you corrupt something that seems such commonplace knowledge? - and still not sure what to think of that idea. I think it's curious that there are so few eyewitness renderings, I think it's curious that so many drawings show "sacrifice victims" having to be physically restrained by a number of individuals even when some of the matching texts might say the victims were drugged into what should have been a submissive state, several cardiac surgeons came out against the idea of the Aztecs having taken people's hearts out, for anatomical reasons (Hales and Robicsek, in a Dumbarton Oaks publication), and etc. Perhaps it might be prudent to try counting the number of persons it seems to take to restrain the alleged (and inexplicably animated) "victims" in some of those drawings?

(I would not be the only commentator, nor the most qualified, to assert the unlikelihood of any conquistadors getting within a mile of a ritual sacrifice for fear of also receiving the same "highest of honors," to the obvious detriment of their eligibility to provide eyewitness testament about such things. Ironically, that is exactly what I do when my own country is invaded, is to offer such "high honors" to the invaders in the most respectful way possible, as my way of saying, "Are you sure you don't want to piss off and go home?" Honestly, we should let some of these archaeologists loose in a modern cemetery and see how well it goes over when they declare that virtually everyone they excavate there was a victim of ritual sacrifice).
Anyway, it might be a good question - did some ancient people "label" a number of water channels by making them in the shape of snakes, even if less from sheer necessity than in remembrance that that most precious of fluids can miraculously appear as if from nowhere?

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"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
This New Material Pulls Clean Drinking Water Straight Out of The Air
This could solve a lot of problems.

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7 MAR 2016

One of the ways of sourcing drinking water in areas afflicted by drought is by harvesting it from the air, and now a new material developed by scientists in the US could make this tricky feat easier than ever.

Researchers at Harvard University have taken inspiration from a variety of water-collecting traits in different natural species to develop what could be an unrivalled composite system for harvesting and transporting atmospheric H20.

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"Everybody is excited about bio-inspired materials research," said chemical biologist Joanna Aizenberg from Harvard's Wyss Institute for Biologically Inspired Engineering. "However, so far, we tend to mimic one inspirational natural system at a time."

Instead, the team's system combines elements from three distinct plant and animal species to create a material that they claim outperforms other synthetic surfaces designed to trap condensation.

According to the researchers, the major challenges in harvesting water from the air lie in controlling the size, speed, and direction of water droplets as they form and flow on a surface. At the core of their solution to this problem, the researchers copy the external bumps of Namib desert beetles, which help the insect to collect water droplets on its shell.

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Aizenberg Lab/Harvard SEAS

Scientists already knew that the bumps' hydrophilic (water-attracting) tops and hydrophobic (water-repelling) surroundings helped them collect water, but Aizenberg's team realised that the convex shape of the protrusions themselves might also be able to harvest water too.

Using modelling, the team found that this natural water-trapping mechanism could be enhanced by mimicking the geometry and slopes of cactus spines, which help drive collected droplets down the slopes.

By combining this further with a nano-coating designed to emulate the slippery surfaces of pitcher plants, the material facilitates greater droplet formation as the water beads downwards.

"We experimentally found that the geometry of bumps alone could facilitate condensation," said one of the researchers, Kyoo-Chul Park. "By optimising that bump shape through detailed theoretical modelling and combining it with the asymmetry of cactus spines and the nearly friction-free coatings of pitcher plants, we were able to design a material that can collect and transport a greater volume of water in a short time compared to other surfaces."

The tandem effect of the system – together with a technology developed by the researchers called Slippery Liquid-Infused Porous Surfaces – helps the material collect water in ways that could otherwise prove impossible.
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"Bumps that are rationally designed to integrate these mechanisms are able to grow and transport large droplets even against gravity and overcome the effect of an unfavourable temperature gradient," the authors write in their paper, published in Nature.

Not only could this technique help to harvest water from the air in areas affected by water shortages, but it could also be of use to enhance condensation in industrial machinery.
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"Thermal power plants, for example, rely on condensers to quickly convert steam to liquid water," said one of the team, Philseok Kim. "This design could help speed up that process and even allow for operation at a higher temperature, significantly improving the overall energy efficiency."

With about 1.2 billion people around the world living with water scarcity and two-thirds of the global population experiencing water shortages on a monthly basis, the potential of technology like this could make a huge difference to so many lives.
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Thanks, EA! - some interesting stuff there (although leave it to scientists, I think the ancient Greeks had specially fabricated constructs designed to promote useful condensation from the air and I believe they referred to these devices as vegetation)? :-)

Atetelco, a suburb of Teotihuacan known for its noteworthy murals, is also home to this diminutive pyramid temple (a similar structure apparently existed at Tetitla). This small pyramid has purportedly been the subject of archaeological restoration, although I still seem to be having difficulties finding any details concerning the restoration or its methodology, and especially any detailed archaeological diagrams and/or measurements concerning the temple. If anyone should happen to know where such data on this pyramid is available, particularly on-line, any pointers would be much appreciated.

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Likewise concerning Cempoala (Zempoala) and its fascinating circular structures (I'm honestly surprised by how many articles on ancient American circular architecture seem to make no mention of these...

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Or other noteworthy sites with circular architecture, like Tancama.

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I have some data from George Andrews on a circular structure at Uxmal that I might just be able to make something out of if I can find the time. Bought a copy of Carolyn Tate's Yaxchilan for fifteen dollars, it's a nice book but the data on monument measurements generally traces back to other sources. Found where three of five volumes of Sylvanus Morley's "Inscriptions of Peten" (her source for data on circular altars) can be read on-line and have cobbled together a few more measurements of circular altars to experiment with. 

The Inscriptions of Peten

Recently, I wrote

I'm not sure what it might mean yet but Tate quotes the height (thickness) of the altar as .33 m = 1.082677165 ft, possibly meaning 1.082323234 feet. I'm not sure how easy it will turn out to be to tell what they intended, as there may well be another instance of the dreaded Ancient Mayan Fake Square Root Trick involved - i.e., 1.082323234 is somewhat near to the square root of 1.177245771: 1.082323234^2 = 1.171423583 and they could have been making an observance of that (see also proposed function of numerical "Hero Twins" previous).

On the other hand, it might turn out to be 1.096622711 ft (.334250602 m) or something..

The Temple of the Calendar The Temple of the Calendar is one of the most significant structures of Tlatelolco. It is a unique edifice whose décor deviates from the norm in that it is ornamented with elements of the Tonalpohualli calendar [Fig. 125]. During Aztec times two calendars were used: the Tonalpohualli and the Xiuhpohualli. The Xiuhpohualli was the civil calendar and it was used to determine festivities, record history, and to date tribute collections. The Tonalpohualli served as the ritual calendar. Tonalpohualli consisted of 260 days while the Xiuhpohualli consisted of 360 plus the five bad days. The Temple of the Calendar is a quadrangular edifice with representations of 39 days; thirteen on each wall painted in blues, reds, and whites [Fig. 126]. 

39/360 = .108333333333 = 260/240

(19.48181818 x 2) / 360 / 10^n = 1.082323234 = 259.7575758 / 240
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
You might be on to something there Ancient Vizier, water was important in rituals all over the world, but most of the cup and ring markings I have seen in UK have been too small or shallow to hold much, or were on sloping rock faces too steep for them to hold any. But then a lot of the carvings above are not cup and ring markings, just cups.
In Celtic rituals the surface of a body of water was representative of the boundary between this and the underworld, perhaps it had similar qualities in other cultures.
This is the first time I have looked at this thread in months,
and good to see that the last few posts have taken a better direction,
because your display of convoluted math is both hilarious and ridiculous.

first and foremost

Quote:Ht Great Pyramid in feet (with paving) 480.3471728 ft Whip

is complete nonsense, 
off by more than a half foot to any historic measures, 
and no competent researcher both historically or currently would agree with your nonsense.
As I showed earlier,
with that height and the {4 / Pi} tangent for the slope {your choice},
the base length 
would mathematically be:

754.5275746 feet  Rofl

when you have both Petrie and Cole and a host of other scientists measures,
all far exceeding that by at least 1.15 feet.
Petrie and Cole averaged together:
755.7666666~ feet

The earth year you fuss-n-fudge-it with in a cesspool of computations:

Quote: 365.0200808 

Jesus Christ ...  man, that's pathetic. 

Sidereal  365.25636
Tropical  365.2422

there were two kinds of count  -- calendar count -- and precision accuracy

calendar count 365
                      365.0200808 --- check accuracy <---

accuracy = 0.99945 = garbage = Shemp

then you offer accuracy that you think is good:

Quote:12.16733603 ft + 13.51926225 ft = 25.6865828 ft, 
probably meaning  Doh
 25.68351851 feet (accuracy 0.99988 !)

That is bullshit accuracy, it doesn't even approach 6 sigma {0.999996}
Here is why your accuracies are garbage:

(accuracy 0.99988 !) Rofl x  Pi  =  3.14121 5662
using six sigma 0.999996       x Pi   =  3.14158 0087

Your accuracy is garbage pail,
six sigma isn't much better than the horseshoes in the sand close to the peg,
but it sure has your accuracy beat.

I use this: 
0.9999996 for accuracy minimum standard. {an extra 9 than 6 sigma}
This at least gives one a pi value of:
3.14159 14  

Quote:Yoda decided that 917.3955239 was the "Grid Lol Latitude" of the Kulkulan Pyramid at Chichen Itza.

Doh Sheep Doh

Quote:..including that my call on "158.98" ft 
would probably have to be 159.1549431 ft -   that's a reciprocal of the mighty Giza constant 2 Pi,

holy Cripe ... 0.9989  accuracy  Reefer

Quote:but the ratio between two major calendrical numbers, 
the "Tzolkin" of 260 days 
and ~225 days of the Venus Synodic Period is 260 / 225 = 1.155555

225 days is the Venus SIDEREAL period in calendar count,
and that value is a function of the Mayan Long Count. 
But you at least have a gasping grasp of Mayan count.

But that at least interests me.
So it's time to make angle tangent magic with ancient numbers.

The "control tangent" for all angles is simply 45 degrees.

This is because this unique angle -- 45 degrees,
has a tangent of exactly ----- ONE,
and the sine and cosines,
are tetrahedral tangents <-----

So you can test virtually any angle tangent,
by adding or subtracting ---> 45 degrees ---> and observing the resulting angle tangent,
and compiling that data.

So we go to ... ancient calendar counts ;

260  days  the mayan tzolkin
365  days  the earth year

we make them a ratio {or fraction} and ---> assign that as an angle tangent <---

365             equals decimal  0.712328767 --- assign as an angle tangent

the above ratio of calendar counts thus yields the angle 35.46336424 degrees

now add the control angle of 45 degrees <----

45  +   35.46336424  =  80.46336424 degrees -----> what is the new angle tangent <---- ?

that new angle 80.46336424 degrees 
has tangent 
= 5.952380 952380 {replicating sequence}

well ... w t f ?

test the angle tangent with ... the MILE in feet,
multiply that new angle tangent by 5280 <----

and the angle tangent magic is completed:

31428. 571428 571428 ~ 
the ancient Egyptian Pi progression fraction {22 / 7}  x 10,000 ... where {22 / 7} = aPi
{4 / aPi} is the correct formula for the GP pyramid Side Face slope angle tangent,
mathematically aligned 
to the exact ancient pyramid formula:
280 cubit height
440 cubit base length

This ancient culturally cosmological "Pi value" 3.142857 142857 ~ {22 / 7}
is the basic founding progenitor of the ancient Pi progressions,
creating a series of descending Pi values which lead to 10 decimal accuracy Pi.
It aligns planetary timelines in ancient calendar count also as one of it's functions.

For instance:
The true Venus sidereal is 224.7 days <---> then  times aPi  =  706.2 ---> a Khafre pyramid base length.
And yes,
all four Khafre pyramid base lengths are uneven just like in the Khufu pyramid.

One could select four ancient pi values,
from the ancient pi progressions {to include true Pi},
and attain the 4 base lengths as a distinct possibility from that method.

That first length yields a Khafre pyramid height of 470.8 feet.

Thanks for sharing your recently acquired expertise concerning my arithmetic (I just love instant experts in any field), but I wasn't quite done explaining it yet. If you're still on about the height of the Great Pyramid, please try paying close attention to the words PAVING, PAVED, and UNPAVED when you're reviewing the material.

BTW, if you ask me my accuracy may actually be pretty good given the multitude of numbers the system in question is prohibited from using for the sake of maintaining interconnectivity within the system, and I've already had enough to say about some of the shortcomings of pure numbers like Phi proper.

I'm taking to referring to 224.8373803 and 225.0000000, apparently representing Venus' Orbital Period, as "VOP1" and "VOP2" respectively, in possible anticipation of a number of others - these two still seem as if they are the two primary intended values, though, in the arithmetic I'm working with.

I think I have most of the data from the collection of George F. Andrews papers tabled up now and about 80% converted from meters to feet. I have a number of instances, albeit relatively few, where Andrews gave us the height of the springline above the bottom of the door lintel, so that we can presumably obtain the height of the door from the floor to the bottom of the lintel across the top, by subtracting that value from the springline height. 

I haven't actually solved any of them yet, but the ratios from the raw data suggest that we could have ancient American doorways serving as "billboards" for some expected major constants like 

1.62231147, Alternate Phi (Chicanna, Structure 1 Room 5)
sqrt 240 (Chicanna, Structure 20 Room 16)
Squared Yoda Meg Yard / 5 (Hormiguero, Structure 2 Room 7)
1.067438159 (Kabah Structure 2C6 Room 8')
11.24186901 ("VOP1" x 5)  / 10^n (Kabah, Structure 2C6 Room 11')
1.216733603, the (primary) remen (Labna, Structure 1 Room 16)
2.107038476 (4 / 18983.99125) x 10^n (Labna, Structure 1 Room 25)
1.718873385?? (MLM Royal Cubit) (Labna, Structure 1 Room 35)
1.351926225 (Reciprocal of the Squared Yoda Meg Yard) (Uxmal, Temple 3, Room 2)
Also possibly
1.290994449?? (Hormiguero, Structure 2 Room 4)
1.698880598? (Kabah, Structure 2C3 Room 9)
1.962076286? (2 / 1.019328359) (Labna, Structure 1 Room 22)
1.911240674 (sqrt 365.2840914) / 10 or 1.921388691 (19.46773764 x Pi^2) / 10 (aka 1 Ellifino) (Labna, Structure 2 Room 3)
1.591549431 (1 / (2 Pi) x 10) and/or 1.601157423 (Kabah, Structure 2C3 Room 5; Labna Structure 1 Room 15; Labna Structure 1 Room 60)

Any of those may be subject to change upon closer inspection, but they all seem like very probable values and seem to take surprisingly little liberty with the source data.

Also there are a very few examples out of all of that where Andrews actually gave values for door widths at the top and bottom, one of them being a doorway in Room 6 of Structure 2C3 at Kabah, where bottom width 1.11 m / top width 1.04 m = 1.067307692 which is probably most safely interpreted as another instance of the much-discussed 1.067438159.

Here is one ancient altar that thankfully, I think is a no-brainer. It's probably from Uaxactun since that is header on the page where it appears, according to my notes

Altar of Stela 12
Raw data from Sylvanus Morley, "Inscriptions of Peten," Vol 1, page 226: Diameter .75 m, Height 48 cm 
(.75 m = 2.460629921 ft, .46 m = 1.509186352 ft, .75 / .46 = 1.630434783)

D = 2.465617776
C = .7745966692
R = 1.232808888
H = 1.519817755
D/H  = 1.622311470
C/H  = 5.096641796
D = Diameter C= Circumference R=Radius H=Height (thickness)

I might also bring up that I've been looking a bit more at another number besides 1.622311470 x 10^n that seems to be prominent in the Pyramid of the Niches at the El Tajin site in Veracruz (some of the architecture at Yohualichan is strikingly similar to to that at El Tajin, but I have no data as of yet), which is 1.1553131312 x 10^n, which I think is probably the primary contender for this value of ~Tzolkin/VOP or ~260/225 (260/225 = 1.15555555555).  

1.1553131312 certainly has some very interesting pedigree - and in fact, all one needs to do to find this in Yoda's Giza Data is divide his 13.60087488 "Hall of Records Grid Coordinate" by any of his instances of 1.177245771, and 13.60087488 / 1.177245771 = 11.553131313; likewise simply half the "AEMY" at Stonehenge and do the same with 1.177245771 which is quite prominent and handy at Stonehenge as 360 / Inner Circumference Sarcen Circle = 1.177245771 (i.e., 2.720174976 / 2 / 1.177245771 = 1.155313131)... 

But 1.155313131 also resists a number of equations so that some very similar values start popping up left and right as if we are seeing the feathers of the serpent flying everywhere (this may be iconographically correct), and I'm not sure what all to make of all of them. I think that 1.155313131 x 10^n is the probably the primary intended value to symbolize 260/225, and probably followed by 1.154923003 x 10^n 

2 / (1.315947254^2) = 1.154923003

I find it intriguing that 1.1553131312 and 1.154923003 appear to be the current acceptable extremes at opposite ends of a very interesting chain based on repeated multiplication by 1.2328088888... This chain includes the reciprocals of 1.622311470 of 1.067438159, 1.082323234 x 2, 1.622311470 / 4, the "Third Meter," and others, not the least of which is 1.424280298, one of the surprises at Tikal, which is first in the series

1.155313131 x 1.232808880 = 1.424280298 = 1.676727943 / 1.177245771 = etc

So, 1.155313131 x (1.232808888^11) = 1.154923003 / 10^n

1.155313131 (or 1.154923003) may be likely numbers to appear in measurements in feet of doorways or altars on account of this, and there is at least one possible example of each currently under consideration as to how much total sense either number would be able to actually make in such situations.

Namely, these are (as raw data)
Yaxchilan, Structure 40, Altar 14 - Diam. = 1.12 m = 3.674549682 ft; D 3.67549682 x Pi = Circ. 11.54391001 ft and
Chicanna, Structure 2, Room 3 - Door Height 2.52 m / Door Width 2.19 m = 1.1506849320

Particularly attentive readers may notice that raw diameter 3.67549682 looks suspiciously like a reciprocal of the Alternate e' Meg Yard: 
1 / 2.720174976 = 3.676234098 / 10, and 3.676234098 x Pi = 11.54923004.

I'm still not sure if the primary intended expression of "260" is supposed to be 259.75757579 but that's certainly how things have tended to go starting at Tikal, and most recently where it now serves a symmetrical Venus equation written as

VOP1 224.8373803 days (VOP1) x 259.7575757 = primary Venus Synodic Period 584.0321292 (292.0160646 x 2) days?
VOP1 224.8373803 days (VOP1) / 259.7575757 = 1 / (1.155313131) x 10^n

Further explanation of the importance of 1.067438159 (and 1.082323234) may appear in association with 1.155313131, where

1.1553131313 / 1.067438159 = 1.082323244
1.1553131313 / (1.067438159^2) = 1.013944682 (365.02008080 / 360)
1.1553131313 / (1.067438159^3) = 189977.2193 / 10^n

Not only showing unusual usefulness of 1.067438159 at the third power, but also giving at least one very significant product.

I may also be seeing a little bit of 5.256289166 in the altars, which might be expected since it's a way of writing a year of 365.020081 days by referring to the number of minutes in it (52562.89166 was also one of Yoda's "Grid Coordinates" for Stonehenge), and certainly there is what looks like some use of the number of hours in the same year also - however, it may be fairly easy to confuse 5.256289166 with one of the reciprocals of the Long Count in days so I'm not sure I have anything of any real certainty to declare yet concerning it. 

As the number of hours in a year, where 365.020081 x 24 = 8760.481938 = 45 x 19.46773764 x 10, this may also serve the representation of the proposed Lunar Year value of 353.9334582 (for 354) days, where

(1 / 8760.481938) x (Pi^3) = 353.9334582 / 10^n
A reminder, mainly to myself, that in addition to other services rendered to mathematics representing Venus, 1.622311470 readily serves the Venus cycle of ~18980 x 2 days, still mainly represented by 18983.99126 x 2 and 18997.72194 x 2 in this work, in a rather direct fashion

5 / (1.622311470^2) = 18997.72194 / 10^n

May not be Phi but it's still damned handy sometimes...

Also, several altars from Yaxchilan show an interesting number in the raw data from Morley 

Yaxchilan, Structure 23, Altar 7 - Diameter .94 m, Radius = .94 / 2 = .47 m =  1.541994751 ft
Yaxchilan, Structure 33, Altar 11 - Diameter .47 m = 1.541994751 ft
Yaxchilan, Structure 33, Altar 12 - Height (Thickness) .47 m = 1.541994751 ft

(Which probably makes for a good example of a measure finding its way around and appearing as different aspects of similar monuments, as I suspect some others, such as 8.760481938 x 10^n and 2.752186570 (.8760481938 x Pi), may be also be doing within the altar measurement data gathered thus far).

Any or all of these might turn out to mean 1.5410111111 (1 / (33.333333333 x 19.46773764) x 10^n)

Which might make some sense in context given that 1.541011111 x 1.232808888 = 18997.72195 / 10^n

(And again, 2 / 1.622311470 = 1.232808888)

Also, adding to its curiosity, 1.1553131313 may (or may not) mark the first recognition of a number where a system-invalid number might have been acknowledged by (even if not utilized by) ancient arithmeticians, and that is where

1.1553131313^2 = 1.334748431, 1.334748431 x 10 = 13.34748431, and sqrt 13.34748431 = 365.3420906 / 100

It's not accurate enough to accept as a mathematical fact, but it's too close to the number of days in a year to completely ignore, particularly for it having come to our attention by appearing in as blatantly a calendrical pyramid as the Pyramid of Niches seems to be.
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911

Your GP material is the worst I have ever seen in any research anywhere.

Man ... it is so far askew and errant,
that looking at the rest of your profuse excess,
is like the watching the skeleton still falling into the abyss 137.0359991 years later.

Quote:1.62231147, Alternate Phi  (Chicanna, Structure 1 Room 5)


Quote:1.911240674 (sqrt 365.2840914) / 10   


Quote:1.351926225 (Reciprocal of the Squared Yoda Meg Yard) (Uxmal, Temple 3, Room 2)

Tp  squared = the cube root of  Pennywise  x Pi

Quote:Any of those may be subject to change upon closer inspection  Rofl 

but they all seem like very probable values Nonono

and seem to take surprisingly little liberty with the source data Rofl

I get it now,
your are a hopeless comedian.
like Bakari Sellers -- black pennywise.

You only know and understand one cubit, and know nothing about ancient cubit systems.
You have no grasp or conceptual understanding of any cubits,
other than 20.62648062 -- one of the Pi cubits.
That's it,
that is as far is your dipshit dipstick goes into the Egyptian Giza Pyramid oil lamp.

You can belly rub the genie in the oil lamp all you want,
but he can't even help you spell or smell the geometry no matter how you cook your Pi.

superior 10 decimal accuracy,
creating Geometry Magic with our ancient calendar counts:

The 365 day Earth year ----->  52  x  365  =  18980  Mayan Calendar Round

The 260 day Mayan Tzolkin spiritual calendar

In the last display, I used the above two values as the fraction {260 / 365},
assigned them as an angle tangent,
and achieved unique results in creating a unique geomtery operation.

We are going to far exceed that,
use the ---> inverse fraction ---> {365 / 260} as an angle tangent,
and create an isosceles triangle.
The isosceles apex angle becomes the target angle and tangent,
in this targeted geometry test.

[Image: lgw3NUe.jpg]

as far as an "alternate phi" goes ... look above to the 162 number sequence 

162 = 3 x 6 x 9
sqrt 1.62 / 9 = sqrt2 / 10 

then look at this equation using the 4 / Pi as the Khufu pyramid slope tangent:

{4 / Pi}  x  1.62  =  Pi cubit 20.62648062 / 10

then take the square root of 1.62 ---> and click arctangent on your hand computer



and PS
the genie in the oil lamp says,
multiply those two Pi cubits together,
and you might learn more about cubit systems in that operation,
than you have in the last ten years.
but then
maybe you won't ... anyways or anyhow  Hi

I agree with V
my 1st Major in College
was Civil Eng
and all I see here
are pages of mumble jumble schematics
going Nowhere 
go build a pyramid
and send us a picture .
Never invite a Yoda to a frog leg dinner.
Go ahead invite Yoda to a Frog leg dinner
Look, Vi - I'm not attacking your work, why on earth do you insist on attacking mine?

Starting with your own models then, if there isn't room for us both to be right, there probably isn't room for your umpteen different models of the same Great Pyramid to all be right either. You ask for us to grant you, what, two, three, four different valid Great Pyramid measures to accommodate all of your models, and if Yoda and I ask license for a fifth, you're going to squeal like a little girl about how my findings are crap when it's the same source data as yours? Seriously?

Lehner and his fancy-pants "linear regression analysis" still can't nail the Great Pyramid sides to any better than give or take half a foot which is no improvement over his previous effort with Goodman, and neither effort has improved over Petrie. Lehner is not coming to your rescue or mine here, I am so sorry to have to keep reminding you. The only thing actually holding up your models as far as I can tell is that they have merit, as do mine.

So how thick a pavement do you think I am talking about here? Have you tried working that out and what it would do to the perimeter length? I'm sure I suggested a rough figure more than once. 

You realize how utterly preposterous it is for you to say "I only know one cubit" after the formulas I've posted here?!?!? 

You do also realize that the Maya had elaborate correction formulas for the Long Count and other calendrical cycles because they do not work out as precisely as that? 365 days to a year puts one as badly in need of a leap year every four years as anyone else because a year is of course not actually 365 days long. Putting more accurate figures into such equations gives you figures more on the order of real life that make your "exact" 18980 as just as purely symbolic as anything I'm using to represent "18980". You've nailed a symbolic figure nicely, but why is your effigy better than mine? 52 weeks of 365.25 days = 18993, I'm using 18997-something as the max. Are you sure you want to crow that loudly about how accurately you've hit a figure that isn't accurate?

You have heard the old expression about people in glass houses, right?

Believe it or not, I didn't actually come here because I have a use for an argument, but I wanted to inform anyone who might give a rip that the suggested study of Andrews' data on the circular monument at Uxmal probably isn't on its way, since another look at Kowalski's diagram of this structure makes it look a bit too badly beaten up for me to take Andrews' measures all that seriously.

Archaeological Excavations of a Round Temple at Uxmal: 
Summary Discussion and Implications for Northern Maya Culture History 

[Image: Figure-3-Lowland-Maya-circular-architect...walski.png]
Kowalski's plan of circular architecture at Uxmal, at upper left

[Image: Figure-1-Map-showing-sites-with-Terminal...ecture.png]
Some sites with circular architecture
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
(08-16-2017, 02:10 PM)Wook Wrote: Well
I agree with V
my 1st Major in College
was Civil Eng
and all I see here
are pages of mumble jumble schematics
going Nowhere 

I'm sure lots of languages look like gibberish if you're not fluent in them. I'm sure Vi's stuff also looks like gibberish if you don't have any background in geometry. I am talking about exactly the same thing as Vi - recording significant data in the proportions of what is probably the most durable medium available, and what's probably bugging both of you is just not being familiar with the mathematics for not having the opportunity to take them for a serious test drive, which is not necessarily a simple proposition.

Richard Hoagland, who introduced me to this particular system of mathematics, referred to it as the "holographic memory of a race" which I continue to think is a very astute description. 

Consider for a minute an ancient monument as being like a holographic data crystal which recalls a particular set of data when a laser is directed at it from a particular angle. By way of analogy, the laser and the different angles that call up different data sets are the different numbers that are tested against that monuments' proportions by multiplication or division.

The numbers I'm using are recursive because they generally don't let the fruit fall very far from the tree, and important numbers can be constructed from numerous other pairs of numbers, which presumably appear in physical form rather than in the purely abstract. This allows the same data to be recorded in many places in many different ways (redundancy, aka data backup) without all architecture having to be identical in order to embody the same mathematics. 

One of the ways to increase the data storage and retrieval capacity is for the user to go back and use different metrological units as "retrieval beams" to retrieve different data, another is to take a basic architectural design and start making little tweaks to it - irregularities that sacrifice aesthetics for data capacity to cram in more numbers, and a third is to use numbers that operate effectively as exponents and give another important mathematical constant for each power applied for as long as the laws governing the precision of mathematics will accommodate this. I've shown multiple examples of where incorporating numbers like Pi / 3 or 1.2328088888 into architecture can be the same as writing as many as ten or twenty numbers, by writing just two.

I'm describing a basic Great Pyramid before the tweaks, and Vi is describing the Great Pyramid after the tweaks, as far as I'm concerned. I think his proposals have great validity because they're impressive. I'm impressed, anyone who gets worked up about numbers ought to be impressed, the ancients were probably impressed, they'd probably have saluted numbers like Vi is showing us - what I don't know is exactly how and where the tweaks were applied - they could have made each side different to accommodate different models, they could have kept the sides equal and make four different tweaks to the edge lengths for all I know. The Great Pyramid supposedly has a twist at the apex that could be involved in accommodating multiple models, but I have no detailed data on that. 

A holographic sort of description is also an apt one because like a hologram, you can recreate the totality out of tiny fragments, out of as few as six different numbers and their products and ratios. I don't even bother to memorize most of them because I know lots of shortcuts using numbers I do remember, I just concern myself with being able to recognize as many of them on sight as possible, which is enough of a chore for one person.

What it looks a lot like, is what would happen when people dink around with geometry for hundreds of years. Having figured out that Radius x 2 Pi = Circumference, people get bored and start wondering what happens if you multiply the circumference by 2 Pi or divide the radius by 2 Pi or the Circumference by the Radius, and etc and etc. and pretty soon you develop a lexicon of numbers that you can fit together in useful ways to express other numbers, rather, say, than trying to write Pi / 3 in doorways by making them little over a foot wide.

The very same thing happens with later architecture concerned with more conventional geometry, someone starts poking around with Phi / sqrt 2 or Phi / sqrt 5 and next you know they're turning up in every cathedral and next someone's published a big catalog out of all the numbers you can make using those numbers as building blocks (it's called "The Ratio Finder" if anyone's interested).

I don't expect for example to find a lot of doorways 1.177245771 feet wide, but I do have a little data that suggests someone was writing the same number backwards as a few 8.494402992 foot wide doorways or temple chambers, so when we wonder what the hell is that, we hopefully go 1 / 8.494402992 = .1177245771. Just more stuff you figure out when you mix mathematics, boredom, and hundreds of years. 

These days it also looks a lot like what might happen if the precise architectural mathematics required so that your temple doesn't collapse or your elaborate aquaduct doesn't fall three inches short of joining up properly, meets the more imprecise mathematics of time keeping, where we can just up and lob roughly 1/4 day off the year if it suits us, or hell, why not lob 5 (and ~1.4) days off and make it an even 360 like some of the ancient Mesoamericans purportedly did?

I know if any of that helps, but I thought I'd give it a try. I really don't have a lot of claims to make here, trying to get geometry and time keeping to play nice together is kind of new to me as previously stated - but most of the numbers I've picked seem to be still holding up as fairly useful in context after weeks of putting them to the test, and seem to be turning up in a diverse number of places, and both of those may well mean something. It's not a perfect system I'm describing, but no system may be a perfect one, which may be exactly what might have made it appealing to use more than one at time, even in a single monument.
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
"if you don't have any background in geometry"

you have No idea as to Civil Engineering
and We all have done this Mayan "stuff" before
I leave you to continue to play with yourself in public .

Never invite a Yoda to a frog leg dinner.
Go ahead invite Yoda to a Frog leg dinner
I am recovering from an illness so I don't have much time for your garbage time.

Quote:Look, Vi - I'm not attacking your work, why on earth do you insist on attacking mine?

there is no "insistence"!
You have been on an endless roll unhindered of playing your game with what you have called, 

Quote:Data dumping  --- a Yodumpa doodle of nonsense numbers 

That is what you do.
You data dump.
Well your toilet overflowed.
That has been going on here for a long time with no interference from me.
At some point, a person can only stand by so long while you fornicate the Giza geometries,
into a fucking mess of silly nonsense.
Your accuracy is a rusted out garbage pail with a hole in it.
All your work is predicated upon the pipe dream height of the pyramid at 480.347 feet,
and as such,
it is all wrong and nonsense.
Everything from that point of your height, on.

People here,
his is a con game developed from absolute boredom, 
and he knows that his material is unnacceptable to any quality Giza research.
{see his next quote displaying his con game}
What he wants you all to do is this:
Completely disregard each and every historic measurement ever taken of the Giza pyramids.
His data is so far askew and errantly devised,
that he still will not admit that with his height as described,
that his base length is over a foot short of:
Petrie and Cole,
historic scientists who both measured a base length average within a half inch of each other,
and over a foot longer than the nonsense GV portrays here.

Quote:I'm describing a basic Great Pyramid before the tweaks, Rofl
and Vi is describing the Great Pyramid after the tweaks, 

Absolute fucking nonsense.
What you are describing NEVER existed.

Quote:The Great Pyramid supposedly has a twist at the apex 
that could be involved in accommodating multiple models, but I have no detailed data on that. 

more nonsense.
It has a slightly offset pyramid peak automatically,
to accomodate the historically measured uneven base lengths,
and that is clearly shown in my previous 3 slope pyramid design,
using Petrie and Cole style base lengths,
arranged with well known and highly researched cubits by a variety of researchers.

Quote:Richard Hoagland, who introduced me to this particular system of mathematics, 
referred to it as the "holographic memory of a race" 
which I continue to think is a very astute description. 

Invoking Hoagland's name will get you nowhere,
and you have absolutely no valid claim to any form of "holographic memory"  Cry
with the nonsense dimensions you have posted.
Hoagland would do very well to distance himself from your "holotrashic memories".

Quote:trying to get geometry and time keeping to play nice together is kind of new to me as previously stated - 

You are such a two faced provacateur.
You never came here to "play nice".
That is clear from the content of your responses very early on.

Your game is to excessively dump useless data {that is useless from the get go with your GP height},
as a venue of attempting to make the huge volume of that screwy oddball data,
somewhat bury itself,
under your cover story of how you think it is so accurate.

You put pyramid names like Uxmal next to your garbage pail math,
in an attempt at painting a muddy fat pig into a pretty pink flower.

You have little concept of any geometry,
all you can do is hurl irrelevantly ill conceived unconnected numbers with absolutely awful accuracy,
into a cesspool of your "holographic" excuse of a memory.

Fucking A, man.
Get a life.
Hoagland's holographic memories have nothing to do with your volumes of litter Whip
I did not want to have my comments affect you as a personal attack,
but man,
you set yourself up with your math for nothing less than total annihilation,
and as such,
any response that points to your glaring errors is going to affect you personally.

Trying to share info with you is a lost cause.
You don't understand cubit systems, or any pyramid geometry, 
or how ancient cultures related to dimensions such as the megalithic yard = 2.72 feet <---
You don't understand ancient calendar count,
because you don't understand how the primes are multiplied in the various count systems.
Your material is the worst analysis of the Giza pyramids I have ever seen.
Sorry, that is just the way it is.

Petrie and Cole aren't your Yoda and the Binkie Math Monkeys.
Petrie and Cole would kick your ass far harder than anything you see from me,
if they read your math and holographic memory crap.

Here is some math that displays ACCURACY Whip
It follows through from my last diagram.
It is actually relatively unimportant material,
just a display 
of how the ancient numbers integrate into an overall complexity,
that has ACCURACY,
and tangibilities to your favorite ancient cubit,
the only one that you barely understand.
The Lunar Month in particular, is one of the most important timelines to ancient cultures.
Modern scientists studying the 29.53059 day period,
have set a one second per Lunar Month allowable factor of error in published math.
This far exceeds 6 sigma,
and the one second factor of error accuracy for the Lunar Month,
is what I use to eliminate all other equations that come close,
in any planetary cycle that I align with geometries,
and often my work goes to 7 sigma and greater.
[Image: C7qxca8.jpg]  
The Tropical Earth Year Cycle at 4821 years is not considered a long term cycle,
but it also isn't short term like others that are more important.
Like I said, 
this is for the most part a test study in high accuracies,
that readily reveals the ancient math number connectivities with quality results.

Well, okay - if you really want to keep drawing attention to the numerous shortcomings of your own models by attacking mine? 

If you're just so sure that You and Only You are right about anything, why don't you kindly remove yourself from my backside and go publish your f--cking book? Come on, you've obviously got all the diagrams done. Go share it with the whole world if you've got such an immaculate airtight model, or are you afraid the real world is going to be harder to impress than us locals? How incredibly Munckish of you to keep preaching to a flock of five - update, now four. 

No, I don't suppose anyone but us would let you get away with trying to give the Great Pyramid four different heights at the same time, would they?

Very well then, the Spendid Wisdom of the Ancients, administered by the unpalatable likes of you so that nobody wants any, then it can be all yours, for that is the true purpose of Humanity's Rightful Heritage, so that you can sit around and stroke your fragile, antisocial, narrow-minded, monopolistic ego with it by Lording it over the denizens of small, quiet, out-of-the-way message boards.

Do you think everyone on this board is so damned dumb that they can't tell you're literally frightened by what I'm showing you because you don't understand it, because it may take YEARS to master that you haven't given it? No, you DON'T understand one thing I'm saying or the first thing you'd understand is that it's no challenge and no threat to your work. You literally had to try to ban Munck's name off this board so you could feel safe and you're still at it! Congratulations on being not one tiny bit better than any mob armed with torches and pitchforks.

And by the way, I came here because Keith is someone I consider a friend, and I'm grateful for the care he's taken of the place since I was here last, and because I literally thought I was dying and wanted to leave a message to humanity to be careful not to blame the wrong thing for it -  how f--cking DARE YOU say anything else about THAT?
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Quote:I did not want to have my comments affect you as a personal attack,
but man,
you set yourself up with your math for nothing less than total annihilation,
and as such,
any response that points to your glaring errors is going to affect you personally.

Pi Whole,I wasn't kidding earlier in the thread that that Vianova basicaly re-wrote the solar system.

Vic has corrected my math on several times several occasions and on many of them has expanded my gnosis.

Not only that but improved upon my modeling and made certain examples make More sense.

Also and in conjunction Vianova would offer in many cases alternate tweaks corrections of posts I made that vary from easily just as valid at minimum to high sigmas I haven't acquired yet as I use Metrics.

My measures have been honed over about a ~decade by Vic 's peer review.
We use different systems of units and the system I use is decimally based on the earth from the north pole to the equator.

Unlike the lengths you refer to.

Quote:Trying to share info with you is a lost cause.
You don't understand cubit systems, or any pyramid geometry, 
or how ancient cultures related to dimensions such as the megalithic yard = 2.72 feet <---
You don't understand ancient calendar count,
because you don't understand how the primes are multiplied in the various count systems.
Your material is the worst analysis of the Giza pyramids I have ever seen.
Sorry, that is just the way it is.


The metric system will have itz final evolution soon.


The international team that is finalising the Updated Metric system will so to speak, say:  "Set in Stone" measures.

And they have that high-sigma drive too.

Collectively was as Vianova is.

Holycowsmile Arrived @  LilD

[Image: C7qxca8.jpg]


if you throw a handful of spaghetti to see what sticks...not all of it will. Sheep If you throw a Pie on the other hand, Itz stuck.
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
EA, in the event I allow myself to be chased off this forum for the second time in ten years by Vi and Wook constantly having to remind forum users which dog gets on top, THANK YOU for acting like a civilized human being toward to me, that is MUCH appreciated!
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
The Math here is way above my humble level, however, if someone is kind enough to point out where I have made mistakes, I am very grateful and do not throw my teddy in the corner. The choice to go is yours, and yours alone, however, in my opinion, it shows a lack of character to have a tantrum and storm off.

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