Hello MJ,
>Sorry, I've lost track of what you mean by "exact".
>How precise in terms of measurement is your "exact" here?
>Are we talking, say, less than a royal cubit or less than a palm, or less than a digit?
I know that you deleted your post because you found the info, but since my last post to Clive Ross there was a strange lull in activity on these subjects. "Exact" may have something to do with it, and so a little contemplation may be in order since the meaning of exact used to be different, when regarding Giza. Like you said, a cubit off here and there was often considered exact, or accurate due to the sheer scale of Giza:
Exact in my case means primarily under the radar, which scans for errors between the layout's recreation, and Petrie's plan. Petrie usually gives a ± tolerance of his particular measurements. 'Exact' therefore means within this ± tolerance. The strange thing however is that in a number of cases the recreation falls dead into the center of Petrie's tolerance range. These agreements are so microscopic they are somewhat hard to explain, unless we invoke the luck of the draw, but since they are strongly supportive of my theory, I'll take them.
The best way to realize how microscopic these agreements are is to personally draw the layout using Petrie's data in some scientific engineering program like Autocad. If you reconstruct the position according to my instructions, you will find yourself constantly zooming in. It's a bit like flying towards the Earth from space, what looked like a thin line suddenly resolves into several parallel lines, which may be a half inch or so apart. You look, and you still don't see the circle or line you've just made from far above. More zooming finally brings it into view, several hundred-thousandths of a cubit apart from the other object. But, being within a millimeter, or half a millimeter would have been just as good.
This scale factor works in favor of much of the stuff you see proposed as parts of the Grand Plan of Giza. With all three pyramids in view, no matter how large your monitor, there is a ton of exactly looking ideas fitting the template. If your display is 1600x1000 pixels, each pixel represents 45 centimeters, or 17 inches of the north-to-south distance between the pyramids. Two lines or circles less than a half-pixel apart will perforce appear selfsame. A lot of theories capitalizes on this aspect of reality to claim being precise and past limits of being construed by coincidence.
Okay, so these theories are not exact in any significant way. Does that make them worthless? Absolutely not! .
Above all, the Grand Plan of Giza was selected out of many possibilities because of the sheer degree of companion coincidences. The Giza planners knew this, and foresaw the later scrutiny, knowing how tricky the solution to their plan is due to this extraordinary intrinsic quality. They knew that the plan will become a mystery, and the mystery will give life to various theories. Giza is not a place of death only, it is a place where ideas are brought into existence. When a man creates a theory, he exercizes his creativity, and is rewarded by satisfaction from the job well done. The world faces a simple geometric construction, which looks exact on a high resolution screen. Usually, such coincidence does not happen without reason, i.e., it is not entirely coincidental. A great example of this is John Legon. He created a beautiful version of the Grand Plan, and got some things right. His observations on square-root values dominating the layout were absolutely correct. I say with certainty that he solved this part of the Grand Plan, because I had the opportunity to put his theory to test.
The large body of alternative designs exists for yet another reason - to illustrate the difference between coincidence and exact planning. Coincidences have their own level of existence, let me call it the zoom level. The Grand Plan itself exists on the next several levels of zoom in. Here you simply follow the correct original idea, and it unfolds before you, taking twists and turns, but the next solution is never too far until you get to the end of the road. One thing is still lacking however - units of measure. This is where I turned to Legon's theory. He said that the north-to south distance was meant to be 1732 cubits, or 1000x square-root of 3. Seeing that the actual value is 1.732050..., 1732.05 cubits gives the benefit of including the succeeding decimal, a zero. Thus the error is minimized to some one-hundredths of an inch over the distance of 35,713.1 inches. As you see, Petrie stopped on the tenths, and so did the ancients, as if they had known..
This is obvious to me, or anybody willing to follow this construction to its sweet end, because only when the south-north distance between the pyramids is scaled to 1732.05 drawing units, the reconstruction suddenly gets more lifein terms of numbers..
As long as I took my measurements in inches, only the physical coincidences of proximity had stood out, but the readings themselves were not immediately prominent. The switch to slightly refined Legon's cubit value brought about a profound change, as the readings suddenly turned into highly calibrated numbers, microscopically close to being perfect tenths, or whole units. This revelation then assisted with final adjustments of the plan.
Every thinking person will recognize that this dramatic turn of events is a clear signal of confirmation for the reconstruction. The planners had made sure to make things clear. One last observation, this final progress would be impossible without Legon's work, and his solution for cubits. Solutions have parts, and levels, and Legon got his part right.