Friday, December 19, 2014

Peak pyramids: the way to ruin is rapid

The graph above is a little exercise in cliodynamics, the attempt of quantitatively modeling historical data. Here, the size of the great Egyptian pyramids is plotted as a function of their approximate building date, taken as the last year of the reign of the Pharaoh associated to them. The data are fitted with a simple Gaussian, which approximates the cycle of the Hubbert model of resource depletion.

The great Egyptian pyramids built during the 3rd millennium BCE are the embodiment of the power and of the wealth of the Egyptian civilization of the time. But why did the Egyptians stop building them? Not lack of interest, apparently, since they kept building pyramids for a long time. But they never built again pyramids on such a giant scale.

Probably, we will never have sufficient data to understand the economics of the Egyptian pyramid building cycle of the 3rd and 4th Egyptian dynasties. But we can try at least to examine the quantitative data we have. So, I went to Wikipedia and I found data for the size of pyramids and their approximate dates. The result is the graph above. Here, I show only the data for completed pyramids as a function of the last year of the reign of the Pharaoh associated for each one.

As you can see, it is possible to fit the data with a Gaussian curve, which approximates the Hubbert curve, known to describe the depletion of a limited, non renewable resource. This suggests that the Egyptians had run out of resources, possibly in the form of the fertile soil necessary to sustain the large workforce needed to build pyramids. Or, perhaps, in an age of increasing warring activity, they were forced to funnel more and more resources into the military sector, taking them away from pyramid building.

Another phenomenon we can note in the graph is the rapid collapse of the size of the pyramids at the end of the cycle. The last pyramid of this cycle, the one associated to Pharaoh Menkaure, is even smaller than the first one of the cycle, the "stepped pyramid" of Pharaoh Djoser. Perhaps, this rapid decline is a manifestation of the "Seneca Effect", a term that I coined to describe economic cycles in which decline is faster than growth. Unfortunately, however, the data are too scattered and uncertain to be sure on this point. But surely there was no "plateau" nor a slow decline after the construction of the largest pyramids andit is suggestive to think that even pyramid building may be described with Seneca's words "increases are of sluggish growth, but the way to ruin is rapid."



  1. Interesting post.

    I wonder how the "seneca curve" would fit in a chart of shopping mall area available in the US since the 50s. Of course, one would have to figure it out a way of compensating for the spread of web-based commerce as of recently.


  2. Yes the way to ruin is likely to be rapid but will outdo even Seneca if some of our TRULY wise leaders manage to get us into a nuclear war. After all it is imperative to safeguard the rights of a few Ukrainian Nazis while also protecting "democracy" in Europe. Not the mention the likely very beneficial geo-engineering effects of the many mushroom shaped clouds and the significant slowdown of peak oil and all sorts of other depletions.

  3. Or, perhaps the Egyptians ran out of resources the way the Bible says they did. When the Israelite slaves which were making their mudbricks and building their structures were saved by God and led out of oppression in Egypt. Isn't the timeframe in line with the Biblical record?

  4. Nowadays it is known that the Israelites were not slaves in Egypt, and that in Moses' time the "Promised Land" was part of the Egyptian Empire. See:
    The Bible Unearthed: Archaeology's New Vision of Ancient Israel and the Origin of Its Sacred Texts

    1. Well, you go with that if you like. I'll stick with the eyewitness account that is preserved for us in the Hebrew scriptures. Many many extant copies of these old manuscripts exist, more than any other document from antiquity. And Sr. Bardi has delivered corroborating evidence.

  5. Ugo
    How about these?

    or these

    or these

    But I am not sure that London has reached ‘Peak Building’ yet.


  6. There is a possibility that many of the pyramid stones were poured and not carved. See

    Critical ingredients may have been mined in the Sinai. The exhaustion of those mines may have caused the Seneca Cliff.

  7. Or, perhaps the Egyptians ran out of resources the way the Bible says they did. When the Israelite slaves which were making their mudbricks and building their structures were saved by God and led out of oppression in Egypt.
    شركة بسمة الرياض وكعادتها معكم تتشرف بتقديم خدمات غسيل المجالس بطريقة علمية ومجربة لضمان الحفاظ على الاقمشة والانسجة فاذا كنت تبحث عن يحافظون على مجلسك فنحن نضمن لك مع شركة غسيل مجالس بالرياض أفضل النتائج الممكنة فنحن نعتمد على عمالة مدربة ومجهزة باحدث الماكينات الحديثة لغسيل المجالس وجميع متعلقاتها حيث اننا نستعمل مجموعة من المنظفات العالية الجودة لضمان الحفاظ على الالياف الداخلية للمجالس فنحن لسنا هواة فى هذا المجال فلدينا باع طويل فى خدمة غسيل المجالس على مستوي المملكة العربية السعودية وبالاخص مدينة الرياض.
    وحتى يتم القيام بعملية غسيل مجالس راقية تقدم شركة غسيل مجالس مجموعة من النصائح والارشادات العامة لاتباعها فى المستقبل والتي هي من اسرار مهنتنا وأولها هو الاعتماد على التنظيف بالبخار بشكل دائم لانه يحافظ على الاقمشة بشكل لا يصدق وضرورة استعمال بعض المنظفات المجربة والتي تعطي للمجالس رونق والوان زاهية بالاضافة للاعتماد على السجاد والموكيت والذين يمثلون مجموعة من أهم المفروشات الخاصة بالمجلس ويجب الاعتناء بتنظيفهم وغسيلهم بشكل دوري حتي يظهروا دائمآ بالمظهر الراقي الذي يليق بضيوفك شركة تنظيف كنب بالرياض.



Ugo Bardi is a member of the Club of Rome and the author of "Extracted: how the quest for mineral resources is plundering the Planet" (Chelsea Green 2014)