Descending Passage Slope Paradox

[Scott Creighton]

So I found this more than interesting and something of a paradox:

The image shows the slope angles of the various pyramids' Descending Passage (DP). Many Egyptologists believe this passage targetted the northern pole star, the point in the night sky where the king's soul would ascend to and be at one with the gods in his celestial afterlife.  Lee Anderson (Thanos5150) gave an excellent post here discussing the star Thuban believed to be the pole star during the 3rd and 4th dynasty pyramid-building age. 

I think even a cursory glance at this image (above) will show anyone the clear and obvious problem - the dates of the DPs run backwards in time against the established sequence of the pyramid constructions. That's the first fairly obvious paradox.  (Note: There is another sequence of the star Thuban during this epoch but those dates are much too young).

The next pecuiliarity here is the angle of DP inclinations seem to follow a pattern (high, medium, low), the values becoming decreasingly smaller from Meidum to Unas (like a pendulum). This swing almost seems like there is a disturbance (nodding motion) of the Earth's axis, giving rise to these 'amplitude oscillations'.

I wonder if any of the traditionalists here might want to offer up an explanation for this apparent paradox of the Descending Passages? Why are the dates reversed / inverted?

The dates also are considerably older than the traditional dates given for the construction of each of the monuments. Arguably, though, these older dates may fit better with the Radio Carbon surveys done.

But that's not all.  If we imagine (for the sake of discussion) that the Earth had once been inverted (as many, many ancient traditions the world over inform us), what might the results of the DPs be from a southern hemisphere perspective, using the brightest southern pole star at the time (HIP 2936 - a brighter magnitude star than Thuban and with an ideal partner, Achernar, to use a plumb-line for determining true north):

Using this southern hemisphere pole star ~3000 BCE, this is what we find with the DPs:

We immediately find that the dates now run in the correct sequence with the accepted build dates of the monuments. We also find that they are much closer to the accepted dates of the pyramid construction dates. We still have the 'amplitude oscillations' suggesting a disturbance of the pole.

So, no matter which way you crack it, it appears that the southern hemisphere pole offers a better fit with regards to the pyramids' various Descending Passages. 

SC

 

Edited November 13 by Scott Creighton

[Antigonos]

No.

Next.

[Oniomancer]

[Kenemet]

Nah.  Otherwise there'd be a very slight difference in the slopes between pharaohs because the location of the pole star doesn't move that much in 20 years.  

[Scott Creighton]

9 hours ago, Kenemet said:

Nah.  Otherwise there'd be a very slight difference in the slopes between pharaohs because the location of the pole star doesn't move that much in 20 years.  

Not quite sure what "slopes between pharaohs" means exactly but your point that the pole star doesn't move that much in 20 years (in normal circumstances) is precisely my point. So, back to the data:

How do we explain:

1) The pole (star) moving ~5.5 degrees in just ~196 years (Djoser 30*47' to Unas) when it should have moved only ~6 arcminutes, a tenth of just 1 degree in that time?

2) The backward trend in the dates of the DPs?

3) The spikes in the date trend (Djedefre, Sahure, Unas)?

SC

Edited November 14 by Scott Creighton

[Kenemet]

6 hours ago, Scott Creighton said:

Not quite sure what "slopes between pharaohs" means exactly but your point that the pole star doesn't move that much in 20 years (in normal circumstances) is precisely my point. So, back to the data:

How do we explain:

1) The pole (star) moving ~5.5 degrees in just ~196 years (Djoser 30*47' to Unas) when it should have moved only ~6 arcminutes, a tenth of just 1 degree in that time?

2) The backward trend in the dates of the DPs?

3) The spikes in the date trend (Djedefre, Sahure, Unas)?

SC

We know the dates for the pharaohs.  We know the order of their reigns (for the most part.)  We also know that no evidence has been found that they accurately measured the stars in the sky until fairly late in the empire.  We know from their water clocks that they used star groupings to map time... but not down to the minute.

The fact that the dates do NOT match anything is a clear indication that they weren't angling the ramps at Thuban.  A better explanation is "that's the angle at which they felt they could conveniently lower the coffin and other materials into the finished pyramid without damaging themselves or the objects" and that it varied depending on what the supervisor/architect's measuring tools showed.  As we all know, hands vary in width (most human palms are between 3 1/2 inches and 2.9 inches) and so did the cubit rods.  Variations in the size of the human whose body parts were the standard for palms and cubits completely explains the differences. 

Edited November 14 by Kenemet

[Trelane]

Wait just a minute...is this another one of those threads that alludes to the Earth flipping during dynastic AE?

[Thanos5150]

2 hours ago, Kenemet said:

We know the dates for the pharaohs. 

Do we? All the RCD points to the OK being roughly 200yrs older than accepted HERE which coincides well with Thuban's closest position to the North Celestial Pole HERE. Recently as noted in the first link, Lehner for reasons I have yet to find revised his dating for Khufu to 2633-2605 BC, some 40+ years earlier than the most widely accepted dates. So all "we know" is a ball park of a few centuries. 

Quote

We know the order of their reigns (for the most part.)  We also know that no evidence has been found that they accurately measured the stars in the sky until fairly late in the empire.  We know from their water clocks that they used star groupings to map time... but not down to the minute.

Creating an angle from ground level to a star or place in the sky is hardly the stuff of "accurately measuring stars". It is quite a simple thing to do using a line of sight, a gnomon and plumb line and has nothing to do with "astronomy". We would note how many megalithic structures several hundred or years if not millennia before, for example New Grange, aligned passages to the solstices or other phenomenon so the notion it required some form of "advanced astronomy" to align a passage to a part of the sky is gobbledygook.  

Quote

The fact that the dates do NOT match anything is a clear indication that they weren't angling the ramps at Thuban.  A better explanation is "that's the angle at which they felt they could conveniently lower the coffin and other materials into the finished pyramid without damaging themselves or the objects" and that it varied depending on what the supervisor/architect's measuring tools showed.  As we all know, hands vary in width (most human palms are between 3 1/2 inches and 2.9 inches) and so did the cubit rods.  Variations in the size of the human whose body parts were the standard for palms and cubits completely explains the differences. 

Good grief. This is bafflingly ignorant. Once again you have no idea what you are talking about, ignoring even what has been discussed here many times before, and instead as usual just make up nonsense. For more than a century it has been widely accepted by Egyptology the descending passages (ascending passages from the perspective of the pharaoh) of 4th Dynasty pyramids were "polar passages" aligned at worst to celestial north i.e. the "Imperishable Ones" which most accept specifically Thuban the pole star of the era. Not only did they align the DP's to it but also used it to make other alignments.  

How the Pyramid Builders May Have Found Their True North:

....The Egyptians most likely used a circumpolar star to align the descending passageways of the Bent, Red, Great, and Khafre Pyramids with due north. Petrie believed the Egyptians used Thuban, the pole star of their time. Using Polaris, I have demonstrated that Petrie’s technique is practical.

The Imperishable Ones

Why did the Egyptians need to align their pyramids with cardinal points? The answer may lie in their vision of the Netherworld. The Pyramid Texts, first inscribed on the walls of the burial chamber of 5th Dynasty king Unas (c. 2356–2323 BC), describe eternity and the deceased’s connection to the celestial world. The king was to “go forth to the sky among the Imperishable Ones” and “go around the sky like the sun.”3 The “Imperishable Ones” were the circumpolar stars, so named because they never set below the horizon.4 The king’s spirit may have been guided on its journey by the orientation of the pyramid’s inner spaces.4 At their northern end, the corridors of many pyramids lead to a “descending passageway” angled up at the circumpolar stars “like a telescope.”3

More: Thuban and the Descending Passages-The Key to Dating the Pyramids?

 

Edited November 14 by Thanos5150

[Trelane]

Yeah, yeah but did the earth invert itself then BAM! flip back around???

I mean clearly that's how they aligned the pyramids and internal constructions therein.

Right??? Guys????? 👀

[Wepwawet]

Here's two questions for anybody. Firstly, when did the soul of the king ascend, ie, at what stage after burial did ascension occur. Secondly, where did this ascension take place.

[Kenemet]

15 hours ago, Scott Creighton said:

Not quite sure what "slopes between pharaohs" means exactly but your point that the pole star doesn't move that much in 20 years (in normal circumstances) is precisely my point. So, back to the data:

How do we explain:

1) The pole (star) moving ~5.5 degrees in just ~196 years (Djoser 30*47' to Unas) when it should have moved only ~6 arcminutes, a tenth of just 1 degree in that time?

2) The backward trend in the dates of the DPs?

3) The spikes in the date trend (Djedefre, Sahure, Unas)?

SC

Unas' supervising architect (or Unas himself) was slightly taller than Djedefre - or his architect (this man is the smallest and therefore cubits and palms from his arm and hand are smaller than Unas' cubits).

Khufu, Khafre, and Menkaure had different supervising architects (or the measurements were taken from whoever was king); who was fairly tall for an Egyptian.

Sneferu's data shows that they apparently made new cubit rods for each new construction  and that the construction crew's cubit rods for the Bent Pyramid were just slightly different in size and that this may coincide with the bent section.  The Red and Medium pyramids may have been made in succession with a similar cubit rod (but not the same one) from the same source.

And that the preferred angle for ramps was about 20 degrees.

[Kenemet]

5 hours ago, Trelane said:

Yeah, yeah but did the earth invert itself then BAM! flip back around???

I mean clearly that's how they aligned the pyramids and internal constructions therein.

Right??? Guys????? 👀

Yeah.  If it flipped, there ain't no Thuban to point at.  Don't know what spot the southern pole star would have been in during that time.

[Peter Cox]

It was those pesky Aliens and the Atlanteans or maybe those 2 are the same.... Just playing the different "angles" here  lol 

[Scott Creighton]

17 hours ago, Kenemet said:

We know the dates for the pharaohs.  We know the order of their reigns (for the most part.)  We also know that no evidence has been found that they accurately measured the stars in the sky until fairly late in the empire.  We know from their water clocks that they used star groupings to map time... but not down to the minute.

The fact that the dates do NOT match anything is a clear indication that they weren't angling the ramps at Thuban.  A better explanation is "that's the angle at which they felt they could conveniently lower the coffin and other materials into the finished pyramid without damaging themselves or the objects" and that it varied depending on what the supervisor/architect's measuring tools showed.  As we all know, hands vary in width (most human palms are between 3 1/2 inches and 2.9 inches) and so did the cubit rods.  Variations in the size of the human whose body parts were the standard for palms and cubits completely explains the differences. 

What Thanos5150 said.

Irrespective of your sloping pharaohs, the consensus view of Egyptology is that these monuments (including their DPs) were astronomically aligned, either by using the stars, the sun or a combination of both. You only have to appreciate the near perfect alignment to the cardinal directions of these monuments, in particular G1 and G2, to understand why they accept that astronomy was involved in their alignments. And they know also that the foundation ritual of their temples and pyramids, the Stretching of the Cord, used the stars to make alignments and that this ‘ritual’ stretches back (no pun intended) to (at least) the 1^st dynasty.

So, accepting the above (as most Egyptologists do), how then do we explain:

1) The pole (star) moving ~5.5 degrees in just ~196 years (Djoser to Unas) when it should have moved only ~6 arcminutes, a tenth of just 1 degree, in that time?

2) The backward trend in the dates of the DPs?

3) The spikes in the date trend (Djedefre, Sahure, Unas)

Thus far I haven't seen much of any serious attempt to answer these questions by anyone. Aliens? Atlanteans? Give it a bleeding rest.

SC

Edited November 15 by Scott Creighton

[Trelane]

Well, by that point in time the Atlanteans had moved operations to Tampa, FL. I mean, that part is obvious for sure.

[Windowpane]

21 hours ago, Kenemet said:

...

 A better explanation is "that's the angle at which they felt they could conveniently lower the coffin and other materials into the finished pyramid without damaging themselves or the objects" and that it varied depending on what the supervisor/architect's measuring tools showed.  As we all know, hands vary in width (most human palms are between 3 1/2 inches and 2.9 inches) and so did the cubit rods.  Variations in the size of the human whose body parts were the standard for palms and cubits completely explains the differences. 

...

This point of view seems to be in the process of becoming unpopular in certain quarters ... but I can't help feeling that there's a fair amount to be said for it.

I live in a house with a chimney (admittedly, only a fraction of the extent of, say, a pyramid shaft), which points at some location in the sky: a location which presumably keeps changing place as the earth turns (unless of course earth is doing one of its periodic flipping events ... )  

For all I know, the chimney might happen to be pointing at Thuban, or Polaris, or Al Nitak (I've not tried to find out).  But what are the odds that the builders of this house designed the chimney that way, rather than just concentrating on putting one brick on top of another ... ?

 

[Wepwawet]

5 hours ago, Scott Creighton said:

And they know also that the foundation ritual of their temples and pyramids, the Stretching of the Cord, used the stars to make alignments and that this ‘ritual’ stretches back (no pun intended) to (at least) the 1^st dynasty.

"They" only know with certainty that this was the case with laying out the foundations of temples, not pyramids, where there is dispute as to whether solar or stellar alignments were used. Also, temples had either stellar or solar alignments, not just stellar as the wording of your post suggests.

Image from page 397 of "A Companion to Ancient Egypt" edited by Alan B. Lloyd 2014 edition

 

Edited November 15 by Wepwawet

[Kenemet]

6 hours ago, Scott Creighton said:

What Thanos5150 said.

Irrespective of your sloping pharaohs, the consensus view of Egyptology is that these monuments (including their DPs) were astronomically aligned, either by using the stars, the sun or a combination of both. You only have to appreciate the near perfect alignment to the cardinal directions of these monuments, in particular G1 and G2, to understand why they accept that astronomy was involved in their alignments. And they know also that the foundation ritual of their temples and pyramids, the Stretching of the Cord, used the stars to make alignments and that this ‘ritual’ stretches back (no pun intended) to (at least) the 1^st dynasty.

So, accepting the above (as most Egyptologists do), how then do we explain:

1) The pole (star) moving ~5.5 degrees in just ~196 years (Djoser to Unas) when it should have moved only ~6 arcminutes, a tenth of just 1 degree, in that time?

2) The backward trend in the dates of the DPs?

3) The spikes in the date trend (Djedefre, Sahure, Unas)

Thus far I haven't seen much of any serious attempt to answer these questions by anyone. Aliens? Atlanteans? Give it a bleeding rest.

SC

Hadn't seen Thanos' post, and I don't intend to read it.  In the past he's been so unpleasant and seems to hunt every tiny excuse to jump all over anything I said (and is sometimes so angry that he misstates my views) that I've blocked him.  But if you think he's made a fair point, please repeat anything you thought was useful and we'll discuss it.  

You've misunderstood my views.   I do NOT disagree that the pyramids are aligned using the sun and the stars.  Far from it.  I support that.  Technically, ANY building you construct that's aligned east-west with a north facing exit... that exit is facing the pole star.  It can't NOT face the pole star, in fact. 

 

EXAMPLE: This building in London (a bus barn, if I've read the labels correctly) is perfectly aligned with the pole star.  Any exit on Lansdowne way will point to Polaris (5,000 years ago it would have pointed exactly to Thuban.) Put a sloping ramp on those exits... 20 degrees or close to... and you get an exact point to Thuban.

 

 

That's because the star is so far away that no matter how far you move laterally on the surface of the Earth, the star seems to stay in the exact same position. (And yes, I know about the stretching of the cord and the "undying stars" as the place where they believed the pharaoh's soul went.)

What I'm saying is that they didn't use the shaft as a pointer to the elevation of the star -- that the angle of the ramp is simply the angle that they determined to be the most efficient way to slide coffin and anything else into (and possibly out of) the tomb --and that the difference in the angles is a result of the difference of the cubit rods they used.  A different length of cubit rod (possibly from having to find a new supervisor or architect) would perfectly explain the differences in the Bent Pyramid as opposed to "make part of a pyramid, stop work, resume work a hundred years later" (as your view seems to imply.)

A "difference in cubit rods" would also align with the known order of succession (whereas -- as you yourself point out ) your data cannot explain why Unas would be succeeded by Djedefre (etcetera)

 

Edited November 15 by Kenemet

[Wepwawet]

28 minutes ago, Kenemet said:

Technically, ANY building you construct that's aligned east-west with a north facing exit... that exit is facing the pole star.

An important point. While it is known that some New Kingdom temples, which I discussed on the "Diagonal" thread, are aligned to stars, predominantly temples for goddesses, when we look at Giza the most notable alignments are solar ones. The Great Sphinx, Sphinx temple, Valley temple and the mortuary temples for G1, G2 and G3 are all aligned on an east-west axis. The Sphinx looks out to the east, the rising sun, and with all the temples the officiants would be facing to the west, which is to be expected in a necropolis. The sun/Ra sets in the west, it is the direction to which the soul departs, at least initially. And as you say, if you have an east to west axis, by default you must also have a north to south axis at right angles.

I don't reject the possibility that a stellar alignment was used, or even paramount with the pyramids, the akh of the dead king does after all end up with the "Imperishable ones" in the northern night sky, but it has to be pointed out that the prime axis of alignments at Giza is east to west.

Edited November 15 by Wepwawet

[Scott Creighton]

3 hours ago, Kenemet said:

...  I do NOT disagree that the pyramids are aligned using the sun and the stars.  Far from it.  I support that. 

Okay - so hold that thought.  ACCEPTING that the Descending Passages targeted Thuban (the star nearest to the pole and the star that appeared to move the least), how then do we explain:

1) The pole (star) moving ~5.5 degrees in just ~196 years (Djoser to Unas) when it should have moved only ~6 arcminutes, a tenth of just 1 degree, in that time?

2) The backward trend in the dates of the DPs?

3) The spikes in the date trend (Djedefre, Sahure, Unas).

ACCEPTING that is what the AEs did (targeted Thuban with these DPs), how do we explain the above. That is all I am asking. If you don't know how it can be explained, that's all you have to say.

SC

Edited November 15 by Scott Creighton

[Stokke]

23 hours ago, Wepwawet said:

Here's two questions for anybody. Firstly, when did the soul of the king ascend, ie, at what stage after burial did ascension occur. Secondly, where did this ascension take place.

Good questions.

Seeing how the Soul was depicted as ascending from the tomb in the New Kingdom (BoD), we might hazard a guess that it happened sometime after the Opening-of-the-Mouth was performed?

What are your thoughts? 

[Wepwawet]

1 hour ago, Stokke said:

Good questions.

Seeing how the Soul was depicted as ascending from the tomb in the New Kingdom (BoD), we might hazard a guess that it happened sometime after the Opening-of-the-Mouth was performed?

What are your thoughts? 

This aspect has always seemed a bit vague to me. At face value it certainly looks as if the soul/s are released at the opening of the mouth, but this ceremony is to re-animate the mummy, indicating that between death and the ceremony it is vacant of any souls. If so, where then are the ba and ka, hovering about near the mummy, nobody says. Then there is the issue of when does the ba enter the Duat, and if not a king, stand before Osiris for judgement. How do the images of the ba of the deceased "living" in the Field of Reeds square with images of the ba also flittering about within the tomb, indeed at times taking the virtual offerings from the mortuary chapel to the burial chamber. It is said that the ba returns to the Duat at night, but this contradicts statements made in the Netherworld texts about the souls of the dead in the Duat living in perpetual twilight except for the one hour that Ra passes through the region they inhabit.

However, I think that the AE enivisaged the ba and ka entering into seperate existances the moment the tomb is sealed, and at that point the ba enters the Duat, otherwise the "roadmap", particularly in royal tombs, doesn't make sense if the ba had already departed the body. What I do not fully understand is if the ba enters the Duat within the burial chamber, it being an extension of the Duat, or does it actually travel to the western horizon, an ever out of reach place in reality. Time and space, in the Doctor Who sense seems to have a place here, as it does in the tomb decorations of kings.

I suspect that with kings, from at least the PT of Unas, the king first enteers the Duat within his burial chamber, then ascends, twice, in the horizon of the rising sun, clearly stated, and also as an akh to the northern sky. This is where "kheperu" comes into play as we have multiple options, the king is in multiple places, his ba is with Ra day and night, and also as an akh in the northern sky. Being an akh, to my understanding, is actually the ultimate goal, a goal wanted by all the dead, eventually, but first they have an existance as a ba and a ka, and that the akh does not come into being straight away at death, but, as Salima Akhram says, is a fusion of the ba and the ka. It has always seemed that it was an aspiration to become an akh eventually, not something that happened straight away, hence my reservations about the descending passage in a pyramid being like the barrel of a cannon "shooting" the akh of the king up to the heavens, he has to have another existance first, going by the PT, which is all we can go by, and which gives both ba and akh options without differentiation. I'll point out that Assmann states that the king wished unequivocally to become an akh straight away and not enter the Duat at all. I don't have a quarrel with that, but think it was more a wish of the king than an actuality, if you have it magically written that you will become an akh, then hey presto, it will happen, but maybe not straight away, and maybe not directly from the tomb, but possible, not least due to the presense of the mummy, a sort of unifying object around which the various parts of the soul can reconbine.

I hope that all made some sort of sense

Edited November 15 by Wepwawet

[Kenemet]

4 hours ago, Scott Creighton said:

Okay - so hold that thought.  ACCEPTING that the Descending Passages targeted Thuban (the star nearest to the pole and the star that appeared to move the least), how then do we explain:

1) The pole (star) moving ~5.5 degrees in just ~196 years (Djoser to Unas) when it should have moved only ~6 arcminutes, a tenth of just 1 degree, in that time?

2) The backward trend in the dates of the DPs?

3) The spikes in the date trend (Djedefre, Sahure, Unas).

ACCEPTING that is what the AEs did (targeted Thuban with these DPs), how do we explain the above. That is all I am asking. If you don't know how it can be explained, that's all you have to say.

SC

As I said, different architects and the different measurements.

Now...they didn't have all the equipment we have. So, just as a thought experiment look out a window and point your finger at some distant object (you can do it with closer things but if you use a distant object, you can see the effect better.)  Look at the angle that your arm makes.

Now crouch down slightly (or if you want to get drastic, sit down.)  You've just changed your "height" by several inches.  Point at the reference object and see if the angle is the same.

If we look at known astronomical implements of the ancient Egyptians, they seem to be very vulnerable to this kind of error

Quote

4. We know that many Egyptian buildings had astronomical orientations. Where did the “astronomers” observe from?

The Egyptian astronomers observed from the terraces of the temples and palaces. From that height they looked for horizons free from obstacles. So, for example, in the papyri of Abusir, of the V dynasty, it mentions “viewers on the terrace of the temple” and in all probability these viewers were astronomers and observers of stellar time. In a stele of the New Empire a personality had the title of “timekeeper/astronomer on the roof of the palace”.

5. What instruments did they have for observation and measurement?

The observational instruments used by Egyptian astronomers were very simple. They had the “bay” a palm frond on whose upper part they had made a Groove to use as a viewing instrument. Then, the merkhet was basically a piece of wood which was placed horizontally and from which a plumb-line was hung. It could be used in combination with the bay. We can also infer the existence of another two instruments for observing: a type of gnomon, which appears drawn on many astronomical roofs; and a type of grommet, which could well correspond to the strange object crowning the head of the godess Seshat. Of course, the Egyptian astronomers also used clepsydras, as well as clocks using the Sun and shadow. And for their observations they had lists of stars with information about risings, settings, and culminations.
(from https://www.iac.es/en/outreach/news/jose-lull-egyptian-astronomers-used-observe-terraces-temples-and-palaces#:~:text=The observational instruments used by,a plumb-line was hung.)

So, a difference in height would account for it.  And they wouldn't have opened the other pyramids to check the angle, though this error could have come from the instructions passed along from one architect to the next generation.

 

 

[Kenemet]

6 hours ago, Wepwawet said:

An important point. While it is known that some New Kingdom temples, which I discussed on the "Diagonal" thread, are aligned to stars, predominantly temples for goddesses, when we look at Giza the most notable alignments are solar ones. The Great Sphinx, Sphinx temple, Valley temple and the mortuary temples for G1, G2 and G3 are all aligned on an east-west axis. The Sphinx looks out to the east, the rising sun, and with all the temples the officiants would be facing to the west, which is to be expected in a necropolis. The sun/Ra sets in the west, it is the direction to which the soul departs, at least initially. And as you say, if you have an east to west axis, by default you must also have a north to south axis at right angles.

I don't reject the possibility that a stellar alignment was used, or even paramount with the pyramids, the akh of the dead king does after all end up with the "Imperishable ones" in the northern night sky, but it has to be pointed out that the prime axis of alignments at Giza is east to west.

I'm a little leery of the stellar alignment myself because the stars move around.  My own wild speculation is that it's more likely the alignment was solar and marked a particular day.  But other than the known examples from the New Kingdom, I have no particular support for this idea.

[Scott Creighton]

3 minutes ago, Kenemet said:

As I said, different architects and the different measurements.

Now...they didn't have all the equipment we have. So, just as a thought experiment look out a window and point your finger at some distant object (you can do it with closer things but if you use a distant object, you can see the effect better.)  Look at the angle that your arm makes.

Now crouch down slightly (or if you want to get drastic, sit down.)  You've just changed your "height" by several inches.  Point at the reference object and see if the angle is the same.

If we look at known astronomical implements of the ancient Egyptians, they seem to be very vulnerable to this kind of error

So, a difference in height would account for it.  And they wouldn't have opened the other pyramids to check the angle, though this error could have come from the instructions passed along from one architect to the next generation.

They could align G1 and G2 (and other monuments) to near absolute perfection to the cardinal directions but because, in your opinion, some dude was too tall or too small that's how they messed up all the others.

Righto!

SC