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The Great Pyramid
Okay, sorry... I'm just getting to know this putative Pole again, perhaps I shouldn't be saying that it's so secular or so unrelated to other proposed ancient metrological units. Took five minutes and a burst of overwhelming curiosity to discover that this slippery little sidewinder of a number is indeed nested between some familiar values and perhaps twice as many if I gave it ten minutes...

Pole 1.981574329 / MLM Cubit 1.718873385 = 1152.83321 / 10^n, which is among other things the number of miles in one minute of equatorial longitude, and possibly the circumference of a circle circumscribed by one of the Great Pyramid's faces, as previously described...

Pole 1.981574329 / (MLM Cubit 1.718873385^2) =  6.70691171 = 4 "LSRs" of 1.67672971 = ((Pi / 2) x (1.622311470^3)

Pole 1.981574329 x MLM GP "Apex Displacement Ratio" 1.040915799 = MLM Royal Cubit in inches 2.062652026

Pole 1.981574329 / ((2 x (Pi^2)) = 1.003877282 

Pole 1.98157432 x proposed M Cubit ("Masonic Cubit") of (33.3333333 / 19.46773764 = 1.7122345679) = 1/2 of Yoda's Map Crap Grid Latitude Chephren Pyramid (that I'm going to ignore until I find it written as a physical measurement somewhere, not as a Mappity-Crappity cartographic one) / 10^n

Pole 1.98157432 x (M Cubit 1.7122345679^2) = 5.809475021 = dh 1 / T Cubit (Thoth Cubit) 1.721325931 x 10^n

(n = me not giving a hoot where the decimal actually goes).

I should have guessed to try squaring the Thoth Cubit sooner, since 5.809475021 = (sqrt 2160) / 8

I'm meaning to write a list of some square roots of the "Pyramid Pi" system like sqrt 2160 and sqrt 8460 that make useful mathematical probes. On the one hand I feel negligent not having done so already, and on the other I rarely have to resort to using them that way. Mainly I'm just exploring things with Pi, the Radian, 360, 2^n, the standard remen 1.216733603 and Yoda's powerful probes 1.177245771 and 1.62231147. Anybody who can remember six phone numbers can reconstruct and interpret a great deal of ancient mathematics as it might have been according to "Pyramid Pi" theory.
"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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Postcard from Tikal #1

A little bit of trivia about Tikal... At least in the one reference work by Yoda that I have handy, the only other physical measurement clearly identified in the material besides the "24.901-something" foot measure atop Temple I that we have already seen diagrammed by Yoda's own hand, is that Yoda's "Master Code Book" also identifies the width of the doorway atop Temple II as being the Squared Yoda Megalithic Yard. While Andrews' data conflicts with the "24.901-something" value derived from Maler's data, it does appear to corroborate that the width of the outer doorway in Temple II is plausibly just what Yoda says it is. 

Doorway Width 225 cm 7.381889764 ft (Maler)
Doorway Width 2.25 m 7.381889763 ft (Andrews)
Doorway Width 7.396853331 ft (Yoda)

Furthermore, although Andrews doesn't give a height for this doorway, the data from Maler provides us what looks like a rather familiar ratio

Doorway Height 265 cm 8.694225722 (Maler)

Height / Width ratio: 8.694225722 / 7.381889764 = 1.177777777

I'll take a wild guess that Yoda interprets this outer doorway as literally a billboard for his "Alternate Pi" 1.177245771, which I would be in agreement with.

That would put the exact intended height at 8.707914303 ft, and there may be corroboration of the intent of this gesture and this interpretation of it in the doorway's immediate mathematical environment. 

So the exact equation in question is 

8.707914303 / 7.396853331 = 1.177245771

Additionally, the product of Temple II's outer doorway's length and height appears to have significance, whereas speaking from experience it is only too easy to pair up different candidates and not have them give satisfactory division ratios and multiplication products both. 

Those are the kind of demands we hope we can put on our "Pyramid Pi System" - not only having interesting width or height values, but that their interactions also be meaningful, so that we can better sort out the messages we think we are seeing from the noise of random coincidence.

Anyway, I thought I'd throw that on the table since to my knowledge Yoda may have done the opposite. Some people have a hard enough time taking him seriously without him leaving out something that I personally consider rather compelling.

I think things are going fairly well with measuring photos of Temple II in order to fill in a number of data points missing from both Maler and Andrews' data. I should want to keep researching what archaeological data is available though, I may need more assistance before things are over - including that the diagram in Maler's text makes it look like the uppermost tier has the same truncation on the edges as the lower tiers, which is not a feature that I've thus far been able to discern in either photo I'm attempting to work with.

Frankly, though, the complexity of these pyramids still often makes it hard to feel certain about how the measurements described are being intended exactly (it's a lot of, "Which width? It's got at least three of them, you know" sort of stuff), and I'd love to find some labelled diagrams for once.

About Tikal Temple II, there's a masonry block in the middle of the upper stairway - from the photo it looks like it may easily have the same width as the doorway - 7.396853331 ft, or one Squared Yoda Megalithic Yard. Using that figure to calibrate a crude pixel-to-meters ratio, I measured its height and width ratio at 1.290-something. Keep in mind I don't have any text to provide confirmation of this and pixel measurement can still be tricky given the available resolution and image geometry (which I am not skilled enough to correct), but smaller measures such as this may come out more accurate, and this to me is highly suggestive of

Width 7.396853331 / Height 5.729577951? = 1.290994448 = (1 / sqrt 60) x 10 = sqrt 1.666666666

Another thing involving the figure of 7.396853331 at Temple II that by Pi Jedi standards looks very much sensible and deliberate.

That would be most gratifying to have corroborated by field measurements since it would constitute the first time I've seen the Radian written outright at Tikal. I've seen figures in Maler's data that resemble the reciprocal of the Radian, the Double Radian, the reciprocal of the Double Radian, half of the squared Radian, and etc, yet this would still be a first.

Interestingly, it's while poking around Tikal lately that I've been learning some important things about the recent figures I've given for the Great Pyramid without upper pavement. Did you know that, for example, my proposed value of Height 481.0235483 ft (without pavement) has a system-valid square root? It's 21.93245423, aka 2.222222222 x (Pi^2) - for those just tuning in to The Pi Program, last ePisode I tried to build a meter out of 3.333333333 x (Pi^2), with some very pleasing results. 

The reciprocal of 21.93245423 (x 10^n) = 45.59453264, aka 450 / (Pi^2), may well be the outer length of Temple II, is how that happened to come up. 

(The data on hand for this is 
Maler: "The front length of the temple (measured not at the projecting base but from wall to wall) amounts to exactly 13 m 95 cm." = 45.76771654 ft.
Andrews: Data not provided?)

I'm not 100% sure of that, especially with no data to corroborate Maler on this measurement except my pixel measures, but what I'm proposing is very compelling as far as I'm concerned, in that it involves the addition of three different figures - the doorway width of 7.396853331, and the figures for the length either side of the doorway, with an air of these having being extremely well chosen to resist the deleterious effects that addition and subtraction usually have on the Pyramid Pi System's "magic numbers".

In fact, the calculations I've done so far imply that the ancient Maya may have generally been approximating with higher precision than the developing standard at Giza, if what I have seen thus far of Tikal is any example.

At this point, I'm extremely intrigued whether, if I ever finish my crude models of Temple I and Temple II, they will end up showing a shared rate of downward expansion in the pyramid tiers reflecting the ratio of 1/3 Pi. Not only might this be an extremely sensible thing to have in the immediate mathematical environment, but I'm learning more about how it may make a powerful mathematical probe in its own right. 

Whereas I wouldn't use 1/2 Pi as a mathematical probe unless everything else had failed, I'm seeing strings of equations involving numbers that may appear in Tikal's temples being linked together by as high as the thirteenth power of 1/3 Pi.

It occurs to me that that's sort of a murky statement about the "immediate mathematical environments" and if only for spreading ourselves far too thin, we Pi Jedi need to work on putting up or shutting up...

Let's take the reciprocal of 1/3 Pi

1 / (Pi / 3) = 9.542965686 / 10

And let's divide that by 1/3 Pi

9.542965686 / (Pi / 3) = 9.118906528 / 10 = 1 / 1.096622711

Andrews gives us data that resembles this number both backwards and forwards. It remains to be seen if these values will fit into their actual surroundings effectively, but the data is

Temple III Room 2 Length 3.35 m 10.99081364 ft = ~10.96622711
Temple II Plat. Height (rear) 2.78 m 9.120734908 ft = ~9.118906528

9.118906528 is twice 45.59453264 / 10 aka interpreted length of Temple II

And let's divide by 1/3 Pi again...

9.118906528 / (Pi / 3) = 8.707914297 interpreted Height of outer doorway of Temple II

So it may not be a matter of just me wondering if they were big on (Pi / 3) because of the possible ratios in the pyramid levels. 

8.707914297, 9.118906528, 1.096622711, 45.59453264 already make four of still very few numbers proposed for Tikal that can be constructed entirely from nothing but 1/3 Pi and in one instance simply halving one of them.

That's more like what I mean about the "immediate mathematical environment" providing a possible sense of corroboration for some of these figures.

I increasingly question Yoda's declaration of "4/5 of the Radian" as a Tikal "site constant" (as the Radian or Double-Pi - and perhaps also their product, 360 - appear to be at Giza) and increasingly wonder if 1/3 Pi may not eventually prove to be a primary site constant for Tikal.

I don't know if anyone else is ever going to believe it, but it really is starting to look to me like the ancient Maya went to the Pi Jedi Academy. Maybe someone should shoot a Pi Wars movie at Tikal?


(05-18-2017, 10:58 PM)EA Wrote: This should interest you PW:

Quote:“It’s going to change the focus and many theories will be enriched or complemented, but mainly it will allow us to make a ... reinterpretation of what Tiahuanaco was,” he said.

Vianova might be corroberated in 3 years or so...?

Thanks for the interesting item, EA. What am I missing here though in regards to your comment? Did Vi do some remote sensing archaeology on this area?
"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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This post here had me wondering about the possibility of using a tetrahedral instrument of some kind for navigation. Supposed you used one to do the same thing this person is doing with their hand here. There may even be a post somewhere with someone having a theory like this, and it may well be on Hidden Mission that I saw such a thing a long time ago?

[Image: moana-navigation.jpg]

But you can also see in my latest geodetic experiments where tetrahedral values may indeed have metrological significance on a global scale - anything that works out to a rational number of standard remens is going to work out to a rational number of "Assyrian Cubits" of 19.4677376 ft or anything made of 19.46773764 x 10^n feet or inches. (What I showed should also be suggestive that maybe someone really was using an ancient system of grads in addition to using the sexigesimal system).

I'm having trouble getting their pages at the moment but I'm hoping that some of the content at "atlantisbolivia.org" may be useful, there's some interesting metrological stuff including that a unit of 19.8 is recognized, and I stumbled across a passage from Berriman's book showing it also recognizes a pole of 1.98 (I haven't located in the book in hard copy yet). Fingers crossed that they give references for sources of monument measures.

The drawback is that most if not all of the material there may be in service of The U Word, as is even Hugh Harleston's work - that they were ancient supergenuises who had to ingeniously reduce everything to rational numbers of their measurements to make things easy on their simple, primitive minds is, to me, clearly a contradiction in terms no matter how many archaeologists have fallen into such a headspace - even though I can see the value of simplified geodetic units. I'm still planning to try to see what I can do with Harleston's materials and any of his proposals for ancient metrological units, but I don't see any way for things at Tikal to all break down into rational values of any single metrological unit, sorry. 

Since the handiest source of any of Harleston's work is likely Tompkin's "Mysteries of the Mexican Pyramids," I stumbled across comments (page 197) about Le Plongeon that I still find intriguing.

"When, from the measurements he made of various Mayan buildings, Le Plongeon found that only the meter gave figures in round numbers, he deduced that the Maya may have divided the circle into 400 units instead of the 360 of the Egyptians, and had taken as their unit of measure a 40-millionth of the earth's circumference".

Michael Morton and I both attempted to do some work with Harleston's "Standard Teotihuacan Unit" in the past but maybe neither one of us worked quite hard enough on it? MLM proposed 1.059521193 meters of (R/2) / 10^n = (sqrt 960) / 10 ft, but maybe if some other proposals for an ancient meter are going to start sticking, it might be time to revisit that? Oddly enough, I may have seen something like 1.059521193 trying to pop out at Tikal, more than once already now, which has added to a fresh sense of intrigue.

At the moment, I'm looking for data on any ancient Mesoamerican construction outside of Tikal that may be well preserved enough for us to have modern measurements of close enough to the original values to attempt interpreting - a lot of ancient architecture is of course beaten up enough that even being carefully measured may not help much. Still looking into what all data is where and what sources I should trust. (Back in the day I never got very far with Mesoamerican or South American archaeology for being heavily focused on North American and British archaeology).

I would love to have a go at something like The Temple of the Bearded Man at Chichen Itza - smallish, easy enough to accurately measure, some nice crisp corners in evidence - but at first glance, at least two archaeologists may have completely overlooked it.

Dunno, sometimes I resent the amount of "woo-woo" that generally accompanies such notions in the scientific community as ancient arithmeticians. To me, I think it's actually a rather pedestrian concept - "The ancients knew long division, big f---king deal, get over it". Very same with ancient navigation - people built boats and got good at using them, and came to the New World centuries before Columbus, I don't know what's ever been so revolutionary about that idea.

(I of course also resent anyone taking sloppy archaeological measures, because I think to an ancient metrologist, archaeologists throwing away measures because they don't personally study them would be like them throwing away bones from an archaeological dig because they don't study paleontology personally - outrage is appropriate, right? - but I will still try to see what usable data might have been gathered).

I don't really know what messages they are sending us, I can look for modern science figures but maybe there's no telling if they would really agree with modern science. Maybe what I'm seeing simply involves the artful use of mathematics, architects using interesting numbers the way a painter would use color and contrast. We have examples of cathedrals and even simple wooden doorways where that may have been the operating principle, as opposed to the "encoding" of some ancient message of cosmic urgency. If you can find the speed of light in my math, be my guest - but I may turn around and ask why the ancient Egyptians didn't express it in remens or cubits. :-)

On an Egyptian note, Mendelssohn's book arrived but I haven't found yet where there are pyramid measures stated therein. He has an amusing note about how the ancients might have "unknowingly" discovered Pi while measuring the progress of a moving cylinder, and a statement that when dressed, the pyramid sides bowed outward. I've likewise found material suggesting that the finished, cased Great Pyramid sides didn't reflect the truncation now visible in photographs. These both strike me as rather impetuous declarations without more details about the location of the casing stones used in making such determinations. The mathematics we've seen here may well suggest to us that the finished pyramid was indeed slightly truncated on at least one side, if not most likely on all four sides.

Also I've been doing some thinking about whether there was a legitimate use for the unsquared Yoda Megalithic Yard - there's a particular equation at Stonehenge involving area that may permit it, and I also noticed an interesting result when applying the same to the Great Pyramid. Even though the unsquared YMY doesn't belong to the number system in question per se, it may be permitted in calculations that call for it to be squared (such as area formulas)? 

Otherwise, you get a variant form of the standard remen from Stonehenge from the formula "generic area of a circle / area of OUTER sarcen circle = 1 remen), which using the "Alternate e' Meg Yard" of 2.720174976 gives 1.2163322743 and not 1.216733603 as the resulting remen value.

That joins another near-remen value at Stonehenge of (1.067438159^3) = 1.216264895 - not close enough to be a true standard remen, and perhaps too close to it not to be.

Whereas if you use the unsquared YMY value of 2.719715671 for what is probably a special occasion, the equation DOES work out to give the standard remen value I've been using all this time of 1.217633603 (ft).

Does either variant remen have improved geodetic accuracy, or any value at all? Was 1.067438159 a standard approximation of the cube root of the standard remen? I really dunno, they never mentioned this stuff at The Academy I went to...
"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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Quote:Posted by Ancient Vizier - 3 hours ago
This post here had me wondering about the possibility of using a tetrahedral instrument of some kind for navigation. Supposed you used one to do the same thing this person is doing with their hand here. There may even be a post somewhere with someone having a theory like this, and it may well be on Hidden Mission that I saw such a thing a long time ago?

[Image: moana-navigation.jpg]
http://thehiddenmission.com/forum/showth...#pid237911
Sounds like you can't quite put your finger on it.

Did you mean Base Ten Metrics.
Ancient Digital  Processes  ???   

Ten fingers, a freemason and the current system of things.

Quote:Monday, February 15th, 2010, 11:59 pm
All men created equal,but vary spatially in 3-dimensions.
Size wise in stature there is the Newly discovered "Hobbit" Hominid and The Even more recently discovered missing link "Ardi" to Dwarfism to giant africans and Basketball stars.
From the very Tall George Washington and Pierre L'Enfant ,near equal in stature...to Pygmy warriors.There has to be a level playing field.
A First American President and 'The Hobbit' are very different so therefore that property is least likely to be a Prime Key. 
It Must be IN the NUMBERS of the Hand /Hand(s).

So I figured [Image: hmm2.gif]

Pure self referential improvisation and the Genius of itself starts to unravel. 


So, I Did the same with both hands in mirror-fashion.
Facing Inward is like alms or scooping water to wash a face.
Facing Outward gestures No thanx X-mas turkey seconds and thirds ,saving yourself for some PIE
This is a closed System of Things.
10=There are Ten whole Digits.
8=There are Eight Spaces between Digits.

Palms inward =18 x 10 = 180 degrees equals Ray/Line.
Palms outward =18x10 = 180 degrees = a Horizon
= 180 degrees = 90 degrees On-Line-Off-line 90 degrees
180x2x10=360 degrees equals a Circle.
There are possible number systems within your digits...Hey itz DIGITAL!!! [Image: applause.gif]


Quote:The Closed System code for a singlehand is almost non-intuitive wich may create a canundrum of sorts.
Looking at single handedness you have Five whole numbers
and four visible gaps.
So how does one derive a Zero...a nothingness?

irregardless ...
If you Start with the Spaces=0 you have four zeroes=zero.
Four nothings and Five somethings = 1.
One Hand in total.

If you prefer binary it would equal=

101010101
if you included both hands it would basically be
101010101101010101

To take this simple code to the Next Level you simply Either make it Binary in the case of single-handedness and get that same number for one hand mirrored input/output
as the one derive from both hands in Either Input or Output mode but [Image: cheers.gif]
Quote:YOUR VERY OWN DIGITAL CALCULATOR 
One of the easiest multiplications to do using your hands is the nine times table, for which there is a little trick that is well known among children, but rather less well-known among those who are older. 

To do your nine times multiplications, simply put your hands on your knees, numbering your fingers left to right as shown in the diagram below.

[Image: article-1052306-0283A1C200000578-626_468x286.jpg]



Now choose which multiple of nine you want. Suppose it's 7 x 9. Simply bend down finger number 7, as shown in the diagram below 

[Image: article-1052306-0283A1BE00000578-764_468x286.jpg]

Now count the number of fingers and thumbs to the left of the bent finger (6) and the number to the right (3), put them together and you have the answer: 63



It works for all ten fingers and thumbs, so you can quickly check for yourself that 3 x 9 = 27, and 9 x 9 = 81

http://www.dailymail.co.uk/news/article ... drums.html


So No Matter What,If you View Both hands or a Single hand.
The Most binary(Off/On)) digits you can Get out of it sums to Nine 

This surrounds both technicalities.
Wether You Consider The Opposable THUMB as a "Finger or NOT" 

Now count the number of fingers and thumbs to the left of the bent finger (6) and the number to the right (3), put them together and you have the answer: 63



It works for all ten fingers and thumbs, so you can quickly check for yourself that 3 x 9 = 27, and 9 x 9 = 81
No matter how you "try" your hand @ IT
Nine Sums it up. [Image: uhoh.gif] 9

A Secret Handshake from a 33rd degree mason likely has some form or another code that will in the end be based on the speed of Lucifer. = C=9
[Image: 0035699df5f.jpg]

[Image: 27481202.jpg]

[Image: 27481201.jpg]
1
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
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Actually I meant more like the fingers and thumb may be forming half a triangle (see tetrahedron)... 

But that's some amazing stuff, as always. Thanks, EA.

It occurred to me that maybe something like a quipu might be adapted to do long division with (possibly with more colors of cord than seen here?)

[Image: quipufeat.jpg]

A. Sutherland – AncientPages.com – Incan Empire – that stretched for over 2000 miles from the north to the south and had a population of an estimated 10 million people – was the largest empire in pre-Columbian America.

To run the empire, the Inca had a sophisticated and organized government. Yet they had no written language, but instead a curious invention, a form of non-verbal communication written in an encoded language similar to the binary code used by modern computers...

The cords were knotted in such a way to represent the decimal system and were fastened at close intervals along the principal strand of the quipus. Thus an important message relating to the progress of crops, the amount of taxes collected, or the advance of an enemy could be speedily sent by the trained runners along the post roads…” (Hiram Bingham, the American explorer who found the ruins of Machu Picchu in 1911, wrote in ‘Lost City of the Incas’.)

Unfortunately, only a few ‘quipu’ arrangements survived to the present time. The truth is that most of the copies were burned. When the Spaniards conquered the Inca State, the Catholic Church ruled that ‘quipu’ are the work of Satan, as such, must therefore be destroyed, and so the Spanish conquistadors did in the 16th century. Approximately 200 of them dating no earlier than about 650 AD have been found and still can be analyzed.)

http://www.ancientpages.com/2015/02/09/s...imensions/



(05-25-2017, 08:10 PM)Pi Whole Wrote:
Michael Morton and I both attempted to do some work with Harleston's STU ("Standard Teotihuacan Unit") in the past but maybe neither one of us worked quite hard enough on it? MLM proposed 1.059521193 meters of (R/2) / 10^n = (sqrt 960) / 10 ft, but maybe if some other proposals for an ancient meter are going to start sticking, it might be time to revisit that? Oddly enough, I may have seen something like 1.059521193 trying to pop out at Tikal, more than once already now, which has added to a fresh sense of intrigue.

Apologies for phrasing that backwards - the Standard Teotihuacan Unit of Harleston is supposed to be about

3.282806350 times 1.059521193 = 3.478202605 ft... 

3.282806350 divided by 1.059521193 = 3.098386941 = (sqrt 960) / 10

Here is a curious thing...

Harleston assigns a value of 56 "Hunabs" (= STUs) the bottom width of the fourth tier (counting upward) of Teotihuacan's Pyramid of the Moon, as measured from the center of the pyramid (Tompkins, Mysteries of the Mexican Pyramids, page 246).

3.478202605 x 56 "Hunabs" = 194.7793459 FEET. Not meters, not STUs, not STFUs... Feet.

For a guy who seems to be on Tetrahedron Patrol (Tompkins, MOTMP,  pages 279-281), I wonder how that one got by him?
"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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Memoirs of a Pi Jedi
Chapter 9
Everybody Must Get Stoned???

[Image: 246_00_2.jpg]

Here is curious artifact... The Aztec "Calendar Stone" or "Sun Stone".

Does anyone know the origin of these measurements? 

"The stone is 358 centimetres (11.75 ft) in diameter and 98 centimetres (3.22 ft) thick"

That is really almost "shocking"...

11.75 / 3.22 = 3.649068323

Looks one hell of a lot like the calendar year, AS A "DECIMAL HARMONIC" RATIO. How incredibly Pi Jedi that would be. 

Now being a bit of a Pi Jedi myself, even when I have no idea where the data came from, it's very hard to resist the interpretation

11.772457711 / 3.225153444 = 365.0200808 / 100

That's once again Yoda's "Alternate Pi" (x 10), last seen lurking about the doorway of Temple II at Tikal, and the reciprocal of Pi cubed:

1 / (Pi^3) = 3.225153444 / 100

We can write the equation forwards as 11.77245771 x (Pi^3) = 365.0200808

Thus Alternate Pi may be a calendrical  number.

That would give the "Sun Stone" a circumference of (Radius x 2 Pi = Diameter x Pi = Circumference) 

(D) 11.7745771 x Pi = 36.98426666, or 5 Squared Yoda Megalithic Yards.

Remind anyone ever so slightly of a doorway at Tikal yet?

A fundamental Pi Jedi premise is that the ancients knew their arithmetic backwards and forwards... literally... so don't hesitate to try multiplying a pair of numbers as well as dividing them.

11.7745771 x 3.225153444 = 37.96798253

What's that? Let's get out the simplest mathematical probe in the book, the number 2 (if that doesn't work, remember to use the Fours, young Piwalker)...

37.96798253 / 2 = 18.98399126

Long Count
Since Calendar Round dates repeat every 18,980 days, approximately 52 solar years, the cycle repeats roughly once each lifetime, so a more refined method of dating was needed if history was to be recorded accurately. To specify dates over periods longer than 52 years, Mesoamericans used the Long Count calendar

Yup, that's probably the most outstanding contender for a "Pyramid Pi System" value for the Mayan Long Count, possibly combining accuracy with resonance (resonance trials currently in progress). Now seen here derived directly from measurements in FEET, boys and girls - Modern "British" FEET - provided we were given any additional incentive to trust the data. (Wikipedia is not  where I usually expect to find usable data).

If I thought for one minute that I should trust these measurements, I might haul off and declare that this may well be a Rosetta Stone of ancient calendrical mathematics and metrology...

But since I've already told a few horror stories (there are more) about what happens when good people get their hands on bad data...

I'm sure it's just a Great Big Aztec Frisbee. Nothing to see here, folks... Move along...

BTW, here's more stuff that isn't here to see...

You remember when I started out with Tikal, I took four raw measurements from Maler given in Yoda's "Master Code Book" and gave them the values that I thought Yoda would give them, and tried to see what I could make out of them. Next you know, I was babbling about how maybe it was time to ponder exactly what 19.48181821 is meant to be, since it seemed to be popping out of my Temple III equations as freely as the ubiquitous 19.46773764?

 (I also mentioned an "ALMOST 19.46773764^3" imbedded in the generic design for the Thom Type A flattened ring that appears to actually consist of 19.46773764 x 19.46773764 x 19.48181821).

19.48181821 x 19.46773764 = 379.2669256 = 189.6334628 x 2

But this is NOT the same thing as 

11.7745771 x 3.225153444 = 37.96798253 = 18.98399126

Until you ask what it's doing in a monument expressing a (360*) circle...

360 / 189.6334628 = 1898.399126 / 1000

Because 1898.399126 is very near to a decimal harmonic of the square root of 360 = 18.97366596 which (to the best of my knowledge) no Pi Jedi has ever accepted as belonging to "The Pyramid Matrix" or the "Pyramid Pi System" or whatever you wish to call it - "ancient mathematics" is fine by me. We've thus far apparently disowned the square roots of 360, the Radian, and Pi (and really haven't missed them any).

Did the ancient Egyptians know about this? I've no idea, but it's certainly a curious coincidence that if we take Yoda's "Giza Constant", the Radian 57.29577951 and divide by the perimeter of the Yoda model Great Pyramid 3018.110298 ft

57.29577951 / 3018.110298 ft = 1898.399126 / 10000

Then there's the part where if we treat the "Sun Stone" like it were Stonehenge, where we divide the 360* degree generic circle by the inner sarcen circle circumference of 305.7985078 to find a magic number

360 / Inner SC circumference 305.7985078 ft = 1.177245771 Alternate Pi

360 / possible circumference of Sun Stone 36.98426666 (5 SYMY) = 9.733868818 =  (1 / 1.027340741 x 10^n). 1.027340741 is also found in the adjusted Thom Type A circle (and currently a strong contender for the distance from the top of the doorway of Tikal Temple II, to its roof, and as may also appear in addition formulas inside the Great Pyramid, as well as 97.33868818 appearing in the Great Pyramid's descending passage (length of roof to ascending passage) and of course as the diameter of the Stonehenge inner sarcen circle, and etc.

Likely a lot of this isn't too surprising since the Squared Yoda Meg Yard is in the mix, but what surprises me is how the Sun Stone's dubious dimensions as shown here may make calendrical  insinuations about the ancient European Megalithic landscape, and perhaps also about the use of these same numbers at Giza?
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Reply
(05-26-2017, 10:21 PM)Ancient Vizier Wrote: Actually I meant more like the fingers and thumb may be forming half a triangle (see tetrahedron)... 

But that's some amazing stuff, as always. Thanks, EA.

It occurred to me that maybe something like a quipu might be adapted to do long division with (possibly with more colors of cord than seen here?)

[Image: quipufeat.jpg]
Knot to khipu in suspense 


[Image: moana-navigation.jpg]

That is exactly why you will note if you read back on all your "Missing -Time" @ THM

There are zero arguments against the best set of counters to any skeptical arguement.

Base Ten Decimal.

I don't care if you are an octopus or an arachnid or a six -footed insect.

That is only a base argument of how you cut the muster/mustard pie no matter square feet.

There is nothing more dactyl when a rosetta stone is Tactile.


Dactyl (poetry)

From Wikipedia, the free encyclopedia

[/url][url=https://en.wikipedia.org/wiki/Dactyl_(poetry)#p-search]
Not to be confused with Dactyly.
Metrical feet Disyllables

[size=undefined]
dactyl (Greek: δάκτυλος, dáktylos, “finger”) is a foot in poetic meter. In quantitative verse, often used in Greek or Latin, a dactyl is a long syllable followed by two short syllables, as determined by syllable weight. In accentual verse, often used inEnglish, it is a stressed syllable followed by two unstressed syllables—the opposite is the anapaest (two unstressed followed by a stressed syllable).
[/size]


The Greek and Latin words δάκτυλος and dactylus are themselves dactyls (and hence autological). The English word poetryis also a dactyl. A useful mnemonic for remembering this long-short-short pattern is to consider the relative lengths of the three bones of a human finger: beginning at the knuckle, it is one long bone followed by two shorter ones (hence the name dactyl).

An example of dactylic meter is the first line of Henry Wadsworth Longfellow's poem Evangeline, which is in dactylic hexameter:


[Image: 250859164_740cb617dd_o.jpg]
Eye can put my finger on it.

I Am amused by a muse use itza always a ruse. (Snake oil y'all !!!)

No matter how you slice it PW

You can't escape the powers of ten.

So Pay A TEN  SHUN



When you decimate as a demarcate the math scales itself by moving the self referential

Without Ten you never arrive @ 3.14... see my point once before.  Arrow

Ten is only a decent raise from zero decadence in the numero Zero/Uno cadence.

Binary to Trinary whatever number combine arrayed Ten itza Zen every now and then as far as Zep Tepi is concerned with Earth Measure/Metric Treasure
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply
Micro to Macro power of 10




Just paying attention to EA as ALWAYS Worship

Bob... Ninja Alien2
"The Morning Light, No sensation to compare to this, suspended animation, state of bliss, I keep my eyes on the circling sky, tongue tied and twisted just and Earth Bound Martian I" Learning to Fly Pink Floyd [Video: https://vimeo.com/144891474]
Reply
And Eye 'em just a peer amid the rest of plain ol' ancient common sense.

Tenure is institutional instructional but Ten Year is Decadal Time-wise.

Recall able Professor of a scalable Progresser You can enlarge a sphere of influence in a 3rd retinal compressor.
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply
Scientists Map The Genome Of Ancient Egyptian Kings, And They Weren’t From Africa  Naughty
[Image: 110418-zahi-hawass-1130a.jpg]
ANDREW FOLLETT
[/url]Energy and Science Reporter



4:56 PM 05/30/2017

[Image: rsz_shutterstock_459353062-e1496168263354.jpg]

The first ever genetic analysis of mummies found that ancient Egyptian kings were more closely related to West Asians than Africans, according to a study published Tuesday by scientists at the Max Planck Institute.
[url=https://www.nature.com/articles/ncomms15694]The research found that ancient Egyptians were most closely related to Neolithic Levantine, Anatolian and European populations. The mummies tested did not share strong genetic links to Africa often found in modern Egyptians.
“This suggests that an increase in Sub-Saharan African gene flow into Egypt occurred within the last 1,500 years,” Wolfgang Haak, who led the research team, said in a statement.
“The genetics of the Abusir el-Meleq community did not undergo any major shifts during the 1,300 year timespan we studied, suggesting that the population remained genetically relatively unaffected by foreign conquest and rule,” Haak said.

It’s further evidence that ancient Egyptians were genetically different than modern day residents. Scientists largely agree that ancient Egyptians were indigenous to the Nile area, but a vocal minority of “Afrocentric” scholars claim that the area’s ancient population was entirely African.

Those scholars claim ancient Egyptians were similar to Sub-Saharan African cultures, arguing that famous Egyptian rulers, including Tutankhamun and Cleopatra, were more African than Caucasian.

Researchers analyzed ancient DNA from mummified Egyptians who lived from 1400 B.C. to 400 A.D., establishing that mummies can be a reliable source for genetic material to study the ancient past.
The study could open the door to further genetic testing of mummified remains. More than 151 individual mummies were examined during the research. Scientists recovered mitochondrial genomes from 90 individuals and genome-wide data sets from three individuals.


Zawi Hawass;  have a Cuppa shut the fuck up!!!

[Image: Zahi_Hawass_Pseudoscientist.jpg]
Scientists Map The Genome Of Ancient Egyptian Kings, And They Weren’t From Africa  Naughty
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply
Bless Zahi, he always had to say Pyramid as quickly as possible, like it was a dirty word - "ptdt"... also he had that adorable habit of spending all day ripping on people for believing the pyramids were built by aliens, then renting out the Great Pyramid at night to people who believe the pyramids were built by aliens...

Well, let's see... I'm about to name a chapter, "Going in Circles" because that seems to be what I'm doing. It describes some of my research interests (stone circles, circular pyramids) and it describes how I'd forgotten what a royal pain it is to research American archaeology. I've already spent years getting run in circles on that subject, and now I've come full circle and it's happening again...

On the one hand, there are things like the treasure-trove of George Andrews' archaeological papers on-line, on the other hand some things are not so freely available and half of that may be items in the hundreds of dollars and available sight unseen as to whether the works even contain any archaeological measurements at all for a given site.

Anyone looking at Yoda's materials might want to pay extra attention to his stuff on the Cuicuilco pyramid, I'm not sure why he can't still be right in interpreting it as a tutorial in circular/spherical mathematics, although if it doubled as a model of the Sun, Venus, Earth, and Mars I suppose we Pi Jedi remain oblivious. I'm pretty sure I'd worked with figures from Marquina before but I'm also pretty sure it's lost in a huge stack of papers now. I'm intrigued that there's a similar one at Guachimontones, and also one there that is purported to have sets of 13 and 4 terraces. Since 13 x 4 = 52, it may well be getting directly into calendrical math, so just maybe it's worth beating my head against all over again?

I'm just going to rattle some stuff off, I'm working on stuff that's new to me so not sure what to make of it.

I think the Sun Stone may have a flexible interpretation, where its thickness may be also be interpreted as 1 / (3.098386677 / 10) as well as 1 / ((Pi^3) / 100) as previously suggested. 3.098396677 is the square root of 960, and it's already managed to be mentioned in the context of Harleston's "hunab" or STU.

Retrofitting that into the equations instead of Pi^3,

11.77245771 / 3.227486122 = 364.7562611

And that may have been another legitimate accounting of the number of days in a year, possibly depending on the particular formulas one is using. It's another very obvious relation to the 360 circle and Pi, consisting of

(360 x 10) / (Pi^2) = 364.7562611

And we may see that corroborated at El Castillo at Chichen Itza. Somehow everyone seems to think this is a calendrical pyramid, contending it has 91 steps on each of four sides and 91 x 4 = 364. Counting the temple on top as one more although I know of nothing that actually instructs anyone to do this, makes 365 days in a year.

This is a curious thing, since 91 not being in the Pyramid Pi System, I'd want to approximate that as meaning (900 / Pi^2) = 91.18906528, which we seem to have been seeing at Tikal, and 

91.18906528 x 4 = 364.7562611

And of course, the difference between our very handy 365.0200808 day year and this proposed alternate 364.7562611 day year is the often-seen ratio 1.00072327...

365.0200808 / 364.7562611 = 1.00072327

It's of course just a proposal, I can visit the ramifications in more detail later.

I sort of ended up with the duty of going back to Silbury and rechecking my dubious complete model.

Grid Point msg board, post #1203 
Thu Feb 20 2003

Was when I first posted that, hot off the presses at the time. Regarding my data sources, these are mentioned in that post 

"Carl Munck, "Whispers from Time, Vol II", p 273...

Silbury: Diameter, 550 feet; Area: 237582.94 feet
Grave Creek Mound: Diameter 317.542 feet, Area 79194.3 feet
(79194.3 x 3 = 237582.94)

All of which, along with Munck's figures for Silbury, are predicted on a slope angle of 30*... 

Carl Munck, "Aquarius", No. 9, pg. 5
"Its flattened upper circle has a diameter of 100 feet" (Circumference= 100 Pi)"

I still can't find my copy of this, about half of these "Aquarius Papers" of his are still gone AWOL, and I really wanted to review whether I should have granted him this indulgence. After all, it makes for a pretty damned boring radius and diameter - 50 and 100 feet respectively, not exactly oozing what we call data at the Academy.
Thu Feb 20 
But we have a Sun Stone that seems to make calendrical use of 1/2 of the Squared Yoda Megalithic Yard, and his "Alternate Pi," which sort of implies they may both be more calendar-related that they've received credit for previously.

So back at the doorway of Tikal Temple II, we have a proposed width of the Squared Yoda Meg Yard, a height/width ratio of Alternate Pi 1.177245771, mandating a height of 8.707914303 feet...

When I went to see if that acts like a calendar number of some kind, I threw the 365.0020808 day year at it, and it came back with

8.707914303 x 365.002080 = 317.8563584 

Which is rather intriguing to me, because one other thing Yoda insisted on is a slope angle of 30* for Silbury, and with my having interpreted the "550-foot" base diameter as 550.4373142 ft

I have (550.4373142 / 2) / (cos 30) = 317.7951315 as the slope height it would have had it were a complete conical shape proceeding all the way to a point at the apex, and back in 2003 I took the liberty of interpreting it as an intentional figure meaning (accuracy .999807375)

317.8563584 = 270 x Alternate Pi 1.177245771

If I indulge Yoda, upper radius 50 ft / cos 30 = 57.73502692 as the missing length of slope, and 

317.7951315 - 57.73502692 = 260.0601046 as the remaining slope, and thatof course looks very much like a number from the Mayan Calendar (the "Tzolk'in" of 260 days).

Back when I posted that in 2003, I was interpreting this as 259.7575757 + y = 317.8563584

Because of the possible relationship of this to Stonehenge, and that is where for the exterior of the Sarcen Circle, I adopted Thom's 120 Meg Yards, assigned the "Alternate e" values of 2.720174976 ft, and got

120 x 2.720174976 = 326.4209971 ft outer Circumference of Sarcen circle

326.4209971 / 1.067438159 = 305.7985078 ft inner Circumference of Sarcen Circle

305.7985078 / 1.067438159 = 28.64788983 = Radian / 2

Which gives a lovely symmetrical framing of 1.067438159...

I have yet to mention that as a consequence, 326.4209971 ft outer circumference give us

326.4209971 ft outer circumference / Pi = outer SC Diameter 103.9030304 (1.066666666 x Pi^4)
outer SC Diameter 103.9030302 / 2 = outer SC Radius 51.95151521 (5.3333333333 x Pi^4 / 10)

51.95151521 / 2 = 259.7575761 / / 10

Which converses with Stonehenge's inner sarcen circle radius to give us Alternate Pi

305.7985078 / 259.7575761 = 1.177245771

And 259.7575761 of course answers the 360-degree circle with 

360 / 259.7575761 = 1.177245771^2

And that also makes for numbers very suggestive of the Mayan calendar (i.e., ~260 and ~52) appearing at both Silbury and Stonehenge...

Back then, I didn't know what a "Thoth Cubit" was, so I had little way of knowing that choosing 259.7575761 for the intended "260" value, with a full (projected) slope of 317.8563584 ft, gives

317.8563584 - 259.7575761 = 58.09878240, which is the reciprocal of (the "Thoth Cubit" / 100) to an accuracy of .999930597 

(1 / (Thoth Cubit / 100) = 58.09485019

Is Yoda's 50 ft / cos 30 = 57.73502692 missing slope for the sake of perimeter of Pi really what we are supposed to be chasing here? Is his "Perimeter 100 Pi" still possible without the model becoming too unstable trigonometrically or having a sudden lapse of accuracy? I do seem to recall finding that, since cos 30 = (sqrt 3) /2, we could use the same (sqrt 3 / 2) value used in constructing the "Alternate e' Meg Yard" and just barely preserve the 30* slope angle, so maybe they accommodated his proposal also by the skin of its teeth, but I'm not entirely sure of too much here. 

I did find it sort of remarkable to think of Silbury being topped with a Cubit after the Great Pyramid's many indications it too is topped with a Cubit, albeit what is likely a different one, the MLM Royal Cubit of .03 Radians.

So that's sort of how Silbury managed to plop itself right down in the middle of an inquiry in to Mesoamerican calendars. I'm expecting evidence, if there isn't already some in my notes somewhere, that approximation of 260 as 259.7575761 could have been fairly commonplace in the ancient Americas.

When we divide this goofy proposal of an alternate 364.7562611 ancient American year by a week of (360 x 19.4677376 = 7.008385550) days (you will recall that 7.008385550 is the title of chapter 7.008385550 of my "memoirs") we get 52.04568991, the form of "52" deriving from Great Pyramid math:

104.0913798 (MLM Apex Displacement Ratio x 100) / 2 = 52.04568991

Which is one of the things that makes them appear as if they are not unrelated.

Now I did say that using 1 / ((Pi^3) / 100) as the thickness of the Sun Stone provides a Long Count with both accuracy and resonance 

But 18983.99126 may have a drawback that if we want to express ~18980 days as hours, minutes, or seconds, that it may leave something to be desired...

Whereas representing it symbolically as the alternate designation 18997.72193 may work better... 

18997.72193 days 
x 24 hrs = 45.59453267 x 10^n
x 60 min = 273.5671960 x 10^n
x 60 sec = 1641.403176 x 10^2

generic Area of a Circle 10313.240131 / 2 Pi = 1641.403176

Also, the reciprocal of that is 1 / (1641.403176 x 10^n) = 609.2348397

Which perhaps make it seems a little less strange, now revealed as also being an obvious variation on the circular geometry theme, that it is the proposed truncated apothem length for the Great Pyramid without paving, Ye Olde 500 "Thoth Remens"

609.2348397 ft / 500 = 1.218469679 ft, the "Thoth Remen" = .1234567901 x (Pi^2)

And 18997.72193 is what we actually get if we do alternate calculations with the Sun Stone based on a thickness given as 1 / (sqrt 960 / 100) in feet...

3.227486122 x 11.77245771 = 37.99544388 = 18.99772194 x 2 (accuracy as Long Count / 10^2 = .9990 over 52 years)

52.04568991 x 365.020081 = 18.99772194

In contrast to 52.00807369 x 365.020081 = 18983.99127 (accuracy as Long Count / 10^2 = .999789756 over 52 years)

So these various candidates begin to look like they may belong to different valid systems of reckoning time, possibly also depending on the need for exact accuracy in a given situation. I still have yet to be able to prove that - in fact, I'm still just getting to know some of these numbers, so I may be a long way from that - but it may well be true that if us Pi Jedi types haven't succeeded at this before, it's because we go chasing "THE" intended value, when there may be multiple valid numbers belonging to multiple valid equations.

Anyway, I thought I'd take the opportunity to show more of what I had for Silbury and Stonehenge. I'm finding no shortage of interesting equations, but I'm still not sure exactly how to work with some of the numbers. I am hopeful that the interpretation of "91 steps" at El Castillo at Chichen Itza is correct, it might help establish more firmly the way we are intended (or allowed?) to interpret such numbers that don't otherwise belong to the particular system of mathematics...

And all of this might help further explain what some of these numbers are doing atop Temple II at Tikal.

I think there may be quite a bit we still don't know about Stonehenge, though, and some of it may be related to approximation... approximation of the square root and cube root of the Remen really are starting to look intended, 

1.067438159 / 1.177245881 = 360 / 326.4209961 = sqrt 1.216322751 (exact value 1.216733603), and
1.067438159^3 = 1.216264895 (exact value 1.216733603)

And approximation of... Well, here...

outer Sarcen Circle circumference 326.4209971 ft MINUS inner Sarcen Circle circumference 305.7985078 = 20.62248930 = ~12 MLM Royal Cubits 1.718873385 x 12 = 20.62638062 ft (accuracy .999806495)

outer Sarcen Circle radius 51.95151521 MINUS inner Sarcen Circle radius 48.66934411 = 3.28217104 = ~Radian Squared / 1000 = 3.282806350 (accuracy .9998064736) 

And possibly representing one or more ancient versions of the meter, depending on the restrictions on accuracy and the sensibility of a particular candidate. (Hint?: I don't think they'd post a meter at Stonehenge, if it wasn't good at measuring Stonehenge - let's hope).

I did wonder what the thickness of the Sarcen Circle was back there in 2003-2004. I've always taken it to mean R^2 / 1000 but now it's starting to look more like those mysterious "6.561" feet figures (3.2805 x 2) atop four of the Tikal Temples that it happens to be just about half of. I presume a single figure belongs to the basic design "on paper" whereas the rough hewn reality made of imperfect stones may accommodate any meter they happened to feel like.

I am looking at a "Fifth Meter" lately, it's 3.287490368 ft. Not sure what it's good for but gosh darn if it doesn't have remen in it too

3.287490368 / 4 = 1 / (1.216733603 / 10)

So there are a few items ticked off my list of things to post about... I wish I thought I could tick them off my list of things still not understood...
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Reply
Ten Late Period tombs uncovered in Aswan
The tombs were uncovered on Aswan's West Bank
Nevine El-Aref , Thursday 1 Jun 2017

[Image: 2017-636319191213493715-349.jpg]
A gilded newly discovered coffin


During excavation work in the area neighbouring the Agha Khan mausoleum on Aswan’s west bank, an Egyptian mission from the Ministry of Antiquities stumbled upon ten rock-hewn tombs.



Mahmoud Afifi, dead of Ancient Egyptian Antiquities at the ministry, said that the tombs can be dated to the Late Period and early studies reveal that the site is probably an extension of Aswan necropolis on the west bank where a collection of tombs belonging to Aswan overseers from the Old, Middle and New kingdom are found.

Nasr Salama, director-general of Aswan and Nubia Antiquities told Ahram Online that the tombs have similar architectural design. they are composed of sliding steps leading to the entrance of the tomb and a small burial chamber where a collection of stone sarcophagi, mummies and funerary collection of the deceased were found.

He said that during the next archaeological season which starts in September, the mission will continue the excavation and begin comprehensive studies and restoration work on the funerary collection uncovered to learn more about who the tombs contain.



[Image: 2017-636319191773929535-392.jpg]a clay pot






[Image: 2017-636319192070995720-99.jpg]a painted mummy mask
[Image: Hawass-Zahi.jpg?itok=bL6wTg98]The painted mummy mask Does not look African or MODERN /Egyptian  ??? 
DNA shall RE-TELL The Tale of the Tape/tepi


Quote:The first genome data from ancient Egyptian mummies

Tue, May 30, 2017 http://popular-archaeology.com/issue/spr...an-mummies



[Image: 2017-636319192396447308-644.jpg]canopic japr





[Image: 2017-636319192655336672-533.jpg]sarcophagus

http://english.ahram.org.eg/NewsContent/...Aswan.aspx


The first genome data from ancient Egyptian mummies

Tue, May 30, 2017

[i]Study finds that ancient Egyptians were most closely related to ancient populations from the Near East.
[/i]

[Image: the-first-genome-data-from-ancient-egypt...=1000&q=70]
MAX PLANCK INSTITUTE FOR THE SCIENCE OF HUMAN HISTORY—An international team of scientists, led by researchers from the University of Tuebingen and the Max Planck Institute for the Science of Human History in Jena, successfully recovered and analyzed ancient DNA from Egyptian mummies dating from approximately 1400 BCE to 400 CE, including the first genome-wide nuclear data from three individuals, establishing ancient Egyptian mummies as a reliable source for genetic material to study the ancient past. The study*, published today in Nature Communications, found that modern Egyptians share more ancestry with Sub-Saharan Africans than ancient Egyptians did, whereas ancient Egyptians were found to be most closely related to ancient people from the Near East.
Egypt is a promising location for the study of ancient populations. It has a rich and well-documented history, and its geographic location and many interactions with populations from surrounding areas, in Africa, Asia and Europe, make it a dynamic region. Recent advances in the study of ancient DNA present an intriguing opportunity to test existing understandings of Egyptian history using ancient genetic data.
However, genetic studies of ancient Egyptian mummies are rare due to methodological and contamination issues. Although some of the first extractions of ancient DNA were from mummified remains, scientists have raised doubts as to whether genetic data, especially nuclear genome data, from mummies would be reliable, even if it could be recovered. "The potential preservation of DNA has to be regarded with skepticism," confirms Johannes Krause, Director at the Max Planck Institute for the Science of Human History in Jena and senior author of the study. "The hot Egyptian climate, the high humidity levels in many tombs and some of the chemicals used in mummification techniques, contribute to DNA degradation and are thought to make the long-term survival of DNA in Egyptian mummies unlikely." The ability of the authors of this study to extract nuclear DNA from such mummies and to show its reliability using robust authentication methods is a breakthrough that opens the door to further direct study of mummified remains.
For this study, an international team of researchers from the University of Tuebingen, the Max Planck Institute for the Science of Human History in Jena, the University of Cambridge, the Polish Academy of Sciences, and the Berlin Society of Anthropology, Ethnology and Prehistory, looked at genetic differentiation and population continuity over a 1,300 year timespan, and compared these results to modern populations. The team sampled 151 mummified individuals from the archaeological site of Abusir el-Meleq, along the Nile River in Middle Egypt, from two anthropological collections hosted and curated at the University of Tuebingen and the Felix von Luschan Skull Collection at the Museum of Prehistory of the Staatliche Museen zu Berlin, Stiftung Preussicher Kulturbesitz.
In total, the authors recovered mitochondrial genomes from 90 individuals, and genome-wide datasets from three individuals. They were able to use the data gathered to test previous hypotheses drawn from archaeological and historical data, and from studies of modern DNA. "In particular, we were interested in looking at changes and continuities in the genetic makeup of the ancient inhabitants of Abusir el-Meleq," said Alexander Peltzer, one of the lead authors of the study from the University of Tuebingen. The team wanted to determine if the investigated ancient populations were affected at the genetic level by foreign conquest and domination during the time period under study, and compared these populations to modern Egyptian comparative populations. "We wanted to test if the conquest of Alexander the Great and other foreign powers has left a genetic imprint on the ancient Egyptian population," explains Verena Schuenemann, group leader at the University of Tuebingen and one of the lead authors of this study.
[Image: 34815201342_fdd3d5b4ef_z.jpg]
 Sarcophagus of Tadja, Abusir el-Meleq. Credit: bpk/Aegyptisches Museum und Papyrussammlung, SMB/Sandra Steiss
[Image: 34815209822_d32dbffc58_z.jpg]
 Map of Egypt, showing the archaeological site of Abusir-el Meleq (orange X), and the location of the modern Egyptian samples used in the study (orange circles). Credit: Graphic: Annette Guenzel. Credit: Nature Communications, DOI: 10.1038/NCOMMS15694
[b]Close genetic relationship between ancient Egyptians and ancient populations in the Near East[/b]
The study found that ancient Egyptians were most closely related to ancient populations in the Levant, and were also closely related to Neolithic populations from the Anatolian Peninsula and Europe. "The genetics of the Abusir el-Meleq community did not undergo any major shifts during the 1,300 year timespan we studied, suggesting that the population remained genetically relatively unaffected by foreign conquest and rule," says Wolfgang Haak, group leader at the Max Planck Institute for the Science of Human History in Jena. The data shows that modern Egyptians share approximately 8% more ancestry on the nuclear level with Sub-Saharan African populations than with ancient Egyptians. "This suggests that an increase in Sub-Saharan African gene flow into Egypt occurred within the last 1,500 years," explains Stephan Schiffels, group leader at the Max Planck Institute for the Science of Human History in Jena. Possible causal factors may have been improved mobility down the Nile River, increased long-distance trade between Sub-Saharan Africa and Egypt, and the trans-Saharan slave trade that began approximately 1,300 years ago.
This study counters prior skepticism about the possibility of recovering reliable ancient DNA from Egyptian mummies. Despite the potential issues of degradation and contamination caused by climate and mummification methods, the authors were able to use high-throughput DNA sequencing and robust authentication methods to ensure the ancient origin and reliability of the data. The study thus shows that Egyptian mummies can be a reliable source of ancient DNA, and can greatly contribute to a more accurate and refined understanding of Egypt's population history.
Article Source: Max Planck Insitute for the Science of Human History news release

[size=undefined][size=undefined]*[i]Ancient Egyptian mummy genomes suggest an increase of Sub-Saharan African ancestry in post-Roman periods. 
Authors: Verena J. Schuenemann, Alexander Peltzer, Beatrix Welte, W. Paul van Pelt, Martyna Molak, Chuan-Chao Wang, Anja Furtwangler, Christian Urban, Ella Reiter, Kay Nieselt, Barbara Tessmann, Michael Francken, Katerina Harvati, Wolfgang Haak, Stephan Schiffels & Johannes Krause  DOI: 10.1038/ncomms15694
[/size]
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Quote:Bless Zahi, he always had to say Pyramid as quickly as possible, like it was a dirty word - "ptdt"... also he had that adorable habit of spending all day ripping on people for believing the pyramids were built by aliens, then renting out the Great Pyramid at night to people who believe the pyramids were built by aliens...

Well, let's see... I'm about to name a chapter, "Going in Circles" because that seems to be what I'm doing. It describes some of my research interests (stone circles, circular pyramids) and it describes how I'd forgotten what a royal pain it is to research American archaeology. I've already spent years getting run in circles on that subject, and now I've come full circle and it's happening again...

On the one hand, there are things like the treasure-trove of George Andrews' archaeological papers on-line, on the other hand some things are not so freely available and half of that may be items in the hundreds of dollars and available sight unseen as to whether the works even contain any archaeological measurements at all for a given site.

According to Mihoubi, when Cleopatra Selene died, he built her a massive pyramid as big as the Giza pyramids.  
Did you know that Algeria has pyramids, and Cleopatra is the reason behind them?

[Image: 582826a7-ddb6-4dfd-b4ab-45f4cb2c22c2_16x9_788x442.jpg]Algerian Culture Minister Azzeddine Mihoubi recently announced that pyramids were discovered in the Tiaret province, 280 kilometers west of the capital. (Screengrab)

Many think that pyramids were only built in Egypt, however, there are pyramids in other countries such as in Algeria.
Algerian Culture Minister Azzeddine Mihoubi recently announced that pyramids were discovered in the Tiaret province, 280 kilometers west of the capital.


He added that the relevant authorities will maintain the pyramids and promote them for tourism purposes.

Following this announcement, many researchers said there are dozens of pyramids and royal shrines.

Mihoubi once wrote an article about the Royal Mausoleum of Mauretania explaining its cultural significance and how it is linked to Cleopatra Selene, the daughter of Queen Cleopatra VII of Egypt.

“Cleopatra Selene’s condition before marrying King Juba of Numidia was to make Egypt’s rituals available where she was. Therefore, she wanted the water of the Nile and pyramids present in Algeria, which was known as Numidia at the time,” Mihoubi wrote.

“King Juba met his beloved’s demands. He made Wad Mazafran in Algeria look like the Nile by decorating it with the same trees and docking the same ships. Pharaonic rites were held at her castle thus everything in Cherchell resembled her home in Egypt,” he added.

According to Mihoubi, when Cleopatra Selene died, he built her a massive pyramid as big as the Giza pyramids. The pyramid however was circular in shape and this was Juba’s desire as he wanted to distinguish his legacy from Khufu, Khafre and Menkaure.

The Royal Mausoleum of Mauretania was thus built as a tomb for Cleopatra Selene.

Last Update: Tuesday, 23 May 2017 KSA 09:34 - GMT 06:34 http://english.alarabiya.net/en/variety/...iaret.html

Chimps found to pass on knowledge to the next generation
June 1, 2017

[Image: chimpanzee.jpg]
Credit: CC0 Public Domain
Passing skills down through the generations, previously thought to be unique to humanity, has been discovered in chimpanzees.



The phenomenon of passing on behavioural traditions, known as "animal cultures" has been seen in other animals e.g. chimpanzee tool use or the migratory routes of birds or even the songs of whales.
However, the ability of humans to evolve these skills over generations by building on previous knowledge, a process known as "cumulative culture," for example the way people have evolved wheeled-vehicles over the centuries, was thought to separate humanity from the rest of nature.
Now, new behavioural experiments with chimpanzees, led by the University of St Andrews, suggests that these apes may indeed share some of the foundations of our remarkable cultural nature.
Primatologists from the University of St Andrews, working with colleagues in the world's largest ape research centre in the US, presented chimpanzees with a novel opportunity: sucking through straws to get juice from a large container just outside their enclosure.
To create the potential for cumulative culture, a range of different objects were available: from sticks to dip in the juice, to various tubes that could be used as straws. The most complicated tool was one which needed to be unfolded, with a valve which needed to be unscrewed to create a long straw to reach the juice from the deep container.
Chimpanzees presented only with this complex option failed to exploit it – it was a very novel challenge for ape minds. However in other groups, where one chimpanzee had been trained to use the complicated tool, other chimpanzees watched and copied them, with this behaviour then spreading through the group.
However, other groups not provided with a trained member, did see some chimpanzees created this complex behaviour by themselves by pooling of partial discoveries by different individuals who had already mastered using the simpler straws.
This discovery shows that complex traditions can arise through collective understanding and cumulative practice.
Professor Andrew Whiten of the University of St Andrews, who led the study, said: "Perhaps the most fundamental thing this study shows is that a group of chimpanzees can appear more intelligent than any single individual – together they can create more advanced steps in cultural evolution.

[Image: Imedghasen.jpg]
Lead author Dr Gillian Vale, of the University of Texas, added: "Our chimpanzees were capable of learning increasingly complex behaviours by observing knowledgeable individuals. 

This and other recent studies are beginning to show that some non-human animals are better equipped to improve the complexity of their cultural behaviours over time than was previously believed."
Algerian Culture Minister Azzeddine Mihoubi recently announced that pyramids were discovered in the Tiaret province, 280 kilometers west of the capital. 
[Image: C2cAuVsWgAMQPg4.jpg]
ancient Egyptians were found to be most closely related to ancient people from the Near East./Algiers.
The researchers emphasise that cumulative progress occurred only when a challenging 'ecological change' was created by the experimenter: simple tools the chimps had been using became no longer available.
The scientists suggest this is significant for understanding what may have happened in the course of human evolution as new skills were required to deal with radical ecological changes as forests gave way to savannas, with "cumulative culture" accelerating particularly during ice ages.
[Image: 1x1.gif] Explore further: Chimpanzees adapt their foraging behavior to avoid human contact
More information: Gillian L. Vale et al. Acquisition of a socially learned tool use sequence in chimpanzees: Implications for cumulative culture, Evolution and Human Behavior (2017). DOI: 10.1016/j.evolhumbehav.2017.04.007 
Journal reference: Evolution and Human Behavior [Image: img-dot.gif] [Image: img-dot.gif]
Provided by: University of St Andrews



Read more at: https://phys.org/news/2017-06-chimps-knowledge.html#jCp[url=https://phys.org/news/2017-06-chimps-knowledge.html#jCp][/url]
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
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Circular pyramid (Ehecatl temple) and Ankh-like structure at Calixtlahuaca

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Cuicuilco Pyramid

Here's one of the more detailed pages I've run across so far on Guachimontones

Los Guachimontones–Ancient Circular Pyramids of Jalisco By Richard Clarke
https://richardarunachala.wordpress.com/...of-jalisco


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The Cuicuilco Pyramid's little brother?

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"La Iguana" Pyramid at Guachimontones before and after restoration

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Model of Guachimontones site

...The Weigands ended up finding a huge obsidian workshop nearby, where millions of blades and sharp pieces of rock were piled up to three feet deep across two acres at the foot of the extinct Tequila volcano. This workshop was evidence of a developed culture, since you are not going to find such a workshop in some small out-of-the-way place.

So in 1970 the Weigands started what was planned as a one-year project exploring the Tequila Valley. This project ended up lasting for the rest of Phil’s life, 41 years more.

The Weigands started by examining aerial photos of the valley. "We found hundreds of buildings shaped like concentric circles, mostly around the volcano," Phil says. "They were everywhere!" A large area above the town of Teuchitlán, called Guachimontones, was especially interesting. "We finally reached a circular compound whose beauty, symmetry, and monumentality far exceeded the expectations we had formed from the aerial photographs." Later, Weigand recalled the moment: “I stood on the largest pyramid, looked around and thought, ‘This is unexpected.’”

From 1970, the Weigands were investigating, interviewing and registering over 2000 archaeological sites which allowed them to formulate the first hypotheses that western Mexico had been home to an unknown civilization, the Teuchitlán tradition. Intensive excavations and restoration of Los Guachimontones started in 1999.

This complex society, responsible for the area’s shaft tombs, reached its peak between 200 B.C. and A.D. 350, when more than 50,000 people may have lived within 15 miles of the Tequila volcano. At its height, the Teuchitlán tradition was the cultural center of west Mexico, with unique, complex architecture and a trade network that stretched from Guatemala to Arizona in the US.

Interestingly, they were not the first Western archeologists to make this discovery. In 1895, the British archaeologist Adela Breton came to the Guadalajara region. His observations and drawings illustrate clay sculptures, high-status burials and the existence of monumental ritual circles near Teuchitlán. However, his notes and articles were forgotten until recently, considered unimportant because scholars already ‘knew’ the prehistory of Western Mexico.


Guachimontones: unearthing a lost world near Teuchitlan, Jalisco John Pint

...Unlike the Aztecs, whose ceremonies resulted in rivers of blood coursing down the sides of their pyramids, the people of Teuchitlán worshiped Ehécatl. a gentle god, who didn't need human sacrifice to satisfy his ego. On ceremonial days, the ring-shaped "patio" was crowded with people chatting and jostling one another or perhaps linked arm in arm, performing the cadena, or chain dance while listening to groups of musicians. Around this walkway, on evenly spaced terraced platforms, the local VIPs gazed out the doorways of buildings that to western eyes might look typically Chinese. They had tall, pointy, gabled roofs which, along with their wattle-and-daub walls, were carefully plastered and beautifully painted in bright colors. The VIPs chatted with the people in the milling crowd, perhaps discussing the latest score of the ball game taking place in the court located alongside the largest pyramid. Directly to the north, a huge crowd of onlookers watched the events from a steep, terraced hillside, a vantage point from which music from the pyramids could easily be heard.

Everyone, of course, was anxiously waiting for the main event of the day to begin. A sturdy pole had been set in the exact center of each steep pyramid. No one today knows exactly what its function was. The clay models show a "flier" balanced on top of the pole, perhaps tied to it so he wouldn't fall off. He probably represented Ehécatl, the bird man, and, as the clay models show us, a crowd of people pushing on the pole caused him to "fly." It is also possible that ropes were wound around the pole, as is still done today in Veracruz, and that fliers tied to the ropes and bedecked with feathers, swooped through the air in ever-widening circles, soaring up and down like the graceful birds, finally to land on the circular walkway around the pyramid. The width of this ring was always the same as a second, exterior ring where the buildings were placed, following a complicated geometrical formula; and the diameter of the pyramid was always 2.5 times the width of the walkway.

(Saints Preserve us, any second now Yoda's going to declare 4/5 of the Radian as the "site constant" of everything south of the Rio Grande?)

...TEMPLES
The Mesoamerican temples dedicated to Ehecatl and other wind gods are distinctive in that they are circular as opposed to the usual square pyramid, or they incorporate a curved end. The roof of such buildings was typically conical too. This design may reflect the desire to make them aerodynamically welcoming for the winds of the god they honour. The doorways are usually formed as the jaws of a giant snake. This may well be in imitation of the caves Mesoamerican peoples considered entrances to the Underworld where the winds were thought to originate from.

(Of course, the Wind is perhaps also of some small importance to those who wish to sail their Itty Bitty Boats around the Great Big Round Thing...)

[Image: ehecatl-pyramid-3.jpg]
Temple of Ehecatl discovered at Pino Suarez Metro Station in Mexico City
"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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[Image: Phil-Weigand.jpg]
"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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A lingering question - if the doorway of Tikal's Temple II is a billboard for the Squared Yoda Megalithic Yard and Alternate Pi, what are the other four Temple doorways at Tikal up to? Currently, the answer is I don't know - or possibly "Ellifino" since the so-called "Ellifino," which I'm proposing was an ancient metrological unit, is the reciprocal of Apex Displacement Ratio-based 52, did anyone notice?

104.0913798 / 2 = 52.04568990 = 1 / (an Ellifino of 1.921388691 ft x 100)

Unfortunately, the other Tikal temple doorways don't seem to be quite as self-explanatory. We might expect to see similar "advertisements" for other Yoda power probes such as what I call "Alternate Phi" or 1.62231147. Such things may actually be present - Maler gives data that looks like 1.62231147 could be written forwards and backwards in the Tikal temples, although Andrew's data seems to differ somewhat on what in Maler's data looks like a backwards occurrence

1 / 1.62231147 = 0.616404444

Temple II - 2nd Chamber - Length 495 cm (Maler) = 16.23015748 ft = ~16.22311470
Temple II - 2nd Chamber - Length 4.95 m (Andrews) = 16.24015748 = ~16.22311470
Temple I - Doorway to 3rd Chamber - Width 188 cm (Maler) = 6.167979003 ft = ~ 6.16404444 
Temple I - Doorway to 3rd Chamber - Width 1.92 m (Andrews) = 6.299212598 = ~6.283185307 (2 Pi)

But what the other outer temple doorways are talking about? Not quite sure and I'd like to be careful given there are occasional discrepancies as seen here, that could be potentially misleading.

A curious fact about "Alternate Phi" is that if you square it, it makes 2 "Cholulas".

1.62231147^2 = 2.631894506 = 1.315947254 x 2

Just as squaring the Cholula makes the representative of sqrt 3 involved in generating the "Alternate e' Meg Yard"

1.315947254^2 = 1.731717294 = ~sqrt 3 (1.732050808); (1.731717294  / 2) x Pi = 2.720175024 

Which leads to the other question I'm working on which is, if this "Cholula" number is supposed to represent the circumference of the Earth in feet, why doesn't it seem to be better represented in the Great Pyramid, which gives many hints of being a representation of the Earth?

Glen Dash's review of Great Pyramid base measurement data including Lehner & Goodman
http://www.aeraweb.org/wp-content/upload...am13_2.pdf

It's noted in Dash's text that the Great Pyramid's platform "extends outward from the casing by an average of 42.3 cm on each side" = 1.387795276 ft = ~Alternate Pi 1.177245771^2 = 1.385907605

Yet another thing I'm working on is trying to figure out just how popular Alternate Pi 1.177245771^2 = 1.385907605 might have been in the ancient Americas, and why.

I've long been intrigued by Tatiana Proskouriakoff's impression of this impressive structure at Xpuhil, with stairs and doorways that may have purely ornamental (or mathematical) purposes, but you can see in the photos how much is(n't) really left of it.

[Image: xpuhil.jpg]

Whereas a similar structure at Rio Bec was found in better condition, and some of its measurements are described by Andrews - although sadly, I can only find where he gives the widths and not the heights of the false doorways atop the towers, so I'm not sure what numbers these "billboards" might be advertising either, even after having been fortunate enough to locate a dataset.

[Image: d23f.JPG]
Rio Bec "Structure B"

A preliminary study of Andrew's data for the Rio Bec structure's interior suggests someone involved in the design may have been very big on Alternate Pi Squared, including the possible presentation of its reciprocal as an approximation of the square root  of the calendrical number 52. I haven't quite figured it out yet but whatever it is does come across thus far as rather clever of them - the room ("Room 2") where this is found may well express an interesting mathematical formula even with incomplete data.

And again, Alternate Pi 1.177245771^2 = 1.385907605 may belong to some circular/calendrical formulas

360 / 1.385907605 = 259.7575759 = ~260 

Clarence Hay's description of the site includes an interesting comment about the structure at Rio Bec

(Hay, Clarence L., 1935. A Contribution to Maya Architecture. Natural History 36 (1): 29-33).

"As in all Maya work, the building is not entirely symmetrical. The central doorway is set slightly to the left as is the double roof comb. An amazing accuracy, however, was reached in the length of the building, for although the north wall had fallen, the measurements taken on the site indicated a length of 84 feet 1 inch on the east side, and 84 feet 2 inches on the west"

As if they'd perhaps have been more accurate about certain things, if they had wanted to be?

[Image: 1000px-Rio_Bec_B_Detail1_1994_03.jpg]
A closer look at one of the Rio Bec structure's towers inspires a question:
Q: Why are there so many doorways in ancient America with teeth?
A: I dunno, how many teeth are there usually in someone's mouth?

It might also be a little curious that if I play around with Wikipedia's Venus data (couldn't possibly be worse than Space.com's excuses for space data, right?) 

Venus Synodic Period 583.92 d / Venus Orbital Period 224.701 d  = 2.598664887 = ~360 / (Alternate Pi 1.177245771^2) = 2.597575757

And that actually IS the ratio between two very strong candidates for "Pyramid Pi System" values for these figures

Venus Synodic Period 584.032129? (292.0160646 x 2) / (360 / (1.177245771^2)) = 584.0032129 / 2.597575757 = Venus Orbital Period 224.8373804?

Which is kind of cool with Venus' reputation for tracing a pentagram in the heavens...

[Image: pentagram_of_venus.jpg]

Because we can construct the proposed candidate for the Venus Orbital Period from two constants closely related to pentagonal geometry: (360* / 5 = 72*), and our "Pi Pyramid Phi" 1.61882914

1.61882914 / 72 = 224.8373804 / 10000

I really want a better idea how all this would fit together, but the questions are probably inevitable given ancient observance of a Venus Cycle stated to be twice the value of the Mayan Long Count (37960 days / 2 = 18980 days)

http://www.chichenitza.com/listingview.php?listingID=49

"Venus also cycles through 5 distinct patterns of movement as viewed from Earth while it moves through these four positions, from evening to morning with 2 periods of invisibility in between. Because of this Mayas devoted 5 pages in the “Dresden Codex to Venus” (one of the Mayas codices) and each page has 13 lines showing 584 days and so for a total of 37.960 days. This is the time which takes the Tzolk’in to correlate to the cycles of Venus and the Sun.

Total 37.960 days = 2x52 or 104 years = 146x260 (Tzolk’in) = 65x584 (Venus) = 104x365 (Sun)

Mayas calculated these five Venus years equal solar years:
5x584 (Venus) = 8x365 (Sun) = Total 2.920 days

Cycle of 2.920 days correlates with 99 lunar months which mean 39, 5 days and 13 sidereal which means 225 days Venus orbits. Mayas also tracked other planets’ movements not just Venus, including those of Mars, Jupiter and Mercury."

Any idea what that is by the way? I found it very interesting after going on about a 887.6223994 look-alike that may also be deliberately present at Tikal, namely 889.5302180...

2 / 224.8373804 =  889.5302180 / 100

But just so I'm sure to be confused sooner or later, 365.020081 / 224.8373804 = 1.623484851 = 1.622311470 x 1.000723277....

Even after 1.177245771^2 x 1.622311470 = 224.8373804 / 100

Hmmmm.... Its it a question of which numbers go with which equations again?

Lovely number, though... 360 / 224.8373804 = 1.601157242, which I'm extremely glad to see. It's 1/3 of Yoda's height for the Great Pyramid / 100. Makes a much better mathematical probe and more interesting number in general than 16 x 10^2.


Several other things I'm rather intrigued with in ancient American archaeology are 

[Image: 440px-Votive_Pyramid_La_Quemada.JPG]
The "votive" pyramid at La Quemada (Chicomóztoc)

[Image: caballitoblanco06.jpg]

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"Structure J" at Monte Alban

Curiously, I am still in search of data on either one, although I did have the good fortune that Daniel Schavelzon (I like this guy!) gives us what looks like data for another novel and possibly related architectural structure, at the Caballito Blanco site 

Caballito Blanco Mound O, Oaxaca, Mexico: A New Plan

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"Mound O" at Caballito Blanco 
Why can't I find data like this for the much more famous "Structure J" at Monte Alban?

Soon as it gets figured out whether these are meters or feet, we might just have something here?
"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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Memoirs of a Pi Jedi
Chapter Ten
Loitering in Doorways
(Postcard from Tikal #2)

(A long time ago, on a continent so close I'm actually standing on it...)

Dimitrios Dendrinos has a paper out on the geometry of the La Iguana pyramid at the Guachimontones site. I don't suppose it's terribly brilliant mathematically, but I did find it helpful - it's actually inspiring the way he managed to extrapolate so much data from one or two stated measurements and photographs. It's a terribly risky thing to do (and of course I linger over why we're having to do so) but having done a fair amount of work on La Iguana now, it's very possible that we actually did get a good piece of data. 

My model isn't finished - like the Tikal temples, I have some hand-drawn diagrams so covered in notations that they're hard to actually make any sense of - and there is still a bug to work out. Specifically, Dendrinos treats the mound as if it were a conical structure, but the fact that it's a stepped structure may mean that if you project a cone that touches the upper edge of each step, it will overshoot the base perimeter - or that if you project a cone from the true base perimeter of the lowest step, it will undershoot the perimeter of the truncated summit. Dendrinos estimates a slope angle of 34* but I'm curious if it will be 30* once the bug gets worked out, which may put La Iguana into a class of ancient monuments that contains true conicals like Silbury (slope angle 30*), Grave Creek Mound (as we have traditionally interpreted it), and others - kindred of the Chephren Pyramid (angles 30*, 60,* 90*), if you will, in embodying the Pythagorean Theorem.

The model I've made thus far is very curious - it reads so much like a basic Yoda reading at first, I'd swear I was back in Pi Jedi Kindergarten... But it may have its reasons for displaying some simple numbers besides just starting off simple for simplicity's sake. If I'm not mistaken, it may indicate that ancient American architects placed high value on decimal harmonics (same string of digits regardless of decimal placement) of

12 Pi^2 = 11.84352528

Hopefully there will be more details to follow on La Iguana when things get worked out, but keep an eye on that number - it may be almost as easy to underestimate as Yoda Himself.

Also, I've been making data tables, trying to get a better grip on ancient calendar systems. I've discovered several formulas that might help, and I'm trying to see where those may lead to. It occurred to me that the number 52 is not only involved in building the Long Count of the Maya, but also in breaking down the year into weeks of seven days as we do in the here and now, so it may be a good opportunity to learn more about ancient approximations of 52 and 7 both.

Let me just say that while 259.7575761 (that's 2 Cholulas x (Pi^2) aka 129.8787880 x 2 and etc) may be useful as 260 in constructing the Long Count, it seems to be rubbish at breaking down any candidate for a year of c.a. 365 days into a useful number of days in the week. I presume the most important numbers that will come out of that study will be the ones that are helpful in constructing a Long Count and breaking down the year into weeks both, but one of those looks to be the value derived as a Great Pyramid "Apex Displacement Ratio" fraction and I've already introduced that here.

Meanwhile, my new hobby being Loitering In Ancient Doorways, let's indulge in that pastime a bit more, shall we?

I've previously described how the doorway of Tikal's Temple II seems to serve as an advertisement for Yoda's "Alternate Pi" (1.177245771) and how George Andrews' width measurement appear to corroborate Maler's measurements which give us what looks remarkably like 1 Squared Yoda Megalithic Yard (7.396853331 ft) as the width, and I've described the rest of the measurements that make it into a billboard advertisement for Alternate Pi. I've stated that preferentially, the width and height of Tikal's temple doorways should not only give an interesting ratio by division (Alternate Pi in the case of Temple II), but an interesting product as well so that we can better recognize them as premeditated acts of arithmetic, but I haven't said much more about that yet, so let's have a closer look...

Ratio = Height 8.707914303 ft / Width 7.396853331 ft = 1.1772245771 Alternate Pi
Product =  Height 8.707914303 ft x Width 7.396853331 ft = 64.41116492

And just what the heck is that? Well, I've also said that the immediate mathematical environment of Tikal Temple I and Temple II may include 1/3 of Pi, that it may be found guiding the proportions of the tiers of both temple pyramids in any finished models of them. Shall we? 

Pi / 3 = 1.047197551
  
64.41116492 x 1.047197551 = 67.45121417 (Radian x Alternate Pi)
64.41116492 x 1.047197551^2 = 70.63474631 (One of Yoda's Tikal "Grid Values" a remarkable number: aka 6 x Alternate Pi)
64.41116492 x 1.047197551^3 = 73.96853336 (Squared Yoda Meg Yard again)
64.41116492 x 1.047197551^4 = 77.45966692 (the powerful probe sqrt 60)
64.41116492 x 1.047197551^5 = 81.11557352 (Alternate Phi 1.622311470 / 2 x 10)
64.41116492 x 1.047197551^6 = 84.94402995 (1 / Alternate Pi x 10^n)
64.41116492 x 1.047197551^7 = 88.95318016 (I've been talking about that one, haven't I?)
64.41116492 x 1.047197551^8 = 93.15155243 (and that one too 93.15155243 / 24 = 38.81314685, which may be featured atop Tikal Temple I as seen in Yoda's diagram previously posted)

Keep in mind that I was not even aware of this progression when talking about  88.95318016 and 93.15155243.

Believe me, I really wish I could just randomly stick any two of our "Pyramid Pi" numbers together or even a good pair with a nice ratio, and get such magic to spill forth. That sort of has deliberate written all over it, if you ask me.

So there is some more of what I mean about the role of numbers in relation to their immediate "mathematical environment" in a setting such as Tikal, and it's a substantial portion of what makes me think that Yoda and I might have actually made the right calls on the original and intended measurements of Temple II's doorway.

Now I've admitted that in spite of what seems like a blatant advertisement for Alternate Pi, I really don't know what any other temple doorways at Tikal are saying, so it still looks like maybe we just got really lucky once and found a pair of numbers randomly stuck together that make us think we're onto something. We could really use more examples of this kind of thing so anyone including us Pi Jedi ourselves, might feel more assured we're not barking up the wrong tree.

Well, let's have a try at loitering around the doorway of Temple III for a minute...

Here's the data I currently have available

T3 Doorway 1 - Width 395 cm = 12.95931759 ft (Maler); 390 cm at rear = 12.5656167 ft, 383 cm at front (Andrews)
T3 Doorway 1 - Height 333 cm = 10.92519685 ft (Maler); no data given (Andrews)

It's a little shaky with a slight discrepancy in the data sets for the width, but there may be a good possibility this indicates an irregular structure just as Andrew's data appears to indicate variability between exterior and interior widths. Not only by experimentation but by comparison, either data set generally seems rather reliable for small measures, so I'm going to go with Maler's call on this one.

Fingers crossed, but I think I just might know what the basic blueprint is giving us here

Tikal Temple III Doorway: Width 12.98787880, Height 10.96622711
Ratio: 12.98787880 / 10.96622711 = 1.184352528 (12 x Pi^2 / 10)
Product: 12.98787880 x 10.96622711 = 142.4280364 

So there's 12 Pi again (I've worked on all of four ancient American monuments now and in an extremely incomplete capacity, but there it is again), and the simplest kind of fraction of the Long Count building 259.7575752-as-260, divided by 2, along with 1.1111111111 x Pi^2 = 10.96622711, which may be an integral part of the exterior dimensions of Temple II pending confirmation in a more complete and verified model of Temple II's exterior

What is 142.4280364? That was the Zillion Cholula Dollar Question. I've really only seen it once before. I've known these were the likely specs for at least several weeks now, but I myself am still only a pitiable upstart of a Pi Jedi who's been having an ongoing pouting festival because I cannot find a way to make it come out 142.1223034. That is after all Yoda's "Holy of Holies" (4523.89341 / 100) x Pi. It's gotta be that, right? What else could it be?

Well, it could be 142.4280364...  I only have one alias for it logged in my puny little catalog of constants, whereas I can more often spot a good number right away because interesting aliases have already been piling up in the log.

For the record, it is ((1 / 675) x Pi^5) / 10^n... And we know that 675 turned up on my first basic table of ancient measurements and how successfully they can or can't measure the world in either simple numbers of units, or at least interesting numbers of units...

Let's try to further our understanding a little by inquiring with the "immediate mathematical environment"

142.4280364 / (Pi^3) = 136.0087562 (the "Alternate e' Meg Yard" / 2, also one of Yoda's "Hall of Records" coordinates)
142.4280364 / (Pi^3)^2 = 129.8787951 (again, already)
142.4280364 / (Pi^3)^3 = 124.0251134 (half of Yoda's Great Pyramid Grid Point, let me tell you about that sometime...)
142.4280364 / (Pi^3)^4 = 118.4352592 (12 Pi^2 x 10 -- that too again, already)
142.4280364 / (Pi^3)^5 = 113.0973417 (360 Pi / 10)
142.4280364 / (Pi^3)^6 = 108.0000000 (the other rational number outstanding in my geodetic tables)
142.4280364 / (Pi^3)^7 = 103.1324031 (generic Area of a Circle / 100)
142.4280364 / (Pi^3)^8 = 98.48419584
142.4280364 / (Pi^3)^9 = 94.04547951

I don't have comments handy about the last two numbers but they should be familiar even to freshmen at the Pi Jedi Academy like myself, so they do count as recovered data.

Lately, I've been experimenting with Venus data. I wouldn't know a star from a planet personally any more than I know where to look for good data on them, but the numbers I've based on a Wikipedia entry like a reckless ass do have a way of standing up for themselves...

They're also an intriguing indicator about the role of Alternate Phi vs Phi Proper, since we can do equations with them using Alternate Phi 1.622311470 that I'm not sure we can get away with using Phi Proper 1.618033989.

Proposed Venus Orbital Period (VOP) 224.8373804 x 1.622311470 = 364.7562612 one form of earth calendar year?
Simplified Venus Orbital Period (SVOP) 225.0000000 x 1.622311470 = 365.020081, our premiere form of earth calendary year

That's after we have constructed 224.8373804 out of 72* and "Not-Phi" 1.61882914 as 1.61882914 / 72 = 224.8373806 / 10^n...

The big incentive though for me dinking around with Venus data is that the Long Count of the Maya is rumored to be half of a "Great Venus Cycle"

http://www.chichenitza.com/listingview.php?listingID=49

"Venus also cycles through 5 distinct patterns of movement as viewed from Earth while it moves through these four positions, from evening to morning with 2 periods of invisibility in between. Because of this Mayas devoted 5 pages in the “Dresden Codex to Venus” (one of the Mayas codices) and each page has 13 lines showing 584 days and so for a total of 37.960 days. This is the time which takes the Tzolk’in to correlate to the cycles of Venus and the Sun.

Total 37,960 days = 2x52 or 104 years = 146x260 (Tzolk’in) = 65x584 (Venus) = 104x365 (Sun)

Mayas calculated these five Venus years equal solar years:
5x584 (Venus) = 8x365 (Sun) = Total 2.920 days

Cycle of 2.920 days correlates with 99 lunar months which mean 39, 5 days and 13 sidereal which means 225 days Venus orbits.
Mayas also tracked other planets’ movements not just Venus, including those of Mars, Jupiter and Mercury."

37,960 days / 2 = 18980 days - so the Long Count and the Great Venus Cycle are really sort of the same thing, simply multiplied or divided by 2.

I've reported finding a little too much lately of what looks like Alternate Pi^2 for my own good, including the still unconfirmed finding at Rio Bec from Andrews' data...

Could part of the reason for a premium on 1.177245771^2 be because we can use it, and Alternate Phi, to construct the proposed VOP (as we saw previously)?

(1.177245771^2) x 1.622311470 = 224.8373804 / 100

So let us now inquire, what does our mysterious Temple III doorway product 142.4280364 know about Venus? 

Dunno... It doesn't seem to like 225 (SVOP) any... Does it speak to 224.8373804 (VOP)?

142.4280364 x 224.8373804 = 32023.14660 = (1.601157330 x 2) x 10^n = (ht Great Pyramid (Yoda) / 15) x 10^n
142.4280364 x 224.8373804^2 = 72.00000000 x 10^n
142.4280364 x 224.8373804^3 = 1.61882914 x 10^2

142.4280364 is a direct extension of the progression that can be used to generate 224.8373804 in the first place.

Never in my years of crunching numbers have I seen such a happy set of "coincidences" - at the risk of being in error, I am perfectly prepared to salute the extraordinary excellence of ancient American arithmeticians.

So we have seen why we might find (12 Pi^2) = 11.84352528 in an environment of (Pi / 3)... Is there a good reason we might find 11.84352528 in the context of mathematics related to Venus?

224.8373804 x (12 Pi^2) = 2662.867201 x 10 (a wonderful number that Yoda and I am always happy to see)
224.8373804 x (12 Pi^2)^2 = 3153773.501 (we've already had some discussion about this number at Giza and in ancient Britain, it's the number of seconds in a calendar year of 365.020081 days)

Now watch this...

224.8373804 / (12 Pi^2) = 18983.99127 / 10^n - our most accurate contender to date to represent the Long Count of 18980 days aka 1/2 Great Venus Cycle

225.0000000 / (12 Pi^2) = 18997.72193 / 10^n - the nominated version of the Long Count that translates effectively into hours, days, and seconds.

More "coincidence," or some ancient indigenous Americans literally counting rings around the likes o' me?
"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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Doing some work on the geodesy tables again today, including trying to add different candidates for the "Palestine Cubit" to put them to the test geodetically... All eleven of them... Not exactly fun but maybe it will help thin down the herd a bit?

Here is a little more that I just stumbled across, concerning the Width x Height products of the exterior doorways of Temple II and Temple III as proposed...

Temple II Outer doorway - Product:  Height 8.707914303 ft x Width 7.396853331 ft = 64.41116492
Temple III Outer doorway - Product: Height 10.96622711 x Width 12.98787880 = 142.4280364 

We already saw how 142.4280364 relates to the proposed Venus Orbital Period of 224.8373806 - it's part of a progression extended from its origin from "Not Phi" and 72, pentagonal constants both, that allows the value to the proposed orbital period clear to the third power to be showcased, which is already an almost preposterous level of demand to place on a set of doorway dimensions...

But the temple doors of Tikal are not done talking yet...

64.41116492 / 224.8373806 = 28.64788976 = 1/2 Radian = 57.29577951 / 2

Well, if there's going to get out a Giza Site Constant (i.e., the Radian)... 

142.4280364 / 57.29577951 = 24858.38182 / 10000 = proposed figure for Polar Circumference of Earth in miles

And I should have known this, but I was so pleased that the 1.00387728 ratio between truncated and untruncated Great Pyramid apothems (slope length at center of a side, from base to apex for complete pyramid) has geodetic value when you throw what is probably the most obvious constant at Giza, 2 Pi...

That I must have let my curiosity lapse (either that or I'm crunching so many numbers lately that I'm starting to forget some fairly unforgettable things)...

We already saw that 1.00387728 x (2 Pi)^3 = 24901.19742 / 10^2, system valid Equatorial Circumference of earth...

It turns out that that equation is only part of a longer chain, that remarkably starts with the cube of Alternate Pi...

(1.17725771^3) = 1.631553867
1.631553867 x (2 Pi^2) = 64.41116492
1.631553867 x (2 Pi^6) = 64.41116492 x (2 Pi^4) = 100387.7284
1.631553867 x (2 Pi^9) = 64.41116492 x (2 Pi^7) = 24901.19747 x 10^n Equatorial Circumference in miles

So in spite of a possible minor obsession with Venus and calendars, the Tikal pyramids may still turn out to be perfectly serviceable geodetically...

In fact, I think even Chinese Cleopatra must be pretty impressed with Tikal and the wheelbarrows full of important numbers that are spewing out of so little as the measures of two doorways and 1/3 of Pi. I certainly am - I know the ancients Egyptians did some incredible work but I've literally never seen anything like this before.
"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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Memoirs of A Pi Jedi
Chapter 11.11111111 (Part One)
Measuring Up... 

On page 4 of Yoda's "The Master Code Book" are found these bittersweet comments

"By the time the Pyramid age had eroded down from the Babylonians, the mile had degenerated from the 5280 feet to 6060. Alexandria had it as 5238 feet, India used 5265 feet - which ancient Europe used. By then the original mile was lost.

The 12-inch foot was likewise eroded by the time Greek metrology was penned. Their "foot" varied between 11.671 inches to as much as 13.779 ft. They could not find it.

As for the inch, Professor F. Petrie covered that in his Inductive Metrology where, on page 111 the wrote, "The inch, as now in use, has not varied by any appreciable amount, on the average, for centuries".

What a mess to sort out. So after digesting a dozen books on this very boring subject, I turned to the ancient global grid system..."

Well, he's got me there. I've read one book on ancient metrology and thankfully it was Berriman's. What Yoda doesn't seem to realize is the possibility that these are NOT degenerated measurements, but deliberately chosen geodetic units and monument decoding keys. I don't have much trouble seeing that, so unfortunately it looks like the biggest victim of Yoda's Map Crap is Yoda Himself. That's really sad because he remains the greatest Pi Jedi the last century and the current one have ever seen.

I might have posted such a link before, but just to make sure... This website probably has a lot to offer including a lot about Prof. Thom's circle geometries, if you watch out for the Urdummheitery - you know, "the ancients were so clever that they created thousands of complex alignments accurate over hundreds of miles, yet they were so stupid they had to do their Ancient Rocket Science in simple fractions". God how that drives me up the very same wall I will probably throw Richard Heath's books at when they get here. 

As if 2/3 of a Royal Cubit were so hard to remember that you need to invent an inaccurate fraction?

http://megalithicscience.org/index.php/n...-metrology

I'm already pissed enough that John Michell's must-read work "The Measure of Albion" is going for around a hundred dollars. Would any of these Urdumheiteers know Pi if it bit them on the Pi Hole? Remind me sometime to help stamp out Urdummheit by helping to turn it into an institution...

What I did instead is to spend forty dollars on my very own copy of Marquina's "Architectura Prehispanica" instead of borrowing one in perpetuity, so I could get a face full of my other favorite heartbreak, which is 1000 pages of the most amazing architectural diagrams, shrunken down so their scale bars are meaningless and their measurements are unrecoverable. It takes DATA to make scale drawings and models - WHERE IS THE DATA?

Here's a sample from "Megalithic Science" with my comments added. I can't guarantee that I've provided the right figures, but it only took me about two minutes to come up with them so who knows what I could do in ten minutes.

Not knocking them, really - these people are smarter than me, no doubt about that, and they do plenty of worthwhile work - but I really think they're probably barking up the wrong tree when it comes to metrology, AND math. I would so love to see what their work would look like if they weren't. Not trying to be a pr*ck, honestly - just trying to be helpful, but I always seem to end up paying for that privilege...

The Twelve Main Measures 
COMMENTS: Where's the Remen? Stonehenge is swimming in the damned thing!!!
There are twelve main measures and usually any measure found is a variation (see later) of one of these rather than the root value. Each root value forms what is called a module. Neal and Michell have identified TWELVE MODULES: 
COMMENT: I have identified 12 Noodles. I have added a spice packet and named it Top Remen. 
Quote:Assyrian Foot 9/10 = 0.9ft When cubits achieve a length of 1.8ft such as the Assyrian cubit they are divisible by two, instead of the 1 ½ ft division normally associated with the cubit length. Variations of this measure are distinctively known as Oscan, Italic and Mycenaean measure.
COMMENTS: They may have actually gotten one right?!?!? An easy one, or Beginner's Luck?
Quote:Iberian Foot 32/35 = .9142857ft This is the foot of 1/3rd of the Spanish vara, which survived as the standard of Spain from prehistory to the present.  
COMMENTS: Apparently it's called the "vara" because it's too damned "vara-iable" to nail down. No Pi Jedi has ever done it that I know of, and fewer have cared to. Meanwhile, 1/ (108 / (Pi^2) / 10) = .913852259. At least Michell knows what 108 is at least as far back as View Over Atlantis, so it's apparently Pi he's never heard of.
Quote:Roman Foot 24/25 = .96ft Most who are interested in metrology would consider this value to be too short as a definition of the Roman foot, but examples survive as rulers very accurately at this length.
COMMENTS: sqrt 240 x (2Pi) / 100 = .9733868822 = 4/5 of 1 Remen 
Quote:Common Egyptian Foot 48/49 = 0.979592ft One of the better-known measures, being six sevenths of the royal Egyptian foot. English/Greek Foot 1ft The English foot is one of the variations of what are accepted as Greek measure, variously called Olympian or Geographic. 
COMMENTS: sqrt 240 x (2Pi) / 100 = .9733868822 = 4/5 of 1 Remen 
Quote:The English and Greek Foot 1 = 1.000000 ft Defined from the Equator of the Earth as one 360,000th of a DAY (angular movement of the Sun in a day) whilst also being one seventh of 1/126th of the mean Earth radius - see chapters 3 and 4
COMMENTS: When someone actually figures out how big the equator is, let me know. It not only depends on mapping datum, geoid height, etc - but it seems to have shrunk from 24901.55 to 24901.461 in the mere 10 years since I was at this last, bringing the error for the ancient ESTIMATE 24901.19742 down from .3525 mi to .2625 mi error, now within about 1400 feet of contemporary figures. 
Quote:Common Greek Foot 36/35 = 1.028571ft This was a very widely used module recorded throughout Europe, it survived in England at least until the reforms of Edward I in 1305. It is also the half sacred Jewish cubit upon which Newton pondered and Berriman referred to as cubit A.
COMMENTS: 1 / .9733868822 = 1.02734074 so now we apparently have to give it a new fancy name like "Reciprocal Egyptian Foot" if we want into the John Neal Top Secret Academy.
Quote:Persian Foot 21/20 = 1.05ft Half the Persian cubit of Darius the Great. Reported in its variations throughout the Middle East, North Africa and Europe, survived as the Hashimi foot of the Arabian league and the pied de roi of the Franks.
COMMENTS: Still working on a whole basketful of "Persian Cubits," thanks. Meanwhile, (Pi/3) = 1.047197551. Turns the whole world into Tikal.
Quote:Belgic Foot 15/14 = 1.071428ft Develops into the Drusian foot or foot of the Tungri. Detectable in many Megalithic monuments.
COMMENTS: Sure it's not another case of the same unit by a different name to .01 foot difference?
Quote:Sumerian Foot 12/11 = 1.097142ft Perhaps the most widely dispersed module of all, recorded throughout Europe, Asia and North Africa, commonly known as the Saxon or Northern foot.
COMMENTS: (1.1111111111 x Pi^2) / 10 = 1.096622711
Quote:Yard and full hand Foot 11/10 = 1.111111ft This is the foot of the 40 inch yard widely used in mediaeval England until suppressed by statute in 1439. It is the basis of Punic measure and variables are recorded in Greek statuary from Asia Minor.
COMMENTS: They got two right by getting the first one right and then inverting it. Is that cheating? THOTH (aka 1.1111111111) doesn't like cheaters. That's why he invented measures in the first place, so people would get the bag o' weed they're being charged for.
Quote:Royal Egyptian Foot 8/7 = 1.142857ft The most discussed and scrutinised historical measurement. Examples of the above length are plentiful. 
COMMENTS: Looks rather like the Double Radian as a metrological unit, or more to the point, simply 2/3 of the MLM Royal Cubit = 1.718873385 x 2/3 = .5729577951 x 2 = 1.145915590
Quote:Russian Foot 7/6 1.166666ft One half of the Russian arshin, one sixth of the sadzhen. One and one half of these feet as a cubit would be the Arabic black cubit, also the Egyptian cubit of the Nilometer.
COMMENTS: Try (sqrt 135) / 10 = 1.161895004 = Remen / (Pi/3)
To this list can be added a thirteenth,
Quote:Inverse Iberian Foot 35/32 = 1.09375 This module that is 1 part is 8000 different to the present Metre is found at Carnac.
COMMENTS: Invert this noodle: 1 / .913852259 = 1.094268784 unless it's another example of 1.096622711 and someone has made two metrological units out of one again. Question: which one makes a better metrological unit? 
"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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Memoirs of a Pi Jedi
Chapter 11.11111111 (Part Two)
Along a Crooked Mile...

Something that might not have helped us Pi Jedi to recover the ancient mile values, is a curious thing that we find at Giza... Did anyone notice

Equatorial circumference of earth 24901.19742 / Height Chephren Pyramid (Yoda) 471.2388980 = 5284.198212

It's meant to be helpful, but for a long time it seems to have just been confusing. It's continued to be, since the proposal that the Earth was taken to measure 131594725.4 feet as the equatorial circumference and 131407229.2 feet as the polar circumference, in relation to their proposed values in miles, does not seem to be aware of this "Chephren Mile"...

Equatorial: 131594725.4 ft / 24901.19742 miles = 5284.674595 ft
Polar: 131407229.2 ft / 24858.38064 miles = 5286.234494 ft

Both of these are probably fairly obtuse figures by the way - the usual mathematical probes are probably good at overlooking them, even when we can show a bit of pedigree for them such as 

Square Root of the Volume of a Sphere 887.6223994 / (360^4) = 5284.674595 / 10^n

Having tabled out the data at long last, it's easy to see that the "Chephren Mile" of 5284.198212 doesn't really seem to relate to the runner-up values either. 

So what did the ancient Egyptians mean by posting "5284.198212" at Giza?

131594725.4 / 5284.198212 = 24903.44228
131407229.2 / 5284.198212 = 24867.95989

(Wikipedia: Equatorial Circumference 24901.461 mi, Polar Circumference 24859.73 mi)

So using the "Chephren Mile" would have us losing accuracy on both figures, particularly the Polar Circumference...

Now I've seen the figure 24903.44228 before, it appeared in just over a dozen posts on the Grid Point msg board about 12-14 years ago now - all of them mine, because I kept puzzling over it, but it never caught on even with me because 24901.19742 as the Equatorial circumference figure blows it right straight out of the water.

The one outstanding alias that kept 24903.44228 from being thrown out with the trash is

Grid Point Great Pyramid (Yoda) 248.0502134 x 1.61882914 = 1 / (24903.44228 / 10^n)

In actuality, the fruit doesn't fall as far from the tree here as one might think, because

248.0502134 x 1.61882914 = 401.5509137 = 4 x 100.3878248

And we now know 100.3878248 x 10^n to be a fairly potent geodetic figure because, once again,

100.3878248  x (2 Pi)^3 = 24901.19746

But why post a mile that's used to construct a much less useful and less accurate value of 24903.44228 instead?

Well, today's fresh hypothesis is that the Chephren Pyramid is a "Mile-o-Matic 2000" that allows interconversion of the two figures. This also includes the recognition previously expressed that the Great Pyramid has separate "paved" and "unpaved" values, and lovely ratios between Great Pyramid and Chephren Pyramid measures that we will want to preserve regardless of whether the Chephren was dressed with pavement as the Great Pyramid appears to have been.

The height-to-height ratio of the two (Yoda model) is

Height Cheops 480.3471728 / Height Chephren 471.2388980 = 1.019328359

The paved-to-unpaved ratio of the Cheops pyramid is thus far given as 

Height Unpaved 481.0325483 / Height Paved 480.3471728 = 1.001426834

Thus a proportionately scaled Chephren Pyramid whether real or imagined (if it had paving of different thickness than the Cheops, that may be even more data presentation) has a height of 

481.0325483 / 1.019328359 = 471.2388980 x 1.001426834 = 471.9112777 ft

(As with the unpaved height of the Great Pyramid, reasons for its existence slowly begin to accumulate)

And finally, when we line up the more complete data, a remarkable and more versatile set of reciprocating formulas for terrestrial circumference seems to emerge...

24903.44228 / 471.2388980 = 5284.674585 = 131594725.4 / 24901.19742
24903.44228 / 471.9112777 = 5277.144976 = 131407229.2 / 24901.19742
24901.19742 / 471.2388980 = 5284.198212 = 131594725.4 / 24903.44228
24901.19742 / 471.9112777 = 5276.669281 = 131407229.2 / 24903.44228

Including an apparent option to treat the earth as equal in the number of miles in the Polar and Equatorial circumference if we are going to have to use different Polar and Equatorial mile values anyway.

(5277.144976 = 2 / (19.4677376^2) x 10^n, just so we get some Vitamin T today).

Interestingly, while I was poking and prodding the Polar circumference, I "discovered" something. I use the term "discovered" more loosely than ever, this must have been discovered a zillion times already but I cannot think of where I have ever seen it. It will be a sad day if the Pi Jedi really beat the Phi Jedi to this, which I doubt very much...

Even I respect Phi Proper as a worthy number with amazing properties even if I don't dabble in it myself

But the square root of 10 Phi = sqrt (1.618033989 x 10) = 4.022479321 = 1 / (24860.28939 / 10^n)

(Wikipedia: Polar Circumference 24859.73 mi)
 
Not that Phi wasn't already amazing, but do you suppose that little trick helped to spark ancient interest in the Golden Ratio?

I also learned another neat little trick today which is very similar. We know that the closest valid approximation to the Great Pyramid base diagonal (Yoda model aka paved model) is 1067.077725 and we discussed how the ancient Egyptians might have tweaked one of the Great Pyramid corners to get one of the actual diagonals to come out the sacred geodetic constant 1.067438159 x 1000 in feet.

Then we did a cool thing at Tikal and acted like we were at Giza, and threw 2 Pi instead of (Pi / 3) at the doorways that have been worked on so far...

Turnabout being fair play (so I've heard), if we act at Giza like we were at Tikal and throw (Pi / 3) instead of 2 Pi

1067.077725 / (Pi^3)^6 = 8.09141258 x 10^n = (1.618282516 x 10^n) / 2

And that IS the square of our best known Pi Jedi version to date of the Polar circumference

sqrt 16.18282516 = 4.022788232 = 1 / (24858.38036 / 10^n)

Hence the Great Pyramid (paved model) may have a geodetic base diagonal whether or not they actually tweaked it, and if they did tweak it, it may have two different ones.

Lastly, a word of caution as if anyone really needs it - I was looking at one of the Thom diagrams at the Megalithic Science site and was reminded that some of the circles are a bit roughed up and the scale of Thom's projected geometry may not always be the best fit. I'll try digging in my electronic texts some more and see if I can come up with anything more useful than that. 

One thing I remember doing when working with some of Prof. Thom's data for unflattened circles was to make a set of tables showing some of what would make for spiffy circle proportions. Fingers crossed I got as far with doing something similar with flattened ones, but even then I seem to recall it looking like the measures of a fair number of the unflattened rings might have been significantly affected by their present condition.
"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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Oh, speaking of that lovely Giza ratio 1.019328359 - what if Yoda apparently getting 1.01740345 (Radian x SRVS) / 10^n and me hedging bets on 1.017876020 ((Area of a Circle x Pi^2) / 1-^n) were both wrong on the Tikal doorways? Still too soon to tell, I'm still seeing fresh support for Yoda's figure...

But if there's one thing I've learned to do at Tikal, it's fling 1/3 of Pi, and in the end it may all come down to which one responds to that best.

Even that often murky figure that appears to be atop Temple I as the platform width in Yoda's diagram (38.81314681 = (2 / 1.618829140) x Pi x 10) responds to this to some degree

38.81314681 / (Pi / 3)^2 = 353.9334579, proposed figure to represent the number of days in a Lunar Year for the "Pyramid Pi" system.

38.81314681 / (Pi / 3)^4 = 3.227486119 = (1 / sqrt 960) x 10, as used in the interpretation of the Aztec Sun Stone.

38.81314681 / (Pi / 3)^5 = 3.082022222 = 1.541011111 x 2 = 33.33333333 / 1.081540981 = 1.027340739 / 33.33333333 = 6 / 19.46773764 = (1 / (19.46773764 x 33.3333333)) x 2 = 1 / (1.62231147 x 2) = etc

Readers may also recall that the proposed Venus Synodic Period of 584.0321292 days may be constructed 19.46773763 / 33.3333333 = 584.0321292 / 10^n, or as twice the cube root of the earth's Equatorial circumference in miles / 10^n

2.920160646 x 2 = 5.840321292 - or if you prefer, as 480 Remens - 480 x 1.216733603 = 584.0321292
"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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Good news, I have found what I did with Thom's books. I hate to do much with Megalithic monuments without having the full texts at hand. Don't know what will get done now but being equipped is a start. If I don't find where I left off at least I have the tools I need if I have to start over.

I'd especially like a closer look at the sites that inspired him to propose additional Meg yard values. Obviously you can get that if you're trying to force a measure to be a rational number of units when it isn't, but on the other hand the multiplicity seen in other proposed ancient units of measurement (and in the act of measuring itself) may well mean he was onto something nonetheless. I'm very curious to see if we can sort that out.

Regarding whatever unit it is that is about 2.09-2.10 something feet, I think I've seen it called a Palestine Cubit, an Assyrian Cubit, a Syrian Cubit, a Persian Cubit and a Hebrew Thingamabob even for still being largely a newcomer to metrology. Make it easy on the new guy, eh?

While I'm at it I might as well review the hypothetical units of measure that serve geodetically in rational numbers. Bear in mind that this is a different thing than units that give significant numbers, and I'll give an example of that too.

Equatorial circumference as 131594725.4 feet
= 40000000.00 x "Third Meter" of 3.289868134 ft
= 108000000.0 x "Thoth Remen" of 1.218468679 ft
= 62500000.00 x "Persian Test Cubit t2" of 2.105515606 ft 

Polar circumference as 131407229.2 feet
= 40000000.00 x "Fourth Meter" of 3.285180728 ft
= 108000000.0 x "Standard Remen" of 1.216733603 ft
= 6750000.000 x "Assyrian Cubit" of 19.4677376 ft
= 62500000.00 x "Persian Test Cubit t3" of 2.102515666

Several additional units in this range provide what is possibly the most dramatic example of units that give meaning values as geodetic measures, as opposed to simply giving rational numbers.

Equatorial circumference as 131594725.4 feet
= 62831853.11 (2 Pi x 10^2) x "Persian Test Cubit t5" of 2.094395102 ft

Polar circumference as 131407229.2 feet
= 62831853.11 (2 Pi x 10^2) x "Persian Test Cubit t6" of 2.091411007 ft

So there are at least four hypothetical "Persian/Assyrian/Syrian/Whatever" cubits in this range of ~2.09 - 2.10 feet having possible geodetic value in this scheme.

In fact, the possibility of the earth itself measuring "2 Pi" (x 10) anything, if Giza, Home of 2 Pi in Pi Jedi lore, actually recognizes the measures involved with good responses, seems very enticing.

Still, the raw value I started with, in accordance with the Vesica Piscis scheme (as previously seen)

Remen 1.216733603 x sqrt 3 = 2.107444419

One or both of several candidates in closer proximity,

2.107038476 = sqrt 240 / (225 / Pi^2) and
2.107850446 = 225 / 1.067438159

may have value in measuring monuments. That could really still use a recent and more careful look. At least we've hopefully been able to assign some value to some of the candidates here. With luck, we'll be able to keep it down to just six of them. :-)

Regarding the new formulas I stumbled upon that I'm testing, I still don't know if they're any use, but the most complicated of them goes like this

a. Divide the number of days in a year into twelve equal months
b. Divide 1 by the number of days in a month to obtain a meter / 10^n
c. Divide the meter by 4 to obtain the reciprocal of a remen

For example

365.0200808 days / 12 = 30.41804008 days 
1 / 30.41804008 = 3.287490367 ("Fifth Meter") / 10^2
3.287490367 / 4 = (1 / Standard Remen 1.216733603 ft) / 10

and 

364.7562611 days / 12 = 30.39635509 days 
1 / 30.39635509 = 3.289868134 ("Third Meter") / 10^2 
3.289868134 / 4 = (1 / putative Remen of 1.215854204 ft)  / 10

and

365.5409038 / 12 = 30.46174197 days
1 / 30.46174197 = 3.282806351 ("First Meter") / 10^n = (Radian^2 / 1000)
3.282806351 / 4 = (1/ Thoth Remen of 1.218469679 ft) / 10

I'm actually rather surprised which parts go together with which in this scheme. If we were actually supposed to do this, it might be a vote of confidence for the "First" and "Fifth" meters, and for another Remen of 1.215854204 (12 / Pi^2) feet
"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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Just puttering around a bit today... 

Trying to figure out just how finished a study of the more obscure Thom Type B modified flattened ring ever got, and going over it again to see if I come up with any alternative ideas about it by starting fresh.

A lot of things have still not been done with these circles, and that includes reworking their geometry based on proposals for intended values to see how the whole things turn out (would be nice to have a script where you can put different values into boxes on a page and have it recalculate the whole thing for you). 

Undone deeds also generally include a lack of actual examples. I need to dig in the literature and find out if more than one example of the Type B Modified Ring was very found. Probably, but very short on subjects for a comparative study currently. The only example I've located in the literature so far is Whitcastle(s), data not handy. Worse, I presume it's this one and it doesn't look to be in that great of shape
https://en.wikipedia.org/wiki/Whitcastles_stone_circle

We even have questions remaining about the intent of rough-hewn materials. Were the ancient Brits really so far behind everyone else that they couldn't have come up with smooth-cut finished stones that lend themselves to more exact measurement and reconstruction, or does the rough-hewn construction say to us, "Don't bother measuring it exactly, there is more than one right answer intended"?

What has set off this alarm most lately is that with five possible meters to consider, all of which may have a time and place for correct use, the thickness of the Stonehenge sarcen circle appears to be "one meter," just as four of five Tikal temples appear to be resting on platforms of "two meters" but it may remain an unanswered question which one where and when. There's also a hint of a meter of some kind embedded in the generic design of the Type B modified ring. Also, there is Phi Proper to be found in Thom's geometry for the Type B Modified Flattened Ring, so I'd love to see what someone like Vianova could do with interpreting something like that, mine may not be the only valid interpretation, just like at Giza.

The data on Megalithic circles has never been scrutinized properly for calendrical, planetary, or even geodetic data by Pi Jedi that I know of - some of that data is in fact pretty fresh with more still just coming into focus only now. What does a circle that's flattened on one half mean, anyway? Does it dramatically represent equatorial and polar ("flattened") circumferences, or does the design trend have some other meaning?

I tried to dig up the history of the proposed Venus Orbital Period 224.8373803. I really don't want to be taking credit for someone else's work. I could only find three posts on it in my main archive of Grid Point points, all three by Michael Morton who amazingly cited it as a Grid Value for Venus in regards to his "archaeo-sky matrix" concept, and no citations for a Venus Orbital Period proposal before although I could swear having the conversation with him about the symmetrical framing with "Alternate Phi"

364.7562611 / 1.622311470 = 224.8373804 Proposed Venus Orbital Period
224.8373804 / 1.622311470 = 1.177245771^2 x 10^n

But I don't think either of us dreamed at the time that some ancients may have used 364.75626211 as a calendrical figure, so possibly we both just scratched our heads and moved on? So thus far, I don't have any old posts just brimming with equations that point to it that I can copy and paste to provide more background on it, sorry.

Also I think "herpetometry" is trying to rear it's ugly head again, I think it was the reptile references relating to Ehecatl got me thinking about a Midgard Serpent that encompasses the earth - that wouldn't happen to refer to measuring the earth's circumference by any chance?

And 14.24280287 given as the product of Width and Height of the doorway of Tikal Temple III, did any of our home viewers notice that "Le Serpent Rouge" serves as a shortcut to it? Using, guess what, Alternate Pi as starting material

"Le (so-called "Serpent Rouge" constant) 1.676727943 / 1.177245771 = 1.424280286

Not half bad for a number that was mistakenly pasted on the poorest excuse possible for a French Serpent Mound, in a fashion that couldn't have been more dimwitted of me.

Mostly what I've done since last post is re-examine the proposed imaginary ratio-preserving imaginary rescaling of the Giza pyramids based on the paved/unpaved Great Pyramid model to try to make sure this makes sense, and to see again how well geodetic concerns have been served. I'm actually fairly pleased with the results, including that the figure of 353.9334564 proposed for the Lunar Year seems to continue to accrue support. It is for one thing 1/2 of the base length of the rescaled Chephren Pyramid:

Height 471.2388980 ft (150 Pi) x scaling ratio 1.00146834 = 471.9112752 ft
Perimeter / Height ratio = 6
471.9112752 ft x 6 = Perimeter 2381.467651 ft
Side Length = Perimeter 2381.467651 / 4 = 707.8669128 ft
1/2 Side = Perimeter 2381.467651 ft / 8 = Side Length 707.8669128 ft / 2 = 353.9334564

35.39334564 also appears to be the likely intended value for the apothem length of the Great Pyramid's pyramidion after being subject to truncation along the apothem proportionate to that exhibited by the whole pyramid.

Definitely some new geodetic formulas I'm seeing... Did you know that the Height of the Great Pyramid in Royal Cubits according to the traditional data 279.4546572 MLM Rcbts (279.4546572 was also known as the "LCS" constant, with the L standing for "LSR"), is geodetic too? I didn't.

(279.4546572^2) / Pi = 24858.38045 proposed valid estimation of Earth polar circumference

How about this one? Rescaled Chephren Height 471.9112752 ft x Pi x "LSR" 1.676727943 = 24858.38034

That also came as news to me. There you go, more "reptilian" geodesy, WTF? Try to put away a stupid concept and see what happens. Want to place bets on whether the "Temple of the Double Headed Serpent" at Tikal might turn out to be the "Temple of Equatorial and Polar Circumference"? Actually does beat hell of thinking they just had tacky taste in decor, I guess?

Oh, and LSR x Pi = 5.267596188. What's that? Why, if it isn't the reciprocal of the more accurate of two proposed values for the Long Count of the Maya.

1 / 5.267596188 = .1898399126 = ~18980 / 10000

So we can write that forwards as 471.9112776 / 18983.99126 = 24858.38047 / 10^n

24858.38047 may not have a valid square root (none that I have logged, anyway), but curiously

sqrt (24858.38047 / Pi) = 88.95318015 = 2 / (proposed Venus Orbital Period 224.8373804) / 10^n

So this 889.5318015 number and its decimal placement variants may be serving both the calendar and geography/geodesy at Tikal.

About this "lovely ratio" 1.019328359 between the Heights of the Great Pyramid and Chephren Pyramid that is undergoing attempted conservation with this imaginary (?) rescaling of the great Giza Pyramids in order to retain it and other very pleasing ratios between pyramid proportions, did anyone try it at home and discover that among other wonderous properties, it is a square root?

1.019328359^2 = 1.039030303 = Outer Sarcen Circle Radius Stonehenge 103.9030303 ft / 100

I think at Tikal it is getting me into trouble to not honor that more myself. I keep holding out for simple fractions of Michael Morton's awesome "Apex Displacement Ratio" figure, they are definitely important to some more oustanding forms of calendar keeping, but we may have already seen them pass over that option once

Temple IV (Raw data from Teobert Maler) 
Outer Doorway: Width 10.17060367 ft Height 10.40026247 ft Ratio = 10.40026247 / 10.17060367 = 1.022580646
Temple V (Raw data from Teobert Maler)
Outer Doorway: Width 7.152230971 ft Height 7.480314961 ft Ratio = 7.480314961 / 7.152230971 = 1.04587156

We have several things that are suggestive of 1.04-something, yet in the final figures for the Doorway of Temple III, we had 

Temple III Width 12.98787880 Height 10.96622711 Ratio 1.184352528 Product 14.24280287 

Where 12.98787880 is apparently used to represent 13, thus the corresponding representation of 104 (13 x 8) may be 12.98787880 x 8 =103.9030304 / 10^n and not 104.09137898 / 10^n... not this time, anyway.

Even if that is going to make for some boring ratios between some of the parts of Tikal's temple doorways (not sure what to think of that as it would be first time I've encountered anything the least bit boring there), it needs to be given more serious consideration.

At least it does begin to look like the doorway of Temple II didn't send us to Silbury without a good reason, since we can observe the same style of approximation of invalid whole numbers apparently at work there and at Stonehenge.

As with our findings concerning "Tikal" numbers at Giza, we seem to be able to see both calendrical homage to Venus and geodesy being served with the same gesture at Tikal here too

Proposed Venus Orbital Period 224.8373803 x Width of Doorway Temple III 12.98787880 = 
2.920160645 x 10^n, cube root of the Equatorial circumference in miles / 10^n

2920.160645 x 12.98787880 = 224.8373803 x (12.98787880^2) = 3792.6.69253 = 1896.334627

That's the "Long Count Builder" we saw back at our discussion of the Aztec Sun Stone - it's that thing we Perfectionist Pi Jedi (all one of us apparently) don't like because it's not a close enough approximation of the Long Count for our tastes, so we take it back to the Circle and trade it in for a different one

360 / 1896.334627 = 18983.99127 / 10^n

Also I beat my head up pretty good trying to figure out what the 819 day period of the Maya means in the Pi Jedi lexicon. Wiki wasn't much help with the rationale for that but it turns out to be pretty complex, and may eventually call for figuring out how our school of interpretation should deal with figures for orbital and synodic periods for the Moon, Venus (one down hopefully), Mars, Jupiter, and Saturn. I figured it probably just meant 364 x 225 = 81900
but boy was I quickly surprised.

This new-agey page probably has the better skinny on that. Might as well post it, the math does seem to check out
http://www.mayafifthsun.com/Mayan_Calendar.html

"Mars, Jupiter and Saturn:  A mysterious 819-day cycle originated at Palenque, related to the 13 Gods of the Upper World, 9 Lords of the Underworld, and 7 Earth Gods (7x9x13=819). It uses 21 (21x13x3) for synodic cycles of Jupiter (21x19 days) and Saturn (21x18 days), and includes Mars synodic cycle (780 days = 3 Tzolk'ins.) The 819-day cycle links with the 4 directions-colors to form a 3276-day cycle that coordinates with the moon every 16 years."

Did someone ask for ancient geniuses? I do think their request might have been granted. I may not be smart enough to actually pull that one off. At least working with calendars, while it's the biggest math headache I've ever gotten, seems somewhat like a bit of a refuge from The Dreaded U Word - we moderns too round off the year into a rational whole number of days, it doesn't mean we don't know better. In fact, some of the Mayan calendrical corrections I'm seeing (more recent observations about the Dresden Codex and an "Ancient Mayan Copernicus" for example) are the complete opposite of simple-minded. They are in fact far too complicated for my own good.
http://www.news.ucsb.edu/2016/017062/mayan-moment

Oh, here is one more thought for the day - little if anything has been done so far by Pi Jedi about mean calendrical or geodetic figures. We probably haven't had enough incentive to think that such acts of inexactitude have meaning, but one flavor of near-Phi we can throw at either proposed Venus Orbital Period is of course plain old 162, it's one of ours too. Just staying simple,

162 x 225 = 364.50 x 100 so there is a nice even mean figure between 364 and 365 to experiment with.

There's also a curious number I'd like to call attention to, it's 

(360 x Pi^3) / 1.000723277 = 111.5419203 x 10^n

It's rather notable because of some of its other aliases - you know that Radian 57.2957791 x Vitamin T 19.46773764 = 1115.420922 is of course going to be semi-sacred at very least.

I first noticed this when I'd just gotten Maler's data home in photocopy over ten years ago, and two minutes after seeing what looks like a "decimal harmonic" of the Earth's equatorial circumference as the width of Tikal Temple I as in Yoda's diagram, I found a temple pyramid measurement that very much resembled it, and squared it to find

(111.5419203^2) x 2 = 24883.20000 as a possible mean figure for the earth's circumference

In fact, it's the most obvious permutation of our Equatorial circumference figure by way of fine ratio

24901.19743 / 1.000723277 = 24883.20000

What to do with it? No idea. All this time later, I'll still working on the how the polar and equatorial figures best serve (or did serve) mankind, and where and how they are still hiding.
"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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We'd like to assure regular viewers of The Pyramid Pi Show that it hasn't been cancelled, we're merely taking our regularly scheduled season break...

Here's a tidbit (I hope) - for the data from Lehner & Goodman via Dash's paper, the average of the mean figures for each side come to 231.175 meters = 758.441627 ft

I'm quickly seeing a lot of good arguments for 758.5338511 ft as the "Intended Figure By Original Design" - including that it may have been their only shot at repeating the fine ratio (a geodetic constant when multiplied by prominent Giza constant 2 Pi, at the third power) that appears across proposed untruncated apothem / truncated apothem lengths, as

Sidelength Great Pyramid Platform 758.5338511 ft ? divided by
Sidelength Great Pyramid (proposed unpaved model) 755.6041600 ft
equals 1.003877283 = Earth Circumference in miles (24901.19743 / 100) / ((Pi^2)^3))

Looks a lot like 360 of the Persian Cubit Candidate 2.107038475... 

758.5338511 ft / 360 = 2.107038475 ft

Such a Persian Cubit gives a pleasing and meaningful measurement of the perimeter of the Great Pyramid (with pavement aka Yoda Model) at

3018.110298 ft / 2.107038475 ft = 1432.394488 = 1/4 Radian x 100

And may be one of the more literal Persian Cubit values to emerge from sacred geometry (see Piscis Design scheme earlier in thread).

How about I just throw that figure of 758.5338511 at the wall and see how long it can stay stuck there?

I think there's another nearby figure also present, the platform may be slightly larger at the bottom as I think is suggested in photos and diagrams earlier in this thread, but I'm not certain if Lehner & Goodman's data is from measuring it at the top or bottom - I'm assuming the top because this affords extention past the pyramid sides by Alternate Pi Squared Feet at each corner with what I think is very good precision, but I'm not really deep enough into the mathematics or the literature to get more guidance there yet.

What I am neck deep and then some is attempts to better comprehend ancient Mayan math. Had the fool idea to look for more guidance on Venus and planetary math in Andrews' data for the INAH reconstruction of the Chichen Itza Venus Platform, which is purported to give more conventional instructions related to Venus tracking on its sides. Unfortunately I do my best work in Complete Smartass Mode, but even a relatively unassuming structure like the Venus Platform can be a humbling enough experience to knock the Smartass right out of someone. It truly is like going straight from the shallow end to the deep end of the pool without swimming lessons, and really a bad time for it since I do also need to devote a few problem solving skills to maintaining my environment.

Hopefully details are forthcoming if I don't drown in numbers - at least offhand it does look the INAH might have done a good enough job with the restoration to preserve the original numbers. That would of course be absolutely wonderful, but it's still hard for me to tell with the possible flexibility in ancient calendar-related math that I'm running into. 

I might dig out Lehner's book eventually for possible clarification on the Great Pyramid platform if it comes to that, if I can resist temptation to get embroiled in the precise details that lead to remarks about his lacking accuracy by a good portion of a mile on pyramid placement at Giza. If he actually is turning up usable data in other areas, I shouldn't overlook it, but I'm really just looking at Giza this moment for a fifteen minute break from Mesoamerica.

Curious what all this may say about ancient peoples - That being a mathematician got very intense on account of ancient specialization, and yet mathematicians might have been generalists at things that required some precise math - namely architecture and astronomy? - and were in a very good position to combine the two into the proportions of architectural designs? Something else I'm looking for in ancient American monuments besides more data on the planets in the Venus Cycle, is something in ancient Mesoamerica that doesn't  seem to have Venus written all over it. Don't know if I've studied such a thing yet. I'm not going out of my way to find Venus referenced everywhere, but it sort of seems to be finding me all too often - but then again, it could have been a standard architectural theme?

Hopefully more time and more examples to study can help sort that out.

That does look like what I'm running into a lot, though, is the work of people who may have devoted a whole lifetime to interesting tricks with numbers and relationships between numbers and finding useful math formulas, compared to my spending not all of a decade doing the same. I should probably fully expect to be up to my neck in that. Perhaps working really hard at designing pyramids was how a lucky few got out of having to help build the things? :-)

I could swear I saw evidence of where someone involved in designing Tikal had worked out where you could build the Polar Circumference in Miles figure I'm using in general, from nothing but the half of the "Alternate e' Meg Yard" and the Squared Yoda Meg Yard - the two primary Meg Yards in use at Stonehenge by my reckoning - yet another thing that makes already familiar numbers seem even more useful and versatile than previously suspected.

Actually very simple: 1/2 AEMY (2.720174976 / 2) / SMMY squared (2.719715671^2)^2 = 24858.380742 / 10^n

It's actually part of a longer series revealed by throwing SYMY^n at 2.72014976 that also finds the inner Sarcen Circle area of Stonehenge as reckoned by Yoda and myself, and the diameter of Silbury Hill as proposed here previously.

So far, I'm not very sure, yet I may actually seeing evidence that the Tikal temple (Temple V) which points North toward the pole actually could be somewhat preferential to math related to the Polar Circumference, as previously speculated. Something else I'm not going out of my way to prove, yet does give possible appearances of being intended by plausible interpretation of the mathematical design. Not sure which page of my notes its on now but I'm pretty sure that formula is one of the ones that came from working on Temple V.

Also, I am wanting to be very careful with some additional work at Tikal. Maler gives data for the proportions of the outer doorway to Temple V as Width 7.152230971 ft, Height 7.480314961 (and I have no data from Andrews here).

These are slightly strange numbers in that if you throw them into the blender while mincing up data to make ratios out of orbital periods and synodic periods for planets involved in the Long Count aka 1/2 Great Venus Cycle, you may see what looks a curious number of ratios being seemingly repeated. I'm not sure what to make of that, and less sure without having more values for planetary periods that I feel are firm. The designers may have gone with several relatively strange numbers for that very reason, rather than with more obvious ones. Very intriguing, though, and certainly deserves some careful thought.

I'd rather get the Tikal doorways figured out before taking on the vaulted rooms - we have enough data from Andrews to figure some out of these vaulted rooms entirely (with the possible exception of where there may be beveling as shown by some diagrams by Maler and/or Tozzer), although only for the first room each of the five Tikal Temples I-V. 

A cursory examination, though, hints that there could have been a practice of selecting lengths, widths, and heights for these rooms that frequently give rational numbered products - something I might have also seen already at Rio Bec Structure B. Fingers crossed there may have actually been a common practice like that to help avoid further confusion on the part of what may have been an aspiring or apprentice mathematician attempting to deduce the original design specifications as an exercise. It's made me curious to see if we will find evidence of this elsewhere such as at Chichen Itza.
"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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Memoirs of a Pi Jedi 
Chapter Twelve
Let 'Em Eat Pi... Fish?!?

I had a curious thing happen... I might have mentioned in passing that a long time ago I worked out a ratio for the Area of a Vesica Piscis, in the sense of the fish-shaped section between two half-merged circles, then found several approximations for it from our "Pyramid Matrix" numbers...

Area Vesica Piscis = Radius^2 x 1.228369699 (exact)

"Matrix Valid Area Vesica Piscis Ratio A" (MVAVPRA) = 1.228047399 
"Matrix Valid Area Vesica Piscis Ratio B" (MVAVPRB) = 1.227936696

Still don't know if it was a good idea to trifle with that but given that Sacred Geometry and "the Pyramid Pi System" aren't exactly complete strangers, it seemed promising at the time. Really don't hear much from them these days, or at least until I started working with George Andrews' data for the Venus Platform at Chichen Itza (it looks like I also ran into 3.728757071 there, that's a long story I can tell some other time but that number was Yoda's "Grid Point" for the Monument to Humanity at Marcahuasi Peru).

Next I know, after looking for data on Palenque (I only have three measurements total from Andrews for that beautiful tower, what a pity) as a fringe benefit I am looking at some data for Pacal's tomb with some of the candidates for measures possibly referencing it and then I learn something I did not know before, that Pacal's sarcophagus is ostensibly hollowed out into the shape of a fish.

So I went to double check, and what I think might have happened is that

a. Ancient Mesoamericans did in fact actually recognize and use this "Vesica Piscis Area Ratio"

b. Because they put this value into calendrical equations that can be highly variable, it gave them an even more variable "Vesica Piscis Area Ratio" and a greater range of constants that they recognized as representing this value

To wit, I think they may have regarded it under the circumstances as (roughly) equal to 2 / Phi, with Phi in context being any number of useful approximations from the "Pyramid Pi System": 1.61882914, 1.620000000, 1.621138938, 1.622311470 and possibly also 1.62348451 treated "as if" Phi for these purposes.

This may afford us at least limited use of additional formulas like possibly

Earth Solar Year x / Lunar Synodic Period = ~VP Ratio = 2 / Phi y = 2 Venus Orbital Period / Earth Solar Year z

Where (thus far), the Lunar Synodic Period and doubled Venus Orbital Period are fixed at the values proposed previously, 
29.58741332 (days) and 224.8373803 (days) respectively.

It may help reinforce a sense that (3600 / Pi^2) = 364.7562611 is "special" because unless I did something really dumb (always possible), this figure is the only one where input Solar Year y = output Solar Year z

Perhaps more importantly, the form of Vesica Piscis ratio in this particular equation is 2 / 1.622311470 = 1.232808888, which may be useful and important enough to account for it probably having turned up already repeatedly in Andrews' data.

In fact, I may have recent evidence of 1.232808888 working successfully as a probe to as high as the twentieth power, which may well be a new record. FWIW, I don't generally expect Pi to be a useful probe at higher than the fourth or fifth power, and even the power probes like 1.177245771 or 1.622311470 generally maxing out by the sixth or seventh power.

Meanwhile, in the proposed formula, the original values 1.228047399 and 1.227936696 might actually serve in the generation of a possible pair of leap year values of just over 366, so perhaps we can see why incorporating this value into their calendar mathematics may have also necessitated departures from the most stringent approximations in order for such formulas to give a proper variety of values for the number of days in a year.

Also, I recently purchased a used Year-O-Matic 2000 just in case we run out of experimental values for the number of days in a year. I'm not sure there is such a thing and I really haven't tested it much, but supposedly it works like this:

13.333333333 / Year x = Year y

(13.333333333 x 10^n) / 365.0200808 = 365.2767074
(13.333333333 x 10^n) / 365.5409035 = 364.7562613
(13.333333333 x 10^n) / 365.8052909 = 364.4926321

And probably etc? (After this it may get strange, but maybe it's supposed to?)

365.5482919 again being a proposed candidate for mean value for the year, and possibly something that's found in the Great Pyramid with some frequency after Capt's findings of 365.2-something are converted back from "Pyramid Inches" to ordinary ones?

It's (1 / (1.177245771^2)) / (2 (Pi^2))* so it's sort of a chip right off the old block of this fondness that ancient Mesoamerica may have had for the square of Alternate Pi 1.177245771.

(*Whereas 2 (Pi^2) / 1.177245771^2 = 142.4280286 / 10^n, previously proposed for product of w x h of a Tikal temple door)

But some of those year figures thus generated are still very new to me in spite of previous attempts to find formulas to generate them, and I'm still not sure what to think.

At least I think I can safely say from looking at Andrews' data for the Palace at (Santa Rosa) Xtampak, that the same kind of mathematics seems to appear there as in temples, so this astronomical cycle-related math may not have been reserved for any particularly sacred type of structures.

Also, I'm finding more instances of what look like the reciprocal of Alternate Pi^2 (presented probably as fake sqrt 52 and possibly as fake 72) in a number of room proportions at places other than at Rio Bec - and quite possibly also at Palenque, perhaps including in the width of Pacal's sarcophagus lid "2.20 meters".

This Piscis business brings up another thing that slows me down on Tikal, though - there is a temple width there that looks about 340-something which I would usually think is awkward, and opt for something just a hair smaller and more resonant, but it turns out that the square of the proposed Venus Synodic Period is right in this neighborhood

584.0321292^2 = 341.0935279

This is also a somewhat awkward figure, yet 341.0935279 x 360 = 1.227936701 / 10^n

So that quick we are getting more Vesica Piscis talk from another aspect of Venus' cycles, and some unfamiliar numbers that might call for extra care.

And of the two Vesica Piscis ratios I previously proposed, it's this one that has its own valid square root, which is 
sqrt (1.227936701 x 10) = 350.4192775 / 10^n, 
which is the proposed circumference of the Thom Type A flattened ring, aka 111.5419203 x Pi etc

Also I don't know if I showed this before - I don't think I did but frankly I'm so swimming in numbers with this stuff that I probably make the same discovery three times in one week and don't realize it... 

But this came out of candidates for assigning possible intended values to the sarcophagii so whether or not we actually find it there, we can call it "The Red Queen's Venus Supreme Equation" (or not) wherein

2.033593767 / 224.85373803^2 = 1 / Earth's Polar Circumference in Miles x 10^2
2.033593767 / 224.85373803^4 = 1.789199025 (a noble number that still awaits a proper introduction)
2.033593767 / 224.85373803^5 = 353.9334588 Proposed Lunar Year in days value

Allowing this Venus Orbital Period value to make a rare display of worthiness even at the fifth power, while directly linking the Polar circumference to the Lunar Year. (Another candidate to come out of the Palenque tomb data may afford a rare opportunity to show off "Not-Phi" 1.61882914 as being useful - on at least the one occasion anyway - to the third power).

Most lately I am using Not-Phi with the Radian to generate the proposed Lunar Year value

57.29577951 / 1.618829140 = 353.9334578 / 10^n 

Which I like to think is itself a vote of confidence for this proposed Lunar Year

We also see the aforementioned noble number come from a string of familiar numbers connected by Alternate Pi, starting at 1/2 the Earth's Polar Circumference divided by Pi

Ignoring correct decimal placement for the remainder of this post

24858.38047 / Pi = 7912.668258
7912.668258 x 1.177245771^1 = 9.315155237
7912.668258 x 1.177245771^2 = 1.096622711
7912.668258 x 1.177245771^3 = 1.290994449
7912.668258 x 1.177245771^4 = 1.519817755
7912.668258 x 1.177245771^5 = 1.789199025
7912.668258 x 1.177245771^6 = 2.016326986

Also in the Pacal data, I have width measurements of 2.85 and 3.75 meters from Alberto Ruz Lhiullier for Pacal's burial chamber

3.75 / 2.85 = 1.315789474 (raw)

Going to take a wild guess here that perhaps Pacal too loved to Do The Cholula 1.315947254

And the ratio of the width of sacrophagus lid to width of sarcophagus

2.20 m / 2.10 m = 1.047619048

Wild guess on this one is 1/3 of Pi = Pi / 3 = 1.047197551

I continue to see a lot of what looks like the "Great Pyramid Apex Displacement Ratio" version of 104 days, namely 104.0913798 as seemed to appear repeatedly at Tikal, now also appearing in the measurements of other sites, but Pi / 3 is easily potent enough to be a fiercely competitive candidate even against the 104.0913798 ratio. A little more about that momentarily...

So now I suppose the question is, are there any other ratios specific to the Vesica Piscis that I probably know even less about?

Also I looked at a few more calendar stones (aka" sacrificial altars") and tried to learn more before I came down with a bad case of Anthropologitis - one can catch that from scouring sixty-page articles all about human sacrifice while just trying to find the measurements of the f---king thing. 

I found at least one example, and possibly several more in the form of circular ornaments from Chichen Itza, that hint at dividing the year into 16 (or possibly 8?) - I have not seen the number 16 enter into discussions of ancient Maya (read: ancient Everybody's?) calendar keeping but it turns out it may indeed belong there.

[Image: Dsc00044.jpg]
"Kukulkan - Sun Symbols. Chichen Itza"
(Item at lower right has 16 notches in perimeter)

365.020081 x 16 = 584.0321293 proposed Venus Synodic Period (days)
= 364.7562611 x 16.01157243 

360 / 16.00000000 = 225.0000000 "alternate" Venus Orbital Period figure
360 / 16.01157243 = 224.8373803 "primary" Venus Orbital Period figure

Also it was proposed that 12 Pi^2 may be a useful calendrical or astronomical figure

12 (Pi^2) = 11.84352528

11.84352528 x 16.01157243 = 1896.334629 "Long Count Builder" = 360 / 18983.88125 

Performing the operation with 16 Proper advises us that this is apparently not the only approximation of the Long Count or Half Venus Cycle that has a "Builder" figure. It turns out that 189.4964045 is NOT "Go away you pesky thing you are not one of the finalists," but actually part of that same process

11.84352528 x 16.00000000 = 1894.964045 = 360 / 18997.72193, the alternate Long Count version derived from the Aztec sun stone and the version that may best break down into hours, minutes, and seconds.

(also ~224-225 = ~16 x 14)

If I did anything wrong at Tikal so far, it might have been related to overlooking that 1/sqrt 60 = 1.290994448 may have been recognized as a legitimate representation of 13. I certainly could have made a mistake for overlooking that possibility.

I also think I found fairly recently, where 720 / Pi^2 = 72.95125222 may have been used in some applications or equations as the calendrical number 73. Also, possibly 73.10818007 (Alternate Pi^2 / Pi)

Yes, their math may have been half as complex as their written language. The Egyptians too. Should I be shocked?

I probably should have seen it back it at the Kukuklan-Pyramid-as-Calendar. On the one hand, it's extremely gratifying to see that (and apparently the Aztec sun stone) apparently operating on the very same logic that Yoda has been using in "decoding" ancient monuments the whole time, but it does also suggest it's a bit of a free-for-all with that "add 1 to make 365" business (and depending on preference, you could say the temple on top has five sides if you count the roof, divide five temple sides by four pyramid sides to get 1.25 to add to 364, to get 365.25)

But yes, this idea of how far we are allowed to drift when this high-precision system collides with a highly imprecise system like calendar counting might even go so far as throwing away everything after the decimal in such situations (once we have arrived at the-number-to-be-mutilated in a meticulously precise fashion of course), in which case

104.7197551 might therefore have actually read the same as 104.0913798 for such purposes, and that is another specific possibility I've previously overlooked.

Such it is that if the previous proposals will continue to hold water, then for the proportions of the door to Tikal Temple IV,

Temple IV (Maler) 
Width 10.17060367 Height 10.40026247 Ratio 1.022580646 Product 105.7769476

Perhaps the most pleasing and sensible interpretation for what was intended could well turn out to be
Width 10.25135528 Height 10.47197551 Ratio 1.021521079 Product 107.3519415

Yup, probably a fake square root trick (Why do I have a strange urge lately to refer to the pairs involved as "Hero Twins"? Was Mesoamerican mythology among any mythologies able to successfully embrace mathematics, as might have been the case with Egypt?) although not quite the square root trick we might have expected?

Although this is still not a terribly well-tested proposal for the doorway of Temple IV (and please don't get me started on lintels, which are one of the reasons none of this doorway data is telling a complete story yet)...

Perhaps the biggest mystery on my mind since I let it wander, is how archaeologists end up thinking the "psychoducting" in Pakal's burial arrangements means he and his wife are getting out that way to go for walks, when perhaps the fish-shaped sarcophagus does double duty as a hint he's going for a wee swim in the underworld instead? Between the "psychoducts" and the Queen's sacrophagus style, I'd swear that Mr. and Mrs. Pacal have heard of this Giza. I hate to go near that sort of stuff at all, but just maybe it would be easier to figure out at Palenque than at Giza what those things are really for?

FWIW, I never paid much attention to Pacal before as Nat. Geo. managed to make him out like the sort of arrogant sh-t to exploit the peasants for his own vanity and so forth, so who gives a rip? It just occurs to me now that even with what may have been a sizable case of Giza Envy, he seemed to have been content with what would most likely be considered as preposterously humble burial arrangement for a Pharoah.

I should just leave that stuff alone and stick to the math but it is interesting that I seem to be able to spot so many apparent ancient cultural contacts that aren't supposed to have happened. I dunno whether Candi Sukuh inspired El Tajin or vice-versa, but I really struggle to believe the striking similarities are coincidence. Worse, archaeologists seem to say a lot of dumb stuff when they're in Isolationist mode. I think I actually read a comment from Lhiullier to the effect that if ancient Asians visited Mesoamerica, why didn't they convert everyone to Buddhism? ROFLMAO! I can see he gave that one even less thought than he gave to getting a complete set of measurements of Pacal's final arrangements.

(I'll try to continue working with his data and see where it leads even though it gives me a creepy feeling how seldom there is anything but a zero in the second and last place after the decimal in that dataset).

Even the ideas archaeologists have about local diffusion of culture seem recalcitrant to me somehow. I'd love to know the story of how neighboring towns got similar architecture but they don't seem to come up with simple straightforward stuff like maybe one of the gubernatorial personages from Rio Bec happened to be passing by Becan and was really impressed with their cosmetic tower, so he got hold of the architect who designed it and said, "Hey those things are awesome, can you come up here to Rio Bec and design us a bunch of those?" - that's one of the sorts of things I wish I could find in the numbers, or maybe a particular mathematical "signature" of a particular architect.

More likely the history books will suggest it was because the architect was taken captive and they tortured tons of work out him before ungratefully ripping his guts out. I know archaeologists say such things even about their own ancestors - ooh, big scary heathen bloodletting altar at Stonehenge! - but really... I mean, unless they were ritually sacrificing their math teachers (which would be perfectly understandable), it's still hard to reconcile that kind of barbarism with the level of civilization visible in the mathematics and astronomy.

I think there's actually a good reason that when I look on the expanses of Palenque or Uxmal or Tulum or Tikal or etc that they nearly scream "College Campus" at me. We are apparently talking about specialization in society here, and for us ourselves that involves specialized education...
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Reply
(06-20-2017, 07:14 PM)Piewackett Wrote: Such it is that if the previous proposals will continue to hold water, then for the proportions of the door to Tikal Temple IV,

Temple IV (Maler) 
Width 10.17060367 Height 10.40026247 Ratio 1.022580646 Product 105.7769476

Perhaps the most pleasing and sensible interpretation for what was intended could well turn out to be
Width 10.25135528 Height 10.47197551 Ratio 1.021521079 Product 107.3519415

I will have to make it a point (mostly for my own benefit) to get around to explaining why these seemed like sensible figures. It's harder to be sure, because in the case of Temple I or Temple II we may have enough data to verify the doorway proportions because of what are hopefully strict guidelines for accuracy on the addition or subtraction involved where for example, we should get

Sensible Temple width - Sensible Door width = Sensible Remainder

or 

Sensible Room height - Sensible Vault height = Sensible Wall Height

To whatever degree of accuracy seems to be the standard.

That's sort of the upside to architecture that involves addition and subtraction, is that given the possible inaccuracy of archaeological measurements, there can be numerous attractive figures near to the stated proportions, but not all of them are going to work together in sensible combinations involving addition and subtraction, which in theory helps to thin down the candidates. It's a lot harder if the supporting data for that isn't present. (I finally had a look at a third data source for Tikal that I mentioned some time ago but it really wasn't any help here - but I'll keep looking). Especially since I am way out on a limb experimenting with the unfamiliar here, I expect something I'm doing lately will call for revision sooner or later.

It's part of the reason I'm wandering into other archaeological sites, though, because there are still a lot of limits on what I can really do with Tikal due to limited data.

The situation is the same with Temple V - I can come up with what I think are sensible figures for the door proportions, but I can't guarantee they'll match a sensible scheme for the remainder of the exterior temple measurements if that data ever turns up.

Regarding Temple V at Tikal

Temple V (Raw data from Teobert Maler, converted from meters to feet) 
Width 7.152230971 Height 7.480314961 Ratio 1.045871560 Product 53.50094033

The ratio could be Pi/3 putting in another appearance, although I'm not sure why that's necessary - for Temples I & II, it seems easy enough to find a licence to fling Pi/3 at the temple measures because Pi/3 may prove to be built fairly obviously into the proportions of their supporting pyramids. Building it into the doorways or temples themselves may imply it's absent in the proportions of their respective pyramids, but I may not have the data to prove that.

Regarding the raw figure of 7.152230971, one candidate, and one that may hopefully help preserve any special relationships between the exact figure and a number of planetary / calendrical values is

7.156796093

Which has several outstanding and attractive aliases

Primary proposed value for Venus Orbital Period 224.8373803 days / Pi = 71.56796093

(What could be more obvious unless they actually had something different on their minds in this case?)

This is probably my favorite, though

Alternate Tetrahedral Constant 19.46773763 / Alternate e' (Meg Yard) 2.720174976 = 7.156796093

Very "Martian" - also very "planetary" or whatever...

But it will be hard to tell just how well this number would fits a scheme for additional planetary values, if I don't either come up with some better guesses for those that are more self-explanatory, or if I don't take the preposterous amount of time required to really kick their tires.

Maybe it will be help that this same figure from the raw data also seems to appear in raw data on Palenque

Temple of the Cross: Room 2 Length 2.18 m = 7.152230971 ft (data from George Andrews)

In that particular setting (fingers crossed) maybe it will be somewhat more self-explanatory?

I found some data for another Aztec calendar stone ("Tizoc Stone from Tenochtitlan: diameter 2.67 m, thickness 92.5 m" as if there were actually singular figures for these things). I know very little about where this data came from or who gathered it (I pulled it out of Pinterest), but even if it isn't half as "in-your-face" as the math for the more famous one seems to be, it's giving some very interesting initial results.

Some of its a little confusing, though - I'm getting my nose rubbed in the fact that a choice equation isn't quite mathematically possible, namely where 

Venus Orbital Period x Venus Synodic Period = So close to Cholula it actually hurts

224.8373803 x 584.0321292 = 131594.7254 131312.2539 which was one of the contestants physically escorted from the building during the Miss-Earth-Circumference-In-Feet pageant. It's still a decimal harmonic of 4 (R^2) and all that, but if preoccupation with Venus took precedence, then maybe the Cholula wasn't quite Pacal's favorite dance after all?

On the other hand, the so-called "Third Meter" of 2.5 Cholulas may be seeing some well-deserved action in the equations arising from the data given for this second calendar stone.

That's about where

4 / Cholula 1.315947254 = 1 / Third Meter  = 30.39635508 / 10^n

but
 
(1/4) / Cholula 1.315947254 = 18997.72193 / 10^n = Secondary value for Long Count in days

Anyway, the only "currently proposed" circumference figure that can be built out of "currently proposed" Venus figures that I can think of is

225 x 584.0321292 = 1314072.291 x 10^n

Which is the figure for Polar circumference in feet, or if you prefer, the Polar and Equatorial circumference in feet using different metrological values for Polar & Equatorial applications.

This might have been an incentive for some individuals to adopt 131407229.1 over 131594725.4 as a circumference figure in their own personal mathematical vocabulary...

Another consolation of this figure is that it is

360 x 365.0200808 = 131407.2292

But would The Ancients have really accepted something like 131594725.4 / 225 = 584.8654462 x 10^n as a useful figure for the Venus Synodic Period? (I'm thinking 131594725.4 / 224.8373803 = 585.2884659 was probably not acceptable, but I'm already wondering just how wrong I could turn out to be for thinking that).

I'm guessing they must have given this a lot of thought once upon a time, which so far seems to disqualify me from being on the same page with them. For the likes of me, it'll be hard enough to finally figure out a preferred figure for a Mars or Saturn Synodic period without all this going on...

At least Cholula doesn't have to feel completely left out of the planetary proceedings, since 1.315947254 still links the primary proposed Venus Orbital Period with the sole proposal thus far for the Lunar Synodic Period

VOP 224.8373803 x 1.315947254 = LSP 29.58741332 x 10

(And just for good measure, and a daily dose of Vitamin T aka 19.46773764 aka 19.47122063

VOP 224.8373803 x (1.315947254^2) = 194.6773764 x 2)

Anyway, the initial experiments with the "Tizoc Stone" data seem to show an interesting collection of data, including some that are easily enough evoked by Maler's Tikal data that Yoda gave them as "Grid Values" for some of the Tikal temples (and, in cases, other major monuments), so it looks like I may be on the right track even if I'm not at all sure where it leads. More importantly, the use of calendar stones to record data (in feet) will hopefully turn out to be a standard practice so that any and all of them that are sufficiently intact will be worthy of study.

Well, while I'm at it... Data (hoping that's what is actually is) says: Diameter 2.67 m = 8.759842520 ft

So I'm wondering if what the "Tizoc Stone" isn't up to is 8.760481938

That is, with its diameter, giving the number of hours in a year 365.020081 x 24 = 8.760481938 x 10^n

Those who've been taking notes may also recognize it as 19.46773764 x 45 = 876.0481938

(Venus Worshippers may wish to observe at this point that 45 / 2 = 22.5)

But there haven't actually been any other contenders for these figures yet so let's maybe give it awhile and see if anyone else shows up for the competition.

At least I think I've tracked down the circumference value for the "Sun Stone" to its source, wherein it is given the same as the data I've been using.

If anyone wants to look at some of the data in question, just let me know and I'll make it more of a priority to post some links. Likewise, if anyone has an ancient monument they'd like me to try and interpret, just holler - I'm easily intrigued by things like that, and better yet if you have any data.

I'll keep trying to sort out this Piscis business - I'm hoping to find, I dunno, maybe a sound geodetic rationale for certain sacred geometry motifs, maybe? - but it does occur to me that further confusion could arise because it's possible to hit the reciprocal of the raw value of 819 days (that murky calendar period of the Maya) without completely departing from values of 1.22-something

1 / 819 = 1.221001221 x 10^n

Although I've generally had probes repeatedly come back telling me that maybe I'd better brace myself that figures more like 820-something may be the inevitability.

Piscis-like figures might include things like truncated apothem Great Pyramid (unpaved) (19.46773764 x Pi x 10) x 2 - or 19.46773764 x (2 Pi) if you prefer - equals 1.223194031 x 10^n.

This comes up yet again partly because I find the Tepozteco Pyramid especially attractive, and I think it would make an excellent study, and of barely eight measurements given by Eduard Seler, we have

9.50 m = 31.16797900 ft (looking suspiciously like the Very Venus-y 1.177245771^2 x 225)
2.50 m = 8.202099738 ft (looking suspiciously like 819 or thereabouts?)
3.73 m = 12.23753281 ft

I may either need to find another data set for Tepozteco, though, or see how just how much data I might milk out of a shrunken architectural diagram for once, reckless as that probably is, to be more certain of any of that.



[Image: 5168145.jpg]


It's still really new to me, I've done some dinking around in the past concerning why we may see ancient monuments whose origin designs may involve the Vesica Piscis but I don't think anyone's ever gone the distance with the question before that I know of. In the present, I'm seeing a number of equations with such figures that do surprise me, so exactly how much total incentive the ancients had for preoccupation with figures in this range (or how carefully they did or didn't distinguish them), I couldn't tell you.

Hopefully we will all continue to live, and learn.

Cheers!
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Reply
Quote:It's still really new to me, I've done some dinking around in the past concerning why we may see ancient monuments whose origin designs may involve the Vesica Piscis but I don't think anyone's ever gone the distance with the question before that I know of. In the present, I'm seeing a number of equations with such figures that do surprise me, so exactly how much total incentive the ancients had for preoccupation with figures in this range (or how carefully they did or didn't distinguish them), I couldn't tell you.

Hopefully we will all continue to live, and learn.

Cheers!
This Volcano-Shaped Pyramid in Peru Has Experts Stumped
By Megan Gannon, Live Science Contributor | June 20, 2017 08:23am ET


[Image: aHR0cDovL3d3dy5saXZlc2NpZW5jZS5jb20vaW1h...FtaWQuanBn]
El Volcán in the Nepeña Valley of coastal Peru has archaeologists stumped as to when and why this mound was built, though it may have served as a place for a ceremony related to a total solar eclipse.
Credit: Courtesy of Robert Benfer


From far away, El Volcán in the Nepeña Valley of coastal Peru might look like a natural feature in the landscape.

But this volcano is artificial, a mound or pyramid built by human hands with a crater dug out of the top. And some archaeologists are trying to figure out what it was used for.
Robert Benfer, a professor emeritus at the University of Missouri who focuses on biological anthropology, had previously found a series of mounds shaped like orcas, condors and other animals in coastal valleys in Peru. He was looking for more of those earthworks by surveying valleys north of Lima when he spotted the volcanic cone that stands 50 feet tall (15.5 meters).[In Photos: Earthly Mounds Shaped Like Animals]

"I knew that a mountain in the valley had a large archaeological site, San Isidro, with platforms oriented to the solstice," Benfer told Live Science. "So with my team, we climbed it to get a better view of the surrounding valley, and I saw the Volcán site from a platform."

In the 1960s, archaeologists had noted the volcano-like mound and identified it as artificial, but Benfer and his team decided to investigate further. As the researchers report in the latest issue of the journal Antiquity, they dug a trench into the inner crater of the volcano, and found a collapsed stairwell that descends below a layer of adobe bricks to a mud-plaster floor.

[img=788x0]https://img.purch.com/w/640/aHR0cDovL3d3dy5saXZlc2NpZW5jZS5jb20vaW1hZ2VzL2kvMDAwLzA5My8xNzIvaTAyL2VsLXZvbGNhbi1zdGFpcndheS5qcGc/MTQ5Nzk2MTMzMw==[/img][Image: aHR0cDovL3d3dy5saXZlc2NpZW5jZS5jb20vaW1h...k3OTYxMzMz]



Archaeologists dug a trench into the inner crater of the volcano-shaped mound, finding a collapsed stairwell that descended to a mud-plaster floor.

Credit: Courtesy of Robert Benfer

They also found a fireplace at the bottom of the stairwell, full of bits of charcoal and shell. Archaeologists can determine the age of such organic material using radiocarbon dating. A sample of burned material from the hearth showed that the last fire was lit sometime between A.D. 1492 and 1602.

Benfer believes this date range is important. During the 16th century, there would have been four total solar eclipses, visible from El Volcán, in short order: in A.D. 1521, 1538, 1539 and 1543. This would have been a rare occurrence. "The chances that four solar eclipses could occur during the probability distribution of the radiocarbon date of the hearth is less than 0.0003," Benfer told Live Science. (That's less than a 0.3 percent chance of occurring.)

In their paper, the researchers wrote that "the people of the northern and central coasts, the Yungas, unlike the later Incas, greeted eclipse[s] of the sun with joy, not fear." Benfer speculated that the fire might be all that's left of a ceremony linked to one of these eclipses.

The researchers are not sure when the mound was first built. It's possible that the original structure might be much older than the hearth. The nearby archaeological site at San Isidro was active during the Late Formative period (900 B.C.to 200 B.C.).
The meaning behind the mound's shape is also still unclear. Benfer noted that there are no volcanoes around El Volcán that would have served as models for its construction, if it was indeed meant to look like a volcano, and no other structures like it have been found in Peru.

https://www.livescience.com/59544-myster...-peru.html


5,000-Year-Old 'Billboard' of Hieroglyphs Contains a Cosmic Message

By Owen Jarus, Live Science Contributor | June 22, 2017 06:39pm ET


[Image: aHR0cDovL3d3dy5saXZlc2NpZW5jZS5jb20vaW1h...Bocy5qcGc=][Image: aHR0cDovL3d3dy5saXZlc2NpZW5jZS5jb20vaW1h...Bocy5qcGc=]

Hieroglyphics found at El-Khawy in Egypt show two storks, back to back, with an ibis between them (left), as well as a bull's head (right).
Credit: Courtesy of Yale University

Archaeologists have discovered a "billboard" of hieroglyphs carved into the rocks near the Egyptian village of El-Khawy. The symbols, which show a message related to the cosmos, are the earliest monumental (large) hieroglyphs known, dating back around 5,200 years.

"This newly discovered rock art site of El-Khawy preserves some of the earliest — and largest — signs from the formative stages of the hieroglyphic script and provides evidence for how the ancient Egyptians invented their unique writing system," John Darnell, a professor at Yale University who co-directs the expedition that discovered the rock art, said in a statement from Yale University. The Egyptian antiquities ministry also issued a statement today (June 22) announcing the discovery.
The archaeologists also discovered another carving, this one showing a herd of elephants, created sometime between 4000 B.C. and 3500 B.C. One of the adult elephants in the scene was drawn with a little elephant inside its body — "an incredibly rare way of representing a pregnant female animal," Darnell said in the Yale statement.  [Photos: 5,000-Year-Old Hieroglyphs Discovered in Sinai Desert]

Only a few similar scenes are known from Egypt. For example, a vase previously found at the site of Abydos depicts a pregnant hippopotamus, Darnell told Live Science.

[img=788x0]https://img.purch.com/w/640/aHR0cDovL3d3dy5saXZlc2NpZW5jZS5jb20vaW1hZ2VzL2kvMDAwLzA5My8zMzcvaTAyL2Vsa2hhd3ktcHJlZ25hbnQtZWxlcGhhbnQuanBnPzE0OTgxNjI5ODY=[/img][Image: MTQ5ODE2Mjk4Ng==]



In this rock carving, a little elephant is shown inside an adult elephant, an indication that the animal is pregnant. It was carved sometime between 4000 B.C. and 3500 B.C.

Credit: Courtesy of Yale University

Political message

The four early hieroglyphic signs were carved around 3250 B.C. And the carvers seemed to be making a statement, as the symbols are about 70 centimeters (27.5 inches) high and had "abright, almost white, color against the patina of the surrounding brown stone" after they were freshly carved, Darnell told Live Science.

"In the modern world, this would be akin to seeing smaller text on your computer screen and then suddenly seeing very large ones made the same way only on a billboard," Darnell said in the Yale statement.

One of the signs shows a bull's head on a short pole, a symbol found at other Egyptian sites. "The bull's head appears to be a symbol of royal power during the formative phases of the Egyptian state," Darnell told Live Science.

[img=788x0]https://img.purch.com/w/640/aHR0cDovL3d3dy5saXZlc2NpZW5jZS5jb20vaW1hZ2VzL2kvMDAwLzA5My8zMzYvaTAyL2Vsa2hhd3ktam9obi1kYXJuZWxsLmpwZz8xNDk4MTYyODcy[/img][Image: aHR0cDovL3d3dy5saXZlc2NpZW5jZS5jb20vaW1h...gxNjI4NzI=]



John Darnell, of Yale University, who co-directs the expedition that discovered the rock carvings, is shown here at the site, called El-Khawy.

Credit: Courtesy of Yale University

The other three signs show two storks, back-to-back, with a bald ibis bird in between them. The stork-ibis-stork arrangement suggests that those three signs are making a "statement about the cosmos through the solar cycle," Darnell told Live Science, noting that similar arrangements of symbols can be seen at other Egyptian sites.

Together, the four symbols were likely "an expression of royal authority over the ordered cosmos," Darnell said, adding that the "inscription was visible to travelers going to and from the early city of Elkab."

The hieroglyphs would have been visible to anyone who passed by during this time, suggesting that many ancient Egyptians were able to understand the signs, Darnell said.
The rock carvings were discovered by a joint expedition from Yale and the Royal Museums of Art and History, in Brussels. The expedition team works in collaboration with the Egyptian antiquities ministry.
https://www.livescience.com/59588-billbo...ssage.html

(05-25-2017, 11:40 PM)EA Wrote:
Quote:Posted by Ancient Vizier - 3 hours ago
This post here had me wondering about the possibility of using a tetrahedral instrument of some kind for navigation. Supposed you used one to do the same thing this person is doing with their hand here. There may even be a post somewhere with someone having a theory like this, and it may well be on Hidden Mission that I saw such a thing a long time ago?

[Image: moana-navigation.jpg]
http://thehiddenmission.com/forum/showth...#pid237911
Sounds like you can't quite put your finger on it.

Did you mean Base Ten Metrics.
Ancient Digital  Processes  ???   

Ten fingers, a freemason and the current system of things.

[Image: 0035699df5f.jpg]

[Image: 27481202.jpg]

[Image: 27481201.jpg]
1

Is it okay for children to count on their fingers?
June 23, 2017

[/url][Image: article-1052306-0283A1C200000578-626_468x286.jpg]
Is it OK for children to count on their fingers? Generations of pupils have been discouraged by their teachers from using their hands when learning maths. But a new research article, published in Frontiers in Education shows using fingers may be a much more important part of maths learning than previously thought.



The article, by Professor Tim Jay of Sheffield Hallam University and independent researcher Dr Julie Betenson, confirms what parents have long felt instinctively - that the sorts of finger games 
children often play at home are central to their education.
The researchers worked with 137 primary pupils aged between six and seven. All the children were given different combinations of counting and number games to play - but only some were given exercises which involved finger-training.
Some pupils played games involving number symbols, such as dominoes, shut-the-box, or snakes and ladders.
Other pupils were asked to play finger games: such being asked to hold up a given number of fingers, or numbering fingers from 1—5 and then having to match one of them by touching it against the corresponding finger on the other hand, or tracing coloured lines using a particular finger.
Both these groups did a little better in maths tests than a third group of pupils who had simply had 'business as usual' with their teachers. But the group which did both the counting and the finger games fared significantly better.
"This study provides evidence that fingers provide children with a 'bridge' between different representations of numbers, which can be verbal, written or symbolic. Combined finger training and number games could be a useful tool for teachers to support children's understanding of numbers," Professor Jay said.
[Image: 1x1.gif] Explore further: Finger tracing can lift student performance in maths
More information: Tim Jay et al, Mathematics at Your Fingertips: Testing a Finger Training Intervention to Improve Quantitative Skills, Frontiers in Education (2017). DOI: 10.3389/feduc.2017.00022 
Provided by: Frontiers


Read more at: https://phys.org/news/2017-06-children-fingers.html#jCp[url=https://phys.org/news/2017-06-children-fingers.html#jCp]
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply
(06-23-2017, 08:03 PM)EA Wrote:
Quote:In their paper, the researchers wrote that "the people of the northern and central coasts, the Yungas, unlike the later Incas, greeted eclipse[s] of the sun with joy, not fear." Benfer speculated that the fire might be all that's left of a ceremony linked to one of these eclipses.
I'm getting the sense that may have been true of a number of ancient people. It's almost more like astronomy was a kind of entertainment before there was television - "Hey come here you kids, look at this - now this particularly alignment right here only happens every 13500 years, how lucky you kids are to get to see this..."

Given the amount of number-crunching and juggling I'm having to do, it's hard to see any cosmic mathematical order that's quite so profound or precise that anyone would think they have to actually worship it or sacrifice anything to it. Rather, there are equations that do impart some sense of cosmic order but I think it comes with the recognition that it may also require some artificial interpretive liberties on the part of Homo sapiens to all work together quite so well, and even then it's still a bit wobbly around the edges.

Of course, maybe some of us decided to make pyramids in the shape of volcanos or craters so The Gods would look down and think they had already sent us recent misfortune. :-)

Not sure what to make of those, EA, but they are certainly food for thought, and all new to me. Wasn't that long ago I was sure I knew where virtually every pyramid known to man was located - if that was ever true, certainly not for long.

Regarding that Piscis business, I'm not sure if this is an old equation or not - it might be, and it might be one that helped put this silly "Piscis Ratio" on the map in the first place

Inner Sarcen Circle Perimeter Stonehenge = 1/2 Great Pyramid Apothem, unpaved model = 305.7985078
Equatorial circumference of Earth in Miles = 24901.19742

305.7985078 / 24901.19742 = 1.228047401 / 100

Still going over candidates for Planetary values - as it was ten or fifteen years ago, probes intended to find values that might be deliberately used to represent "686.971 days" and "779.96 days" - Mars' Orbital and Synodic Periods respectively, primarily come back with 

687.5493542 days (21600 / Pi) and
779.2727283 days (8 x (Pi^4)

As likely the most the useful candidates. There are additional candidates, and most likely the contemporary "textbook" figures can be more closely matched if need be, but these may well be fairly serviceable figures overall for general purposes. That's what may have been elusive previously is that maybe it's okay not to sacrifice the level of resonance of these proposed figures for the sake of more accurate but less resonant ones, if the more accurate ones are frequently going to have their exactitude rounded off anyway as soon as calendars enter the picture.

I seem to be feeling unusually confident today about Saturn's Orbital Period of "10,759.22 days" probably being best represented by a "decimal harmonic" of the reciprocal of sqrt 8640

1 / (sqrt 8640) = 10758.28707 / 10^n

Still not entirely sure about any intended interpretations of Saturn's Synodic Period of "378.09 days" - as may be the case with Venus, there may not be any singular candidate given the variable nature of some of the possible equations...

Note that this "378.09" figure is awfully close to 18980 / 2 = 379.6 / 10

But whether the ancients thought it was worth trying to "make" it work out that way (more evidence of man's required participation in cosmic order?) I'm not sure. In fact, I found at least one candidate for the "378.09 days" figure that I'm completely unfamiliar with that may be showing a fairly impressive amount of resonance, so I will have to give that some more thought.

I've also taken to wondering if our ancient mathematical system doesn't also recognize the additional Lunar Months, with the radius I've proposed for Silbury Hill of 275.2186571 feet representing 10 times an adapted version of the "27.554549878 day" Anomalistic Lunar Month, along with possible representation of the Lunar Tropical and/or Sidereal Months represented by the reciprocals of several candidates for a "Leap Year" worth of days. 

Also there is the Draconic Lunar Month of "27.212220817 days" - the fact that have a similar figure that turns up from time to time and then quickly gets tossed aside for not being 27.20174976 is what originally prompted my renewed curiosity about Professort Thom mentioning several possible ancient variations on his Meg Yard (dunno, I still haven't got back to his books yet) - not that one probably couldn't get away with using 27.20174976 or other proposed Meg Yard values, but there really is a distinct pair of available numbers in this range, for whatever that's worth.

Ideally, there may be some ancient Megalithic sites that might put these numbers into situations where they are a little more self-explanatory, if I can't figure out how to extract a clarification from Stonehenge.

For what it's worth, the second figure in question besides the familiar "Alternate e' Meg Yard of 2.720174967 x 10, is 27.21223218, which is

(Generic) Area of a Circle 10313.24031 / (19.46773760^2) = 27.21223218

If we were ever intended by the ancients to get much use out of that figure, it's still not something I've learned to do, but it certainly is tempting when it would probably be one of our most accurate approximations ever.
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Reply
I got back into Professor Thom's data just a little, it was actually handier to dig out electronic data tables that I made a long ago with some of the calculations already done than to start over. I think the flattened rings were hopefully mostly worked out well back then, but I don't think much was ever done with ellipses. There's some enticing data, particularly for the elliptical stone circles at 

Meikle (Mickel) Findowie, where the inverse of the eccentricity of the ellipse comes out in the raw data as 1.175742574, being very suggestive of Alternate Pi 1.177245771, and

Lee Moor, where the inverse of the eccentricity of the ellipse comes out in the raw data as 1.217391304, being very suggestive of the value of the primary remen, 1.216733603 (feet)

It's not something I should actually try to do in a day, but I've come up with a tentative model for Meikle Findowie. I might end up having to revise it further down the road, but here goes...

This may be even more given to future revision considering the shape the circle is in.

Meikle Findowie
http://ukra.jalbum.net/brac/Scotland/Per...index.html
http://www.themodernantiquarian.com/site...dowie.html
http://www.megalithic.co.uk/article.php?sid=14744

Nonetheless, Thom's description of the circle may make some sense. Thom describes the geometry of this circles' design as being based on a right triangle of 5, ~8, and 9.5 Megalithic Yards respectively (involving two violations of his fundamental premise of the use of the Megalithic Yard in whole number values in all of three figures)

1. 5.0 MY x 2.72 = 13.60 ft = 2 a (a = minor radius) 
2. 8.0 MY x 2.72 = 21.97 ft = 2 b
3. 9.5 MY x 2.72 = 25.84 ft = 2 c (c = major radius = hypotenuse)

And I am taking these to mean

1. 13.60087488 ft (5 Meg Yards of "Alternate e'' = 5 x 2.720164976)
2. 22.06485532 ft (8.111557354 Meg Yards of "Alternate e'") = 8.111557354 x 2.720164976)
3. 25.97575757 ft (1 / (Pi / 3) x 10) Meg Yards of "Alternate e'" = 9.549296571 x 2.720164976

25.97575757 ft / 22.06485532 ft = 1.177245771 ("Alternate Pi)
25.97575757 ft / 13.60087488 ft = 1.909858315 (6 / Pi; the square root of putative calendar figure 364.7582611 / 100)
22.06485532 ft / 13.60087488 ft = 1.622311470 ("Alternate Phi")

I haven't reviewed the origins of the perimeter value, but I've adjusted it as being intended to mean 75.85338501 ft (The data table implies that Thom provides the figure of 75.2355 ft but his interpreted proportions are slightly different which of course results in some variance in the perimeter value - I did try my best to conserve his original perimeter / major radius ratio in coming up with my figure).

= 4 x 18.963346250 = 360 / 18983.99129 (1/2 Venus Cycle) / 10^n
= 36 "Persian Cubits" of 2.017038473 feet (a favored "Persian Cubit" for measuring the Great Pyramid?)

It doesn't necessarily give the most dazzling responses, but it gives some Giza-related data in response to Alternate Pi and Alternate Phi, and it somewhat dramatically conserves an important and familiar geodetic ratio

75.85338501 ft / 25.97575757 ft = 2.920160646 
75.85338501 ft / 2.920160646^2 = 889.5318005 ((2 / Venus Orbital Period) x 10^n)
75.85338501 ft / 2.920160646^3 = 1 / Radian Squared = 3.046174195 x 10^n

So it's essentially the Reciprocal of the Squared Radian x Earth Circumference in Miles

Of which, ignoring decimal placement, 2.920160646 is the cube root.

There's also the part where 1.227936700 ("Matrix Valid Area Vesica Piscis Ratio B") / 1.61882914 ("Not Phi) = 75.85338501 / 100

75.85338501 ft / 22.06485532 = 3.437746766 (Double MLM Royal Cubit = 1.718873383 x 2)

75.85338501 ft / 13.60087488 ft = 5.577096009 ("Giza Vector" / 1000)

So it's perhaps a bit picky who it talks to, but it does seem to have a very good grasp on some things worth talking about

Lastly, putting up with 22.06485532 as probably not the most flamboyant constant may also have been done at Giza

1 / 22.06485532 = 453.2094072

I guess I have yet to publish my Great Pyramid exterior data set in entirety (pretty sure I've shown most of it and the rest really merits some good explaining), but 453.2094072 appears in this data set as what most likely becomes of the 452.3893421 "Holy of Holies" (Yoda) height of the Great Pyramid, without capstone, when the upper layer of paving is removed (i.e., the "unpaved height" without capstone)

And this usurper is tolerated there probably largely because in reciprocal form it is hotcha for Alternate Pi

22.06485532 x 1.177245771 = 25.97575751 (as also seen at Silbury and Stonehenge)
25.97575757 x 1.177245771 = 30.57985080 (1/10 Inner Sarcen Circle Circumference Stonehenge)
30.57985080 x 1.177245771 = 360 / 10

In a manner that is very suggestive of Stonehenge, which is in turn closely related mathematically to the classical "Pyramid Matrix" values for the Great Pyramid (i.e., the "Yoda Model") where Inner Sarcen Circle Stonehenge x Pi^2 = Height Great Pyramid (Yoda)

This isn't entirely certain, however - in this case, what mostly needs explaining is the allowance of a departure from the use of a scaling ratio that I believe is otherwise applied stringently, but we do already know that the results of addition and subtraction where they are also applicable compete with the results of applying scaling ratios, somewhat dampening the prospects of there being "one right way" to arrive at the correct raw value.

Being that the construction of the right triangle for Thom's Meikle Findowie ellipse involves superposition of the height B (minor radius) onto A (the major radius), we are somewhat "obligated" to determine the remainder of the major radius, and we can optionally also apply this operation to the other values of the right triangle to search for more intended data. Here are the remainders along with interpretation, and the emerging, rather homogeneous-looking, standard of accuracy for operations involving addition or subtraction for this particular rough monument

25.97575757 ft - 22.06485532 ft = 3.910902250 = 3.924152570 = (3.333333333 x 1.177245771) - accuracy 0.99662
25.97575757 ft - 13.60087488 ft = 1.237488269 = 1.232808888 = 2 / Alternate Phi 1.622311470 - accuracy: 0.99621
22.06485532 ft - 13.60087488 ft = 8.463980440 = 8.443431970 (.1 / (12 x (Pi^2))) - accuracy: 0.99757

Please note however that all of this has been worked out at a scale of 2:1 rather than 1:1

(I went with the data as presented by Thom rather than converting it. Note that ratios should not be affected by scale).

Could be wrong but I suspect my "Stone Age Genuises" are slightly more ingenious than Thom's. 

In my opinion, this is a VERY nice elliptical circle mathematically, it's managed to hit plenty of important numbers even with this little exploration.

One down, thousands to go? :-)

BTW, I am saddened to announce I'm having to take back the one point I gave to the metrology of Heath, Neal and Michell. I was flattered to think that if 1.111111111 were a metrological unit, I could say I constructed my unpaved Great Pyramid perimeter of two ancient metrological units 1.11111111111 x 2.720174976 = 3022.416640 ft / 1000, but 1.111111111 may actually be a somewhat nonsensical or redundant metrological unit because it's the reciprocal of simply 9. Anyone interpreting needs only throw 3 at it twice, just as I throw 2 to the nth power at numbers as a blatantly obvious analytical method which I continue to use because it continues to work.

Both of Heath's books have finally gotten here, though, and I will keep an eye out for anything interesting or useful when I get a chance to browse them. Thought it might be worth attempting to hear him out at ten apiece - after all, I'm still pretty far out to lunch on things like distances to outliers and azimuths so that's one place they may have some valuable input even if they have figures that might need a slight tweaking?

Oh, and lastly, I'd forgotten that I've already dealt with the proposed perimeter of Miekle Findowie back in post #122 of this thread - it is 1/10 of the proposed side length of the Great Pyramid's platform - so that should provide a bit more background on that particular figure.

So many numbers, so little brain, apparently... There will be none left by the time the Maya are done with me.
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Reply
(06-25-2017, 06:44 PM)Ancient Vizier Wrote:
(06-23-2017, 08:03 PM)EA Wrote:
Quote:In their paper, the researchers wrote that "the people of the northern and central coasts, the Yungas, unlike the later Incas, greeted eclipse[s] of the sun with joy, not fear." Benfer speculated that the fire might be all that's left of a ceremony linked to one of these eclipses.
I'm getting the sense that may have been true of a number of ancient people. It's almost more like astronomy was a kind of entertainment before there was television - "Hey come here you kids, look at this - now this particularly alignment right here only happens every 13500 years, how lucky you kids are to get to see this..."
Arrow
'Great American Total Solar Eclipse' Just 1 Year Away

By Joe Rao, SPACE.com Skywatching Columnist | August 19, 2016 11:00am ET


[Image: total-solar-eclipse-2016-nasa-totality.j...side|660:*]

The total solar eclipse of March 8 to 9, 2016, reaches totality in this still image from a NASA webcast from Woleai Island in Micronesia.
Credit: NASA TV

Aug. 21, 2017, is a red-letter day for eclipse enthusiasts.

On that date, the sun will be partially eclipsed over an immense area that includes all of North America, the northern third of South America, much of the eastern Pacific Ocean (including the Hawaiian Islands), virtually all of the north Atlantic Ocean and a slice of western Europe. For much of the United States, at least 80 percent of the sun's diameter will be eclipsed by the passing new moon. Some eclipse chasers have billed it as the "Great American Total Solar Eclipse."
And a total eclipse will be visible along a narrow track that runs diagonally from northwest to southeast across the Lower 48 — the first such event that's visible for this part of the world since February 1979. It will also be the first time that the path of a total solar eclipse will go coast to coast across the U.S. since 1918. [Total Solar Eclipse 2017: When, Where and How to See It]

Although many people have viewed a total eclipse of the moon, few have been lucky enough to see a total solar eclipse. In the 21st century, total eclipses of the sun occur on an average of once every 17.6 months, but they're often only visible over open water or from sparsely populated areas. 

Indeed, Americans under the age of 40 who have never ventured outside of the country have never witnessed a total solar eclipse. Since 1960, just three such events have been visible from the U.S. mainland — on July 20, 1963, March 7, 1970 and Feb. 26, 1979.  

But at long last, next summer, this greatest of celestial roadshows will be coming to a sky near you.  

[img=553x0]http://www.space.com/images/i/000/057/662/i02/solar-eclipse-2017-usa.jpg?1471578193?interpolation=lanczos-none&downsize=640:*[/img][Image: solar-eclipse-2017-usa.jpg?1471578193?in...ize=*:1400]



Map showing the path of totality for the "Great American total solar eclipse" of Aug. 21, 2017.

Credit: Fred Espenak/NASA GSFC

The path of the moon's shadow

This August 2017 eclipse will have a potential viewing audience of at least 12 million people who already happen to live within the totality path. However, about 220 million people live within a one-day drive (about 500 miles, or 800 kilometers) of the totality zone.

At local sunrise on Aug. 21, 2017, the dark umbral shadow of the moon will first touch Earth at a point in the North Pacific, about 1,500 miles (2,400 km) northwest of Hawaii. And then, for the next 193 minutes, the shadow will first head east-northeast, then east and finally southeast, darkening a narrow strip of North America along the way.

For the first 28 minutes, the shadow will only touch open ocean. The shadow will make its first landfall along the coast of Oregon at Yaquina Head, a headland extending into the Pacific Ocean north of Newport. 

As it traverses the United States, the total eclipse will be visible within a path of darkness stretching from Oregon through Idaho, Wyoming, Nebraska, Kansas, Missouri, Illinois, Kentucky, Tennessee, Georgia, North Carolina and finally South Carolina. The path will average 67 miles (108 km) in width, but it will widen to a maximum of 71 miles (114 km) while moving through western Kentucky, about 12 miles (19 km) northwest of the town of Hopkinsville (population 3,000). 

Because the moon's shadow will be moving at a tremendous speed, totality will not last very long in any one place. The duration of the total phase is always longest along the center of the shadow's path; as one moves away from the center, the duration of totality time decreases, becoming zero along the path's edges. [Solar Eclipses: An Observer's Guide (Infographic)]

At the Oregon coastline, totality lasts less than 2 minutes, as the shadow will be traveling at more than three times the speed of sound (2,400 mph, or 3,860 km/h). Heading southeast along the center line, the totality time slowly lengthens, reaching a maximum of 2 minutes and 40.2 seconds at a spot in southern Illinois about 12 miles (19 km) southeast of the city of Carbondale.  

The shadow will slow to 1,450 mph (2,330 km/h) as it moves through the Tennessee Valley, and then speed up; subsequently, the duration of totality will begin to diminish. Indeed, when the eclipse arrives at the South Carolina coastline, the duration of totality will have dropped to 2 minutes and 34 seconds. The shadow then exits out to sea, finally leaving Earth 75 minutes later at local sunset in the North Atlantic Ocean, 390 miles (628 km) southwest of the island nation of Cape Verde.   

Notable cities that fortuitously find themselves inside the totality path include Idaho Falls; Casper, Wyoming; Lincoln, Nebraska; Columbia, Missouri; Nashville, Tennessee; and Columbia and Charleston, South Carolina. The metropolitan areas of Kansas City and St. Louis straddle the southern and northern edges of the totality path, respectively.  
A number of cities and towns lie just outside of the totality zone, and their residents will see the sun cut down to an exceedingly thin sliver of light. These include Portland, Oregon; Boise, Idaho; and Knoxville, Tennessee. But a partial solar eclipse pales in comparison to a total one, even when more than 99 percent of the sun's disc is obscured. The great show can only begin at the moment when the last speck of sunlight is extinguished.  

On the edge!

Earlier, I said that 12 states lie within the eclipse path, but to be more precise, there are actually 14; the shadow will also give glancing blows to two other states. About 5.4 square miles (14 square km) of the southernmost tip of Montana's largest county, Beaverhead, will be tucked just inside the northern limit of totality, providing up to 50 seconds of total eclipse. And an even tinier plot of land — 0.7 square miles (1.8 square km) — in the extreme southwest corner of Iowa's Freemont County will be barely nicked by the shadow's northern edge; there, totality will last up to about 30 seconds. 

And if you live in either Kansas City or St. Louis, you'll want to know where the boundary line will run between a 99.9 percent partial eclipse and the far grander spectacle of a total eclipse. In Kansas City, the southern edge of totality lies very near to the Central Avenue Viaduct Bridge in the Central Industrial District; the farther north you go, the longer the duration of totality. Totality will last longest in the neighborhood of Ferrelview, with a duration of about 2 minutes.  

In St. Louis, the northern edge of totality runs close to the Hi-Pointe and Forest Park South East neighborhoods; heading south will lengthen the time of total eclipse. Totality will last longest in Patch, the southern tip of the historic Carondelet neighborhood, with a duration that's close to 80 seconds. [Incredible Solar Eclipse View Shot During Alaska Airlines Flight (Video)]

The table below provides local circumstances for 21 cities that are within the path of totality. For each location, it gives the local daylight time (LDT) of the beginning of the partial phase (First Contact), the start of totality and its duration (Dur.) and the altitude (Alt.) of the sun above the horizon at midtotality. Finally, there's the end of the partial stage (Last Contact). "P.A." is the position angle of the point where the sun's and moon's discs touch. It is measured clockwise around the sun's edge from 0 degrees at the north point of the disc. Hence, the value 42 degrees for Yaquina Head means that the first "bite" out of the sun will appear in the upper right part of the solar disc.

[img=553x0]http://www.space.com/images/i/000/057/663/i02/aug-21-2017-schedule.jpg?1471578676?interpolation=lanczos-none&downsize=640:*[/img]

Weather prospects

To help observers pick the best opportunity for cloudless skies on Aug. 21, 2017, many experts are scrutinizing climatological records in and near the path of totality. Climatological cloud amounts are consulted only because there are no reliable alternatives. 

Unfortunately, meteorological weather forecasts for eclipse day are not possible more than a week or so ahead of time. The best probabilities of clear skies for eclipse viewing appear to be in the region running from western Oregon through Wyoming, where, on average, the odds for fair skies are on the order of about 70 to 80 percent. Going farther east, the odds gradually diminish; across the Piedmont plateau to the Atlantic coast, it appears to be just about a coin toss: 50-50, except perhaps less than 50 percent for people in the western mountains of North Carolina and the coastal plain of South Carolina.  

People living around the immediate Pacific coast of Oregon, with its gusty onshore winds and frequent bouts of low cloud and fog, appear to have the lowest odds of seeing the eclipsed sun — probably only around 40 percent. Regardless of where you plan to be, staying mobile to dodge cloud cover will always enhance your chances.

Space.com will be providing more details about the "Great American Eclipse" in the coming months. But for now, be sure that when you get a 2017 calendar, you put a big red circle around Aug. 21!



Editor's Note: This coming Aug. 30 at 7 p.m. EDT, Space.com Night Sky columnist Joe Rao will be giving a special presentation at New York's Hayden Planetarium titled, "Countdown to Totality." Joe will detail all the specifics concerning next year's big solar sky show and, utilizing Hayden's state-of-the-art Zeiss IX planetarium projector, will attempt to replicate the sights and sounds that accompany an actual total eclipse of the sun. 
Full details can be found here: http://www.amnh.org/learn-teach/adults/h...o-totality



  
Angular size wise Was as 33.3 is

Table:   Frequency of Solar Eclipse Types 
        for 2000 BCE--3000 CE  at Nodal Alignments
_______________________________________________________
    Type       Number   Percentage
_______________________________________________________
    total       3173       26.7
    annular     3956       33.2 
    hybrid       569        4.8
    partial     4200       35.3 
    all types  11898      100.0
_______________________________________________________




On average, the Moon appears to be slightly smaller than the Sun as seen from the Earth, so the majority (about 60%) of central eclipses are annular. It is only when the Moon is closer to the Earth than average (near itsperigee) that a total eclipse occurs.[16][17]

 
Moon
Sun
At perigee
(nearest)
At apogee
(farthest)
At perihelion
(nearest)
At aphelion
(farthest)
Mean radius
1,737.10 km
(1,079.38 mi)
696,000 km
(432,000 mi)
Distance
363,104 km
(225,622 mi)
405,696 km
(252,088 mi)
147,098,070 km
(91,402,500 mi)
152,097,700 km
(94,509,100 mi)
Angular
diameter[18]
33' 30"
[Image: 56px--Phase_of_the_moon_NO.16.jpg]
(0.5583°)
29' 26"
[Image: 49px--Phase_of_the_moon_NO.16.jpg]
(0.4905°)
32' 42"
[Image: 54px-The_Sun_by_the_Atmospheric_Imaging_...100819.jpg]
(0.5450°)
31' 36"
[Image: 53px-The_Sun_by_the_Atmospheric_Imaging_...100819.jpg]
(0.5267°)
Apparent size

to scale
Order by
decreasing
apparent size
1st
4th
2nd
3rd


It's almost more like astronomy was a kind of entertainment before there was television

Where's my remote control???



Did you know eye was the first person age of electric frontman ever signed an autograph for?
I Got Drunk @ his Parents table @ a GIG wayyyyyyyyyyyyyyy back in the day.
My ex-girlfriend back then probably tossed it out with the rest of her mementos Doh

Star TV is an attitude of latitude and tempus' prolong imbued by  longitude.

~19.5
Quote: Wrote:The two points where the Moon's orbit crosses the inclination to ecliptic are called the nodes. The line that connects the nodes passes through the Earth. This line is called---very imaginatively---the line of nodes. The line of nodes rotates westward ~19.4 degrees per year.

anabibazon [Image: 0257fd0006daad8eba41929948e918cc.jpg] catabibazon

Frequency of Solar Eclipse Types 
        for 2000 BCE--3000 CE  at Nodal Alignments
_______________________________________________________
    Type       Number   Percentage
_______________________________________________________

    annular     3956       33.2 
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~33.3 + ~negative 1
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England’s first prehistoric stone ‘circles’ may have been square
It is believed to be the first prehistoric "stone square" ever discovered – in Britain or continental Europe [Image: avebury.jpg][img=788x0]https://static.independent.co.uk/s3fs-public/styles/article_small/public/thumbnails/image/2017/06/28/20/avebury.jpg[/img]Stones at the Avebury stone circle PA Archive/PA Images

One of Britain’s most famous prehistoric monuments  - Avebury in Wiltshire – may be substantially more ancient than previously thought.



Investigations within the UNESCO World Heritage designated stone circle - the largest in Britain - have revealed a hitherto unknown, and probably very early, series of ancient standing stones, are arranged, not as a circle, but as a 30 metre by 30 metre square.


It is believed to be the first prehistoric "stone square" ever discovered – in Britain or continental Europe.  It is conceivable that the newly discovered monument, which would have originally consisted of around 17 standing stones, was built up to a thousand years before both Stonehenge’s  and Avebury’s surviving stone circles.

Most of the newly discovered stones (or in some cases the holes they had stood in) had been buried (or, in the case of stone holes, filled in) at some stage in prehistory – or, more probably, in mediaeval or early modern times.


What’s more, at the centre of the square, archaeologists, re-analysing pre-war archaeological records, have discovered the remains of a substantial Neolithic timber building – constructed in mid-fourth millennium BC style.

That would make the ten metre long, six metre wide building the oldest feature yet found at Avebury. It would also raise the possibility that the stone square, constructed around it, is equally old or was built slightly later but while the building was still standing (i.e., up to a few hundred years later). The sides of the building and the sides of the stone square are aligned with each other – so a relationship between the two is likely.



If the building does indeed date from some five and a half thousand years ago, the discovery helps push back the date of the origins of Avebury by up to a thousand years.



[Image: avebury-skycopter-still.jpg][img=564x0]https://static.independent.co.uk/s3fs-public/styles/story_medium/public/thumbnails/image/2017/06/29/00/avebury-skycopter-still.jpg[/img]
The exact area where the archaeologists have found the prehistoric 'stone square' and timber building (National Trust)


If the newly discovered stone square also dates back to the fourth millennium BC, then it would potentially be the oldest standing stone complex in England – and around the same age as the oldest ones in Scotland.



What’s more, the square shape of the newly revealed early Avebury standing stone enclosure is totally unique – indeed without parallel anywhere. 



It is likely that both the rectangular building and the stone square surrounding it were of religious or ceremonial significance – but so far the archaeologists have found no clues as to the precise nature of any ritual or ceremonial activities that may have taken place there.



The early date for the stone square (and the building it appears to enclose) is also supported by two other pieces of evidence from Avebury. Both the site of the timber building and the stone square itself were located in the centre of a  100 metre diameter stone circle (in the southern half of Avebury) which was probably built at a later date – perhaps in or by the mid-third millennium BC.



A second identical stone circle was erected, presumably at around the same time, in the northern half of Avebury.


video: http://www.independent.co.uk/news/avebur...13421.html

Man finds ancient medieval city on border of England and Wales

Significantly a group of three massive standing stones stood at the centre of that northern circle – and has been scientifically dated to somewhere between around 3500 and 2800BC.



The stylistic dating of the southern circle’s timber building and the scientific dating of the northern circle’s central standing stones both point to very early ceremonial activity at the centre of what would eventually become Avebury’s still surviving northern and southern stone circles.



Additional support for an early date for the newly discovered  timber building and stone square is also provided by fragments of pottery all dating from between 3600 BC and 2800 BC found many years ago in that specific area.



The discovery of a stone square, arguably pre-dating most British stone circles, raises the possibility that other similar monuments were built in the fourth millennium BC – but have simply not been discovered. The find therefore has the potential to completely rewrite the evolution of standing stone complexes in Britain.



The Avebury  UNESCO World Heritage Site, cared for by the National Trust, contains three stone circles – including Europe’s largest which is 330 metres across and originally comprised around 100 huge standing stones.


A research team led by the University of Leicester and the University of Southampton used a combination of electrical resistivity, ground-penetrating radar and archival research to investigate the site.

http://www.independent.co.uk/news/avebur...13421.html
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A couple of items - I think I've made some progress lately but it's kind of soon to really tell... it LOOKS to me like there is most likely at least one more important approximation of Venus' orbital period, namely 225.3210359 (days). I've been trying to avoid making this concession, but the figure seems to be pedigreed and versatile, and tentatively appears to be the missing piece in at least some important equations. If there is another version of the Long Count that comes along with it, I couldn't tell you yet. There actually is something that is about 18990 (days) but I've really been trying to avoid complicating the proceedings with that one also, so I haven't even really explored the question anywhere near as well as might be done.

Also, the Thom Type A Flattened ring has a particular value that's intriguing, it is "angle Theta = 19.10660535*" and I'm increasingly convinced that is intended to be interpreted as 19.11240674 (degrees). I often used to wonder that back when I was originally working on it but was never quite that sure (10 Ellifinos was the other thing I kept wondering about). 19.11240674 x or / 10^2 continues to accumulate some evidence of respectable pedigree (back in the day when I was wondering, I posted some aliases of this figure doubled), and it's finally come to my attention, since attempting to understand Mayan math has seemingly justified my trying to be more conscious of squares and square roots, that

19.11240674^2 = 365.2840914

This would automatically build this days-of-the-year figure into all stone circles classified as Thom Type A Flattened Rings.

365.2840914 is in turn beginning to reveal just enough pedigree that it might be best to try to take that figure seriously as another valid expression of the number of days in a year. It's just as much a setback as it is progress, though, to try to go back and work out where these figures fit in as carefully as I've tried to do with most of the other figures recently commanding attention.

FWIW, after many equations showing the relationship of "Alternate Pi" 1.1772245771 to ancient Venus math, there is

225 / 1.177245771 = 191.1240673

So the figure has gotten that much harder to ignore lately, even if I'm not half sure what it really is.

This figure for the year seems to belong to the proceedings to some or other degree

365.2840914 / 225 = 1.623484851 = 1.622311470 x 1.000723277 = 365.020081 / 224.8373804 = 12.98787878 / 8

Also I've developed a case of "The Seventy Two Problem," which is that that I've finally realized that some of what looks like often-repeated use of 7.215488220 (1 / (1.177245771^2)) most likely means 7.200000000, but combining the use of the meter with the lack of data at the third place after the decimal, means that the data just isn't going to be precise enough to help sort that out of itself - both 7.2 and 7.215488220 are going to come out looking like 7.215488220 (or the other half of the time 7.2 will get rounded down to 7.185039370) - and instead, finding the original intent is left up to trial and error. Thus I may have some fairly elaborate equations to recheck to make sure I didn't miss an appearance of "72 Proper" somewhere. 

2.19 m = 219 cm = 7.185039370 ft
2.19456 m = 219.456 cm = 7.200000000 ft <--invisible to archaeologists using the #$&*@!! centimeter/Metric system? 
2.20 m = 220 cm = 7.217847769 ft (7.215488220 = (1 / (1.177245771^2)) x 10) 

It's one reason I haven't made any declarations on the rooms at Rio Bec based on Andrews' data yet, it occurred to me that I should be seeing some versions of some of these equations that actually use 72 / 10 as 72 / 10. Likewise regarding the length of the Rio Bec building as mentioned previously,

(Hay, Clarence L., 1935. A Contribution to Maya Architecture. Natural History 36 (1): 29-33).
"As in all Maya work, the building is not entirely symmetrical. The central doorway is set slightly to the left as is the double roof comb. An amazing accuracy, however, was reached in the length of the building, for although the north wall had fallen, the measurements taken on the site indicated a length of 84 feet 1 inch on the east side, and 84 feet 2 inches on the west"

These look remarkably like 18980 / 225 = 84.355... to me but I'm just not quite sure what is meant exactly. Both could be meant as (1 / (12 (Pi^2) x 10^n) = 84.43431970 which belongs to equations involving both current candidates for the Long Count of the Maya, but there are actually as many as a half dozen interesting candidates in this range and another Long Count figure may be on the horizon, and the small disparity noted by Hay may well mean that a particularly good pair was selected rather than any single figure for both east and west walls.

I have been working on the iconography again, though. I'm as convinced as ever that the mythology is directly reinforcing some of these mathematical concepts - that we see monster mouths, teeth, fangs, skulls, serpents and human beings flayed alive not for reasons of an oppressive religion or morbidity, but for reasons of arithmetic - which is not at all unlike what we might expect from some other ancient cultures. 

In fact, one of the things I think is that all you have to do is permit more than one concentric band of hieroglyphs on a circular calendar stone, and you've probably created the inevitable forerunner to the tortoise shell motif as can be found in "altars" at Copan. (I'm not entirely sure yet but examples of a "transition" model between the two might have appeared at places such as Yaxchilan if these aren't already reiterations of even older iconography).

Another thing I think is that as far back as La Venta ("altar" 4) you can see some of this in iconographically-correct context including what may be an underappreciated early appearance of Xipe Totec or Coatlicue, which may be telling us (among other things mathematical) that ancient calendar math and geodetic math have been woven together for convenience for quite some time. 

[Image: altar_4_la_venta_side-14FD6E8AECD2F0502BA.jpg]
La Venta, "Altar" 4
Left hand of figure at left protrudes from second ("flayed") skin twisted into (earth) "serpent"? 
Since these "flayed" deities may represent the serpent shedding its skin, their use may carry responsibility for serpent-related 
(i.e., metrological and geodetic) concerns and mathematical figures? 
This monument, like numerous others, may be a conceptual and mathematical representation of the earth?

[Image: LCM+Tlaltecuhtli+drawing.jpg]
Tlaltecuhtli Disc at Xihuacan
Demonstrates awareness of Venus' orbital relationship to pentagonal geometry, invites division of circle into 5 segments of 72* each, and links this to iconography (and mathematics) of a double-headed serpent, which (or alternately, the duality of the shedding serpent and the shed skin) may symbolize the duality of geodetic measurement of divergent polar and equatorial values (and / or the duality of circumference as reckoned in both miles and feet?)
(The artifact may also exhibit, in my personal opinion, what may be considerable Peruvian design influence? - and yes, that may actually be the Pi symbol under the circle in the center?!?)

[Image: p22.jpg]
"Stellar Venus symbol from Teotihuacan, dispensing influence downwards towards the earth. Compare with picture 8 in Egypt Gallery 6"

The same is probably true of the spiral eyes we find in some of this work - see Chenes culture - i.e., that it refers to the utility of constants related to spirals, like Phi and e and/or their various approximations, although this part may be harder to prove given that while George Andrews provided tons of data including doorway widths at many sites, so far its looking like it was mainly at Tikal where he bothered to get data for the height of doorways, so what exactly we see these spirals motifs adorning in terms of arithmetic may be harder to determine. Even though I'm still experimenting with the idea, I do think things are probably looking good for a good part of the reason we see the Chenes "monster mouths" to be because they really are referencing the number of teeth that human beings can boast, which according to Wikipedia totals 52, the same number of weeks in a year. 

[Image: X0674C-Chicanna-Structure-II-House-of-th...loured.jpg]
"Monster Mouth" Door at Chicanna
The number of teeth you were expecting, divided or multiplied by the number of teeth that actually appear, is one of the rules?

[Image: foto02.jpg]
"Monster Mouth" at La Venta (and elsewhere):

Naturally, Le Serpent Rouge continues to struggle valiantly to maintain identity as a "serpent-related" number for no good reason, as can be seen in this combination of spiral related constants

Alternate e' 2.720174976 / Alternate Phi 1.622311470 = Le Serpent Rouge 1.676727943

This form of "52" - 51.95151522 reacts with Alternate e' to produce

51.95151522 / 2.720174976 = 19.09859317 = 60 / Pi = sqrt 364.7562611, our second most valuable figure thus far for representing the 365 day year...

And it reacts with our new friend 19.11240674 to produce a more e-like value (logarithmic e = 2.71828182845)

51.95151522 / 19.11240674 = 2.718208960 

And that would probably be another point for Professor Thom's Stone Age Geniuses as well as for the Maya...

Although the precise results may of course depend a great deal on exactly which of a number of possible representations of "52" that we choose to work with.

Hopefully I will find time in the next week to cover some of these things and a few others in a little more detail.

Also I've begun to wonder if some of the ancient UK Megalithic "cup and ring"-marked stones might not constitute maps of nearby monuments rendered not-to-scale, but it sounds like just the kind of hypothesis someone else would have beaten me to, so corroboration of that, if there is any merit to the idea, could already be out there somewhere? (It occurred to me that such maps might be readable even when travelling at night without a suitable light source).

As to the reasoning behind this daring proposal

"Temple IV (Maler) 
Width 10.17060367 Height 10.40026247 Ratio 1.022580646 Product 105.7769476

Perhaps the most pleasing and sensible interpretation for what was intended could well turn out to be
Width 10.25135528 Height 10.47197551 Ratio 1.021521079 Product 107.3519415"

This gesture locks both unexpected figures 10.25135528 and 1.021521079 into a remarkable series using the now traditional Tikal (Pi/3) probe. What it sets up literally display forwards and backwards in a far more interesting manner than using would using 10.39030304 and the square root of 103.9030304 = 10.19328359 to announce that particular square root relationship. Here's the series forwards, as far as I recognize it with out additional analysis (I have to say, it looks a bit like it might have been a fairly typical Maya practice to try to find ways to start a series such as this a little higher or lower than we might usually think to - at first you think you're on the wrong track and then suddenly at least five really hot responses in a row).

1 / 1.021521800 = 9.789323197 / 10
9.789323197 x (Pi^3) = 10.25135528
10.25135528 x (Pi^3) = 10.73519415 = 1 / .93151552369 = (38.81314682* x 24) / 10^n 
10.73519415 x (Pi^3) = 11.24186902 = 2.248373804 x 5
11.24186902 x (Pi^3) = 11.77245771 = 10 Alternate Pi
11.77245771 x (Pi^3) = 12.32808889 = 20 / Alternate Phi 1.62231147
12.32808889 x (Pi^3) = 12.90994449 = (1 / sqrt 60) x 100
12.90994449 x (Pi^3) = 13.51926226 = (1 / Squared Yoda Megalithic Yard) x 100
13.51926226 x (Pi^3) = 14.51733833 = (1 / (6 x 1.177245771)) x 100
14.51733833 x (Pi^3) = 14.82553003 = (1 / (57.29577951 x 1.177245771)) / 10^n
14.82553003 x (Pi^3) = 15.52525874 = 31.05051749** = (1 / 64.41116483***) x 10^n 
*= (see previous info on Temple I outer proportions & Yoda's diagram)
**= (see previous info on Great Pyramid & Pyramidion) 
***=(see previous info on Tikal temple doorway proposals)

I could be wrong but I'll be hard pressed to come up with anything better, even it really is only a previous Tikal proposal that's reframed and reiterated even more dramatically, showing off (Pi/3) as active in context to about the twentieth power.
"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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(07-01-2017, 09:10 PM)The Pi Piper Wrote: In fact, one of the things I think is that all you have to do is permit more than one concentric band of hieroglyphs on a circular calendar stone, and you've probably created the inevitable forerunner to the tortoise shell motif as can be found in "altars" at Copan. (I'm not entirely sure yet but examples of a "transition" model between the two might have appeared at places such as Yaxchilan if these aren't already reiterations of even older iconography).

Okay, sorry... This one I have to take back already. There is indeed such an example of a calendar stone with multiple rings of hieroglyphs in "Altar" 22 at Yaxchilan...

[Image: IMG120069.jpg]
"Altar" 22 at Yaxchilan

However, what really might have prompted this symbolism more than anything else is how often tortoise shell can expected to exhibit a certain number of major divisions. I really don't know what's typical but I just looked at a dozen different and rather diverse looking examples of turtle shells and they predominantly showed 14 major divisions (one showed 13), which is of course a significant calendrical number.

Eventually, we get

[Image: 18RabbitLo2.jpg]

[Image: 5647543968_d2f1aaaa94.jpg]
"Altars" at Copan
"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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(07-01-2017, 12:45 AM)EA Wrote: The Avebury  UNESCO World Heritage Site, cared for by the National Trust, contains three stone circles – including Europe’s largest which is 330 metres across and originally comprised around 100 huge standing stones.

I should go back and see what Thom had to say about Avebury since it's dangerous to accept measures that look this round, but 330 m = 1082.677165 ft = 3401.330629 / Pi ft and that is ringing some bells. I'll try to look it up but knowing me, if this were to be treated as a perfect circle the way you might at first treat the Great Pyramid as a perfect pyramid that isn't indented on the sides before moving on to the fact that is indented, I probably called it 1081.540980 x Pi = 3397.761197 

4 / 1.177245771 = 3.397761197 = 360 / 1.059521194 = ((1 / 57.29577951) x 19.46773764), or
19.4677376 / 57.29577951 = .3397761197 while
19.4677376 x 57.29577951 = 1115.419203

I'm a little less sure given that the Maya do indeed seem to have more surprises for me at right about 3.40-something, but at the time the proposed 3397.761197 ft circumference would have been fairly well tested - I was trying to be really careful reauthoring any of Yoda's data on Stonehenge, Avebury, or Silbury at the time, and tried to make sure things fit together really well. Time for a review, though, if I can find more of my old data on the Megalithic Landscape.

This reminds me that another idea I'm experimenting with is whether the door proportions of the Tikal temple doors were so carefully selected that they have significant diagonal values, which is a mathematically related noted because one looks like it might be 16.98880598, which happens to be half of 33.97761197. Still not sure what to think of the proposal, largely for lack of more working examples.

You never know, though - I probably still swear by SRVS 887.6223994 as a "can opener" for interpreting irregular monuments, and "Dos Ellifinos" x 887.6223994 = 3410.93528 = 584.0321293^2 / 10^n, 584.0321293 being still our sole candidate for the Venus Synodic period...

[Image: dosequis.png?itok=rJ_CARoD]
"I don't always do math, but when I do, I drink DOS ELLIFINOS...
Stay curious, my friends!" 

Yoda may get more points for the prospect of SRVS somewhere in the workings at Tikal, given the most recent Venus orbital period proposal is equivalent to

2 / SRVS = 2 / 887.6223994 = 225.3210376 / 10^2

And that btw IS what you get via

(Alternate Phi 1.62231147 / 72) x 10^n = 225.3210376

In contrast to the usual figure I'm using

(Not-Phi 1.61882914 / 72) x 10^n = 224.8373806
"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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