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Re: Petrie's measurements — forever the best
Author: Jiri Mruzek ()
Date: December 13, 2022 01:44AM

Ever since the appearance of Google Maps some use them to measure the mutual positioning of the Giza pyramids. Because of a shift in the Earth axis since the time the pyramids were built, such measurements are misleading. Using the present position of the True North extends the span of the pyramids from North to South substantially.
In the effort to determine what the position of the True North was at the time of building, the pyramids themselves furnish a reliable testimony, I believe. My belief stems from the fact that the pyramids show incredibly perfect control by their builders over the alignment of their sides.
Quoting Petrie from "The Pyramids and Temples of Gizeh"
Chap. 13. Positions and Orientation of the Pyramids
"Hence, in 4,000 to 6,000 years — the age of the Pyramids by different chronologists — the change of Greenwich latitude would amount to just about 1'. Thus, as far as observation can lead us, it seems to show a shift of the earth's axis in longitude 0؛ to a fifth of the extent shown in longitude 121؛ by the Pyramid orientations; and therefore a change of the same order, and not improbable in its extent.
[p. 127]Assuming a change of place of the axis amounting to 1' in 1,000 years, ....
Thus the apparent change in the axis of rotation shown by the orientation of the Pyramids, is of the same order as a change actually observed.
and: "On the whole, considering the various values of the data, – 5' 40" ± 10" may be taken as a safe statement of the suggested place of the pole, at the epoch of the Pyramid builders."

The present consensus pegs the Giza pyramids' age at about 4,400 - 4,600 years. By Petrie's estimate of the True North axis changing 1' per millennium, the pyramids' orientation would then move out of alignment with the True North by about 4.5' since the time of their building.
Let's make the North to South span of the pyramids 1,732.05 cubits, the value posited by my theory. To do that, we have to rotate the True North 4'37'' from its present position. This rotation is then in sync with the estimated age of the pyramids and Petrie's estimated rate of axial travel.
Rotate CCW by the midsides so the N-S span = 7,026,552.425 Survey Units‬ = 1,732.05 cubits = 35,713.1"

.................. our angle of rotation from Petrie's arbitrary North = 1º7'45"
= 1.12908817º
Petrie's angle of rotation to the True North of the modern era = 1º12' 22" ± 6"
difference = 4'37'' add 56.5" (see below why this value) = 5'33.5" which is in range with Petrie's estimate of 5'40" ± 10"
Alignments of pyramid sides to the True North at the assumed time of their building
East side G1 angle in XY Plane __ = 89.98882923 _____(0.01117077)   = 40"  
off the perfect 90 degrees
West side G1 angle in XY Plane __ = 89.98807670 _____(‭0.0119233‬)    = 43"

North side G1 angle in XY Plane__ = 359.97856857_____(‭0.02143143‬) = 1'17"

South side G1 angle in XY Plane - = 179.98433279 _____(0.01566721‬)__= 56"
G1 average fault  54''

North side G2 angle in XY Plane__ = 180.01489946 _____(0.01489946)_= 54"
East side G2 angle in XY plane __ = 270.02921273 _____(0.02921273)_= 1'45"
West side G2 angle in XY Plane __ = 269.99558146 _____(‭0.00441854‬)_= 16"
South side G2 angle in XY Plane__ = 0.01734014 _______ 0.01734014)_= 1'02"

East and West sides of G1 = 3 seconds difference in alignment
South side of G1 and North side of G2 = 2 seconds difference
South side of G1 and North and South sides of G2 = three sides within  8 seconds of each other
Five lines are within the narrow range of 22'
of each other orthogonally.
The data on alignments showcases the builders' capacity to make pyramid sides absolutely parallel, whenever they wish. Based on that observation, it is reasonable to conclude that they could also make the pyramids absolutely square but did not do so for some reason.
Given Petrie's stated margin of error in measurement of 6 seconds for G1 and 16 seconds for G2, there remains a theoretical chance that altogether five sides are absolutely parallel or orthogonal to each other.
Either way, these alignments exhibit unprecedented accuracy. To position massive mantle blocks over long distances with such absolute accuracy would still present a most difficult challenge in our time even when using all the means at our disposal.
Why then do three of the sides - the northern side of G1; the eastern and western sides of G2 - diverge slightly albeit noticeably from the uniform direction?
Given the builders' capability to be accurate, I believe that these divergencies are deliberate:
Petrie's stated margin of error for G2 is 16 seconds. After we rotate Petrie's plan so that its North to South span becomes 1,732.05 cubits, the western side of G2 reads 16 seconds off the True North (90 degrees in the x,y plane of our scheme).
Therefore, it is possible that the actual error in Petrie's measurement is that 16 seconds, and that the western side of G2 points exactly to the True North, as it was at the time of laying out the pyramids.
Encoding the exact direction of True North in at least one side seems natural. The other sides can then be used for some other purposes.
Manu wrote on January 11, 2022
Quote Manu shouldn't be so trusting of shadows dancing on the wall. He should trust my CAD operations more,
Manu: lol, that's a brilliant jab. Loved it. The rest of your post goes downhill fast. I almost sent your post to Glen's daughter Rebecca to let her respond to this flaming nonsense you whipped up there.

I gave a point-by-point critique of Dash's dissatisfaction with Petrie's approach. You could have addressed it point-by-point; I guess you leave that chore to Rebecca.
Manu: At first I was mystified where this fervor is coming from. Then I checked the maximum span on the Giza Plateau Map and it dawned, and I quote you:

Jiri: My hypothesis was that in doing so, the pyramids' orientation will shift much closer to true North, and therefore indicate that this span was truly the builders' intention. . 7,026,552.425 Survey Units‬ = 35,713.1"

Manu: And of course the Dash-map of Giza doesn't show that. I did all four possible maximum spans based on the two sets of two corners and you are not even close. No wonder the indignation. Yes, I see shadows on the wall...I see a dog and a pony, Jiri.
What you don't see is that Dash works with the present True North, and I don't. The analysis of Giza for planned design has to take the shifting of the True North into account.
Manu > This, all the while, Dash confirmed that his measurements of the four socket markers matched those of Petrie. I am going to address your major misconceptions in just a moment, but this is exactly the issue I raised with your comrade Chiginn: If a theory melts away in the sun when distances less than error margins are called significant and, thus, allegedly intentional, then you cannot distinguish it from any of many that do the same.
So, if I get it right, comrade Manu, you don't like the fact that my theory fits into Petrie's margins of error and, in fact, duplicates his data. Moreover, you claim that there are many other theories that do the same. Name one!
Yes, there is one other theory that does so partially - Legon's. He has some pioneering ideas, three of which I incorporated into my theory:
1) The North to South span of the pyramids in cubits equals 1,000 times √3.
2) The eastern side of G2 is 250 times √3 or 433.0127.. cubits westwards from the N-S axis of the Great Pyramid.
3) Derivation of the size of G3 in cubits by a neat construction:
Draw a square 555 cubits per side, with a circle inside of 250 cubits radius.
Draw a container square for the circle with sides rotated 45° to the first square.
Each side of the new square slices off a triangle from the first square whose hypotenuse equals the diagonal of G3. The resulting pyramid is 201.446 cubits ( 4,153.6 inches) per side, exactly as specified by Petrie.
This brilliant modern era solution for G3 must also be the true solution, because we find a strong confirmation for it in the Engraving _ it integrates with the engraving and the engraving's Mother Star. As usual, its authors know everything we know. Let's take a look.


At this resolution, the green circle and one side of the green square fit neatly into the Mother Star's position.

Legon's construction imported into the engraving fits as seen above. G3 is colored yellow.
One diagonal of the big square is tangential, as perfectly as can be, to what some call the figure's pocket. By the way, the pyramid itself will fit this pocket really well when moved there.
The green line along the pocket's line edge has the exact angle of a golden diagonal.
The golden diagonal from the NW corner of G3 is perfectly tangential where pointed to by an arrow and mirrors the other diagonal.
The right side of the big square seems to hinge on engraved lines.
1) Glen wanted to import Petrie's data into a modern (1984) control grid that's cardinally oriented. That's it. His choice of words has nothing to do with irreverence. He deferred to Petrie for G2 and G3. He confirmed Petrie's G1 distances. Your indignation, I now see, is merely a rhetorical device you use to reject what Dash did because Dash kills your theory. I get it. But then you slam his credentials and expect me to trust your CAD, and, trust you?? Do you know that Glen Dash has staked out the Giza Plateau with almost 2000 measurements.

"our 2012 and 2015 work did not include a systematic survey the bases of the Menkaure or Khafre pyramids"

So, what do his 2,000 measurements contribute on the positions of G2 and G3?

He confirmed Petrie's G1 distances? If he were right about there being only 196,713 Petrie's survey units to an inch as opposed to Petrie stated 196.750 per inch, then the average length per side of G1 would have to be 2.8 inches longer:
9,068.8 x 0.062 = 562.2656
562.2656 : 196.713 = 2.86 inches longer
But Dash's result differs by only 4 millimeters on average. By confirming Petrie's data, Dash seems to be rejecting his own. So, which is it?
He has no theory to push. You do.
You make it sound like I would lie and cheat to push some snake oil on the gullible. Yet, the theory you condemn is intrinsic to the artifacts in question. It is there for anyone to distill. I saw the Stone Age engraving in a book; and it was enchantment at first sight; it's that good. I don't push this theory; it pushes me.
Ever since learning of the engraving's true nature, I face the challenge of making it known to the public. Although it deserves better, it's stuck with me as its sole champion. My mission remains unaccomplished, the discovery undiscovered. Maybe I ought to be more assertive and do more of that 'pushing'. I'm certain that others with the same information on their hands would.
What have you done? Sit on your ass and play with CAD? No thanks, I pass on your CAD.

News flash from Manu! Doing research while enclosed by library or study walls, and using CAD is not the real McCoy! True archaeologists must wear western hats like Charlton Heston in The Treasure of the Incas, crack a whip like Harrison Ford who wore Heston's hat in the Raiders of the Ark, and ride donkeys around Giza like Manu!
Speaking of theories to push - didn't you publish one such on your projection for the architect behind the Great Pyramid? That would explain your zealous denial for my findings - they shunt your story into the realm of fairy-tales.
The Giza plan precedes your architect designate by more than a hundred centuries; it is prominent in a 15,000 years old engraving from La Marche. The young lady portrayed there is the avatar for the real architect of Giza, because the Great Pyramid dominates the design of her head (while the Square and the Second Pyramid also contribute their share). The symbolism behind this fact is clearly manifest _ she is a scientist with pyramids on her mind.

The Engraving holds absolute supremacy among all the world's artistic drawings in the category of Mathematics. It is a lot more than just art. Nothing in this world comes close to it. Picasso, Leonardo da Vinci, Dürer, Escher and other rivals known as leaders in this particular category are just apprentices next to the author(s) of this engraving. I'm not putting into question the greatness of these masters; it's strictly just this one category where they are not up to par. It's none of their fault. The Engraving serves primarily scientific and encoding purposes and that makes it an apple among oranges.
I expect you to disagree. However, your denial cannot possibly be supported by any evidence to the contrary.

"You owe Glen an apology in heaven. He passed away a couple of years ago. Bless his soul.

I am sorry to hear of Glen's passing away. Petrie himself is not with us anymore; Glen's manner of describing Petrie's work carries negative undertones in the specific instances under review; so I thought I'd mention those. However, having read more of Glen's writing on Petrie, I do admit that in general he does treat Petrie with all due respect.

You assume the pyramids were aligned to due north. How do you know this?

The designers of Giza pyramids (and also of Nazca Lines and La Marche engravings) do not play the second fiddle to us in science. So, it's only logical that they knew the exact position of the True North at that time.
Moreover, if we confer a complete autonomy upon the pyramids, i.e. allow them to set their own x,y plane by their mutual alignment, that alignment happens to coincide with the estimated position by Petrie of the True North at the time of their building. No problem here one way or another.

4) I looked again at your Athena. Your geometric figures do not well capture the drawn lines.
The key points of your squares and circles cannot be divined from the drawing with ease.

No one said that it should be easy. If it were, many others would long ago catch onto the true nature of these drawings.

Is it impossible to establish specifically what circle or line the designer had in mind? Not if the designer wants to help the decoder! This subject deserves a thorough consideration, and I would devote an entire post, or two to it, if need be.
For now, I'll just say that once an arc or a line has a thickness, then the greater the thickness, the greater the range of circles and lines passing through. Yet, there are factors that can help us with making the right choice. Some arcs have at least one perfectly circular edge, thus indicating a particular circle clearly. Some others are fairly long and not so regular and that reduces the number of circles that can pass through the arc without leaving its confines to practically just one. The same rules apply to lines.
When you base a circle on an arc, does the rest of the image visibly integrate with that circle? Does the circle nest among lines; does it set limits for them? Do these circles integrate with other elements to form abstract design?

You have been a critic of my findings for some years now, Manu. I recall that your objections were chiefly aimed at the two main figures of the engraving's geometric system _ the Cone which translates into the Mother Star, and the Square, which is directly descended from the Cone and becomes a major player in the system. These two main figures are then ancestral to others, for instance, the Mother Star is ancestral to the Giza ground plan. None of these descendants seem to suffer from genetic defects, which we should expect if their parents were in any way defective in the first place. You doubt the fundaments, yet, they support a magnificent edifice.
Let me give you a concrete example so you can respond with a specific critique rather than just bashing in general. In it, we see a 5-pointed star which dictates a number of accurate limits for the head's elements, especially, the face. Such harmony certainly does not appear accidental. It is too perfect for that.


The point, Manu, is that this star is one of the 'child' objects of the Square whose very existence you doubt. The Square (lines 'a' and 'b' are two of its sides visible in the diagram) has its golden circle centered in one of its corners (the intersection of 'a' and 'b') and inscribed with this star.
How could this star relate to the image in orderly fashion if its progenitor were random?
I leave it up to you to observe this special order on your own. It's there; if you cannot see it, I will describe it for you if you wish - just ask.

The same golden circle makes orderly appearances in other locations in this image, as well; if you wish, I can provide more examples.

Here is my question: Did you superimpose the Giza plan over this drawing and then do pattern recognition or did you start with the drawing and derive, from first principles, the Giza map?

I did a bit of each. In fact, the first part of the plan is already implicit in the Mother Star. If you choose the "13-step" method of design for the Mother Star (the designer's favorite method) the base of the Great Pyramid appears automatically; and there is a number of vectors which place it into its Giza position as a natural development of the geometry of the position - no engraving needed. Geometrically - the GP is in a true Power Position!
I can't help wondering what applications this geometry may have in real life. Let's not forget that in the engraving the Pyramid covers the area of Athena's frontal lobe - does this geometry have something to do with the organization of cognitive processes?

The point X in the diagram is mere 4 millimeters from Petrie's position for the southern side of G2. The containing square for the pyramids is also given. Read the Giza plan reconstruction chapter for details.

Typically, I learned things about the Nazca Monkey from the Engraving, and about the Engraving from the Monkey. Due to the Engraving I felt at home with the Giza plan, and subsequently, the Giza plan was my key to learning a whole lot of new things about the Engraving. So, this roadmap, or flow-chart, is not quite what you ask for.
In order to process the 1,500 engravings from La Marche, we need AI. A quantum computer would identify Petrie's Giza map in the engraving in a millisecond, as a part of the system. No need to mention that this greater system is missing from Giza.

Any object can be enclosed from three sides into an open container which can then be completed into any desired shape such as a square or a golden rectangle, etc. The method of image exploration by containing rectangles was missing from my toolbox until I got around to studying the Nazca Monkey which is notably conducive towards adoption of this method. Thereafter, its application to the Engraving and the Giza plan had proved most productive.
However, out of sheer negligence, I did not use it consistently. If I had, I would have learned some crucially important things much earlier. For example, the following:

Leonardo da Vinci, Piero della Francesca and Luca Pacioli would love this 'Divina proportione'.
The width of the face (1) extended by (0.618) sets the extent of the white space in the helmet.
The image contains other notable geometric details, whose appreciation is left to the reader.
The blue square is set by the width and the bottom of the face.

The same square fits 1.5 times into the width of the left foot. Considering the magnification (what you see on your screen is most likely larger than the entire engraving in lifesize), the fit is extremely accurate.
There is a vertical line edge marking the exact half of the whole rectangle, and another marking the exact square (from left to right).
The latter two lines are connected by a line with one edge perfectly coinciding with a golden diagonal (from an upright golden rectangle).
Two more such diagonals rise from the 1/3 and 2/3 points of the rectangle's bottom. These diagonals are perfect tangents to nearby line ends. Another diagonal (from a horizontal golden rectangle) rises from the bottom right corner and is also a perfect limit to the nearest line end.
All these tangents are perfect as far as can be seen. Further magnification makes it too hard to see where the actual edges are due to blurriness.
Even just by itself, this is an example of immaculately implemented geometric order. Using superlatives in its description cannot be avoided; they are true.
That said, it's time to get to the point _ only after we insert the Giza ground plan into the drawing, we learn that these squares are none other than the square of the Second Pyramid!
At least, that would be the script if I had used my method methodically. In real life, the procedure was reversed — mea culpa. It is a fact that I could have 'divined' the square of the Second Pyramid' on 'your' first principles, although not in its proper position in the Giza plan. Instead, some time after inserting the Giza plan into the engraving, I just tested the square base of G2 — first over the face and then over the feet. Then it worked like a charm!

It is Mission Impossible to divine the G2 square into its present Giza position, at least for a human. The actual placement of G2 is the result of creative use of the all-encompassing knowledge by the designers of the potential inherent in the basic position. The Mother Star sets up something like a Chess-board - a deceptively simple field offering a near infinity of logical entanglements. You can analyze a game afterwards - you cannot predict its course after a few opening moves.

Onward to G3 - its position is entirely discoverable - unlike G2. Lines a,b,c,d,e as well as lines '1' '2' and 'f' in the diagram below all have golden diagonal angles of the Mother Star system. Lines 'a' and 'b' in combination with line '1' set up a golden rectangle. The golden rectangle based on G3 is one-fourth of this rectangle. (Line 'f' serves as a spectacular confirmation)

Once again, although discoverable, I have not discovered G3 by analysis. Elon Musk says of the former world chess champion Kasparov - "He plays chess almost as well as my I-phone!" Similarly, one day soon, an I-phone will tell me about all I had missed in my analysis :)

In fact, Petrie may have been aware of the problem. In Chapter XXI of The Pyramids and Temples of Gizeh, Petrie compares his measurements to the earlier work by Watson and Gill. Where both had measured common baselines, Watson and Gill’s measurements were longer than Petrie’s by 1 part in 4500. If Watson and Gill were correct, the Petrie’s conversion factor should have been 196.706. That number differs from my estimate of 196.713 by just 4 parts in 100,000.

He was aware of that, of course. And yet, he decided to stick with his own measurements.
Note that nobody is questioning Petrie's measurements given in survey units. It is his conversion of those to inches or meters, which is being challenged; and that is something of no concern to me (because ratios remain constant during conversions), but rather only to those who look for the meaning of those measurements in various ancient and modern units of length.
Finally, but three stations are really common to both triangulations, and fairly fixed. The result of comparing these is a mean variation between the two surveys of 2" of angle, or 1/100000 equal to 1/10 inch. This is a variation such as professedly may exist in either of the surveys; and there is no reason therefore for doubting the professed accuracy of the survey of 1881, which results from the combination of dozens of check observations.

From the vantage point of the Athena-engraving, Petrie's survey of Giza blows off the mists shrouding the bridge between it and Giza. The Giza plan becomes a template dictating the position and contours of multiple major parts of the engraving.
I continue to provide you with examples showing that the engraving is the result of exact design, not unmeasured free-hand drawing. That fact alone constitutes a revolutionary paradigm changing discovery. In conjunction with the Nazca Lines and Giza pyramids, it adumbrates a hidden parallel reality complexifying our history.

p.s. sorry about taking time to reply - better late than never