Hi Chris,

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Supposing you are watering the garden with a hosepipe. Would you arrange the whole length of the hosepipe in a straight line with whatever part of the garden you want to water? - I don’t think so. You just pick up the nozzle at the end of the hosepipe and point it at the ‘target’ - all that matters is that you accurately point the nozzle - whatever bends and curves the hosepipe makes behind you is irrelevant.
The shafts are thought by some to be model passageways for the ‘spirit’ of the King to ascend to significant areas of the sky. The architect had to make sure that as the ‘spirit’ of the king exits his pyramid, he would see his destination and head in the right direction. Thats why the angle of incline for the final section is crucial, which means we can use it to determine a possible date for the design.

Thanks for the clarifying analogy. It made me smile. I imagined how Khufu's soul is fired by a shaft and by inertia flies to the desired stellar target, like water from a watering hose.
On a more serious note, this analogy will help me to explain what I mean when I talk about "selective approach".

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Gatenbrink: “The "Mankiller" tunnel is accessible from the outside of the Pyramid, so we could manually measure the angle of shaft inclination through this section. The average angle is 31.20°, determined by 5 measurements made over a length of 11 m.”

Gantenbrink states that the average angle of the Mankiller tunnel is 31.20°. To return to your analogy, we have a watering hose with a tip that is "straight on average". Or better yet, a pistol with a "roughly straight" muzzle. Can a pistol with a roughly straight muzzle hit the target?

Let's take a look at the data on angles for the northern shaft (data for the Mankiller tunnel according to Petrie).



As you can see, three separate measurements give different angles of slope in the section under consideration, and the values varie within 1.3°, that corresponds to a ~200-year interval of the altitudes of the stellar target.

Obviously, if we talk about the average angle based on the results of three measurements, then the Mankiller tunnel points to Thuban at 2508 BC, but each of these three sections separately points to Tuban at different times. The question is, how long is the shaft considered a “hose tip” and why? After all, if we take only two of the three values (which are closer to the outside), then corresponding "average" section would point to Thuban at a later time (~2455 BC), if only one - even more later (~2415 BC). But what if we assume that the "hose tip" is twice the length of the Mankiller tunnel? How does this affect the dating by Thuban, considering that the average angle of the northern shaft is 32.6° according to Gantenbrink, i.e. the shaft must be steeper to the inside?

It is not difficult to notice that by choosing a larger or smaller section of the shaft consisting of subsections with different slopes, we thus influence the average value on the basis of which we make dating, and therefore it is possible to choose such a length of the shaft, starting from the outside, that dating by the average angle value would give dates preferred by us.

For the southern shaft, the situation is similar:



If, for example, we consider only three first values (so that the “tips” of both “hoses” are of the same length), then the resulting date for the southern shaft is approximately from the middle of the 25th century BC (for Alnilam as the middle star of Orion's belt).

In my opinion, the only solution that will not be selective is to consider each shaft as a whole, calculating its angle from the known position of the entrance (after the horizontal part) and outlet.

Alex.



Edited 2 time(s). Last edit at 11/13/2020 02:42PM by keeperzz.