Course thicknesses of the Great Pyramid

[aarvai]

The thickness of each course of stones in the Great Pyramid shows an overall trend for the courses to get thinner the higher up they are. This makes sense since it is harder to lift heavier stones. However there is also a periodic pattern where the thickness decreases for some number or courses and then abruptly increases. Here is a diagram:

 

The horizontal axis is the course, with the bottom course on the left and the top course on the right. The vertical axis is how thick each course is.

This paper analyzes the course thicknesses and they appear not to be random, but to be integer multiples of the cubit, the palm and the finger. The explanations for the thickness variation I've seen are:

1. The variation is due to the natural variation in thickness of the limestone

2.  In the process of quarrying the raw blocks, there would have been various thicknesses. Rather than rough shape them all to the same exact thickness they probably stockpiled blocks in groupings of similar thickness, then sent them to the pyramid as a group...layer by layer.

3. There is some unknown religious or symbolic meaning to the variation in course thicknesses.

The first two explanations don't explain why the thicknesses decrease and then abruptly increase. They also don't explain why the course thicknesses are multiples of the cubit, the palm and the finger.

The pyramid is estimated to have been built in about 20 years and there are about the same number periodic patterns in the course thickness, so this could indicate there is some yearly pattern. So I propose a simple explanation:

4.  Each periodic pattern of course thickness represents 1 year of construction. When the workers started working, the weather was cool and the workers were well rested so they could lift heavier stones. As the weather got hotter and the workers became tired, the thickness of the stones was decreased. This pattern would repeat every year.

Let me know if you believe any of these explanations or prefer some other one.

[Hanslune]

Howdy aarvai

Welcome to the forum

This was discussed recently on another board: *Snip*

[Still Waters]

5 hours ago, Hanslune said:

Howdy aarvai

Welcome to the forum

This was discussed recently on another board: *Snip*

It was the OP who posted it on the other board.

[Hanslune]

10 hours ago, Still Waters said:

It was the OP who posted it on the other board.

Yeah I guess he didn't get the answers he wanted there.

[jmccr8]

20 hours ago, aarvai said:

There is some unknown religious or symbolic meaning to the variation in course thicknesses.

Hi Aarvai

Do you have any supporting documentation for this bit, and if is unknown then why include it if you can't give reference?

jmccr8

[aarvai]

21 minutes ago, jmccr8 said:

Do you have any supporting documentation for this bit, and if is unknown then why include it if you can't give reference?

Hi Jmccr8,

I included this as one explanation I've heard for the variation in the course thicknesses. I don't think there is any evidence for this nor do I believe this explanation is correct.

aarvai

[jmccr8]

15 minutes ago, aarvai said:

Hi Jmccr8,

I included this as one explanation I've heard for the variation in the course thicknesses. I don't think there is any evidence for this nor do I believe this explanation is correct.

aarvai

Hi Aarvai

Okay thanks but what did you hear, where was it written/discussed as I would like to know,

jmccr8

[Hanslune]

25 minutes ago, aarvai said:

Hi Jmccr8,

I included this as one explanation I've heard for the variation in the course thicknesses. I don't think there is any evidence for this nor do I believe this explanation is correct.

aarvai

So what data is there for all the other pyramids with tiers? Is there any correlation?

[jmccr8]

3 minutes ago, Hanslune said:

So what data is there for all the other pyramids with tiers? Is there any correlation?

Hi Hans

That is where I was trying to go with his comment and was hoping that he was willing to give some answers.

jmccr8 

[aarvai]

13 minutes ago, jmccr8 said:

Hi Aarvai

Okay thanks but what did you hear, where was it written/discussed as I would like to know,

jmccr8

Hi Jmccr8,

The author of the paper I referenced in my original post has a second paper which he sent me a copy of. I don't want to post the paper since it's unpublished, but here is a quote from the paper:

Quote

The perhaps not so practical question is, why did they do this?  It required an enormous amount of effort to plan the course thicknesses in this non-intuitive manner.  Possibly some kind of information  was coded into these thicknesses.  It could have been historical  information or possibly religious information.

You can contact him directly and he will probably send you a copy of the paper. The second paper has a much more mathematically detailed analysis.

aarvai

[jmccr8]

1 minute ago, aarvai said:

Hi Jmccr8,

The author of the paper I referenced in my original post has a second paper which he sent me a copy of. I don't want to post the paper since it's unpublished, but here is a quote from the paper:

You can contact him directly and he will probably send you a copy of the paper. The second paper has a much more mathematically detailed analysis.

aarvai

Hi Aarvai

Thanks and I can understand not wanting to post his unpublished paper at this time, just thought it was curious that it was included without definition in your OP.

jmccr8

[aarvai]

9 minutes ago, Hanslune said:

So what data is there for all the other pyramids with tiers? Is there any correlation?

I don't know of any other data measuring the course thicknesses for any other pyramids. It would be very interesting to see more data.

[Hanslune]

45 minutes ago, jmccr8 said:

Hi Hans

That is where I was trying to go with his comment and was hoping that he was willing to give some answers.

jmccr8 

As far as I know there is no additional information on tiers. I believe there is some for Maya temples but cannot find it presently.

If the tiers heights had some sacred meaning then we should see it on other pyramids - but given they cladded not sure what the point might have been

[jmccr8]

1 minute ago, Hanslune said:

As far as I know there is no additional information on tiers. I believe there is some for Maya temples but cannot find it presently.

If the tiers heights had some sacred meaning then we should see it on other pyramids - but given they cladded not sure what the point might have been

Hi Hans

Yes of course it is the first time that I have heard of this and have to wonder if the same pattern would have shown up in the cladding as well as each course would be supporting the cladding so would have to be structural in support. We have never seen a fully cladded G1 so it seems speculative in nature.

jmccr8

[cladking]

21 hours ago, aarvai said:

1. The variation is due to the natural variation in thickness of the limestone

If deposition of stone occured chiefly at the peaks then bedding planes might well lie in a pattern like the course thicknesses;

https://link.springer.com/article/10.12942/lrsp-2013-1/figures/18

 

Of course there are endless possibilities for both natural and unnatural means by which these courses might exist.  

But there is no evidence of armies of stone draggers so it seems unlikely that it's caused by the men getting tired.  If it were so simple one would expect that there would be thicker courses in the summer when temperatures cooled and a nice breeze from the sea picked up.  Logically,  they must have taken what was available.  I propose that it was done in bedding planes principally because would keep adjacent blocks the exact same thickness AND because it would be easy to adjust for errors in previous courses.  There is the fact that each course is apparently wedge shaped and this is consistent with using limestone as it was deposited.  Maunder minimum would likely even leave a visible plane so that crews could stay on the right one.  

There's a great deal of research on the pyramids which has simply never been done because those who should care do not.  

[openozy]

Riveting stuff.

[Nobu]

3 minutes ago, openozy said:

Riveting stuff.

I don’t think any of this stuff used rivets. Levitating magnets and liquid stones perhaps. Rivets. Nope.

 

[Hanslune]

2 hours ago, Nobu said:

I don’t think any of this stuff used rivets. Levitating magnets and liquid stones perhaps. Rivets. Nope.

 

As I have noted before they used awfully large amounts of cheese which Egyptologist and fringe theorists have mischaracterized as 'Gypsum' mortar.

[aarvai]

5 hours ago, cladking said:

If deposition of stone occured chiefly at the peaks then bedding planes might well lie in a pattern like the course thicknesses;

First let me readily admit there is no proof the "tired worker" theory is correct, and unless some ancient papyrus is discovered documenting this, it is unlikely any proof will ever be found. However it does explain all the data with reasonable assumptions.

On the other hand, the limestone bedding theory might one day be proven true if bedding planes are measured. Presumably very similar bedding planes should exist in areas which were not quarried and could be examined. As far as I know this has not been done.

The problems I see with the bedding planes theory are:

1. Does not explain why course thicknesses are integer multiples of the cubit, the palm and the finger.

2. Relies on the unusual and periodic patterns of thicknesses naturally occurring sequentially in the limestone.

3. Does not explain why there are about 20 periodic patterns of thickness.

4. At the top of the pyramid much less limestone is required per layer. One bedding plane which was adequate for one lower layer, should be adequate for very many upper layers.

 

I'm suggesting the weather may have had a large impact on the workers. Here is a plot of humidity comfort levels in Giza:

The Nile would flood from June-September when no farming was done. I suggest the workers may have worked from around May-September. As the humidity (and discomfort) increased, the thickness of the stones would be decreased to compensate.

Quote

There's a great deal of research on the pyramids which has simply never been done because those who should care do not.  

Yes, I agree

[Hanslune]

24 minutes ago, aarvai said:

Yes, I agree

Yes and that applies to all ancient buildings.

[Gaden]

Do we actually have a time line on the layers' construction, or is this just speculation? Are we trying to use present day humidity calculations for a time period 4500 years ago? Have we considered how indigenous people are acclimated to their environment, or are we simply using our own discomfort levels as evidence? Why wouldn't stones placed in the early morning be larger than the ones later in the day, if energy level was the deciding factor? If smaller stones are adequate, why use larger ones at all?  

[Thanos5150]

On 2/8/2021 at 7:17 PM, aarvai said:

The thickness of each course of stones in the Great Pyramid shows an overall trend for the courses to get thinner the higher up they are. This makes sense since it is harder to lift heavier stones. However there is also a periodic pattern where the thickness decreases for some number or courses and then abruptly increases. Here is a diagram:

 

The horizontal axis is the course, with the bottom course on the left and the top course on the right. The vertical axis is how thick each course is.

This paper analyzes the course thicknesses and they appear not to be random, but to be integer multiples of the cubit, the palm and the finger. The explanations for the thickness variation I've seen are:

1. The variation is due to the natural variation in thickness of the limestone

2.  In the process of quarrying the raw blocks, there would have been various thicknesses. Rather than rough shape them all to the same exact thickness they probably stockpiled blocks in groupings of similar thickness, then sent them to the pyramid as a group...layer by layer.

3. There is some unknown religious or symbolic meaning to the variation in course thicknesses.

The first two explanations don't explain why the thicknesses decrease and then abruptly increase. They also don't explain why the course thicknesses are multiples of the cubit, the palm and the finger.

The pyramid is estimated to have been built in about 20 years and there are about the same number periodic patterns in the course thickness, so this could indicate there is some yearly pattern. So I propose a simple explanation:

4.  Each periodic pattern of course thickness represents 1 year of construction. When the workers started working, the weather was cool and the workers were well rested so they could lift heavier stones. As the weather got hotter and the workers became tired, the thickness of the stones was decreased. This pattern would repeat every year.

Let me know if you believe any of these explanations or prefer some other one.

5) structural reasons. 

6) Annual Nile flooding allowed for deeper canal waters allowing boats to carry larger blocks.  

[cladking]

11 hours ago, aarvai said:

First let me readily admit there is no proof the "tired worker" theory is correct, and unless some ancient papyrus is discovered documenting this, it is unlikely any proof will ever be found. However it does explain all the data with reasonable assumptions.

On the other hand, the limestone bedding theory might one day be proven true if bedding planes are measured. Presumably very similar bedding planes should exist in areas which were not quarried and could be examined. As far as I know this has not been done.

The problems I see with the bedding planes theory are:

1. Does not explain why course thicknesses are integer multiples of the cubit, the palm and the finger.

2. Relies on the unusual and periodic patterns of thicknesses naturally occurring sequentially in the limestone.

3. Does not explain why there are about 20 periodic patterns of thickness.

4. At the top of the pyramid much less limestone is required per layer. One bedding plane which was adequate for one lower layer, should be adequate for very many upper layers.

 

I'm suggesting the weather may have had a large impact on the workers. Here is a plot of humidity comfort levels in Giza:

The Nile would flood from June-September when no farming was done. I suggest the workers may have worked from around May-September. As the humidity (and discomfort) increased, the thickness of the stones would be decreased to compensate.

Yes, I agree

You raise several good points only some of which I can address.

I am not aware that course thicknesses are multiples of the measuring units.  Since most courses appear to be wedge shaped this seems unlikely.  Of course varying heights of the courses could be caused by other factors including measuring error.   I am aware that many of the higher courses are about 1 cubit.  

There is a cyclical nature to everything so limestone deposition should be included.  While tree rings tend to be thicker during years with more sunspots it would hardly be surprising if this affects limestone as well though the mechanism is much less apparent.  

I agree that the pattern is not entirely expected for exactly the reasons you state.  But the divergences can mostly be explained by working different parts of the quarry effectively "stockpiling" varying thickness stone in the ground.  They worked at least two quarries for G1 and possibly as many as four.  

The weather may have affected the work if men were dragging stones up ramps.  It did get very hot in the summer and the structure would block the wind and reflect heat back to the stone draggers on ramps.   Even if they built the pyramid the easy way that is clearly evidenced (pulling the stones straight up) men working the step tops would have very onerous work despite being able to work in the shade with a breeze.  Of course the number of men on any kind of lift determines how hard each man must work.  A stone that's hard for 50 men might be quite easy for 120.  

It should be noted that the climate was different in 2750 BC when carbon dating says the pyramid was built.  In those days (up until ~ 2300 BC) a monsoon in very late spring hit Ethiopia  which was the headwaters of the Blue Nile raising the river level but also ushering in a change in wind direction at Giza.  It switched around to the NE and was cooler.  There was twice as much  rain in those days as well and much more in the summer.  There was likely a major river just north of Giza flowing to the east but it may have dried up late in October.  Floods often came up to the Sphinx.  While there were very hot days in summer they tended to be dry air from off the Sahara and sometimes included dust storms. 

There could well be any number of reasons for the course thicknesses.  If I believed they were superstitious there could certainly be religious or "magical" reasons to build as they did.  There could be any number of reasons they wanted this exactly as it is. I don't have a great deal of evidence to support my hypothesis but it is a "best guess" with the tiny bit of information the linguists at Giza have provided.   My guess is based as much on my understanding of "cultural context" as much as anything else.  There are interesting writings about quarries all through Egyptian history and I believe several mentions of them in the Pyramid Texts. 

 

[aarvai]

3 hours ago, Gaden said:

Do we actually have a time line on the layers' construction, or is this just speculation? 

There are about 200 layers and it is estimated that the pyramid took 20 years to build, so a rough estimate would be that about 10 layers/year were built.

> Are we trying to use present day humidity calculations for a time period 4500 years ago?

According to this the climate was about the same:

Quote

The climate of ancient Egypt was much the same as it is today; a hot, dry desert climate with very little rainfall.

> Have we considered how indigenous people are acclimated to their environment

They would certainly be more acclimated to their environment, but I'm assuming they would still feel relatively more discomfort as the temperature and humidity increased.

> Why wouldn't stones placed in the early morning be larger than the ones later in the day

It would have taken multiple days to complete a level and all the stones on a given level are about the same thickness.

> If smaller stones are adequate, why use larger ones at all?

I don't think anyone knows for sure why they used the size of stones they did. Larger stones are more stable but harder to move, so there was probably some compromise. If you believe that the thickness of the stones was based on the natural thickness of the limestone layers, then they just used thicknesses which were naturally available.
 

[aarvai]

2 hours ago, Thanos5150 said:

5) structural reasons. 

There is some evidence for this. The rule for a doorway to a pyramid was that it occupy 1 or 2 courses. There is a passage which exits on course 19. Instead of making the doorway one unusually thick course, they made it two shorter courses (20 and 21). You can clearly see this and how it interrupts the pattern of gradually decreasing stone thicknesses.

> 6) Annual Nile flooding allowed for deeper canal waters allowing boats to carry larger blocks.  

The Nile was not used to carry the blocks which are now on the exterior of the pyramid. These were brought from a nearby quarry. The Nile was used to bring the exterior casing stones, which are now missing.