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The Great Pyramid
Is Carlotto's geometry supposed to apply to it in 2-D or 3-D?
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
...that would be 2-d.
[Image: 11915938413_490895347f_o.jpg]
I think he intended it as the underlaying floor-plan / geometry of the 'foundation'.(The Base)

in 3-d...the angles of the five 'facets would of course be different as well as both side lengths up to the apex.

The Base-lengths would be the same in 2-d plan and 3-d plotting
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Okay... Can I give you a Ted Talk on finding ways to reduce geometry to right triangles so you can continue to apply the Pythagorean Theorem? Remember that triangles with angles of 60* are equilateral (60* x 3 = 180*) so they'll be equal on all sides.
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Never mind me here, I'm just going to rattle off a few things while I happen to be thinking of them. One is that I'm intrigued to see how things turn out on Mars because it may mean that for the first time I'm going to have to contend with figuring out what a Pyramid Pi Meter looks like. I've been starting to see hints of one in the Great Pyramid interior and then I ran across a webpage where I thought someone was doing a halfway respectable job of arguing that the ancient Egyptians must have been familiar with the meter.

The ratio between the squared radian and the meter is pretty fine... We can make a "Pyramid Pi Meter" if we choose, using one of our fine ratios - particularly the handiest fine ratio 1.000723277...  

57.29577951^2 = 3282.806350 / 1000 = 3.282806350
3.280839895 = (1/.3048)
3.282806350 / 3.280839895 = 1.000599375
3.282806350 / 1.000723277 = 3.280433687775 - It's been proposed before as a "Matrix-Valid Meter"...

Although historically I don't think know of anyone thus far ever having gotten it to work well, or of having figured out exactly how it would fit into the number system it comes from, or of having gotten any geodetic value out of it. We've so far gotten away, as far as I know, with treating the meter like it isn't one of ours, and hating it for how annoyingly often that using meters instead of feet allows archaeologists to get away with being even sloppier than usual (not yet including archaeologists converting figures into feet and then the reader having to convert them back again without a stated conversion key).

1.000723277 is the reason (so to speak) that the Yoda Great Pyramid Height isn't a rational number of feet
480.3471728428 ft / 480 ft = 1.00072327675

At the moment, I'm reviewing Egyptian Metrology according to Wikipedia - not terribly authoritative but the values given seem to be working reasonably well for the most part, so I'm curious to see where it goes. I've never been able to force myself to be all that preoccupied with Digits and Palms before partly since the usual formulas don't wholly belong to the Pyramid Pi system and partly since the few Egyptian units I seem to be working with (which seem to be the most important ones) seem to be working well enough without that.

It's encouraging to me that if one lays out the measures for the GP inner architecture in a small spread of metrologies, one might be able to both find the most promising metrological schemes, and avoid some of the pitfalls of trying to sort out whether we really see the use of 7, 11, 14, or 28 at work in the main metrology. In the King's Chamber or Queen's Chamber, there are some confusing candidacies - for example

King's Chamber, Height
Lehner, "Complete Pyramids" - 19.02887139 Feet =
228.3464567 Inches =
11.07054862 Cubits (of .03 Radians ft)
15.63930786 Remens (of e'/sqrt 5 ft)
6.995908599 Megalithic Yards

How many people would take this unquestioningly to actually mean that 11 Cubits = 7 Megalithic Yards, literally - provided they're even willing to entertain the thought of a contested Megalithic British measurement in the Great Pyramid in the first place? That's the kind of stuff that can happen if one doesn't insist on greater accuracy - something else we're not likely to get if someone thinks that isn't to be found among ancient works either - but hopefully these mistakes are less likely to happen dealing with the relatively large measures of the Giza pyramid interiors than when dealing with individual units of numerous, mostly small metrological units where errors are reduced to mere 1000s of a foot or less. Lots of stuff looks "close enough" at that level of magnification... (and there are, what, maybe 5 people in the whole world who realize that 7 and 11 may belong to a 7-11 Store and not to your basic pyramid math?)

Using larger numbers of these units - i.e., 500 remens or 77.60 Squared Yoda Meg. Yards in a pyramid apothem, for example - should help take some of the guesswork out of it for the humble seeker, which is why I'm inclined to refer to such things as metrological standards. At the scale of most of given ancient units, it may be extremely hard to sort out by actual measures whether, for example, a

"Fist" of "11.25 cm" = 0.36909448819 ft means 
exactly 1/10 of a Squared Yoda Meg Yard (SYMY) .3698426665 ft, or 
exactly 6 Palms of 1/5 of 1 remen .2433467205 ft x 6 = .3650200806, or

The later is part of the specified formulary progression, but the former is a considerably closer match for the given value, and who's going to have an easy win in an argument over 5/1000 of  foot?

Even so, some of the figures we see in the basic interpretations of parts of Great Pyramid's interior such as chambers of ostensibly 10 cubits x 20 cubits x 10 ellifinos appear as if they may be also intended as metrological standards in spite of their scale, being we seem to see very simple rational values of multiple units involved even after our system has taught us time and again that things like that are about as exciting as watching paint dry. 20 cubits / 1 cubit = 20 probably isn't exactly newsworthy.
The most successful thing currently seems to be to take these alleged cubit fractions as assembled by Wikipedia and treat them as remen fractions instead, something I should have guessed long ago when having great success working with Algernon Berriman's remen fractions.

I have to say, I'm inherently skeptical about a "20.61" ft cubit because even if this eventually found favor with Petrie, his measures of the Pyramid interiors as I have them (I still need to review Petrie's texts) still seem to make pretty good cases for the "20.62" royal/sacred cubit.

However, if it served a purpose 20.626480624 / 1.000723277 = 20.611572747 would probably be the quickest way to generate a cubit of "20.61" to experiment with, and I did just pull that same trick with the squared Radian to make a makeshift meter, so there might still be more at work here than anyone has guessed yet?
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Before the Meter was Based on the Speed of Light...It was Based as one ten-millionth of the distance from the equator to the North Pole.

And the Great Pyramid has been identified as a scale model of the Earth's Northern Hemisphere from wich the arc of the distance from pole to equator was definately decimally derived. Arrow

If They Modeled the Northern Hemisphere and Gizah/GP was the prime meridian...the 'meter' would be "Natural" as a decimal based unit for a system of measures.

Cubits smchmubitz

Quote:The metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole.


From Wikipedia, the free encyclopedia

This article is about the unit of length. For other uses of "metre" or "meter", see meter (disambiguation).
Unit system
Unit of
Unit conversions
1 m in ...
... is equal to ...
   SI units
   1000 mm
 1×10−3 km
   imperial/US units
   1.0936 yd
 3.2808 ft
 39.370 in
   nautical units
   0.00053996 nmi

Look up metre in Wiktionary, the free dictionary.

The metre (international spelling) or meter (American spelling), (from the Greek noun μέτρον, "measure") is the base unit of length in the International System of Units (SI). The SI unit symbol is m.[1] The metre is defined as the length of the path travelled by light in a vacuum in 1/299 792 458 seconds.[2]
The metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole. In 1799, it was redefined in terms of a prototype metre bar (the actual bar used was changed in 1889). In 1960, the metre was redefined in terms of a certain number of wavelengths of a certain emission line of krypton-86. In 1983, the current definition was adopted.
The imperial inch is defined as 0.0254 metres (2.54 centimetres or 25.4 millimetres). One metre is about  3 38 inches longer than a yard, i.e. about  39 38 inches.
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
On Mars there IS a Datum Level.
On Earth The Meter WAS the Datum Level.

Quote:The problem with this approach is that the exact shape of the Earth is not a simple mathematical shape, such as a sphere or oblate spheroid, at the level of precision required for defining a standard of length. The irregular and particular shape of the Earth smoothed to sea level is called a geoid,

Meridional definition[edit]
In the 18th century, there were two approaches to the definition of the standard unit of length. One favoured Wilkins approach: to define the metre in terms of the length of a pendulum which produced a half-period of one second. The other approach was to define the metre as one ten-millionth (1/10 000 000) of the length of a quadrant along the Earth's meridian; that is, the distance from the Equator to the North Pole. This means that the quadrant (a section/distance  14 of the Earth's circumference) would have been defined as exactly 10 000 000 metres (10 000 km) at that time, with the total circumference of the Earth defined as 40 000 000 metres (40 000 km). In 1791, the French Academy of Sciences selected the meridional definition over the pendular definition because the force of gravity varies slightly over the surface of the Earth, which affects the period of a pendulum.
To establish a universally accepted foundation for the definition of the metre, more accurate measurements of this meridian were needed. The French Academy of Sciences commissioned an expedition led by Jean Baptiste Joseph Delambre andPierre Méchain, lasting from 1792 to 1799, which attempted to accurately measure the distance between a belfry inDunkerque and Montjuïc castle in Barcelona to estimate the length of the meridian arc through Dunkerque. This portion of the meridian, assumed to be the same length as the Paris meridian, was to serve as the basis for the length of the half meridian connecting the North Pole with the Equator. The problem with this approach is that the exact shape of the Earth is not a simple mathematical shape, such as a sphere or oblate spheroid, at the level of precision required for defining a standard of length. The irregular and particular shape of the Earth smoothed to sea level is called a geoid, which literally means "Earth-shaped", but does not correspond to the actual shape of the earth, but rather is a mathematical model of its shape. Despite these issues, in 1793 France adopted this definition of the metre as its official unit of length based on provisional results from this expedition.

Quote:What is the relation between radian, degree and grad?
Posted by Ancient Vizier - Today, 01:46 am

Quote:Okay... Can I give you a Ted Talk on finding ways to


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2 Answers
[url=][Image: -3-images.new_grid.profile_pic_default_s...fedf49.png]
Sachin Maurya, works at Accenture
Written 21 Jun 2015

1 degree = 1/360 of a circle 
1 radian = 1/(2pi) of a circle 
1 gradient = 1/400 of a circle (and is much less used than the others) 
1/400 of a datum Circle is 90 degrees or the Distance of the North Pole to Equator along any Prime Meridian.(where you derive your meter from naturally)
Degrees and gradients are arbitrarily chosen using convenient divisors (360 and 400). 

1 radian = the angle created when the radius of a circle is laid out along the circumference. 
Since C = 2 pi r, there are 2 pi radians in a full circle. 
1 radian = about 57.3 degrees = 63.66 grads.

So question arises is :-
 Why does anyone want to divide a right angle into 100 grads instead of 90 degrees?
grads are a decimal unit, and are subdivided into simple 100ths, just like the meter is subdivided into cetimeters..Degrees are not decimal units--they are subdivided into 60 minutes and then another 60 Page on every time you want to do a simple calculation (say, adding two angles), you have to do first do TWO extra steps--convert the seconds into decimal minutes, then convert the decimalized minutes into decimal degrees. (most pocket calculators have a simple button that does this, but it still requires you to press an extra button before doing the actual calculation that you want to complete.

try this example--add two angles : 75 degrees, 45 minutes, 20 seconds plus 25 degrees 15 minutes 10 seconds. 
or add 75.753 plus 25.251 
Which is easier?

Land surveyors (those guys you see on the side of the road with an instrument mounted on a tripod) make hundreds or even thousands of angle measurements during a day's work.

Grads are great!!! :)

33.30 gons=
33.3 grads=
29.97 degrees=
29 degrees 58 arc minutes=
523.1 mrads=
0.5231 radians

Great Pyramid of Giza set at 29:58:50.952 N = ~33.30 GONS

The Great Pyramid is located at 29:58:50.952 N =~33.3 grads
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Right, right... Sir Fig Newton used to think stuff like that, which is one reason I'm Proud To Be A Pyramidiot. I will be in his Distinguished Company in hell someday and I'll get to ask him face-to-face, "How do you like your thermodynamics now, b**ch?" since entropy is always the stock answer why the power bill is so damned high.

Not that I'm arguing but you do realize there are implications in finding a geodetic unit of measure on Mars, right? Aliens schmaliens...

[Image: 11915938413_490895347f_o.jpg]

Okay, let's start from the ground up with the 2-D model first so that I don't have far to fall when I land on my face. So you have sides of 3333 meters and 2356 meters, do I have that right? And we have three equilateral triangles so all of their edges will be 2356. So the height of these triangles is sqrt ((2356^2) - ((2356/2)^2))) = 2040.36 since according to Pythagoras a^2 + b^2 = c^2 and c is the hypotenuse of known value 2356.

c) 2356^2 - b) 1178^2 = a) 2040.36^2

For some reason, the Chephren appears to be a model of Pythagoras' formula and it may be the only thing at Giza that Vi and I agree on (until we start measuring it anyway), so cherish it accordingly.

So the length of this object from midbase at the bottom of the picture to the points-at-the-face tip is 2040.355851 + 2356 = 4396.355851 m

If the height of the apex is 1947.1 m, the slopes are

a) 1947.1^2 + b) 2356^2 = c) 3056.46^2 


a) 1947.1^2 + b) 2043^2 = c) 2822.24^2

So the length along the ground is 
2040.36 + 2356 = 4396.36 m

and the length up the side, over the apex, and down the other is
3056.46 + 2822.24 = 5878.7 m

We'll call them l(g) 4396.36 and l(a) 5878.7 on those accounts.

And the max width (w) is going to be the height of two of the triangles = 2040.36 x 2 = 4080.72 m

The total base perimeter (p) is 3333 + 3333 + 2356 + 2356 + 2356 = (3333 x 2) + (2356 x 3) = 13734 m

And we'll call our two edge values and e(a) 3333 (<--you're famous!) and e(b) 2356 

So here are some statistics to start out with...

p / l(g) = 13734 / 4396.36 = 3.123947993
p / l(a) = 13734 / 5878.7 = 2.336230799
p / w = 13734 / 4080.72 = 3.365582544
l(a) / l(g) = 5878.7 / 4396.36 = 1.33717439
l(g) / w = 4396.36 / 4080.72 = 1.077349095
l(a) / w = 5878.7 / 4080.72 = 1.440603619
p / e(a) = 13734 / 3333 = 4.120200000
p / e(b) = 13734 / 2356 = 5.829371817
e(a) / e(b) = 3333 / 2356 = 1.414685908
l(g) / e(a) = 4396.36 / 3333 = 1.319039904
l(g) / e(b) = 4396.36 / 2356 = 1.866027165
l(a) / e(a) 5878.7 / 3333 = 1.763786379
l(a) / e(b) 5878.7 / 2356 = 2.495203735
w / e(a) = 4080.72 / 3333 = 1.224338434
w / e(b) = 4080.72 / 2356 = 1.732054329

I haven't worked with the height yet, nor have I even begun analyzing those numbers (several probably don't require analysis)... (In fact, being a Pi Jedi, I wouldn't know Phi if it bit me on the Pi Hole).

However, I'm particularly encouraged by this one

p / h = 13734 / 1947.1 = 7.053566843

Also I could point that the width 4080.72 m looks intelligible already

4080.72 / 1500 = 2.72048 = ~e' (.9999194889)

(Also I might emphasize that "decimal harmonics" of 15 are tetrahedral - I don't know who all is in the habit of thinking that, but 1 / 15 = .6666666666 / 10 and we know why that is a tetrahedral number already... but also, while I don't have the proofs handy, I do have in my notes that 1.5 is the ratio between the surface area of a tetrahedron and that of the corresponding double tetrahedron).

I submit this for your entertainment and possible enlightenment (and most importantly, for second opinions on accuracy since being a Pi Jedi doesn't actually keep me from sucking at math and geometry and I'm just terribly prone to boneheaded mistakes in general).
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Memoirs of a Pi Jedi
Chapter 3
Recent Remen-iscences

Meanwhile back at ancient Egyptian metrology, we seem to have some missing units of measurement (should have suspected this when most of the Wikipedia list are wee ones). One of them is the Ellifino, but there may be others. More understanding seems to be available from placing some of these measures in situ, such as measuring the diagonal of a square of 1 remen x 1 remen, or 1 cubit x 1 cubit. This motif has also been helpful so far

[Image: seedoflifesquareroot.jpg]

If  HE = 1 Royal Cubit of 1.718873385 ft,
EA = 2.430854053 = ~the Double Remen 2.433467205 ft = 1.216733602 x 2
EG = 3.843517733 = ~the Double Ellifino 3.8427772041 = 1.921388602 x 2
CD = 2.977176034 = ~the Double Short Cubit (Wiki: Short Cubit 45 cm = 1.476378 ft x 2 = 2.952756)

The question being which Double Short Cubit

a. 2 x 1.460080322, the prescribed value for the Short Cubit as "6 palms or 24 digits" derived from the remen
(1.216733603 x 1.2 = 1.460080322 = 2.920160646 / 2)

b. 2 x 1.480440658, the squared remen (1.216733603^2 = 1.480440660) 

c. 2 x 1.479370666, 1/10 of the Double Squared Yoda Meg Yard (7.396853331 x 2 = 14.79370666) / 10

(If there's a contest between them, I suppose accuracy favors His Most Highly Accurateness himself?)

If  HE = 1 Ellifino of 1.921388691 ft
EA = 2.717253945 = ~2.720174976 = 1 Megalithic Yard
EG = 4.297022562 = ~4.297183463 = 2.5 cubits of 1.718873385?
CD = 3.327942833 = ~3.346257609 = 1.718873385 x 1.946773764?

If  HE = 1 Meg Yard of 2.720174976 ft
EA = 3.846908343 = ~Double Ellifino of 3.842777381 = 1.921388690 x 2
EG = 6.082496157 = ~6.083668013 = 5 remens
CD = 4.711481263 = ~4.712388980 = 1.216733602 x sqrt 15? (careful with that one...)

If  HE = 1 Remen of 1.216733602 ft
EA = 1.720721162 = ~1.718873385 = 1 Cubit
EG = 2.720699046 (e' exactly) = ~2.720174976 = 1 Megalithic Yard
CD = 2.107444419 = ~2.107038476 = sqrt 240 / (225 / Pi^2) = the (so-called?) Palestine Cubit?

Note also that a rectangle of 1 cubit x 1 remen has a diagonal of

sqrt (1.216733602^2 + 1.718873385^2) = 2.105935985 ft.

I get a kick out of historians who refer to the Double Remen as a Roman Pace. Picture ancient Romans sitting around inventing their metric system: "All we gotta do is just double the remen precisely, and no one will ever know we stole it from the Egyptians"...  


So why can't I seem to find reference to this rather ostensibly ancient Egyptian Ellifino? (wait for it...) Ellifino!
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
I'm still looking for some data sheets I made where the latitudes of the vertices of additional Platonic Solids were worked out including some formulas I created from scratch since I couldn't locate any other examples even with all the math stuff on the Internets. I'm not even sure I can find most of the formulas at present even though I've got a set of printed sheets with their proportions and ratios. (It needs double-checking and it would be 1 Royal Pain^2 to re-type so still hoping for an electronic version). 

I just found this, though - I think it's probably a fairly even mix between some tetrahedral statistics and my attempts to project "generic" values for their proportions using the Radian value 57.29577951 as the Radius value in the equations, then trying to find Pi-related values that would serve to represent them. IIRC, I think the finished products are what you get if you use the Meg Yard value 2.720174976 as e'

excerpt from:
The Enigmatic Matrix Double Tetrahedron & Other Curios
Wed Sep 11 16:34:34 2002
Grid Point msg board
Previously, we used this approach

we wish our Circumradius (aka Radius, aka Radian) to be the generic Radian value of the Pyramid Matrix, 57.29577951 (the Radian in arc-degrees). With the Edge Length/Circumradius ratio of 1.632993161855, if the Circumradius is 1, the Edge Length will be 1.632993161855. So... if the Circumradius is 57.29577951, the Edge Length will be 1.632993161855 x 57.29577951, which equals 93.56361609

Then, we used the formulas EL2 x SA. Ratio= Surf. Area and EL3 x Vol. Ratio= Volume

Which we later corroborated using the known surface area and volume of the Sphere and the known ratios between them and the surface area of the tetrahedron (e').

Since our radius (Circumradius), like our diameter, for the "protruding" tetrahedron, is now 1/2 of the figure used for a single circumscribed tetrahedron, we repeat this replacing R (57.29577951) with (R / 2)... 57.29577951 / 2 = 28.65788976; 28.65788976 x 1.632993161855 = 46.78180805, which is the Edge Length of the smaller tetrahedral "protrusion" or "cap," and precisely 1/2 of the Edge Length of the larger single circumscribed tetrahedron 93.56361609 / 46.78180805 = 2.

Previously, for the single (larger) tetrahedron, we did essentially this:

R (57.29577951) x 1.632993161855 = EL 93.56361609
EL^2 (8754.15027) x el^2 / sa ratio sqrt 3 (1.723050808) = SA 15162.63302
For the surface area, and 
EL^3 (819069.9538) x el^3 / vol ratio (0.117851130) = VOL 96528.31619
For the Volume.

For the smaller tetrahedral "protrusion", we now do the same

R / 2 (57.2957791 / 2 = 28.64788976) x 1.632993161855 = EL 46.78180805
EL^2 (2188.537564) x el^2 / sa ratio sqrt 3 (1.723050808) = 3790.658255 SA
For the surface area, and
EL^3 (102383.7442) x el^3 / vol ratio (0.117851130) = VOL 12066.03995

For the surface area, as we add a smaller tetrahedral protrusion to the larger tetrahedron, we are actually covering up the bottom side and an equal area of the face of the larger tetrahedron, so what we actually gain in surface area is equal to 1/2 the total surface area of the smaller tetrahedron.

3790.658255 SA / 2 = 1895.3291131 gain in surface area for each small tetrahedron x 4 small tetrahedra added = 7581.316145 total gain in surface area, and adding this to the surface area of the large tetrahedron... 15162.63302 + 7581.316145 = 22743.94947

22743.94947, Surface Area of the Double Tetrahedron 

Referring to the Double Tetrahedron inscribed by a sphere of Radius = 57.29577951, our "generic" Pyramid Matrix format)...

For the volume, we simply add four times the volume of the "cap"- one "cap" for each side of the larger tetrahedron, to arrive at the total volume of the double tetrahedron.

VOL 12066.03995 x 4 "caps" = 48264.1598
VOL Tetrahedron 96528.31619 + total Vol of 4 smaller caps 48264.1598 = 144792.4760

14479.4760, the Volume of the Double Tetrahedron


It's not likely that these exact figures per se belong to the Pyramid Matrix, and in this case, when we seek close approximations there are a number of possibilities that present themselves. It would probably be most prudent, in spite of clear possibility of multiple intended Matrix-oriented to try to follow our previous approximation style...

"Alternate Tetrahedral Surface Area" ? 15165.55436 for 15162.63301
"Alternate Tetrahedral Volume" ? 96546.91716 for 96528.31961


96528.31961 / 15162.63301 = 6.366197714, the reciprocal of (1/2 Pi / 10)

41252.69124 / 2.720174960 = 15165.55436

& etc.

22743.94947, Surface Area of the Double Tetrahedron
14479.4760, the Volume of the Double Tetrahedron

Probably the simplest is to sample the ratio between the values for the single tetrahedron and the double tetrahedron:

22743.94947 Surface Area of the Double Tetrahedron / Surface Area of the Tetrahedron
15162.63301 = 1.5 

144792.4760, the Volume of the Double Tetrahedron / Volume of the Tetrahedron 96528.31961 = 1.5

Preserving this wonderful ratio, and applying this same ratio to the previously proposed Alternate Tetrahedral Surface Area 15165.55436 x 1.5 = 22748.33154, a possible "Alternate Double Tetrahedral Surface Area" 

96546.91716 x 1.5 = 144820.3757

The ratio between the Volume of the circumscribing Sphere and the double tetrahedron is now
787873.5293 / 144820.3757 = 5.44034995 = 2.72017496 x 2, or twice Alternate e'

The ratio between the Surface Area of the circumscribing 
41252.69124 / 22748.33155 = 1.81449973 = 2.72017496 x 1.5
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
[Image: video_encoding.jpg] Test Video
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Holey Smokes!!! google PRO is a free download now. LilD who knew??? Doh

Quote:Tuesday, May 2nd, 2017, 05:56 am

Is Carlotto's geometry supposed to apply to it in 2-D or 3-D?
Google Mars Pro has a unique feature where you draw a polygon in 3-d and then click on itz properties and there is a function where you can clamp your model polygon to the ground below or you can toggle it to a setting called Absolute.

The Absolute setting flattens your 3-d model to 2-d and floats it as an incorpereal outline above the 3-d object.

In Absolute mode you get Carlotto measures.
In Clamped to ground setting all the angles of the dangle change as the polygon envelopes the 3-d landform by draping itself over the dtm/image.

I must practice itz utility and we'll see what happens when I compare the Nadir "Absolute" 2-d angles to the different "clamped" to Ground/Truth 3-d angles.

2-d The same/difference  3-d
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
It continues to intrigue me that I seem to be able to get working data out of preposterously blunted metric system values, current case in point being the Wikipedia page on ancient Egyptian measurement...

I found the original posting regarding Berriman, which probably hasn't seen the light of day in some time. I might preface it with a remark or two - one thing that might be worth mentioning is that originally it seemed like Berriman was describing units that might fit into two categories - those descended from the remen, and those descended from Pi. Accordingly, there may be some confusion remaining exactly what some of the intended values are, and that may be reflected in the original work - it certainly continues in the current work.

There are several probably absurd or obscure concepts offered - the "Alnilam Cubit" (current faith level in an "Alnilam Cubit" = 0) and "Herpetometery" (long story), but there are some numbers included that may speak for themselves so I've avoided redacting such goofy remarks. The original text may also feature the groundwork for the realization that divergence of the remen itself may not be a terribly bright idea (outside of possibly extenuating circumstances?)

I can't find enough older material currently to have a good idea exactly how well road tested some of these figures were. Obviously the first thing you want to do with them is measure some pyramids and see what the results look like, but back then I may have regarded most of them as incidental, or mere curiosities as far as pyramid decoding goes. It looks like I'd attempted to diversify the cubit in accordance with various sources, but I'm really not sure how well it went the first time. Certainly, at the time I was lacking the formula "(360 / Remen) = ~Royal Cubit^2".

I am still at something of a loss for the proliferation of smaller measures as seen in Wikipedia - much of what's displayed could be spared simply by using remen (or possibly cubit) fractions, and remembering to use simple rational numbers as well as irrational ones, as mathematical probes. That remains an effective strategy because most of us may be lucky to memorize some of these units in multiples of one and probably don't recognize many simple multiples on sight.

Such a plethora of measures for objects most likely under a foot almost sounds as if many of these units exist because they were remeasuring their junk for bragging rights: "Yeah? Well MY Big Juan is 42.5 half-digits long, howdya like THAT?" - that's unforgivably pedantic of me in anything remotely aspiring to be a scholarly discussion and I'd have been better off refraining, and yet it borders on another ancient metrological mystery, because I'm anything but the first person to bring up metrology and human body parts, what with measures named after hands, fists, elbows, feet and etc. I find these too curious - these would be metrologies based on anything but a stationary reference, and taken literally they would be virtually useless to young students. So, what's up with all that?

Anyway, for whatever it may or may not be worth, here is the original post as it originally appeared.


When I SAY, "Everybody Loves Remen"...
Wed Jan 22, 2003
Grid Point msg. board

When I SAY, "Everybody Loves Remen", I bloody well MEAN, "Everybody Loves Remen" :-) Department:

Maybe in a year I will look back on this and think, "gee what a dribbling moron I was back there", but... 

Summary of Linear Units from Algernon Berriman, "Historical Metrology".

(image: scan of page 29 from Berriman's book, page titled "Summary of Linear Units")

Summary of contents: The usual cloud of palm, finger, and digit juggling where "x is 24 / 25 of that which is 174 / 175 of that which is 9 / 8 of that which is sqrt 3 / 2 to that which is..." you know, that kind of crap that nobody wants to deal with, written with little notation about contemporary equivalents, making for 40 pages of recalculating it all to find out where you came across what, since the whole book amounts to one long running equation that will take a year to re-write, and you are so grateful that rods and reeds and everything else was left out, that you really don't care about the oversight.

That, to quote a very wise person, "just ain't right, dammit".

Tips on unravelling ancient metrology: 

Okay, let me make this simple- don't make this simple. Make it hard on yourself. 
Bite off way more than you can chew, attempt to take on so many units at once that you can't remember whether you're working in inches or feet, and when it doubt, just keep desperately throwing 12 at things hoping to find your way back from totally lost.

If I can simply impress upon the reader the importance of DESPERATELY FLAILING, then he or she too can create for themselves the same experimental (scholarly term for "I haven't the foggiest clue what I am doing") metrological overview for themselves in under an hour:

Remen Centered:

DIGIT, in Inches: .7300401615
DIGIT, in Feet: .0683668013
FINGER, in Inches: .7604585008
FINGER, in Feet: .06337154174
GREEK CUBIT, in Inches: 18.25100404
GREEK CUBIT, in Feet: 1.520917003
ASSYRIAN CUBIT, in Inches: 19.4677376
ASSYRIAN CUBIT, in Feet: 1.62231147
PALESTINE CUBIT [Forumalaic*], in ft. 2.102515665
PALESTINE CUBIT [Forumalaic*], in Inches: 17.52096388
TALMUDIST CUBIT, in Inches: 21.90120485
TALMUDIST CUBIT, in Feet: 1.825100404
ROMAN FOOT, in Inches: 11.68064256
ROMAN FOOT, in Feet: .97338688
2.16 Roman Feet, in Inches: 25.23018793
2.16 Roman Feet, in Feet: 2.102515661

GREEK FOOT, in Inches: 12.167033603
GREEK FOOT, in Feet: 1.013944669

Pi / Radian-Centered, 1.111111111-Centered, Herpetometric and Divergent:
"Alnilam Cubit", in Feet: 1.70010936 = 10 "LSC" Fingers
"Alnilam Cubit", in Inches: 20.40131232 in
Royal Cubit MV-B [Middle R. Cubit of Stecchini] in Feet: 1.722570927 
Royal Cubit MV-B [Middle R. Cubit of Stecchini] in Inches: 20.67085112
1.722570927 = dh "Alnilam Cubit" / Pi^2 
Roman Foot B, ("Roman Carpenter's Foot") possible, in Feet: .972
Roman Foot B, ("Roman Carpenter's Foot") possible, in Inches: 11.664
(Remen centered Roman foot = "Roman Mason's Foot"?)
Sumerican Cubit B, in Feet: dh (2R) x 12 = 1.65011843 Feet
Sumerian Cubit B, in Inches: dh (2R) x 12^2 = 13.75098708 Inches
Royal Foot, in Feet: 1.14591559
Royal Foot, in Inches: 13.75098708
Assyrian Cubit B, in Inches: 19.44 (cf. "Idealized Apothem Length" Grt. Pyr. dh 1944 Pi)
Assyrian Cubit B, in Feet: 1.62
(+ Possible Additional Assyrian Cubits based on "Phi in Feet" approximation?)
3 / 4 Remen = 12 digits, in Feet: .912205201
3 / 4 Remen = 12 digits, in Inches: 10.95060242
3 / 4 Remen = 12 digits: Divergence A, in Feet: .913852259
3 / 4 Remen = 12 digits: Divergence A, in Inches: 10.96622711 = dh MVB Cubit / Pi
3 / 4 Remen = 12 digits: Divergence B, in Feet: .909025652
3 / 4 Remen = 12 digits: Divergence B, in Inches: 10.90830783
3 / 4 Remen = 12 digits: Divergence C, in Feet: .908689065
3 / 4 Remen = 12 digits: Divergence C, in Inches: 10.904268783 = 656.5612701 / 12
Assyrian Foot, Divergence A: 1.08 Feet
Assyrian Foot, Divergence A: 12.96 Inches
Assyrian Foot, Divergence B: 1.08154098 Ft
Assyrian Foot, Divergence B: 12.97849176 Inches
Sumerian Foot, in Inches: 1.0904268783 = cf 12 digits of Divergence C
Sumerian Foot, in Inches: 13.1312254 = 6.565612701 x 2
Sumerian Foot, Divergence A, in Inches: 13.14072289
Sumerian Foot, Divergenence B, in Feet: 109.5019075

Chinese Ch'ih of "7.07" inches, in Feet: .589889096
Chinese Ch'ih of "7.07" inches, in inches: 7.078669163

Additional possible divergences:
Roman Cubit: 17.496 Inches (as above in Berriman's Table); "Roman Carpenter's Cubit"?
Greek feet of 12.15 and 12.15854204 Inches ("Greek Carpenter's Feet"?)
The Palestinian Cubit can be expected to further diverge in the event that it does not prove in practice to be an adequate value. Ostensibly, at least, the suggested forumulaic value here seems to be adequate.

Remaining enigmata:
"Nilometer Cubit" = harmonic of Squared Remen?
Additional species of Royal Cubit.

Note on 25.3018798 for Cubit A: dh Remen x (12^4)

How can I say all this with any confidence? Okay, let me try it without getting cranky...

Either I can or I can't; the same question applies to anyone, how can anyone say anything about all this with any confidence? Guys have some nerve with all this about "Geodetic Feet", we can't even, not even now, measure the equator to within a mile. Don't believe me? Follow that hot tip on the International Datum being more accurate than WGS 84 because of what went into it, and see what the International Datum gives as the Equatorial Circumference of the Earth if I am not sadly mistaken.

But that is me getting cranky...

What contributes to this logic?

The observation of true statements in Berriman's equivalents column if we assign these values, using the established Matrix Remen of (e' / sqrt 5) feet.

The observation that of true statements in Berriman's equivalents column if we assign these values, using the established M. L. Morton Royal Cubit of .03 Radian feet.

The observation that Pi and Radian logic is clearly at work in some of these figures.

The prior experience with the Double "Matrix Royal Cubit B" in mensuration of the Great Pyramid and Stonehenge.

The contrivance of "Mason's feet" and "Carpenter's feet" to differentiate some of these units, based on the fact that we can expect measurements in stone to be permanent, while those in wood outside of extenuating circumstances (i.e., Hermetically Sealed with Pyramid Rays pointed at it) are not, hence the possibility of a set of "everyday" measures which are easier to calculate than the Remen-centered values. I personally find this, if it will hold up in the long term, a lot more plausible than some of the "geodetic logic" that's out there.

The huge swaths cut across the equivalences of proposed values in both major categories (and additional major contstants of the Pyramid Matrix, or the coincidence of values of measurement of major monuments in other units) based on 12, exponents of 12, and multiples of 12, not to mention the small parade of Matrix Constants that already appear as proposed values here.

Digit .7300401615 inches
.7300401615 x 12 = 8.760481038
.7300401615 x 24 = 17.52096388
17.52096388 x 12 = 210.25156665
210.25156665 / 12 = 1.460080323 
1.460080323 / 12 = .1216733603

Finger .7604585008 inches
.7604585008 x 12 = .912550201
.912550201 x 12 = 109.5060241
109.5060241 x 12 = 1314.072289

GREEK CUBIT, in Inches: 18.25100404
18.25100404 x 12 = 2190.120485
18.25100404 / 12 = 1.520917003 
18.25100404 / 24 = .760458501
(18.25100404 x 2 = 36.50200808) 
18.25100404 / 2 = 9.12550202

You get the idea, right?

(Note for Geodesy nuts: .7604585008 / 12 = .063369159; .063369159 / 12 = dh 5280.763286... now, I am not going to tell you that 5280.763286 is a "Sumerian Carpenter's Mile", since I don't see measuring any pieces of wood a mile long...

In fact, we know little about the Mile other than that it (allegedly) works in the Pyramid Matrix, but as far as origins, we can only categorize it as the work of a very small and very confused group of people who are BOTH Masons and Carpenters, who were So confused, they even added instead of muliplied: 19.47 = 33.33 = 52.80

But that is really all we know... but note: 5280.763286 x (2.920160646^3) = 1314.97329... where is that going? A: Somewhere I don't want to go until my datum quits quivering...

Also note: 18.25100404 / (24^2) = .0316857709... hmmmm...????? Again, not until...).

Okay, lastly, what precipitates the delusion that my proposed list is logical, is after all that about the Greek Foot (and I apologize for confusing Remen-feet with Greek-foot inches, which is confusing enough isn't it?; from remarks I've made not long ago, you would think the Greek Foot is c.a. 1.215 Feet; it is not it is c.a. 12.15 Inches)...

In Berriman's hands, at least, the c.a. dh 1.215 figure is no one's actual measure than I can (pardon the accidental pun) fathom; rather it is the MEAN the results of two sets of measures of the Parthenon, made c. a. 100 years apart.

Berriman, "Historical Metrology", pp 118-119:
Stuart (c.1750), Attic foot, based on platform measurements of Parthenon:
W 12.137, L 12.138
Penrose (c. 1888), Attic foot, based on platform measurements of Parthenon:
W 12.16, L. 12.167

While neither gives 12.15 nor 12.15854204 (120 / Pi^2), Penrose's give the "Matrix Remen" in foot value x 10, to as many as three places after the decimal: 12.16733603

If any conclusions were forced based on this information alone, it might have to be that the Greek foot was calibrated to the Egyptian Remen in the ratio:

10 Remen = 12 Greek Feet

This simple 10 / 12 ratio may pervade the proposed list of Remen-centered values.

The management apologizes for any coincidence, accidental or intentional, between the 5/6 calibration ratio and the 5/6 symmetry of the D&M Pyramid at Cydonia.

Tentative nature of proposed figures:

The reader should note that the massive oversided unprintable table showing the Great Pyramid and Stonehenge measured in all of the above values has not been composed, therefore, if this is one of the better available tests of these values, it has not actually been performed, with the exception of variants on the "Alnilam-foot", which may be in evidence at Avebury, etc.

Using sacred geometry relationships to project the Roman Pace x sqrt 2 value gives 3.441442358, which appears to be 3.4451418337, which turns out to be the Double 
MV-B Royal Cubit rather than the Double "MV-A" Royal Cubit of Michael L. Morton:

3.445141853 / 2 = 1.722570972
3.437746771 / 2 = 1.718873385

Stecchini, while overlooking the logic of .03 Radians for the "A" Cubit (our tentative local terms, which do not necessarily agree with the terms used by Berriman; the logic of the (e' / sqrt 5) Remen and Pi logic both evade Stecchini), gives the value of our "B" cubit:

Thompkins, "Secrets of the Great Pyramid", pg 320

"Correspondingly, the study of the monuments and of the measuring rods indicates that there were three values of the royal cubit:

524.1483 mm
525.0000 mm
528.3231 mm"

Hence, I have (arbitrarily, in relation to other material, i.e., Berrmiman's) named them, in order, A, B, and C.

524.1483 mm x .0003281 = 1.719735072 ft
525.0000 mm x .0003281 = 1.722525000 ft
528.3231 mm x .0003281 = 1.733428091 ft
(sqrt 3 = 1.732050808; it is unclear whether this third cubit is an embodiment of a sqrt 3 approximation, and if so, which, or whether it is the result of using a ratio of a sqrt 3 approximation to relate the "C Cubit" to some other unit of linear measure).

Granted that there are many other texts to consider, such as Stecchini's; i.e., ideally, we can re-write such texts entire and demonstrate the full logic along the way, and furthermore while highly recommended and the only less-geographically localized whole text to come to mind, many other units are omitted from Berriman's work obviously, and as so have yet to be considered here). The search continues for other measures based on Sacred Geometry, which either require identification with common names, or may have been lost hitherto.

I apologize again for any confusion, disorientation, or discomfort caused by the above, probably preposterous excuse for a disseration, but you know the old expression: "Give 'em an inch..."

Yours inquiringly,


I haven't checked on the original source or to see if it's still available yet, but the file search for "Berriman" also brought up a bit of biographical information that I still find interesting although I have to soundly disagree with the author on probably a number of points. (You get what the author is systematically doing wrong in asserting multiple correct values and then saying that Berriman isn't correct?) At the bottom of the page it gives an email for John Neal at Secret Academy so that is probably a clew where it came from.


Algernon Berriman

Berriman, an engineer, published his book, Historical Metrology, in 1953.  He was inspired to write it by the fact that in May 1951, the Departmental Committee on Weights and Measures Legislation published a report recommending the abolition of the imperial standards in favour of the complete adoption of the Metric System.  He realised that a heritage of great antiquity was to disappear from daily life.  

His interest in the matter may have stopped there but for the chance reading that a royal Egyptian cubit may be expressed as 20.6265 inches.  He recognised this number as the radius of a circle of which the perimeter would be 129.6 inches, this led him to believe that the English inch had geometrical significance as a sexagesimal division of the circle.  Inspired, he continued on to study the weights and measures systems of antiquity and reached many conclusions about these systems that the majority of other serious researchers had inevitably arrived at.  That is, the linear units have a geodetic appearance, in as much as they seemed to be devised from the lengths of the meridian degree and from the length of the polar axis.  He quoted Jomard as being the first to arrive at this conclusion around 1800, and that Sir C M Watson, in 1915, in his book Babylonian Measures of Length, had also commented upon the geodetic appearance of the Greek linear scale.  (One Greek foot being the 360,000th part of the meridian degree).  

Many others, not quoted by Berriman, have reached the same conclusion, the Architect, Francis Penrose, who measured the Parthenon in the 1880s, made the same remark regarding the Greek foot.  According to Stecchini, the fact that the earth had been accurately surveyed in antiquity was not only taken for granted by those interested members of the French Academy of Sciences during the Nineteenth Century, it was a fundamental premise.  So neglected a subject had ancient metrology become, that by the time Berriman wrote his book his conclusions of a geodetic origin for these ancient measures was mooted in the manner of a new discovery.  The concluding sentence in his preface is the question:  "Was the earth measured in remote antiquity"?  

Unfortunately, although he must have been well aware of the variations in values that are accepted as standard expression of the measures, he tried to relate everything to a single value.  As did Alexander Thom with the Megalithic Yard, and Stecchini with his definitive values of the Roman foot and Egyptian cubits.  No attempt was made to explain these differences and the fundamental unity of the systems as a whole completely eluded him, although he knew it was so.  When a measure is exactly identified its integrated nature with other values is clearly visible.  The equation that first inspired him, that of the 129.6 inches of the perimeter which would yield a royal cubit radius, was obtained by using true pi.  Had he divided this number by 22/7, as was done by tradition, then his value for the royal Egyptian cubit would have been exactly right, at 1.71818ft it is the value identified by Petrie at Giza.  Instead, he believed this cubit to be 1.78873ft, close enough, but the numerical aspect of metrology is completely ruined, and all subsequent values are mere approximations.  Although his general conclusions were largely correct, his work inspired no further developments to the study, the errors outweighed the facts.  In spite of his inexactitudes, his work is often quoted as authoritative, which underscores the lack of knowledge about the subject in general.
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Memoirs of a Pi Jedi
Chapter Four
Some Curiosities I Have Known

I have a few more cards I haven't put on the table yet. Wasn't saving them, just hadn't got to them yet. Thought I'd get them out for Star Wars Day. Not a big Star Wars fan myself (not since Jar Jar Binks anyway) but as you recall, my mentor is short, green, and hairy - so May The Fourth Be With You.

SRVS = Square Root of the Volume of a Sphere (as reckoned with "generic" Radian value of 57.29577951 as the radius) = 887.6223994. This proved to be a very useful reference figure. It was introduced by Yoda, who at one point proclaimed it the key to the decoding of (blatantly?) irregular monuments, something he may have later recinded although I haven't.

IMY = Incidental Megalithic Yard = Squared Yoda Meg Yard / "AEMY" "Alternate e' Megalithic Yard" as I sometimes refer to 2.720174976 as in order to hopefully help prevent confusion.
(2.719715671^2) / 2.720174976 = 2.719256444
This too hopefully qualifies to receive the admiration of RCH as "an idealized average of e and e'" which is how he long ago described the Yoda Megalithic Yard in his "UN Briefing" Video (my introduction to RCH & Cydonia 20 years ago). It's "incidental" in origin - i.e., it exists as a consequence of formulas, much as some of the cubits resulting from the formula 
(360 / Cubit) = ~Cubit Squared = Cubit x times Cubit y
might also said to be "incidental," although in anything related to "Pyramid Pi" Math, I question whether anything is really incidental.

RS(Y)MY = Reciprocal of the Squared Yoda Megalithic Yard. 1 / (2.719715671^2) = 1.315926225 / 10
I probably found the reciprocal form of (2.719715671^2) to be even more useful as a mathematical probe than (2.719715671^2) in regular form.

Not-Phi B = Besides "Pi Pyramid Phi" 1.61882914 formerly known as "Not-Phi A" there is 1.618975080 within the "Pyramid Pi System". I don't know if anyone discovered what it's doing there, but the sole entry in my "master list" of "Pyramid Pi" constants explaining it relates to the equatorial circumference of Earth reckoned as a decimal harmonic of 2.920160646^3, so it may have some geodetic significance that has yet to be discovered.

LSR = 1.676727943. This number originally appeared as the putative "Grid Point" for the head of "Le Serpent Rouge," featured in a number of works on "The Mysteries of Rennes-le-Chateau". While the cartographic significance of this number has ceased to exist as long as the science of monument mapping remains largely in limbo, the number itself survives as a possible metrological unit, thus the origin of the idiotic term, "Herpetometric" - possible metrological significance of mathematical values associated with serpent or reptile related monuments, including Ohio's Serpent Mound. 

I think it still carries a connotation that if nothing else, a serpent may have been used euphemistically to significate a measuring cord. Cord. Rods, schmods. It would take a lot of rods laid out end-to-end to measure a big Giza pyramid, or so many individual measures that it's likely to throw the total measures off considerably, the way I reckon things at least.

As goofy as the concepts got, the numbers were never quite so goofy. The height of the Yoda Model pyramid in Royal cubits (sensu stricto) of 2.794546573 x 100, was also once known as the "LCS" constant, another "Herpetometric" expression whose complete origins have now escaped my memory but I'm pretty confident the "L" in "LCS" refers to the "LSR" "Le Serpent Rouge" constant (and the "S" is quite possibly the Ohio Serpent Mound).

You should have seen the look on my face the day that, after having constructed the "LCS" value from the hokiest stuff imaginable, I took Morton's cubit to Yoda's pyramid and that popped out.

At present, I can still no more produce a specimen of a measuring rod for this value in feet than I can for the "Ellifino," yet what creates the strong suggestion of the "LSR" constant as a possible metrological unit is that, given the statistics for the Yoda Great Pyramid model (i.e., the pyramid above the pavement?) of Height: 480.3471728 ft and Perimeter: 3018.110298 ft...

Height: 480.3471728 ft / 1.676727943 = 286.4788976 = 10 Radians / 2
Perimeter: 3018.110298 ft / 1.676727943 = 180.00000000 = 360 / 2

TAP ("The Appointed Time," novo nomenclature) = 2012.073533. I think this first turned up when I was trying to see if the Great Pyramid's entrance was indicated cartographically so to that people wouldn't have to do to it what Al-Knucklehead went and did just to get into the thing. I may have told that story before, it's a case study in the follies of working with substandard satellite data - I came up with fantastic numbers but I turned out to be totally wrong. They might describe a second entrance further up the slope but they cannot actually indicate the known entrance.

It's more folly that refuses to go away in spite of its absurd origins. This thing was so remarkably resonant within numbers already established at Giza that I was a hair away from being convinced that it was an ancient decree for opening the Hall of Records (that technically I don't actually believe in) at the end of the Mayan Calendar. 

I don't know what it is really (and Zahi never coughed up the goods anyway, I think he must have just taken GH&RB down a shaft and bribed their ordinarily healthy curiosity into submission or something? - so records, schmecords), but one often sees a decimal harmonic of 1/2 this figure as the ratio between other "Pyramid Pi System" constants.

2.012073533 / 2 = 1.006036766

Speaking of, it's a flaming wonder that Yoda did not come up with the "Alternate e' Meg Yard" himself. One of his Grid Coordinates for the Hall of Records is a decimal harmonic of 1.360087488, which probably makes it pretty sacred stuff in his reckoning. Observez-vous,

1.360087488 x 2 = 2.720174976
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Oh happy day (of 1440 minutes or 86400 seconds)... Not certain of the accuracy, but now I just found a short page giving Platonic Solids latitudes and the manner in which I obtained formulas for the dodecahedron, icosahedron, and truncated icosahedron.

Notes say that the Becker & Hagen scheme of planetary Platonic Solids results in a truncated icosahedron. I was wondering why I had data for the truncated icosahedron, although there may still be some confusion over that, it says

"The materials available do not seem to make it clear what the correct orientation of the Truncated Icosahedron is inside the planetary sphere."

(As to why I worked out my own formulas when maybe Bruce Rawles or someone was already giving those to us, well first off I didn't want to just take anybody's word for anything, and second, no source I had gave the formulas involved in arriving at the given formulas. The given examples normally do a terrible thing, which is give key values as 1, and it can be difficult to infer the formulas from such examples since 1^2 = 1 and sqrt 1=1 and it isn't necessarily clear what's been done to a radius or edge length value of "1" in order to arrive at the specified value).

Latitudes of Vertices of Circumscribed Platonic Solids

TETRAHEDRON - 19.47122063* = 19* 28.27323808' = 19* 28' 16.39428456"
HEXAHEDRON - 35.26438968* = 35* 15.8633808' = 35* 15' 51.80284800"
OCTAHEDRON - NONE (seriously???)
DODECAHEDRON "A" - 52.2263185* = 52* 13.5791100' = 52* 13' 34.74660000"
DODECAHEDRON "B" - 10.81231683* = 10* 48.73900980' = 10* 48' 44.34058800"
ICOSAHEDRON - 26.56505113* = 26* 33.90306780' = 26* 33' 54.18406800"

I may have more material (possibly also any applicable corrections) after I've looked around a bit more...

Update: I'll want to see the proofs before I believe it, but another later page has data representing the Truncated Icosahedron, so possibly it got worked out?

T-ICOSAHEDRON - "Latitude 1" 73.87593125* = 73* 52.55587506' = 73* 52' 33.3525036"
T-ICOSAHEDRON - "Latitude 2" 56.25921741* = 56* 15.55304460' = 56* 15' 33.182676" 
T-ICOSAHEDRON - "Latitude 3" 30.99196869* = 30* 59.51812140' = 30* 59' 31.08728400"
T-ICOSAHEDRON - "Latitude 4" 09.88314545* = 09* 52.98872703' = 09* 52' 59.32362137"

This later page also gives the value for the Dodecahedron "A" Latitude as 

DODECAHEDRON A - 52.62263185* = 52* 37.35791238' = 52* 37' 21.4747280"

But doesn't explain when or how a correction came about. (Given that the old and new figures for degrees both end in "...63185" it may well be that a brief moment of dyslexia was involved somehow).

And another page purports to give their central and dihedral angles

Tetrahedron - Central: 109.4712206° - Dihedral: 70.52877936° 
Octahedron - Central: 109.4712206° - Dihedral: 60° 
Hexahedron - Central: 70.52877936° - Dihedral: 90°
Icosahedron - Central: 63.4349488° - Dihedral: 138.1896852°
Dodecahedron - Central: 41.81031488° - Dihedral: 116.5650512°
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Searching for Artifacts of Ancient Technological Species in Our Own Solar System

Posted by Greg at 05:40, 05 May 2017

[Image: alien-city.jpg]
Since its birth around a half century ago, SETI has largely focused on looking for alien civilisations beyond our own solar system, searching for radio signals from prominent or nearby stars. But what if there were earlier technological civilisations in our own solar system, or even here on Earth?

That's the question explored in a new paper posted to (and soon to be published in the International Journal of Astrobiology), "Prior Indigenous Technological Species", by astronomer Jason T. Wright.

Quote:SETI typically focuses on interstellar radio signals or other studies of objects beyond the Solar System, however an alternative search avenue has been appreciated for nearly as long: the search for alien artifacts within the Solar System. This has not only been a topic for science fiction (e.g. 2001: A Space Odyssey) but in the SETI literature. Indeed, the apparent lack of such artifacts has been used as evidence that humanity must be the only spacefaring civilization in the Galaxy (Hart, 1975). Despite Hart’s claim, we can hardly rule out such artifacts in the Solar System, as demonstrated by Freitas (1983a) and Haqq-Misra & Kopparapu (2012).

In these discussions it is assumed, implicitly or explicitly, that the origin of such artifacts would be not just extraterrestrial (Haqq-Misra & Kopparapu, 2012, refer to them as “Non-Terrestrial Artifacts” (NTAs)) but extrasolar. But if such technology were to be discovered, we should consider the possibility that its origin lies within the Solar System, and potentially on Earth.

After all, given that the bodies in the Solar System are at least five orders of magnitude closer than the nearest star system, and given that we know that not only are the ingredients of and conditions for life common in the Solar System, but that one of its planets is known to host complex life, it is perhaps more likely that their origin be local, than that an extraterrestrial species crossed interstellar space and deposited it here. At the very least, the relative probabilities of the two options is unclear.
In this paper, I discuss the possibility for such prior indigenous technological species; by this I mean species that are indigenous to the Solar System, produce technosignatures and/or were spacefaring, and are currently extinct or otherwise absent.

Wright notes that one of the great difficulties in finding evidence for previous technological civilisations in our solar system is simply the passage of time - old stuff disappears. "The Earth is quite efficient, on cosmic timescales, at destroying evidence of technology on its surface," he notes. "Biodegredation can destroy organic material in a matter of weeks, and weathering and other forms of erosion will destroy most exposed rock and metals on a timescale of centuries to millennia, if human activity does not erase it faster.

Wright points out that, at the very longest, some "large and durable structures, in the right environments" - such as the Giza pyramids - might last for 'just' tens of thousands of years. Given complex life has existed on Earth for over 400 million years (40,000 sequential periods of 10,000 years), you see the problem in searching for 'ancient aliens'. Not least, because, on timescales of hundreds of millions of years "plate tectonics will subduct almost all evidence for technology with the crust it sits upon, erasing it from the surface entirely.

Regardless of those difficulties, where should we look? Wright suggests that Venus - with a thinner atmosphere in the past - and Mars, once covered in water, would be good candidates. And he reminds us that search should also include Earth (though he disavows the topic of 'ancient aliens' on his blog). Furthermore, he notes, "while all geological records of prior indigenous technological species might be long destroyed, if the species were spacefaring there may be technological artifacts to be found throughout the Solar system."

It's a fascinating hypothetical topic, though it is worth pointing out that Jason Wright is not particularly happy about "all the wrong kind of attention" the paper has received "from the yellow press and the is mortifying...Now excuse me while I answer all these emails from Coast to Coast and ufologists sending me pictures of clouds."
No doubt his frustration has arisen from the "astronomer says ancient aliens existed in our own solar system" headlines that the paper has generated, with many mis-judging what the words "may" and "is possible" mean, in terms of likelihood of ancient alien civilisations. As Wright says on his blog, he put his paper together...

Quote:...not because I think they exist, but because we’re at the point where it should be possible to say for sure that certain types of them didn’t. The end of the paper is all about the things we can do to start drawing some conclusions.

I recommend - as I have to SETI people before - that it might be worth engaging with the ufologists and Forteans, rather than dissing them, as they could be some of your staunchest advocates, even if there is some disagreement over assumptions and conclusions.

Paper: "Prior Indigenous Technological Species", by astronomer Jason T. Wright.
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
On his blog I wrote this reply:
Dr. John Brandenburg of the Viking missions found Xeon^129 in the atmosphere of Mars and relted it to the Xeon^129 in Earth’s atmosphere since that isotope is ONLY made in nuclear explosions. PERIOD. You can his video and also the Ares Face Properly Processed and not the “CATBOX” that was released April 5, 1998:
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:]
Quote:Nuclear activities will create not just unnatural, short-lived isotopes, but unnatural isotope ratios from the stable daughter products of decay that might be obvious essentially forever. Humanity seems to have had a sufficient impact on the Earth that it has created an unambiguous geologic record of its technological activities (the “anthropocene”, e.g. Zalasiewicz et al., 2011). A prior species with a similar effect would thus probably have been noticed in the geological record.

 "Prior Indigenous Technological Species", by astronomer Jason T. Wright.

On Graham Hancock's Website forum there is a variant of my ~333 light speed formula
Quote:Many hypotheses for why alien artifacts might exist in the solar system involve a system that monitors the Solar System or announces itself (a “beacon,” Burke-Ward, 2000; Haqq-Misra & Kopparapu, 2012, and references therein).

Paper: "Prior Indigenous Technological Species", by astronomer Jason T. Wright.

a “beacon,”
Magical Equation for the Speed of Light 

Quote:Therefore, your calculations for the “Speed of light in air” should read thusly: 

33×3×333 √1.2345678987654321×108 = 2.996999997003 × 10

> The equation can also be written: 

> Speed of light in air = 33 x 
> 33 x 333 x 1234,5679 

33×33×333×1234.5679 = 2.996999997003 × 108 

> The equation for the speed of light in a vacuum 
> can be written 

> Speed of light in vacuum = 33 x 
> 33 x 333 x 1234,947 

Your calculation for the “Speed of light in a vacuum” should read: 

33×33×333×1234.947 = 2.99792028879 × 10

According to Wikipedia: 2.99792458 × 108
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Let's see, where was I? Right... So apparently, ancient Egyptians declined the invention of pants in order to facilitate frequent remeasuring of their own junk with a mind-boggling proliferation of superfluous small measures, much as ancient Middle and Southern Americans ostensibly declined industrial use of the wheel... 

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The translated heiroglyphs concur with the pictographic message:
"The blessings of Anubis are bestowed upon he who measureth his junk as he measureth the Mighty Pyramid"

Oh, sorry, wrong page...

This might be worth making a note of - I can't think of where else I've seen the info. You'll notice my first experiments with Berriman's metrology gave a different possible value for the Palestine Cubit than one I've given more recently. There's actually another good candidate that turns up a lot, and I'm still trying to sort these out as carefully as possible. In light of that, the following sounds intriguing and possibly useful

"A short cubit was equal to six palms (44.9 cm) which was roughly the length from the elbow to the thumb tip. After the Saite Period, however, the royal cubit was used by artists. During the Persian occupation, however, the royal Persian cubit of 64.2 cm was sometimes used, although a reference cubit for this measure discovered at Abydos is actually 63.85 cm in length."

64.20 cm = 2.106299213 ft
63.85 cm = 2.094816273 ft

Those look like the ones...

Also I'm trying to dig up some of Professor Thom's materials. Can't find his books but I should have some of his data tabled electronically and there may be some interesting things in it to share. Not sure where now but ran across a note about Thom's ideas being contested on the grounds that he ended up with variations on the Meg Yard before long. As I understood it, his detractors identified the possibility that the ancients were NOT necessarily using whole number units of the Meg Yard (duh!!!), but unfortunately seemed to proceed to think this somehow means he's wrong about this that and the other thing. I guess Urdummheit is kinda like the common cold, it can happen to even the best of us?

I wouldn't mind if I can take the time to investigate more carefully whether there was any call for variations on the Meg Yard by looking at the data for the variant monuments in question, since I'm trying to take a more thorough inventory of ancient metrology.

(05-03-2017, 08:18 PM)EA Wrote:
Quote:try this example--add two angles : 75 degrees, 45 minutes, 20 seconds plus 25 degrees 15 minutes 10 seconds. 
or add 75.753 plus 25.251 
Which is easier?

Land surveyors (those guys you see on the side of the road with an instrument mounted on a tripod) make hundreds or even thousands of angle measurements during a day's work.

Grads are great!!! :)

So far my answer is yes and no - I wouldn't rule out that such a system was used, but if so because it facilitated the mathematics, not because it made things easier. The right answers may not always be the easiest. (I'm having to remind myself of that a thousand times a day just to keep from going all Urdummheit on the King and Queen's chambers myself. It's like a cold, I tell ya).

Also, the Babylonian system may have the seniority that it warrants respect and conservation.

"Although it is no longer used for general computation, the sexagesimal system is still used to measure angles, geographic coordinates and time. In fact, both the circular face of a clock and the sphere of a globe owe their divisions to a 4,000-year-old numeric system of the Babylonians."

I'd say grads are great when they're working, and you do have examples of them working. Personally I wouldn't go near an ancient monument without 360 in my toolkit, though, and 400 I'd get just from lobbing simple mathematical probes. How many sides to a pyramid? 4. Let's throw 4 at it...

But maybe Thoth did indeed decree that both systems may be used?

400 / 360 = 1.11111111111

Do you know anything about tetrahedral instruments or tetrahedral geometry being used for navigation? It's starting to bug me to have so much "19.47" coming out of what so far has had to serve for earth-measuring geodetic math. Okay, I get it, planetary tetrahedra, gotcha - but the use of "19.47" may even more insistent than just referencing that, and with the geodetic context it does make me very curious what all else might be meant. Is there some way that "19.47" might serve navigators?
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Memoirs of a Pi Jedi
Chapter Five
Giza and Stonehenge: Circular Logic?

The earliest recognition by modern man that Giza's pyramids represent mathematical constructs is the recognition of elements of circular mathematics. When I say that simple circular mathematics serves as an "entry-level" for ancient mathematics at Giza, I'm referring to something that is a matter of historical record.

A Pi Jedi recognizes at Giza not one but two colossal monuments to the ratio of double Pi, the ratio between radius and circumference of a circle

Radius x 2 Pi = Circumference

Using the radian value as the "generic" radius for circles of unknown or unspecified proportion,

57.29577951 x 2 Pi = 360*

The formula for the area of a circle (Area = pi x r^2) is rendered in the same way as 

57.29577951^2 x Pi = 10313.24031 Area of a Circle (AC)

Note that this is a "decimal harmonic" (decimal point moved) of 1/2 of the geometrically-derived value of the Royal Cubit in inches

10313.24031 x 2 = 20626.48062 
Royal Cubit in feet 1.718873385 x 12 = 20.62648062

Had Berriman only noticed (see biographical data previously posted) that he'd inadvertantly squared the circumference (perimeter) value of the generic circle (360^2 = 129600)...

"His interest in the matter may have stopped there but for the chance reading that a royal Egyptian cubit may be expressed as 20.6265 inches.  He recognised this number as the radius of a circle of which the perimeter would be 129.6 inches"

The formula for the surface area of a sphere (4 Pi x R^2) gives us

4 x Pi x (57.29577951^2) = 41252.96124 Surface Area of a Sphere (SAS)

i.e, four times the area of the corresponding circle, or a decimal harmonic of 24 Royal Cubits in feet
1.718873385 x 24 =  41.25296124

The formula for the volume of a sphere (V = 4/3 Pi x R^3) yeilds the generic construct

1.3333333333 x Pi x (57.29577951^3) = 787873.5239 Volume of a Sphere (VS)

Those exploring ancient mathematics may wish to be aware of these values in case they encounter them. As previously mentioned, the square root of the Volume of a Sphere may often serve as a useful mathematical probe or reference value.

sqrt 787873.5239 = 887.6223994 Square Root of the Volume of a Sphere (SRVS)

Having recently revised the Pi oriented Great Pyramid model in these very pages to a "Thoth model" which may represent the proportions of the Great Pyramid sans pavement, this affords us (as previously mentioned) an apothem value which is a close and recognizable approximation of 611.5970155 feet, and I have posted data suggesting the length of the descending passage roof to the point where it meets the ascending passage, is a convincing likeness for 97.3386882 ft.

611.5970155 / 97.3386882 = 2 Pi

To review our data for Stonehenge (based on measures by Petrie and Thom), the inner sarcen circle has a radius of 48.6693441

Radius 48.6693441 x 2 = Diameter 97.3386882; Radius x 2 Pi = Circumference 305.7985078 ft

Given these figures, we can say that the length of the passage roof in the Great Pyramid's descending passage is equal to the inner sarcen circle diameter of Stonehenge, and that the apothem length of the Great Pyramid (unpaved) is precisely twice the inner diameter of the Stonehenge sarcen circle

GP Apothem 611.5970155 / 2 = 305.7985078 Stonehenge SC (sarcen circle) inner circumference

Those searching for the tracks of tetrahedra may wish to observe that 

611.5970155 / Pi = 194.6773764 
97.3386882 x 2 = 194.6773764

Because the Pi Jedi considers that the Stonehenge sarcen circle is a 360* degree circle, we apply that value to these figures

360 / SC Circumference 305.7985078 = 1.177245771 Yoda's "Alternate Pi"

(Or we can apply the Radian value to the  SC Radius 

57.29577951 / 48.6693441 = 1.177245771 Yoda's "Alternate Pi"

360 / SC Radius 48.6693441 = 7.396853331 The Squared Yoda Megalithic Yard (SYMY) = (2.719715671^2)
1440 / 7.396853331 = 19.4673764

This will be the third time I have related the story of how I found the apparently Top Secret, allegedly "Hall of Records locating" number 1.067438159 at Stonehenge, as the outer/inner sarcen circle ratio, using my "Alternate e' Meg Yard" (AEMY) value of 2.720174976

Outer: 120 Meg Yards = 120 x 2.720174976 = 326.4209964 Outer Sarcen Circle Circumference

Outer / Inner = 326.4209964 / 305.7985078 = 1.067438160

However, if we were to work purely with the inner sarcen circle data, it is still available to us

Inner SC Circumference 305.7985078 / Radian 57.29577951 = 5.337190809 = 10.67438159 / 2

When you have important data, you tend to want to make backups.

Last night I reviewed the geometry of the Thom Type A flatted circle. Treating that too as a circle of unknown measures and therefore providing it with a generic radius of 57.29577951 = Radian, I managed to derive from it most of the data shown thus far for Stonehenge, and more.

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Professor Thom's flattened circles: Left to right are Type A, Type B and Type D.

Also an interesting thing happened - finding an unsolved version of it, I presumed it had never been solved, so I set out to finish it. Awhile later, I found a version that did have some of the solutions worked out after all, and was quite taken with the fact that the solutions I plotted last night are the same as when I worked on it ten years ago. I don't know that the trigonometric functions have been solved, but I noticed I seemed to have gotten further toward finding meaningful solutions (if there are some) in that respect ten years ago than I did last evening.

What I have on my paper from either attempt shows at least several values derived from the flattening that are strong responders to "Alternate Pi" 1.177245771, answering back to 1.177245771 as a mathematical probe with significant figures to as high as 1.177245771 to the fifth power.

I have no idea yet if there were ever any real-life examples of Professor Thom's Type A circle that were solved by any Pi Jedi (or anyone), but for tetrahedra trackers there is in the generic design a value that can probably be taken with considerable confidence to mean either 2 x (19.46773764^2) or 2 x (19.47122063^2) depending on one's preference - and because that's encoded into their basic design, it appears in all ancient circles with the Type A motif regardless of their actual measurements.

(Some Type A flattened circles, according to Professor Thom: Duloo, Moscar Moor, Botallack, Black Marsh, Mitchell's Fold, Castle Rigg, and Dinnevar Hill in England, and Loupin Stanes, Aviemore, Callanish I, Seven Brethren, and Farr West in Scotland. No doubt there are more examples at large. If I recall correctly, Thom probably only made these types of pronouncements for stone circle cites he was able to carefully survey personally).

I know I've already been on my soapbox in this thread about the perils of allowing one's self to become distracted while attempting the mathematical decoding of Giza (i.e., my very large and very dusty map collection), but having recently announced that the Great Pyramid seems to represent a "fusion" of multiple designs, I've become freshly intrigued with Thom's flattened circle motifs as representing "fusions" of multiple circular-oriented designs. It's definitely the flattening that makes them considerably more interesting than ordinary circles, even when their regular circular component simply has them spouting simple radian fractions.


AO = OM = ON = 57.29577951 (Radian / 1)
OE = EC = ED = OK = KH = KC = 28.64788976 (Radian / 2)
AE = EK = 75.79519188
EF = FK = 24.80980029
OF = 14.32394488 (Radian / 4)
AF = 71.61972439 (Radian / 8)
Angle (theta) = 19.10660535*
Angle (beta) = 40.89339465*
Perimeter of arc from O = 240.0000000
Perimeter of arc from A = 69.65793147
Perimeter of arc from E = 20.44669733
Total perimeter = 350.5513216
Total area = 9329.067655

I've also been reminded that the ancient British, Scottish, and Irish circles still have a few things left to teach me, that for all I know may still complement my understanding of Giza's mathematical messages.
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
As an addendum, another curious artifact I could have included in Chapter Four is the Giza Vector.

Giza Vector = 5577.096019. Yoda gave this as the cartographic "Grid Point" value combining the "Grid Longitude" of the three small Cheops subsidiary pyramids (07.396853331" East of the Great Pyramid Apex = SYMY) and the "Grid Latitude" of the three small Mycerinus subsidiary pyramids 41252.96126, even though this intersection doesn't seem to be otherwise marked by a physical monument.

41252.96126 / 7.396853331 = 5577.096019

Isn't it amazing, you pull some absolutely boneheaded stunt like that only to discover that

360 x sqrt 240 = 5577.096019 = SRVS 887.6223994 x 2 Pi = (57.29577951 / 2) x 19.46773764 x 10 

This is another piece of data I was able to extract from the generic Thom Type A flattened circle with remarkable ease.

Here's my call on the intended interpretation of the generic perimeter of the Type a flattened circle:

Total perimeter = 350.5513216 = 350.4192775 (accuracy .99962)

That's 360 / 350.4192775 = 1.027340740

Anyone recognize it? No? Let's try turning it the other way then...

1 / 1.027340740 = 97.33868822 / 100 = 194.6773764 / 200

Radian 57.29577951 / 1.027340740 = 55.77096019
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Quote:Do you know anything about tetrahedral instruments or tetrahedral geometry being used for navigation?
It's starting to bug me to have so much "19.47" coming out of what so far has had to serve for earth-measuring geodetic math. Okay, I get it, planetary tetrahedra, gotcha - but the use of "19.47" may even more insistent than just referencing that, and with the geodetic context it does make me very curious what all else might be meant. Is there some way that "19.47" might serve navigators?
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Polynesian Stick Charts

The Polynesians, scattered as they were over 1,000 islands across the central and southern Pacific Ocean, were master navigators who tracked their way over a huge expanses of ocean without any of the complex mechanical aids we associate with sea fairing. They didn’t have the astrolabe or the sextant, the compass or the chronometer. They did however have aids of a sort, which though seemingly humble, were in fact the repositories of an extremely complex kind of knowledge. Called Rebbelibs, Medos. and Mattangs, today we call them simply “Stick Charts.”
There are three kinds of stick charts.

[Image: stckchrt2.jpg]

The “MATTANG” or “WAPPEPE” is a small, square shaped chart which shows wave patterns around a single island or atoll and was used for teaching purposes only.

[Image: stckchrt3.jpg]

The “REBBELIB” is a general wave navigational chart mapping an entire chain, showing the relationships between the islands and the major ocean swells.
[Image: stckchrt4.jpg]

The “MEDO” covers only a few islands and is useful for specific voyages.
[Image: stckchrt5.jpg]

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The charts were made by men from thin strips of coconut frond midribs or pandanus root. They were then bound together with coconut sennit in geometric patterns depicting sea currents around the low lying atolls. Small money cowrie shells or coral pebbles indicated islands and curved sticks represent wave patterns.

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They were not carried on a voyage and the adult navigator gauged the wave patterns represented in the Stick Charts entirely by his sense of touch. “He would crouch in the bow of his canoe and literally feel every motion of the vessel.” As with ripples in a pond they “concentrated on refraction of swells as they came in contact with undersea slopes of islands and the bending of swells around islands as they interacted with swells coming from opposite directions.”

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A fascinating aspect of the charts is that they varied so much in form and interpretation that they were “readable” only by the specific navigators who constructed them. Evidently the knowledge contained in each was a closely guarded secret.
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Wikipedia says: “The stick charts are a significant contribution to the history of cartography because they represent a system of mapping ocean swells, which was never before accomplished. They also use different materials than is common in other parts of the world. They are an indication that ancient maps may have looked very different, and encoded different features from the earth, than the maps we use today.”

[Image: stckchrt13.jpg]

[Image: stckchrt14.jpg]

Use of stick charts and navigation by swells apparently came to demise after World War II, when travel between islands by canoe halted. They continue to be made in Polynesia, though very few people are able to use them as navigation aids. They are made and sold instead as tourist souvenirs.
For much more info see the following (images and text were adapted from these):
Wikipedia entry.
Reading Patterns in the Waves.
Ethnomathics Digital Library.
Digital Micronesia.
Micronesian Stick Charts.
Mariner’s Museum.
The Leek-Green Sea.
Stick Charts.
Visit Marshall
THe British Museum.
The Met.
World Weather, Climate, and Society Projects.
And Lastly I’d like to recommend the following for some interesting context-
Varieties of Unreligious Experience.
Hope you enjoyed.

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~19.5 wave  Hi
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
I'm cross-posting this from the Back To The Garden thread since I think this might be a good place for at least part of the discussion?

(05-07-2017, 12:23 AM)Ancient Vizier Wrote:
(04-24-2017, 05:07 PM)EA Wrote: Ancient stone pillars offer clues of comet strike that changed human history
April 24, 2017 by Bob Yirka report

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Prior evidence based on ice cores taken from Greenland has suggested that a strike by a comet may have led to the onset of the Younger Dryas—a period of Earth cooling that lasted for approximately 1000 years. Other evidence also suggests that the cooling period caused groups of people to band together to cultivate crops, leading to the development of agriculture, which in turn led to huge leaps in technological innovations and societal developments, i.e. Neolithic civilization. In this new effort, the researchers describe evidence they found on a stone pillar at Gobekli Tepe (the oldest known temple site) that aligns with the ice core findings—that a comet struck the Earth in approximately 10,950 BC.

I'm not going to actually say that this means anything, but as we know, the central angle of a tetrahedron is 109.4712206*.

Between this and some of Thomas Brophy's numbers (I did not know until recently that Brophy seems to have gone on to collaborate with Bauval &/ or Hancock?) - which are some "BC" dates that look like they were lifted straight out of Yoda's mathematical work...

I'm tempted to broach the subject of who might have been counting time backwards, and why. Any ideas?

I've referred to Brophy several times now, once in this thread in relation to Yoda's mathematics. I probably shouldn't try to hold any of Brophy's work up as evidence that Yoda is right about anything (partly because they require a backwards count), but I still find this very interesting, even though I've about washed my hands of archaeoastronomy. Been there done that, that someone works out an brilliant alignment theory using Star Software X and then next person comes along and says, "No, no - your theory is complete doodoo because Star Software Y says you are in error by seven million years and half a parsec" - sound familiar?

Yoda has a value at Giza he calls the "Sphinx Azimuth" - it's 30 Pi. I can't currently find documentation but I think it's supposed to be the deviation between the orientation of the Sphinx and a straight north-south bearing?

I don't suppose this value has any useful trigonometric functions, but it's 30 x Pi = 94.24777962*

Brophy, "The Origin Map," pages 86-87 

"Further, a fourth (Queen's chamber northern) shaft was measured by Gantenbrink with less precision certainly because his measuring robot encountered physical barriers. But the best value from Gantenbrink (39 deg 07 min 28 sec) aligns it with the ritually significant star Kochab in 2,368 BC - essentially simultaneously with the Galactic Center and the other two stars.

Zodiac Clock
The two primary Orion's Belt star alignment dates (11,772 BC and 9420 BC) are separated by 2,352 years and 32 degrees of general precession. The two dates bracket the Galactic Center culmination alignment date as well as the Orion's Belt culmination dates. This suggests that the Giza monuments, as well as marking the date and location in the sky of the Galactic Center maximum culmination, function as a clock marking the passage of the Zodiac, the duration of a Zodiac period (30 degrees of general precession), and a calibration to the zero pint of the Zodiac: culmination of Galactic Center."

Michael L. Morton was the first person to point out that "11,772 BC and 9420 BC" look remarkably like decimal harmonics of "Alternate Pi" 1.177245771 and 30 Pi 94.24777962. (While we're at it, 30 degrees of general precession looks remarkably like 30 Pi / Pi, allegedly coming from something rather suggestive of a Zodiacal character).

I may have been the first person to point out the resemblance between 2368 BC and 240 (Pi^2). It's been affixed to some contentious things before, but that's still a very significant number to a Pi Jedi (and it has 240 in it, and as you may recall, Yoda has it that 240 is a signature of "Thoth" - he also gives the length of the Sphinx at 240 feet long and asserts that "Thoth" had a hand in that decision).

240 x (Pi^2) = 2368.705056 

Where is this marked at Giza? I'm still not quite sure yet. However...

What catches your eye at Giza first? Is it by any chance the three big whopping pyramids that dominate the landscape?

Reckoned according to Pi Jedi tradition, 

Cheops = perimeter / height ratio = 2 Pi (a three-d model of double Pi)
Chephren = perimeter / height ratio = 6 (a three-d model of the Pythagorean theorem)
Mycerinus = perimeter / height ratio = 2 Pi (a three-d model of double Pi)

2 Pi x 6 x 2 Pi = 236.8705056

I'm sure someone could try passing it off as a decimal harmonic of the diameter of Venus to within about 60 miles, just as I might try passing off 360 / AEMY 2.720170746 as a decimal harmonic of Mars' equatorial circumference (based on what was current NASA data 10 years ago) but either one sounds a bit impudent even to an impudent b*st*rd such as myself. I do think 236.8705056 is there for a reason, though, and quite possibly an important one given its prominence.
But yes, how in the Ellifino would they have known in 11772 BC that is WAS 11772 BC? 

Without that answer on the table, it seems rather reckless to me to suggest anything in this post means anything at all. Just some curious numbers I felt like sharing.

This missing answer might also have to have been involved with their ability to reckon the speculative "Appointed Time" of 2012.073533 AD as seen above (not to be confused with Zep Tepi, the first time I saw Led Zeppelin live).

TAP ("The Appointed Time," novo nomenclature) = 2012.073533

2368.705056 / 2012.073533 = 1.177245771
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
(05-07-2017, 12:23 AM)Ancient Vizier Wrote: In this new effort, the researchers describe evidence they found on a stone pillar at Gobekli Tepe (the oldest known temple site) that aligns with the ice core findings—that a comet struck the Earth in approximately 10,950 BC.

I'm not going to actually say that this means anything, but as we know, the central angle of a tetrahedron is 109.4712206*.

Between this and some of Thomas Brophy's numbers (I did not know until recently that Brophy seems to have gone on to collaborate with Bauval &/ or Hancock?) - which are some "BC" dates that look like they were lifted straight out of Yoda's mathematical work...

I'm tempted to broach the subject of who might have been counting time backwards, and why. Any ideas?
Yep Tepi.

[Image: 234293304_3ed499fbfc_o.jpg]

Depends on your calander Eye guess.

[Image: 4738565865_c0eb5c4bf6_o.jpg] Eye Luv the 4th of July. LilD

Tuesday July 4 1947

Tuesday is a day of the week occurring after Monday and before Wednesday. According to some commonly used calendars (esp. in the US), it is the third day of the week. According to international standard ISO 8601, however, it is the second day of the week. The English name is derived from Old English Tiwesdæg and Middle English Tewesday, meaning "Tīw's Day", the day of Tiw or Týr, the god of single combat, victory and heroic glory in Norse mythology. Tiw was equated with Mars in theinterpretatio germanica, and the name of the day is a translation of Latin dies Martis.
[Image: 2239878223_e44c992962_o.jpg]

[Image: RoswellDailyRecordJuly8%2C1947.jpg]

[Image: alien-city.jpg]
Since its birth around a half century ago, SETI has largely focused on looking for alien civilisations beyond our own solar system, searching for radio signals from prominent or nearby stars. But what if there were earlier technological civilisations in our own solar system, or even here on Earth?

That's the question explored in a new paper posted to (and soon to be published in the International Journal of Astrobiology), "Prior Indigenous Technological Species", by astronomer Jason T. Wright.
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
(04-17-2017, 08:19 PM)EA Wrote: [Image: concave2.gif]
Focus of the locus?
[Image: GreatPyamidBaseContruct.jpg]

Could you Imagine the Light beam that shone off the focal facets?
The mirror polished white limestone concentrating sunlight  and reflecting back like a lighthouse beacon.

[Image: 35c78c7b103d83a3113e119c5f7b0319.jpg]

The sides of the GP are not perfectly flat because they were reflectors.IMO.


[Image: egypt46_large.gif]
 Bulk parameters
   Sun    Sheep    Earth   
1,988,500. Mass (1024 kg) 5.9724  (Sun/Earth)Ratio 333,000 : 1 / Ra = 333kKiloEa
132,712. GM (x 106 km3/s2) 0.39860 (Sun/Earth)Ratio 333,000 : 1 /Sol = 333kiloEa

[Image: Pyramid-Egypt.jpg]
Quote:Many hypotheses for why alien artifacts might exist in the solar system involve a system that monitors the Solar System or announces itself (a “beacon,” Burke-Ward, 2000; Haqq-Misra & Kopparapu, 2012, and references therein).

Paper: "Prior Indigenous Technological Species", by astronomer Jason T. Wright.

Focus of The Locus   >>>  The Great Pyramid is located at 29:58:50.952 N =~33.3 grads

calculations for the “Speed of light  in air” should read thusly: 

[Image: pyramid-polished.jpg]

33×3×333 √ 1.2345678987654321 ×108 = 2.996999997003 × 10

[Image: pyramids-white-giza.jpg][i]“Speed of light  in air” Beacon[/i]

Quote:Many hypotheses for why alien artifacts might exist in the solar system involve a system that monitors the Solar System or announces itself (a “beacon,” Burke-Ward, 2000; Haqq-Misra & Kopparapu, 2012, and references therein).

Paper: "Prior Indigenous Technological Species", by astronomer Jason T. Wright.

The Great Pyramid shined like a star. It was covered with casing stones of highly polished limestone

The Great Pyramid of Giza was originally covered with casing stones (made of highly polished limestone). These casing stones reflected the sun’s light and made the pyramid shine like a jewel. They are no longer present being used by Arabs to build mosques after an earthquake in the 14th century loosened many of them. It has been calculated that the original pyramid with its casing stones would act like gigantic mirrors and reflect light so powerful that it would be visible from the moon as a shining star on earth. Appropriately, the ancient Egyptians called the Great Pyramid “Ikhet”, meaning the “Glorious Light”.  How these blocks were transported and assembled into the pyramid is still a mystery. ([url=]source

“Ikhet” = zep tepi first wish to see light @ ~.333 / ~33.3
Get your degree here!   THM You Know Verse City
@~33.3 grads per sol.

Quote:Okay... Can I give you a Ted Talk on finding ways to

In Duck Tedx~19.5   youareaduck   Inductedx~333
[Image: images?q=tbn:ANd9GcQ4U5V62J5NP7FAYknZMKg...TzSV89wPsg]
What is your second wish?

(05-07-2017, 05:20 AM)Ancient Vizier Wrote: I'm cross-posting this from the Back To The Garden thread since I think this might be a good place for at least part of the discussion?

A first-ever find in Egypt: A funeral garden

Fri, May 05, 2017

Excavation has discovered a 4,000-year-old funerary garden at a tomb entrance.

[Image: a-first-ever-find-in-egypt-a-funeral-gar...=1000&q=70]
SPANISH NATIONAL RESEARCH COUNCIL (CSIC)—The Djehuty Project, led by research professor, José Manuel Galán, from the Spanish National Research Council (CSIC), has discovered a 4,000-year-old funerary garden- the first such garden ever to be found- on the Dra Abu el-Naga hill in Luxor, Egypt. The discovery comes during the 16th year of archaeological excavations which are sponsored this year by Técnicas Reunidas and Indra.
The discoveries made by this project shed light on a key epoch when, for the first time, Thebes (now Luxor) became the capital of the unified kingdom of Upper and Lower Egypt about 4,000 years ago.
Dr. Jose Galán explains, "We knew of the possible existence of these gardens since they appear in illustrations both at the entrances to tombs as well as on tomb walls, where Egyptians would depict how they wanted their funerals to be. The garden itself consisted of a small rectangular area, raised half a meter off the ground and divided into 30 cm2 beds. In addition, next to the garden, two trees were planted. This is the first time that a physical garden has ever been found, and it is therefore the first time that archaeology can confirm what had been deduced from iconography. The discovery and thorough analysis of the garden will provide valuable information about both the botany and the environmental conditions of ancient Thebes, of Luxor 4,000 years ago".
Galán continues, "The plants grown there would have had a symbolic meaning and may have played a role in funerary rituals. Therefore, the garden will also provide information about religious beliefs and practices as well as the culture and society at the time of the Twelfth Dynasty when Thebes became the capital of the unified kingdom of Upper and Lower Egypt for the first time. We know that palm, sycamore and Persea trees were associated with the deceased's power of resurrection. Similarly, plants such as the lettuce had connotations with fertility and therefore a return to life. Now we must wait to see what plants we can identify by analysing the seeds we have collected. It is a spectacular and quite unique find which opens up multiple avenues of research".
"Digging in a necropolis not only allows us to discover details about the world of funerals, religious beliefs and funerary practices, it also helps us discover details about daily life, about society and about the physical environment, both plant and animal. The necropolis thus becomes, as the ancient Egyptians themselves believed, the best way to understand and embrace life", concludes the CSIC researcher.
The garden, or funeral garden, was unearthed in an open courtyard at the entrance of a Middle Kingdom rock-cut tomb very probably from the Twelfth Dynasty, circa 2000 BCE. The garden, measuring 3m x 2m, is raised and is divided into a grid arrangement of 30 cm2 beds distributed in rows of five or seven beds.
According to experts, these small beds may have contained different types of plants and flowers. In addition, at the center of the raised garden there are two beds which are set higher than the others where small trees or shrubs probably grew.
In one corner, the researchers recovered a still upright tamarisk shrub complete with its roots and 30cm-long trunk, beside which was a bowl containing dates and other fruit which may have been given as an offering.
In addition, attached to the facade of the tomb, which the garden is related to for the time being, a small mud-brick chapel (46cm high x 70cm wide x 55cm deep) with three stelae, or stone tombstones, in its interior was also uncovered. These are dated later than the tomb and the garden, coming from the Thirteenth Dynasty, around the year 1800 BCE. One of them belongs to Renef-seneb, and the other to "the soldier ("citizen") Khememi, the son of the lady of the house, Satidenu." On each, reference is made to Montu, a local god from ancient Thebes, and to the funerary gods Ptah, Sokar and Osiris.
[Image: 34467504605_4dd329fd26.jpg]
 Aerial view of the funerary garden discovered by CSIC's research team. Credit: CSIC Communications
"These finds highlight the importance of the area around the Dra Abu el-Naga hill as a sacred centre for a wide range of worship activities during the Middle Kingdom. This helps us understand the high density of tombs in later times as well as the religious symbolism that this area of the necropolis holds", concludes the CSIC researcher.
Article Source: Spanish National Research Council news release
Thanks for the post on stick charts, EA. A fine presentation. I'd never heard of them, they're pretty cool. Also it does help bolster my faith that the ancient Egyptians could have made pocket calculators out of sticks.

Also the NASA countdown. That occured to me after I'd posted that after they say ten they ritually say the name of Thoth backwards 9.876543210... (A Pyramid-Pi System valid number!) so to speak before launch. Don't quite know what to make of that, but good point.

Folks, in my long post interpreting Berriman's data, I think I'd toss out everything that follows the opening section on the Remen. On closer inspection, it does sort of look a lot like someone's first attempt at a grand unifying scheme of ancient metrology. It looks a bit like too much homage to Pi and especially too much of a formulaic approach might have tripped me up. I do apologize for not just leaving that stuff out.

Hopefully the more involved one I'm working out better, including that I'm trying to see how many approaches one can run at once for additional guidance, but (just as it might sound) it's pretty intensive and I've no idea yet how well it will all work out. I'm hoping to really see how much mileage the Vesica Piscis scheme shown above really offers.

Thought this was interesting, I already showed the Egyptian Cubit-O-Matic 2000™ that uses 360 to make a remen-cubit exchanger in case it works to create a cubit that measures the Great Pyramid at the proscribed 440 x 280 cubits (there are claims that even shorter cubits than this would require might actually exist but I still haven't experimented that much on the lower end yet)...

I was mulling over that 360 / Meg Yard = Circumference o' Mars nonsense (?) when I stumbled across this....

Introducing the new Assyrian Cubit-O-Matic 2000™. Megalithic Yards go in, Assyrian Cubits come out - what could be easier?

57.29577951 (the Radian, aka 360 / (2 Pi)) / Megalitic Yard x = Assyrian Cubit y?

Dunno, maybe it's a piece o' carp, I've barely got it out of the box yet. Lemme kick it a few times and see if the tires hold.

Might as well see how much I can do with the metrology, though - something to do while I await the arrival of books. Can't find Lehner's "Complete Pyramids" for the life of me nor my copy of Mendelssohn's book. My data tables say Lehner gave the same measure for both the King and Queen's chambers which I think is in contrast to Petrie. Could be Lehner's mistake if it doesn't turn out to me mine but I need to have another look at the original source. Things are still a little to murky to try to make a call on the original measures so any source may be helpful. I also need to track down who was giving real, varied measures and where they are, and who was giving mean figures. I'm tabling out the candidates thinking that the winners will be the intended mean proportions, while the four runners up may be represented by the actual somewhat irregular measures, and eager to see if that idea holds water.

Also, while I'm thinking out loud, I ran across two works in the same day about what may be monuments aligned to indicate the position of other monuments. One is - I think it was - one of the circles that Thom worked on, so possibly it's in the link to the page with Thom's diagrams? The other is that I still keep wondering if Mississippi's Emerald Mound wants to be Carlotto's D&M when it grows up but I don't know if anyone's ever worked out Emerald Mound's geometry. Was looking for a good pic (none found yet) when I found an archaeological website that suggested that in the direction it points, small mounds and a striking large mound are found on that axis. I have a certain fondness for the idea that one of the functions of ancient monuments may be (where applicable) to provide landmarks, as well as considerable fondness for Watkins' book "The Old Straight Track".

It might be worth looking into since the geographic positioning theory (all the map stuff at the Pi Jedi Academy) can't seem to get its act together. Curious if the direction to the next monument is indicated if we could expect the distance to be indicated also. Just some thoughts, I'm not at all sure offhand if most ancient monuments would even make good pointers per se. Then again, dirt mounds may not be very good at preserving sacred numbers for posterity, either - which is precisely what made the idea of milking one last bit of data out of the global position of what's left of one such an attractive proposition.
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Memoirs of a Pi Jedi
Chapter Six
Geodesy? We got lots of that!

I seem to remember the subject coming up of a different value for the remen that my favorite one. To be fair, I have been forced to conceed diversification (the "Thoth Remen") and there may be others. So I took a remen of 12 / Pi^2 and fed it too into the Cubit-o-Matic 2000 ((360/ Remen x) = cubit y x cubit z)).  

I noticed it seems a little strange I am calling 1.721325932 a Thoth Cubit when a theoretical cubit of 33.33333333 / 19.46773764 = 1.7122345672 has a little bit of Thoth in it too...

If I put my favorite cubit in the Cubit-o-Matic 2000 and input 1.7122345672 as a candidate, I get back as its pair a figure of 1.728000000, which I thought was intriguing.

If I put the 12 / Pi^2 remen into the Cubit-o-Matic 2000 and input 1.7122345672 as a candidate, I get back as its pair a figure of 1.729249823, which I thought was even more intriguing. You might say that's an old friend of mine. I've never hauled off and called it a cubit in the past, but it's a rather interesting number.

Where have I seen it before? Silbury Hill (the terrestrial counterpart of Cydonia's "Tholus" in David Percy's reckoning - his concept of some of Silbury plain's monuments as a model of Cydonia sans Face is probably the reason I ever bought a Hoagland video in the first place). In a model I made of Silbury, there was something fairly remarkable in the way it pulls off an approximated trigonometric function that I still think is really cool.

Here's a post from my initial exploration of Silbury's proportions. Please pardon any Munck Junk not weeded out. I'm not going to censor his name at every turn here, sorry.

excerpt from:
"Ah found mah three-ills... on Silbury Hill..."
Thu Feb 20, 2003
Grid Point msg. board

For sure I should be wearing one of those "Don't Follow Me, I'm Lost" bumperstickers... thing about being lost, sometimes you think you were in a great place until you figure out you were lost... and you can even make up your own names for the territory, like "Indeterminant Geometry", but that really doesn't have a lot of inherent ability to change the fact that you're lost, if that's where you actually are...

Silbury Hill... would like to have more data on this. I'm the guy who decided it was a bright idea to re-write all of Carl Munck's model on Stonehenge, Silbury, and Avebury into "WGS 84 datum", I almost feel personally responsible for making sure that the "WGS 84" is satisfactory in every last detail... one of the troubles being that I've never actually seen a model of any of these three in every last detail... although at this second I have virtually every Carl Munck product in existence in my possession... 

Another problem being the question of who has the Silbury data to begin with... I have a shelf starting to brim with works on Stonehenge and Stone Circles, that don't actually even begin to represent British archaeology, but alas, poor Silbury, mightiest monument in the Isles it may be, does not happen to actually be a Stone Circle... I'm sure we're all dying to know how it answers the Megalithic Yard, but Thom's indices don't even give it honorable mention...

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)

Aside from Munck's Grid Values, 67858.40132 / 2662.867199 = 2.5483208098... although I have a model of how he got those figures... That's really all the data I have... 

Now, I'm sure I'm likely to get us all into trouble trying to steer the boat through long-charted waters myself... but should we just give up there...? Hmmm... where would we all be, if "give up" were in our vocubulary?

Seriously, there are two things I commend, one of them is when Carl Munck does not even want to touch a monument because he doesn't have enough physical data, and the other is when someone is not going to let a lack of physical data be an obstacle. There are cases out there where we may never get that physical data, and I refuse to accept that it means even the Grid Values of those monuments are irretrievably lost. Quite the contrary, I like to think the Matrix means that even if there's nothing left of a monument but an unmeasurable crop stain, the ancient voices haven't been silenced... 

Okay, let's look at what Carl Munck has here: Diameter 550
D / 2 = R, R^2 x Pi = Area, so... (550 / 2)^2 x Pi = 237582.9444

Carl Munck, "Whispers from Time, Vol II", p 273...
Silbury: Diameter, 550 feet; Area: 237582.94 feet

So... we know his figure for area is based on 550 feet EXACTLY, and we know the formula is for the area of the Base that Silbury rests on, not all of Silbury's exposed surface...

I've said this before, and I've been trying to put it to the test lately... 550 is NOT in the Matrix as far as I've been informed... but I know two figures that are very close... one of them is 550.4373139, exactly 1/100 of Carl Munck's Grid Latitude for Monk's Mound at Cahokia.. 

What could you think if Silbury had a Diameter of 550.4373139 feet?

Interesting thing, Silbury is stone underneath... we've known that for a long time... we know that it's a very bizarre looking structure, split into radial divisions into an octagon or nonagon (archaeologists do not sound sure which yet for some reason). My guess is that it's a nonagon, nine sides, and 9 Radians = 515.6620156, which is 1/100th of my Grid Longitude for Silbury... now I'm not in favor of basing any values on anything that was had to be discovered by invasion of a monument, there are other ways... in fact, that's another one I got from Carl Munck's new publications, and that is the partnership of the Area of a Circle and the Surface Area of a Hemisphere... 

No, it's not really a strange case where addition works well for the Matrix, it's really multiplication...

The Surface Area of a Hemisphere is 4 times the Area of a Circle, so adding the two really means 5 times the Area of A Circle... Area of a Circle 10313.24031 x 5 = 51566.20125...

Maybe right there is where we are warned that maybe we shouldn't take this "Cone" stuff too seriously... ?

Anyway, say we have a Silbury with a Diameter that's a decimal harmonic of the Grid Latitude of Monk's Mound... they're different forms, of course... Silbury is something in the circular family, Monk's Mound is a more rectangular species... so what have they got in common besides just being "major monuments"? 

Well, it's too late to predict it now, but speaking of monument invasion, guess what they found at Monk's Mound underneath? Who'd have guessed, but just like Silbury underneath, stone...

Maybe it's more to the point here that 550.4373139 seems to belong to the British Landscape as well... 

Proposed Diameter Silbury 550.4373139 x WGS 84 Grid Point Silbury Reciprocal of the Squared Yoda Meg Yard, RSYMY 1.351926225 = 744.15060399, decimal harmonic of our customary Area of Stonehenge, one of those Carl Munck figures I wouldn't waste a second arguing with, and good luck to anyone who cares to... That's just an example...

I have considered 550.0394833 feet... not off my much... in fact, over at the Celtic New Zealand site, they suspect this although they can't figure it out and I'm not surprised...

550.0394833 feet x Pi = Circumference 1728.0 isn't that cool? CNZ thinks it's 1728.0...
(God, they're brilliant, I just wish they'd wake up and smell the Pyramid Matrix)

One problem is that 550.4373139 x Pi seems to belong even more to the British Pyramid Matrix than does 1728.0... in spite of 1728.0 having at least several very glowing items marked on its resume...

550.4373139 x Pi = 1729.249822

And this "affinity" of 1729.249822 over 1728 includes something very important in context, which is the ability to resonate with Silbury's own (WGS 84) figures...

They're not necessarily the most obvious, but 1729.249822 is in the middle of a run of responses to at least 5 powers worth of 1.351926225, the Reciprocal of the Squared Yoda Meg Yard, RSYMY  the "WGS 84" Grid Point of Silbury... 

There's also this: 51556.20156 / 1729.249822 = .0298199833

That IS a decimal harmonic of what is so far the most recognizable figure for approximated WGS 84 reciprocal flattening... which is probably even more "navigational", to borrow CNZ's phrase, than is 1728...

1729.249822 is also "navigational" in the sense that 1729.249822 x 4 = 6916.999288, which is a decimal harmonic of the "miles-per-degree-of-equatorial-longitude" figure associated with 24901.19742 miles, which is a Matrix Valid figure obtained by cubing the WGS 84 Stonehenge Grid Point, that comes within one mile of the "almanac" figure for the Earth's equatorial circumference, and answers the Apex latitude at Giza in a substituted Munck equation, addressing the Michael L. Morton Apex latitude value for the Great Pyramid, which also addresses the Grid Latitude of the D & M Pyramid on Mars...

24901.19742 / 360 seconds = 69.16999284 miles per degree / 60 minutes = 1.5283321 miles per minute / 60 seconds = .0192138869 miles per second, .0192138869 being a decimal harmonic of 19.4677376 x Pi^2...


And that's the way it was. 

(note on: 1.5283321 miles per minute...should read 1.152828584 = dh perimeter of inscribed circle on face of Yoda model pyramid in feet, more geo-modelling?)

The way it is, is that I'm incredibly tempted to just haul off and declare 1.729249823 a "Geodetic Cubit".

Another way of saying the above is that 24901.19742 / 144 = 172.9249821, allowing a Silbury Hill a base perimeter to serve as a scale model of the earth using a ratio involving modern feet and miles.

On a vaguely related note, I was going over that academic article on the cubit

Table 2 has some "Hebrew Linear Measures"

After some deliberation, I decided that the best way to interpret a "Span" of "8.745" inches might well be as = 8.760481938 inches. (I get decimal harmonics of 8.760481938 into my calculator by remembering that 45 x 19.46773764 = 8760.481938)

That gives a value of 8.760481938 inches / 12 = .7300401615 feet (a remen fraction), which is one of two values vying for identification with the Egyptian Small Span along with a Squared Yoda Meg Yard fraction.

Of the measures stated by source, a common scale cubit of 17.49 in / common scale span of 8.745 = 2. 

Accordingly, the corresponding cubit = 8.760481938 inches x 2 = 17.52096388 inches, or 1.460080323 ft.

1.460080323 x 2 = 2.920160646 = (cube root 24901.19742) / 10
17.52096388 x Pi = 55.04373141 proposed diameter Silbury Hill / 10
17.52096388 x Pi^2 = 172.9249922 proposed base circumference Silbury Hill / 10

When we observe that our basic concept of Silbury essentially has a circular base and exercise the prerogative to throw icons of circular mathematics at it, such as 360, the radian 57.29577951 or Pi

1729.249822 ft / 360 = 4.803471728 = Yoda Ht. Great Pyramid / 100
1729.249822 ft / 57.29577951 = 30.18110298 Yoda Perimeter Great Pyramid / 100

It's rather suggestive that there may be geodetic concerns built into that model of the Great Pyramid that may not have received sufficient focus before.

24901.19742 / 480.3471728 ft Yoda Ht. GP = 51.84, as in 51.84* Great Pyramid angle

24901.19742 / 55.04373141 proposed diameter Silbury Hill / 10 = 452.3893421 ft proposed height Great Pyramid with paving but without pyramidion, and

24901.19742 / (55.04373141^2) = 452.3893421 / 55.04373141 = 8.218725921, or 1 / one-tenth of my favorite remen of 1.216733603 feet

I thought that was pretty good for just being me copping a whiny attitude that "550 isn't in the 'Pyramid Matrix'"
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
But wait... There's more! A little more geodesy for you...

Idealized apothem Great Pyramid (paved) = 194.4 Pi = 610.7256119 feet
Idealized apothem Great Pyramid (unpaved) = 194.6773763 x Pi = 611.5970155 feet (equals 1000 Ellifinos / Pi)

610.7256119 x 611.5970155 = 373517.9615 -- and what's that?

373517.9615 x .0666666666 = 24901.19743 

373517.9615 = 15 x 24901.119743

Idealized apothem Great Pyramid (paved) = 194.4 Pi = 610.7256119 feet
Truncated apothem Great Pyramid (paved) = 500 remens = 1.216733603 x 500 = 608.3668015

610.7256119 / 608.3668015 = 1.003877283

Being the Pi Jedis have it figured for a 2 Pi pyramid, let's throw Double Pi

1.003877283 x (2 Pi)^3 = 249.0119743 = 24901.119743 / 100

I think Vianova is the first person to actually make me think they have truly found a Sidereal Year value encoded in a pyramid design. A number of people have tried and failed, which has made me terribly wary of such claims in the past. In fact, Capt has the annoying habit of framing all measures in "Pyramid Inches" in order to find "the Sidereal Year" inexplicably scrawled all over the Great Pyramid's interior at the probable expense of much other data contained therein, so that every measurement in Capt's book has to be converted back into normal feet using a conversion ratio that isn't easy to find in his book unless you're not looking for it (case in point, I'm not finding it in order to be able to tell you what figure he is using).

The Pyramid Pi System has multiple candidates for conversion of a "Pyramid Pi Year" of 365.020081 into more Sidereal Year-like figures, starting with the most obvious 365.020081 x 1.000723277 = 365.2840914, but to date this sort of tactic hasn't generated much excitement or enthusiasm among any Pi Jedi that I'm aware of. Perhaps the Sidereal Year is something to keep an eye out for, though, since we have a slightly new model of Giza in front of us now? 

For the moment, why not try to take a little closer look at 365.020081?

Memoirs of a Pi Jedi
Chapter 7.008385550*
Time and Motion?

Yoda used to write chapters with titles like this, full of what is probably an even mix of the remarkable and the fancifully absurd. Don't have any handy at the minute but you can be sure he'd do stuff like

24 hours x 60 minutes = 1440; 1440 x 60 seconds = 86400 seconds in a day, and probably next we'll look at the sqrt of (86400 / 10) = 92.95160031, one of our useful significators and mathematical probes.

If the earth's equatorial circumference is reckoned at the "Pi System" valid value of 24901.19742 miles, and the earth is making 1 complete rotation in a day, it may be suggested to be rotating at a speed of 

24901.19742 miles per day
/ 24 hours = 1037.549893 miles per hour
/ 60 minutes = 17.29249821 miles per minute
/ 60 seconds = .288208303 miles per second

If a year is reckoned as the "Pi System" valid value of 365.020081 days, it may be suggested to have a value of 

365.020081 days per year
x 24 hours = 8760.481944 hours per year
x 60 minutes = 52562.89166 minutes per year
x 60 seconds = 31537735.00 seconds per year  


24901.19742 miles per day rotation x 365.020081 days = 
9089437.100 miles per year
(9089437.100 = 3.60 x (Pi^4) x 25920)

Hmmm... several figures I've just introduced (17.29249821 and 8760.481944) appearing here, aren't there? (In fact, if you've been to the Pi Jedi Academy you've likely seen most of them before). But 31537735.00? What are we supposed to build that monstrosity out of - sticks? 

How about stones?

305.7985081 inner sarcen circle circumference of Stonehenge in feet x Area of a Circle 10313.24031 (equal to 6000 royal cubits in feet) = 31537735.00

Or mounds?

1729.249821 proposed base perimeter Silbury Hill x (R / Pi)  = 31537.73496

Is there an easier way to remember that? 

How about building it out of tetrahedra?

1620000.000 x 19.46773764 = 31537735

Or out of the putative symbolic Precessional Cycle of 25920 years?

1 standard Remen in feet 1.216733603 x 25920 = 31537735 / 1000

I wonder what it says to the "Holy of Holies" 144 Pi (452.3893421 feet, proposed height Great Pyramid with paving, sans pyramidion)

31537735 / 452.3893421 = 69.71370352 x 1000

You recall this figure from the Thom Type A circle, Perimeter of arc from A = 69.65793147?

69.71370352 (sqrt 4860) is my call for the intended interpretation of that figure. 

Note also from the post with the Thom diagrams my call on the perimeter

Here's my call on the intended interpretation of the generic perimeter of the Type a flattened circle:

Total perimeter = 350.5513216 = 350.4192775 (accuracy .99962)

Does Thoth approve of all this?

350.4192775 / 1.1111111111 = 315.37735

Well if the boss okayed it, I guess it's okay by me... that would also mean that

31537735 x 1.234567901 (1.1111111111^2) = 38935475.31 = 19467737.65 x 2

Back to the Great Pyramid's Holy Height (sans pyramidion)...

31537735 / (452.3893421^2) = 154.1011111

What's that interesting looking number? Should we know it?

It's a decimal harmonic of the reciprocal of 6.489245878. 1 / 6.489245878 = .15410111111

And what's 6.489245878?

19.46773764 x 33.33333333 = 648.9245880

Radian squared, divided by Pi (57.29577951^2 / Pi) = 10313.24031 "generic" Area of a Circle / (Pi^2) = 1044.950284...

31537735 / 1044.950284 = 30181.10298 = Perimeter Great Pyramid (with paving) x 10

31537735  x 1.177245771 = 37127665.16

We haven't covered that yet, have we? It's Morton's generic figure for the Volume of a Torus

Though it isn't the proper formula, we can nonetheless construct it too from simple circular math: 360 degrees of a circle x 10313.24031 generic area of a circle = 3712766.512

Remember this one? 575.1793153? I barely do, it's one or other of the Great Pyramid apothems with the pyramidion missing (the slope length up to a height of 452.389341 ft)

It's an unwieldly figure that seems to answer clearly to relatively little, yet it still serves as a "metrological standard" for the SYMY (Squared Yoda Megalithic Yard) figure of (2.719715671^2) = 7.396853331 ft

575.1793153 ft / SYMY 7.396853331 ft = 7776.000000 / 100

31537735 / 575.1793153 = 58431.13555 = dh ((1 / 57.29577951) x Pi)), another permutation of the Radian and Pi, or perhaps more straight forwardly, Pi / Radian = 0.05483113555

Is 31537735 Radian-friendly, then?

31537735 / 57.29577951 = proposed base diameter Silbury Hill 550.4373144 x 1000
31537735 / (57.29577951^2) = 9606.943463 = perimeter Great Pyramid (paved) / Pi
31537735 / (57.29577951^3) = 167.6727943 = "Le Serpent Rouge" constant 1.676727943 x 100

Let's go back here a minute where we showed how to build the earth's equatorial circumference from 1.003877283 and 2 Pi

Idealized apothem Great Pyramid (paved) = 194.4 Pi = 610.7256119 feet
Truncated apothem Great Pyramid (paved) = 500 remens = 1.216733603 x 500 = 608.3668015

610.7256119 / 608.3668015 = 1.003877283

Being the Pi Jedis have it figured for a 2 Pi pyramid, let's throw Double Pi

1.003877283 x (2 Pi)^3 = 249.0119743 = 24901.19743 / 100

31537735 / 1.003877283 = 31415926.53 = Ten Million Pi

Dunno what 1.003877283 is but sure seems kinda handy sometimes.

*Seven itself does not belong to the Pyramid Pi System as far as any Pi Jedi are acutely aware of.
7.008385550 = (360 x 19.4677364) / 1000
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Lehner's book got here. Looks like his mistake and not mine on the chambers. He might be the Supreme Commander of Shart Shard Dusters but I still don't see where he's a scientist yet. It's too bad, I think Vi is every bit on target with his sentiments about Petrie and the royal cubit.

Petrie's data is making the Queen's Chamber (cleverly disguised as a first exercise in Kindergarten Cubits) look like ancient Egyptian rocket science. I have honestly never seen the likes, and do not really know what to make of it precisely, but I do know exactly what I'm looking at essentially. I thought the Cubit-O-Matic 2000 was hot stuff, this thing's got a Cubit-O-Matic 2000 BC with an adaptor that slices, dices, and makes dozens of Julienne Phis.

According to the actual measures given by Petrie, it's got cubits as low as 1.716 and 1.715 ft (we are getting into cubits you could measure the Great Pyramid's exterior with at c.a. 440 x 280 cubits too, I think).

Here's how it works:

(1 / Phi) / 360 = 1.71676108 / 10^n; (1 / ~Phi y ) / 360 = ~1.71676108 / 10^n= "Phi Cubit" z  

Looks very much to me like they intended us to find a particular pair of their favorite forms of Phi, possibly from Pyramid Pi math. They may have written 1.618033988 as literally as possible then set it next to something (Perfected Pi Pyramid Phi 1.61882914 or Pi Phi 1.621138938?) that they wished us to consider to be equivalent in proper context - or they set true Phi next to the natural form of Phi in a 2 Pi pyramid, or something. Some combination of two forms of Phi that has meaning, at least... or,

Maybe they wanted it just blurry enough to keep us guessing so we get to add our big pile of guesses to our Catalog of Pyramid Pi Constants. I'm definitely seeing some that haven't been on the radar before.

I might have hinted before that such a thing was in theory possible, but I think in the QC we may actually be seeing it in situ. I hadn't expected to find it there.

The advanced setting looks like:

3 or 4 of the most important Pyramid Pi System constants between 1.02 and 1.04 go in, cubits and Phis come out. They also seem to be trying to simultaneously add constants to form values for "Phi Cubits" in feet from them on the North and South sides.

I'm still fairly sure that 1.033542556, 1.027340740 (as seen in the Thom Type A flattened ring), and 1.032759559 were intended. Not exactly sure what the fourth is or how they combined them exactly, but for example, one proposed combination is

+ 103.2759559
206.0100299 inches = 17.1675024 feet; 17.1675024 x 360 = 6180.300897 = 1 / 1.618044197 x 1000
206.0200000 inches = Petrie's mean stated value for south to north below the QC's apex

If the Great Pyramid is not a Phi pyramid, they almost seem rather apologetic about that.

For a long time I thought 1.031324031 was going to be one of the included favorite Pyramid Pi System constants, but we can dispense with that one since there will be buckets of it at the Kindergarden Cubit level (Six Royal Cubits of 1.718873385 ft = 10.31342031 ft = 206.2648062 inches = (103.1324031 x 2) inches). The Kindergarten QC is, I think, 10 cubits wide by 9 cubits tall + 3 cubits to apex = 12 cubits max.

BTW, these numbers look very much like the stuff I'm pretty sure I was seeing in the most careful measurements of the King's Coffer lid.

Really very glad I heeded John Michell's warning about Urdummheit-itis, even though he was still suffering a fairly bad case of it himself at the time. (Even the official Urdummheiters themselves were most likely busy scouring the Vedas for ancient technology and so forth - a bit like standing at a bus stop with a thousand dollars cash in your pocket and announcing as loudly as possible to everyone, "There certainly isn't a thousand dollars in my pocket" - yes, there certainly weren't any ancient geniuses, were there?) Hopefully I am done now with the U Word.

I should live so long to see this get figured out, let alone that this is one pyramid, still full of surprises 20 years later. It's literally made me seriously depressed to realize there probably isn't even time in this life to get on to Mesoamerican Pyramids. I can't even dream of that anymore even though technically, those I could just get in a car and drive to (and there are probably, what, more pyramids at some of those individual sites alone than in all of Egypt, or something like that?) Frankly I find Mesoamerican archaeology about 10 times more interesting than Egyptian, but I am unworthy.

That field is depressing enough, I gathered piles of shit marshmallowy data from Mexican archaeologists who seem to have no clue how brilliant their own ancestors were, and how they are managing to cover it up with shit marshmallowy data. (Yoda's even gone so far to suggest, after composer James Furia pointed out to him the analogy between the Giza and Teotihuacan pyramids, that Teotihuacan may have been the ancient prime meridian marker before Giza, implications probably intended).

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(Teotihuacan layout stylized to accentuate correspondence).

Looking a bit more all the time like the Ancient Astronauts wore loincloths, not space suits. Ancient rocket science... Try pointing one of those SETI dishes downward sometime...

Whatever our ancestors were, they were not stupid, and demonstrably so.

It might take ten like me to complete a mathematical analysis of Giza in my lifetime. That's a disturbing feeling, since I haven't seen any evidence of work by Munck or Morton in the last ten years. I may be the only one like me now, which is trying to motivate me into much more than I'm really up for. What did we expect though? Should it take any less time or any fewer workers to decode their mathematics than their hieroglyphs?

(Also, I've been looking again at the physical measures of the outside. Whatever else it may achieve, it may be very well possible that one reason the Great Pyramid was tweaked was because it may have meant more to them to make one of the base diagonals - probably the NW to SE? - into 1067.438159 than I'd realized. Hell, if it points right at any "Hall of Records" while Yoda's coordinates point to its entrance I shouldn't be surprised. What we were supposed to do, go straight to the Hall itself and start dynamiting?)

Lastly, I've seen signs of several interesting phenomena - more important constants stored between the measures of the paved and unpaved Great Pyramid models, and how constants from the unpaved model (i.e., my idiotic invention the Thoth Remen) can help resolve strange and seemingly incidental constants that are otherwise purely a thing of the paved model - also some exceptional square root tricks that don't seem like usual Pyramid Pi System fare, but may help answer the question of how we were expected to guess the proportions of the pyramid without the paving, without pulling up the paving. Pay close attention to those apothem values...

Strictly speaking, for any 2 Pi pyramid, using specs according to Yoda (paved) here, the edge length / apothem ratio is 

el / apo = 717.9062172 / 610.7875012 = 1.175378041

Wouldn't it be cool if that could be the mighty Alternate Pi, 1.177245771?

Sorry, not mathematically possible.

However, for the model minus the paving, the edge length calculates at 718.9305496, which numerous mathematical probes suggest is deliberately intended to indicate 718.9741438 feet...

And the ratio across 718.9741438 and the adjusted 610.7256118 (194.4 Pi) untruncated apothem value is 

718.9741438 / 610.7256118 = 1.177245771 Alternate Pi

More ways they attempted the mathematically impossible so they could cram more numbers and more confirmation into the Great Pyramid.
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911

1 Astronomical Unit(AU) = ~.666/ ANU = Earth

1 Astro Numerical Unit(ANU) = ~.999/ ANU = Mars 
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Bulk parameters
                        Sun       Earth     Ratio (Sun/Earth)
Mass (1024 kg)              1,989,100.    5.9736   333,000.
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I noticed the equation that governs Earth’s gravitational sphere of influence is all threes. The Sun’s mass is 333000 times greater than Earth’s mass. AU stands for astronomical unit, the mean distance from the Earth to the Sun.
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In the microcosm, every proton in the universe is made of 2 up quarks and 1 down quark. The charge on the up quark is +0.666666… and the charge on the down quark is -0.333333…, netting a charge of +0.999999…, polarized oppositely to the electron. The neutron has 1 up quark and 2 down quarks as you can see, netting a zero charge.
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Repetitive sixes and threes suggest triangles. This leads me finally to another epiphany (e-π-Φ-ny) I had, that the infinitesimal gap in what would otherwise be a perfect Pythagorean triangle connecting e, π, and Φ suggests the question, “Why can’t we ever rationalize the transcendental?”
[Image: The-Mystery555.png]This mystery is drawn to scale
Logically, the answer is that it is an irreducible eternal mystery, and I’m down with that.

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When I drew an equilateral triangle inside the Great Pyramid’s two-dimensional elevation I was surprised to see my computer report that it measures 555.5 Feet or 6666 Inches on edge. Each edge of the inverted equilateral triangle inscribed within is exactly 3333 Inches in length. The lunes drawn above are arcs whose centers are on the midpoint of the pyramid’s base and at the midpoints of its two faces. The total perimeter of all 3 arcs is 3333 Feet. Do you chalk this up as a lucky coincidence or perceive it as an intentionally encoded design? Do you believe there is a conspiracy spanning millennia preserving the Imperial system of units? What purpose might that serve? Is something deeper going on? Why does Earth’s equator bulge .33% beyond being a perfect sphere? Why does Earth’s orbit bulge 3.3% out of round? Why does sound travel at 333.3 m/sec at 3.3°C in Earth’s atmosphere? Why is escape velocity 33 times the speed of sound? Why is the Sun 333000 times more massive than the Earth? Why does your spine have 33 bones? Reflect on the Eye of Horus! 

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Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Perhaps I'm being too kind in making Munck my Yoda. I think maybe he is more like my Darth Vader, perhaps he has gone over to the Dark Side a long time ago. I'd sort of like to make a Light Sabre out of a bunch of rolled-up maps that he duped me into buying with his Map Crap and take him off at the knee with it.

Worse yet, I could do it because I think it set the stage for Michael L. Morton (my Obi-Wan?) to go off on the Grand Folly of an "Archaeo-Sky Matrix" - I could name you a dozen reasons this is a boneheaded thing to do, but let's start off with the idea that it's stellar cartography's equivalent of Map Crap. What a terrible waste of someone like Michael with such a phenomenal command of ostensibly ancient Pi and geometry-based mathematics.

What I should have said to Michael is probably, "Look, dude - we can't even seem to map the ground properly. Can we figure out how to do that first?" - but I just kept crunching numbers and tendering support for his theories when I found it, which I seem to remember doing often.

The latest bitter pill is for hatching aspirations of hunting down Michael and seeing what he thinks of my latest work on Giza. We'd had enough of those just with Munck sending his students out in the world to be made mincemeat out of in a minute because our Great Pyramid is eight inches shorter than everyone else's, and we are never given any way of defending that. Being a scrappy little bastard, I've made my own way at long last. I could point out that if we set the Map Crap aside for a moment, the only physical data we have for the exterior of the Great Pyramid from His Smugness Munck is the height and perimeter. 

All the rest of it - four heights, eight apothems, measures with and without pyramidion, all come from me. Thirty years crunching away at Giza numbers and that's all Munck has to show for himself, is height and perimeter - unless it's yet another indulgence of his most annoying habit of keeping the best cards up his sleeves and going on like we who are his faithful are unworthy of viewing them. I can't begin to tell you how thin that Secular High Priest bullshit of him acting all Pi and Mighty has worn with me.

We are in no way prepared for New World archaeology thanks to this bullshit. There are twenty times more numbers in the exterior of a Tikal temple that we have ever seen out of the exterior of a Giza pyramid, minimum. Any one of them makes Giza look like kindergarten, and Grand Master Munck never got any of us past that into first grade.

I should think it peculiar if either Munck or Morton ever stopped irrepressibly crunching away at numbers, but I can't find much on later work from either. 

My latest Google searches suggest that I am not going to be getting a second opinion from Michael L. Morton, the one person in the entire world who might truly be able to appreciate some of the work I've done lately, because for some seven years now Mr. Morton may not be here to give one.

If that is so, may Giza's Great Pyramid with what I take to be its firm declaration that the Michael L. Morton Royal Cubit reigns over all others, stand in his memory.

I will say this, I still consider the work of either one as worthwhile as that of someone like Hugh Harleston, even while I can easily think of Munck as someone with the right numbers and the wrong attitude. The upside of our folly is that we have after all made many important discoveries during our wild goose chases, and we actually have gotten good practice out of it.

If one is crunching numbers and finds one of Munck's "Pyramid Matrix" Grid values, it would be wise to stop right there and reflect. Those numbers are well-tested, they are resonant nodes in Pi & Selective Square Root based mathematics that many numbers point to, so that these "Matrix" "Grid Values," Map Crap though they may be, still have meaning that may be applicable to architecture and metrology. Same with Morton's work and his Pi in the Sky - one new to the school of though can still learn a great deal from the available works of either. Watch out for their many mistakes, rejoice in the many successes they may have achieved.

Ironically, after Morton and I having been labelled "pirates" (yo ho ho, ahhhhhhrrrrrr me hearties) by Munck for getting on the Internet and not only telling everyone his "Pyramid Matrix" was the greatest invention since sliced bread, but actually acting that way too - like it really was so right and true it was worth us devoting out lives to it - nowadays you can apparently find Munck's videos on YouTube. There is your chance to study with my Master yourself at no cost (good, because I am so done with being a volunteer salesman for his Map Crap) whichever of the Star Wars characters he most closely corresponds to.

If you are watching one of his videos and are tempted to be taken in by his infectious level of overconfidence in his Map Crap, just remember - been there, done that, oops. This guy may be a bona-fide prodigy in ancient arithmetic and a worthwhile tutor, but it has yet to be established that he can map his way out of a paper bag - literally.

What he did was a fine job of proving you can find order in nonsense - just the opposite of what we are supposed to be trying to prove - and misled others into doing the same. I would grant him that "archaeocryptography is a science in its infancy" but those are his own words yet he turns out to be the one who seems to be most in need of reminding of that. "We must exercise curiosity," asserts Munck. Truer words were never spoken. Maybe just a little humility too, though.

Here's also a quaint little tour of some his curious notions (ooh, look - they made him a f--king King - that probably didn't make it any easier for him to measure his head).

If time allows, I hope to discuss some of this in more detail. My wish is that it be established as firmly as possible that just one American Pyramid (North or South, anything) reflects the same mathematical design logic that I can hopefully demonstrate being on display at Giza. That's at least fuel for much discussion since just one New World Pyramid may represent more numbers than you-know-who ever taught us how to deal with.

It might also give me something better to do than soapbox and sound too sure of myself - two things I might easily have learned at the feet of The Master that I'd kind of rather I hadn't.

Let's just say I'm curious how my latest projects turn out. No promises they'll amount to anything. As long as it isn't more projection of order onto chaos, I'm at present intrigued if not encouraged. Not like I don't have enough f-----g hobbies as it is, but who knows? Maybe I really am The Last of the Pi Jedi? Who the f--k else is going to it, eh? Thankfully spring is here and I'm rejoicing in just being able to give a sh-t about anything but freezing my ass off. I'd be too miserable to crunch one single number in the winter anymore.
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Hopefully I have most of the intended basic exterior physical data on the Great Pyramid by now with the exception of internal angles and the radius of an inscribed sphere. Things are still a little dicey with the diagonal but they were maybe supposed to be. Other than that, one way of framing it is that the Great Pyramid sans pavement has particularly good edge and apothem values - they are the values that countless mathematical probes have suggested were there, and now we hopefully know why. We can also see in retrospect how the mathematics (arrogant as this must sound) have been telling us they were there the whole time - more of how we were supposed to know what was under the pavement without vandalizing it, just as this model's pyramid with paving is the pyramid that Munck's mathematics have always told us was there.

If I've assessed things correctly, nothing goes to waste in this model, nothing is purely incidental or by chance. Apothems, diagonals, vertical edge lengths were all intended to mean something. Anything less than the most ideally stupendous is seemingly tolerable only because it has some interesting property, such as the curious incidental apothem length that works out to a decimal harmonic of rational units (7776 / 100 = 77.76000000) of "Squared Munck Megalithic Yards". 

These may often be showcases for the utility of mathematical probes at higher powers, for example I believe the awkward-even-if-intended height of the Great Pyramid sans pavement and sans pyramidion turns out to be a notable responder to Pi to as high the ninth or tenth power before beginning to lose resonance. Reponders to unusually high powers of other common probes such as the Radian value may also be in evidence. For what it's worth, in my way of reckoning, the Great Pyramid's proportions appear to have been just that carefully selected.

So far, I have not been forced to accept any inaccuracies in approximating calculated values for the Great Pyramid in excess of ~.9996, so that is trying to become something of a standard. It still may not clarify the intended diagonal but to approximate the raw calculated diagonal value of ((3018.110298 / 4) x sqrt 2) = 1067.063129 with the sacred 1067.438159, and it may yet be of interest that this very desirable approximation would involve an accuracy of ~.99964 without physical distortion of the most basic equal-on-all-sides model.

Have I shown before that whatever his number 1.067438159 may be, we might expect to see it frequently enough even aside from any purported context of any "Hall of Records" because it appears to be, among other things, a geodetic constant? Just that, 360 and 2:

(1.067438159 / 2) x (360^3) = 24901.19737 as if we haven't found the Earth's equatorial circumference in the expanded Munck model Great Pyramid enough already.

I'm presently pouring over Tikal data - I've dug out Teobert Maler's original report, and I've also been looking at a second dataset from George Andrews - there are some discrepancies but there may be a lot of useful corroboration as well. I could just dig into tossing out data, but it occurs to me that with Maler's data making it look so much to me like Tikal's pyramids respond well to the traditional "Pi Jedi" logic, that we have a different thing than the mathematics of Mayan calendrical or astronomical math and this may be a good opportunity to try again at something I don't think any of us have succeeded at before, which is reconciling these together.

Obviously, any Pi Jedi knows that numbers like 52, 260, 891 or 1898 do not belong to "Pyramid Pi" mathematics per se, however anything we might use to represent them and any applicable rules haven't exactly announced themselves, but working it out not only requires me to try a lot of calculations, but also brushing up on things like lunar constants and other astronomical data, which I have a very poor grasp of, from the ground up. It is starting to occur to me that in the past we may have failed to comprehend our intended version of some constants precisely because they are not constants, but are variable over time. Certainly enough to foil any Pi Jedi with their supreme devotion to any and all precision possible.

One of the illustrations on the Munck pages I linked to shows Munck's own diagram of Tikal Temple I, where straight from Maler's measurements we get a value in feet of the Earth's equatorial circumference / 10^n. Andrews gives a different figure for this measurement so I am going to want a third or fourth dataset if I can find them before I invest too much in that proposition. Munck finds the literal, present-day "almanac" value for this, whereas I've experimented with my "Matrix-Valid" value of 24901.19742 which is much easier to find (and more often) in the numbers than the "almanac" value.

The story of this number is a strange one. I didn't know it existed until I found 2.920160646 at Stonehenge and cubed it just for fun. Munck has an equation where to his accounting, the Great Pyramid has a second intended latitude on the North face which allows him to do a bankshot off the symbolic precession cycle value of 25920 to find the Earth's equatorial circumference, also involving an "apex displacement ratio" of 25920 / Earth's equatorial circumference. 

Michael Morton adjusted this figure by the slightest to make it not only "Matrix-valid" but also conversant with Munck's "Grid Values" for the D&M Pyramid, bringing the ratio to 1.040913799 precisely and therefore that is his discovery (another for the miscellaneous constants list above), but he didn't seem to have thought to give it back to the equation, giving us 25920 / 1.040913799 = 24901.19742. I was actually quite surprised after having found a circumference value that would be probably be bursting out in many monuments, when I took that value and applied it to Michael's equation to see that they fit perfectly.

One of the things I'm intrigued with in Maler's data, if it will hold up, is that for Temple IV, his data shows a doorway measurement of Height 317 cm = 10.40026247 so one of many new projects is working on whether the original designers might have intended that value to mean 10.40913799. It may be relevant to the issue of Mayan calendrical or related data in that

104.0913799 / 2 = 52.04568993; 1040.913799 / 4 = 260.2284497

There are some alternate candidates, but it's also sinking in that perhaps there were not any single intended approximations, any more than "Pyramid Pi" math affords any single approximation of the square root of two, and particularly not if this mathematics is going to integrate with diverse metrology, or at least on the Egyptian side of the Atlantic. It may have thwarted us before to be looking for "the" value previously under such circumstances, when there may have been multiple approximations that belonged to multiple valid formulas. So that's very new to me, and I'm very curious to see how it all works out this time, but I expect it could take quite awhile.

I spent a considerable amount of time yesterday just exploring 353.9334581 as a potential candidate for representation of a Lunar Year value of 354 days. It's a remarkable number that none of us seem have noticed before, but I may even have already found it providing some linkage between the paved and unpaved Great Pyramid models, so its possible role in the rationale for that kind of multiplicitous pyramid design might also be something worth exploring. Was the Great Pyramid a "Lunar" pyramid that becomes a "Solar" pyramid when you add the paving? No idea really, it's all completely new to me.

Going over Maler's data has also provided considerable fresh insight into the probable origins of most of Munck's numbers for the Tikal pyramids, woefully incomplete as they may be, so in spite of it all I may be nearly equipped for an opportunity to demonstrate the logic he used and even to discuss possible alternatives related to any broader picture that may be possible. If the ancients were thinking about calendars and he wasn't, it's possible he overlooked something.

I might add something else while I'm thinking of it... Not that it matters now, but Michael Morton bless him used to drive me up a wall with some of his "Archaeo-Sky Matrix" values for stars allegedly related to Giza's layout. He determined Grid Values of 33121.22149 (1.111111111 x (Pi^9)) and 194.818182 (2 x (Pi^4)) for Alnilam for the point in time that his dataset refers to. I eventually thought it was completely absurd not to take these to mean 33333.33333 and 194.677364 which I believe were within acceptable error tolerance. It always seemed to me rather like seeing how close one could get to Richard Hoagland only to give him a slap in the face when you get there. Eventually this actually managed to help drive a wedge between Michael and myself, even when I thought we made a great team - and of course we are talking about a very slim ratio of 194.818182 / 194.677364 = 1.000732377 as we often are. Nerds splitting hairs and arguing over almost literally nothing, to any causal observer.

I have never wanted to question that 19.4677376 is THE intended representative of the Tetrahedral Constant 19.47122063 in our system, and this is just the point of my argument - 33121.22149 and even 194.818182 are secular constants that generally aren't referenced that often whereas 194.677364 x 10^n is all over the place as I've shown here. I got out the Thom Type A circle specifically to show what a bucket of 19.467737 that thing is, generically. However, it almost also succeeds in expressing the cube of 19.467737, but if I'm not mistaken, what it actually expresses is 19.467737 x 19.467737 x 19.4818182. Why was that permitted?

I was playing with four (uncorroborated?) measures that Munck gives for one of the Tikal pyramids just for fun because I'm pretty sure I know how Munck would interpret that raw data, and ended up looking a fair amount of both 19.467737 and 19.4818182 in the numbers as if they might be skillfully juggling the two and pointing out to us a number of places where 19.4818182 may have been overlooked in our mathematics. It may be just about time to finally seriously ask whether the ancients regarded 19.4818182 also as if it were 19.47122063. Should I up and christen 19.4818182 as "Alternate Tetrahedral Constant B"? (Yeah, I know - who's gonna argue, but is it really the right thing to do???)

Another thing I've run into at Tikal is some values beginning with 88-. The obvious one is 887.6223994, the Square Root of the (generic) Volume of a Sphere, it certainly looks like Munck interpreted it that way for at least some purposes, but I've encountered what may be the possibility of another, which is the height of the Munck model Great Pyramid in MLM Royal Cubits, divided by Pi

Ht GP 480.3471728 / MLM Rcbt 1.718873385 = 279.4546573; 279.4546573 / Pi = 88.95318016. 

Any independent mathematical explorers of Tikal may wish to be aware of the possibility that its designers may have been adeptly juggling these two similar values also. I'm only beginning to explore that myself.

As for Mayan metrology, I haven't any clues yet. It might be that the complexity of their pyramids owes to the simplicity of their metrology, whereas the Giza pyramids may be exactly the opposite - having multiple metrologies may have afforded them simple pyramids that are mathematically as ornate as the New World pyramids often are physically. We shall see where all this leads if I'm up to it, but I have already found some intriguing equations. Stay tuned, as Richard Hoagland used to say.
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
I may as well go ahead and rattle off a little bit more as I noticed a couple of things while tidying up my notes, if nothing else this will serve as a note to myself in a convenient place.

As I said, it seems as if Munck may have detected the presence of SRVS 887.6223994 at Tikal. We can see this in some of his "Grid Values" for Tikal's temple pyramids. There is what may be something of a recurring figure in Maler's data, that is also seen in some of Andrews' - for example

Temple II Room 1 - Height (floor to springline) 3.10 m. = 10.17060367 ft. (Andrews)
Temple IV Exterior Doorway Width 310 cm = 10.17060367 ft. (Maler)
Temple IV 1st Chamber Width 124 cm  = 4.068241470 ft = 1.017060368 x 4 (Maler)

It's a bit soon to tell but it may also occur as the Width / Height ratio of Temple I's exterior doorway in Maler's data, and it may well occur a number of other places within the Tikal temple pyramids.

I'd rather think things through more carefully, since just starting out, this could mean

Area of a Circle 10313.24031 x (Pi^2) = 10.17876020 / 10^n

(1.031324041 is also the ratio between the "Pyramid Pi Calendrical Year" of 365.020081 and the experimental candidate for a system-valid Lunar Year: 

365.020081 / 353.9334584 = 1.031324041 )

But I think Munck may have chosen to interpret the figure as a decimal harmonic of 1.017140346?

2 Radians (57.29577951 x 2) x SRVS 887.6223994 = 1.017140346 x 10^n

(And yes, curiously enough, I haven't found anything that looks like Pi or the Radian at Tikal in either dataset, although I've seen plausible occurrences of both the reciprocal of the Radian, and the Double Radian).

Likewise, we find Munck's "Grid Point" for Temple 1 of 44.368111997 to be 88.76223994 / 2

And we find his "Grid Point" for Temple 4 of 70.63474622 to be 44.368111997 / (2 Pi)

Whether it's because he has interpreted Maler's figure of "88.58" feet for the height of Temple I to its platform as meaning 88.76223994, or Maler's figure of 271 cm = 8.891076115 ft for width of the exterior doorway of Temple I as meaning 8.876223994 (or both) it's hopefully safe to say it appears Munck may believe he has found decimal harmonics of 887.6223994 at Tikal and proceeded accordingly with his calculations.

His "Grid Point" for Temple 3 of 73.00401681 is hopefully enough to raise a red flag in the here and now that he may have hit, whether he realized it or not, an intended value for the ratio between 18980 / 260 = 73

"Arithmetically, the duration of the Calendar Round is the least common multiple of 260 and 365; 18,980 is 73 × 260 Tzolk’in days and 52 × 365 Haab’ days.[17]" (Wikipedia)

(And yes, 73.00401681 = 60 Remens in feet and etc.: 1.216733603 x 60 = 73.00401681)

I'm still a bit inclined to heed Munck's figure of 1.017140346 on several grounds which may be unknown to him, one of them being that 1.017140346 x (Pi^2) = 1.003877301. This ratio occurs in the Great Pyramid at least once, and as we have seen, it serves as an encoding of the Earth's equatorial circumference especially in an environment of 2 Pi, because that is all we need to convert it into the circumference figure

1.003877301 x ((2 Pi)^3) = 249.0119789 = Earth's equatorial circumference value 24901.19789 / 100

I have begun to wonder if the four Tikal temple pyramids that face East and West (parallel to the earth's equator) might specialize in numbers relevant to equatorial figures, with perhaps the North-facing Temple V being a good place to look for equations related to whatever is supposed to be the Pi System's value for the Earth's polar circumference?

It's also piqued my curiosity, however, to discover that 360 / 1.017140346 = 353.9334581, the experimental candidate for a "Matrix-Valid" Lunar Year. Did Munck manage to discover some calendrical and astronomical values at Tikal by following the resonance of the numbers, rather than by thinking calendrical and astronomical thoughts?

BTW, regarding Maler's figure of 1183 cm = 38.81233596 for the length of Tikal Temple I (the temple itself atop the pyramid) that sits next to a possible very literal Earth circumference figure

[Image: 112311f.gif]

One of the most literal ways to account for this figure that as far as I know remains unexplained by Munck, is as the value 38.81314683. That's an interesting figure to find atop a pyramid anywhere outside of Giza, since that value is equal to 

Height Great Pyramid in MLM Royal Cubits 279.4546572 / (360 x 2)  = 38.81314683 / 10^n

That also gives it a special and easily detected relationship to the Great Pyramid's proposed Pyramidion Volume / Base Area ratio of 9.315155235 

As we Pi Jedi like to put things when we are showing off, did Thoth order this dumb number to be placed atop Tikal Temple I? Let's ask him...

38.81314683 x 240 = 9.315155235 x 10^n

It may be that Maler might have often been more exacting in smaller measures like this and the doorways and chambers, and less exacting in larger ones, with Andrews perhaps having been the other way around. It's at least one reason I'm hesitant to be too hasty questioning Maler's data even in the face of discrepancies between additional datasets. 

There's a third dataset quoted by Wikipedia that I haven't gotten hands on yet but to my reckoning it's still no better than Maler's for certainty about the height of Temple II's levels. I've measured two different frontal photos of Temple II and they both suggest to me that the thicknesses of the bottom two tiers may be equal while the third tier is somewhat less. If that's the way it really is, I don't think any of them have gotten that right yet.
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
This 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...?

Unexpected Finds Increase Mystery Surrounding Tiahuanaco Citadel

[Image: 12887223w.jpg]LA PAZ – Several unexpected archaeological finds at the ancient Tiahuanaco (or Tiwanaku) citadel, part of a project sponsored by Unesco and headed by Spanish archaeologist Jose Ignacio Gallegos, are enhancing the research into and the mystery surrounding that long-vanished western Bolivian culture.

The Unesco consultant explained to EFE that the preservation and conservation work being undertaken at the site, 70 kilometers (45 miles) from La Paz, took a surprising turn when studies using topographic imagery, satellite technology and a drone found that the archaeological complex is larger than previously thought.

Tiahuanaco, which came before the Inca civilization, started out as a village about 1580 BC but grew into an Andean empire that began to spread about 724 AD, although it then went into decline about 1187 AD, according to historians.

“The aim of the project was not scientific discovery. The aim is to provide a set of tools that later will allow us ... to create appropriate policies for work at the site,” Gallegos said.

Nevertheless, eight drone flights over the complex to gather imagery have shown that the site encompasses at least 650 hectares (1,675 acres), of which 411 hectares are included in the topographical study.

Among the key finds is that the Puma Punku area, one of the least-researched and most enigmatic portions of the complex because it includes extensive ruins and a terraced earthen mound faced with stone blocks, extends for at least 14 hectares.

Archaeologists have found that there is a large underground plaza and two platforms considered to be part of a pyramid, which Bolivian authorities want to excavate.

This is a find that could change the view of the archaeological site, the director of the CIAAAT research center at Tiahuanaco, Julio Condori, told EFE.

“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.

The work being carried out also leads researchers to believe that near the Kalasasaya temple, there is another buried stone construction, possibly another temple.

Condori said that the work has also revealed signs of a network of water channels at the site.

Also, researchers have detected about 100 circular “domestic units” – or living quarters – underground at the site, and Condori said that excavations will possibly be launched in September to verify the topographic data.
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Memoirs of a Pi Jedi
Chapter Eight
Give 'Em an Inch... 
(or, Let's Do The Cholula!)

Let me start off with a note that the only Yoda material I've dug out of the mothballs is The Master Code Book, so I'm using that entirely thus far to review his take on various subjects. Pages 171-178 of this work provide various information relating to Tikal (punctuated with plenty of Map Crap including the massive non-sequitur of the "Grid Values" of a Florida hot spring - that's Map Crap squared - I bet if I squint at the page, it will try to tell me that's the Fountain of Youth or some such bullshit). There's other bonehead stuff, including (if I'm not mistaken) that his diagrams are labelled with total pyramid measures that are actually clearly labelled time and again by Maler as measures taken at the first step of the respective Tikal temple pyramids.

His diagrams note a value of "6.56" feet for the height of the platforms on which the Temples rest, and on page 177 he states that this feature is common to Temples I through IV, the east or west facing Tikal temples. This is rather intriguing in the face of my proposal that these pyramids may have a particular concern with Equatorial circumference, and moreso in the face of the prospect that they may serve as a standard for an ancient metrological unit very similar to the meter (2 meters = 6.56 feet), although no one has ever been able that I'm aware of to dispel the idea that they represent 6.565612079 feet, which is 1/100 of Yoda's "Grid Point" for the Cydonia Face using his traditional Map Crap. 

Even though this is more Map Crap squared - Are you kidding? Martian Map Crap? We're still trying to figure out how to measure and map the earth properly, FFS -  this has long invited speculation that an ancient meter was derived from the squared Radian:

57.29577951^2 = 3282.806350 = 3.282806350 x 1000 = (656.5612701 / 2) x 10

Things at Tikal become even more intriguing given some additional measures

Temple III - 1st Chamber, Width = 161 cm = 5.282152231 ft (Maler)
Temple I - 3rd Chamber, Length = 5.28 m. (Andrews)

Both rather suggestive of the 5280 foot mile / 10^n

Naturally a Pi Jedi gets all excited that just maybe if we study Tikal really, really hard, we will find some Grand Unification of the Maya Calendar, geophysical and astronomical constants, and several perennially elusive ancient measures, complete with instructions for their use.

I have yet to begin such studies of the Tikal data, unfortunately. However, in order that I might be better prepared for such endeavors, I took the liberty of making some geodetic tables, and while I've only begun to be able to interpret their full meaning, I discovered several interesting things already.

Now I've conceded that maybe Yoda's Map Crap wasn't a total waste of time since it includes him doing plenty of testing for mathematical resonance, so there's a good chance his calculations hit something real and important, even if it has nothing to do in reality with maps or any "Pyramid Matrix". Mainly, I'm just trying to forget about these numbers until they can be convincingly located in the physical measures of ancient monuments - I'd take his "Holy of Holies" 4523.893421 and toss it right out the window except for an incredibly compelling case that the height of the Great Pyramid sans pyramidion may indeed actually be 4523.893421 / 10 feet.

(Well, that and that 452.3893421 is precisely twice the height of the Mycerinus Pyramid as we Pi Jedi have traditionally reckoned it - my replacement copy of Kurt Mendelssohn's book is apparently arriving by Snail Mail literally, but that is our credited source for that, at least).

Let me introduce here several of Yoda's many "Grid Points" for ancient monuments

Hoosick Mound, NY - Grid Point 1.081540980 (Sqrt 240 / (Radian / 4))
Cholula Pyramix, MX - Grid Point 13.15947254 (1.33333333 x Pi^2)

And let me introduce another figure here, this is what we (meaning Michael L. Morton and myself) used to experimentally take for our intended value for the Earth's polar circumference 24858.38064 miles

It's pretty precarious, every source I look at gives different values for polar (and equatorial) circumference, and there are different ways of reckoning things (which is why our Founder of Pyramidiocy Isaac Newton is an idiot, how would he or anyone else know what "one zillionth of the Earth's polar circumference" looks like if it bit him on his perfumed and powdered arse with all of that going on?) but let me just put that number on the table since good luck finding it elsewhere on the Internet these days.

In the past, we Pi Jedi may have made the habitual mistake of expecting a "Matrix Mile" to be a figure with a self-explanatory level of resonance. Perhaps we should know better, because given what an absolute annoyance we know the modern mile to be, the best we can realistically hope for may more likely be simply a figure that serves as an adapter to more resonant planetary values, rather than being a remarkable thing unto itself, or translating in to some profound value of remens or cubits. I've tried for going on 20 years to find any intended "Matrix Mile" and have still failed, likely for those very reasons.

Now, using my value for the Earth's equatorial circumference,

24901.19742 mi x 5280 = 131478322.4 feet

If we knew how to interpret that figure, that should tell us what our Matrix Mile is (not that there is necessarily any single value any more than there is necessarily a single value for the cubit or the remen or whatever). 

So rather than having the occasional poke at this with a mathematical probe or two, I've decided to table the results of that experimentation for more convenient reference, unruly beast though it is because I'm looking for values that are sensible in multiple ancient metrological units if I can get them.

In the past, a lot of mathematical probes have hit the figures 131407229.2 and, yes, here it comes - 131594725.4

Reviewing the tables, it turns out that these two by far give the most pleasing results when rendered into multiple metrological units.

Now there may be multiple ancient intended values for polar and equatorial circumference figures - it all depends on how you do the math and what you use for the mile, doesn't it?

But at present I'm not certain what else to do but take those two as ancient and intended figures for the Earth's polar and equatorial circumference in feet, respectively - and yes, if 1.315947254 feet were someone's ancient idea of a metrological unit, it would measure the earth at exactly one zillion of them (one hundred million = one zillion).

It turns out this figure, while it responds well to a number of ancient metrologies as I reckon them, is nonetheless a fairly crappy responder to nominated meter values of (R^2 / 1000) = 3.282806350 feet and the obvious choice for a more precise value, (R^2 / 1000) / 1.000723277 = 3.280433687.

What it actually responds well to is a meter of 3.289868134 ft = (.3333333333 x Pi^2) ft, since 

131594725.4 3.289869134 = 4 zillion, exactly

And not that a rational number is always the best response (that's part of the Art of the Pi Jedi to know when it is and when it isn't), but guess who else gives a rational value in reply to the application of an ancient metrology?

It's this boneheaded Thoth Remen I came up with while desperately flailing away to explain why Yoda's pyramid is smaller than everyone else's

.1234567901 x Pi^2 = 1.218469679 = "Thoth Remen" = Desperately Flailing Bonehead Remen

131594725.4 / 1.218469679 = 108 zillion, exactly

Let me note here if that 1.315947254 really were someone's ancient metrological unit - let's call it The Cholula in honor of where Yoda misplaced it with his patented Map Crap...

That this figure - I'm calling it a Third Meter because it was my third choice, but then I noticed it's 1/3 x (Pi^2) so this stupid name is already trying to stick like cold spaghetti - of 3.289869134 = 2.5 Cholulas precisely

3.289869134 / 1.315947254 = 2.5, which is really simply the backwards way of stating that 

131594725.4 3.289869134 = 4 zillion, exactly

But it does inspire curiosity where these two came from, and if they are indeed some ancient metrological units, whether they didn't share a common source

Now these...

Hoosick Mound, NY - Grid Point 1.081540980 (Sqrt 240 / (Radian / 4))
Earth's Polar Circumference? 24858.38064 miles

Where is 24858.38064 written at Giza, if this is intended? I'm not really sure exactly, it certainly needs a fresh review. However, the proposed half-diagonal for the Great Pyramid's pyramidion as seen here is 31.04003279

We simply need to invert this number and throw circles at it

(1/31.04003279) / 360^2 = 24858.38026 / 10^n

(You see how much mileage I've been getting out of 360 as a mathematical probe these days?)

This Hoosick business I'm bringing up because 1.081540980 is another number that appears to be encoded across the two Great Pyramid models, with and without paving

Perimeter GP, without  paving 3022.416640 ft / 10.81540980 = 279.4546574, height of Great Pyramid with paving in MLM Royal Cubits

But it also appears in my tables as the number of standard remens in the earth's equatorial circumference reckoned as A Zillion Cholulas

One Zillion Cholulas 131594725.4 / Standard Remen 1.216733603 ft = 108154098.1

Meanwhile, while the experimental value for the Earth's equatorial circumference comes to a rational number of "Thoth Remens," the experimental value for the Earth's polar circumference of 131407229.2 comes to a rational number of standard remens:

131407229.2 / 1.216733603 = 108000000.0 = 108 Zillion

(Surprisingly, it also works out to a rational value for a fourth experimental value for a meter, 3.285180728, which is made from  

(R^2 / 1000) TIMES 1.000723277 = 3.285180728

In contrast to the second experimental meter of (R^2 / 1000) / 1.000723277 = 3.280433687.

Were we really intended to do any of this or am I just dinking around in the wind here?

Well, here is a curious fact hot off the presses... Since we're exercising our curiosity as we should, if 131407229.2 ft and 131594725.4 ft were the ancient and intended polar and equatorial circumference of the earth, respectively, how many feet are there in a degree, a minute, or a second of longitude?

131407229.2 / 360 = 36502.00811 ft / degree; 36502.00811 ft / 60 = 6083.668019 ft / minute
131594725.4 / 360 = 36554.09030 ft / degree; 36554.09030 ft / 60 = 6092.348399 ft / minute

Which would make my proposed truncated apothem values for the Great Pyramid of

500 standard remens = 608.3668019 ft (paved) and 
500 "Thoth Remens" = 609.2348395 ft (unpaved) 

Into precisely 1/10 minute of polar and equatorial longitude respectively.

I'll have to have another go at Capt's book again, too - IIRC, he was finding the "solar year" or some such all over the Great Pyramid's interior by applying a "Pyramid(iot) Inch" to a recurring figure that may bear suspicious resemblance to 365.5409030 ft. Hmmm...

It will be interesting to see what is really written at Tikal as referred to here, if I ever get that far.

Also, please pardon my "zillions" bullshit. One upside to being irresponsible with decimal placement - i.e., the "decimal harmonic" concept - is that if you just write everything with the decimal after the first digit, it's a great benefit to being able to find a particular figure with a browser's "find on page" function, whereas accurate decimal placement is the opposite. Hence I give could a rat's rip where the decimal point actually goes or how many zeros there are in 100 million.

But "A Zillion Cholulas" does have kind of a nice ring to it...


Half-Baked Postscript: On the subject of metrology, amongst the books I've been hunting for these days is one that I recall as probably being by Rennes-le-Chateau author Henry Lincoln. I found a note regarding a metrological unit he discussed called the "Pole" - it's a different value than the unit of the same name found in discussions of ancient Egyptian metrological units (likewise we will have to go back and sort out our "Assyrian cubits," where one value is c.a. 19.46773764 feet, and other is 2.-something feet, quite a difference). 

I've finally found the source, it's Lincoln's "Key to the Sacred Pattern" (pages 208-212), which was in my ancient astronomy books rather than with my books on Rennes-le-Chateau. He describes this Pole as 198 inches (or "1/320 of a mile"). My note points out that the closest obvious constant in my catalog is 1.981574330, which may be a contributor to my wingnut "herpetometric" nonsense because I also have a note explaining that it can be constructed from "Le Serpent Rouge" (also from the work of Lincoln, Wood and Campbell, the head of this alleged entity technically being a hill above the French town of Peyrolles, IIRC) and a constant that Michael L. Morton affixed to Alpha Draconis in his "Archaeo-Sky Matrix" - also known as Generic Volume of a Torus (Morton) / Pi.

"LSR" 1.676727943 x 1.181810286 = 1.981572971

What I've been doing with it lately is experimenting with it in the Vesica Piscis 1 : sqrt2 : sqrt 3 : sqrt 5 metrological scheme seen earlier on this page. It may come from the same source as some other metrologies, as 2 MLM Royal Cubits / sqrt 3 

(1.718873385 x 2) / sqrt 3 = 1.984784023

Other cubit values may approximate it even more closely via the same route, but I haven't checked yet

In experimenting with it recently, in spite of its particularly absurd "herpetometric" origins and its seemingly secular traits, I've observed that

1.981572971 x 4 = 7.926291884

And what's that? It's a decimal harmonic of the Earth's equatorial diameter using my 24901.18035 mile equatorial circumference.

7.926291884 x Pi = 24.90118035 = 24901.18035 / 1000

(Curious thing though it is, I guess, that we should find a "Pole" to be related to equatorial mathematics?)

You can also generate it with a much more respectable pedigree than this mega-dippy "herpetometric" stuff, from a number I recently mentioned

(Area of A Circle 10313.24031) x (Pi^2) = 1.017875321 x 10^n; 1.017875321 x 19.46773764 = 1.981582971 x 10^n

But it remains a difficult number for me to understand. In spite of these equations, it still seems to relate poorly to other metrologies, and appears to be rubbish at measuring the Great Pyramid's height or perimeter, with or without paving. 

I'd say "Go figure" if it weren't an utterly asinine thing for an arithmetician to say.
Finally, since it's somehow impossible to write anything about ancient mathematics without bringing up 33.33333333 and 19.46773764 on a daily basis...

It's not entirely surprising if we recall that 16 standard remens (1.216733603 ft x 16) = 19.46773764 ft, but the proposed polar circumference in feet figure of 131407229.2 ft therefore also translates to a rational number of the longer "Assyrian Cubit" of 19.46773764 ft.

131407229.2 / 19.46773764 = 6,750,000.00

If it isn't newsworthy in itself, it will at least make a good way for someone (probably me) to remember the proposed polar circumference figure.
"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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