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Systems Engineering The Pyramids

by Prof. Derek K Hitchins

Contents

Nerertari 
* Fourth Dynasty - State of Development
* Looking at Systems
* Emerging Picture
* Hemon, Overseer of the Kings Works - Architect of the Great
Pyramid
+ Situation Facing Hemon the Architect
* Planning the Great Pyramid of Khufu...
* Notional Strategies to Achieve Pharaoh's Vision
+ Notional Strategy to Achieve Emergent Property 1
+ Notional Strategy to Achieve Emergent Property 7
* Behaviour Diagram for Khufu's Pyramid
* Organization
* What's at the end of the Ventilation Shaft, Khufu's Pyramid,
Queen's Chamber South?

Fourth Dynasty - State of Development

* No wheel, block and tackle.
* Primitive mathematics with binary multiplication and fractions. No
zero. Could calculate:
* areas of triangle, rectangle, trapezium
* area of circle by squaring 8/9 x diameter.
* volume of pyramid(!), truncated pyramid and cylinder
* Long architectural tradition-design of pyramids reaching
apotheosis at Giza
* Pyramid design had evolved over the 100 years since Imhotep¹s
first. Slopes had changed:-
* Bent Pyramid - 14:10 (54d31m) then 19:20 (43d21m) Snefru
* Red Pyramid - 19:20 (43d40m) (first true) Snefru
* Khufu's is 14:11 (51d50m)
* We can deduce that the ancient Egyptians, like the builders of
mediaeval cathedrals, were less concerned with angles, more with
proportion.
* Proportion seems to have been a powerful guiding principle behind
architecture, painting, astronomy and many more.
* Pyramids, cathedrals and renaissance paintings stand testimony to
the considerable power of proportion
+ It is far from being some "rough-and-ready" guide.
+ Instead, it seems to be offer great insight.

Looking at Systems

* Following Job Trees show how jobs at the "top of the tree" depend
upon the existence of other jobs which supply them with their raw
materials, tools, supplies, etc.
* From the trees, it is possible to discern something of the
complexity and sophistication that must have existed for some time
before the building of pyramids could have even been seriously
considered.

Job Trees

Job Trees in the Fourth Dynasty

Emerging Picture

* Complex, sophisticated, well-trained, highly-skilled,
partially-literate population
* Skills honed, maintained, improved by continual challenge-new,
ever-more demanding projects-palaces, temples, pyramids
* Integrated astronomy, theology, architecture suggests
³university²:-
+ observation, recording and research over many decades, even
centuries
+ technique, method, developed, handed down

Start
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Hemon, Overseer of the Kings Works - Architect of the Great Pyramid

Three basic theories about the method of building:-
1. Long ramp stretching out into the desert, continually lengthened
and heightened as pyramid grew
2. Sand ramps built spirally around the faces of the growing pyramid
3. Herodotus (5thC, B.C.) - built as a series of terraces, raising
blocks on all four sides simultaneously using 'contrivances made
of short timbers'

Situation Facing Hemon the Architect

* Uncertain life-span of Pharaoh-how much time is available to build
the Great Pyramid?
* Standing army of 4000 artisans
* Willing work force, up to 100,000, but only during 3-months of
Inundation
* Copper tools. Strong ropes (f ¾ 5in). No mechanical aids. No block
and tackle. No wheel.
* Cost irrelevant, quality paramount, failure disastrous-especially
for Hemon!
* Great Pyramid part only of Imhotep's Grand Plan
+ pyramids by Nile like stars by Milky Way
* must create Khufu as part of overall star-plan
+ scale on ground represents scale in heavens?
+ major astronomical siting task
+ major surveying task over tens of kms
* Only then could Hemon conceive, design, plan and manage the
construction of mighty Khufu¹s Horizon
+ magical formulae, angles, relationships, directions
+ traditional architecture - innovative features:-
o star shafts,
o multiple chambers in masonry,
o Grand Gallery,
o hidden rooms...

Start
_________________________________________________________________

Planning the Great Pyramid of Khufu...

* Reductionism has not yet been invented - c.2000 years to go before
those Greeks !
* Mercifully, Henry Ford and Taylorism have some 4,500 years to go !
* Happily, ancient Egyptians instinct was to build-so...
* "Big" was good, "Takes many years" was fine, "Cost" was no problem
* Not yet spoilt by conscious fear of failure and risk
* Still, Hemon dare not fail - "Egypt and Khufu must be eternal, or
none of us will live for ever"

SE Model

Systems Engineering without Reduction

Notional Strategies to Achieve Pharaoh's Vision

1. Numinous open-air Cathedral for burial of Kings and regular
religious ceremonies - aesthetic, temporal, behavioural
2. Site to legitimize new Pharaoh as Horus, store past Pharaoh as
Osiris, maintain Ka - functional, aesthetic
3. Pyramid annually revitalized celestial "seed" for all Egypt,
giving rebirth with Inundation? functional, temporal, aesthetic
4. Khufu's Pyramid as Osiris - celestial channel for annual rebirth
of Egypt? - physical, functional, aesthetic
5. Grand Plan for Giza (at least) to represent part of the star (&
solar) mythology on Earth? - physical, functional, aesthetic,
temporal
6. Large, star white/gold pyramids laid out to represent Osiris'
phallus near Milky Way? - physical, aesthetic
7. Pyramids to be v. large: impress; mark spot from heavens(?);
defeat robbers; contain traps, decoy chambers...yet support
regular ceremonies - rebirth, offerings to the Ka...physical,
functional, aesthetic, behavioural
8. Giza and pyramids to contain magic symbols, relationships, angles,
but within a sound, impregnable architecture - aesthetic,
physical, behavioural (c.f. Christian cruciform cathedral facing
East)

(Following Strategies exemplify the Process, but address only
Strategies 1 and 7 for brevity)

Notional Strategy to Achieve Emergent Property 1

1. Grand Plan for Giza (at least) to represent part of the star
mythology on Earth Strategy, Principal Activities
+ Observe mythological stars,
+ record passage, angles,
+ choose scales on Earth,
+ locate site w.r.t. Nile/Milky Way,
+ survey potential sites,
+ select Giza.
+ set up observatory at Giza.
+ record star angles from Giza.
+ note effects of precession.
+ mark cardinal directions.
+ mark and record heliacal risings and culminations

Notional Strategy to Achieve Emergent Property 7

7. Pyramids to be v. large: impress; mark spot from heavens(?); defeat
robbers Strategies and Principal Activities
+ Conceive pyramid design based on experience.
+ Introduce new features - star shafts, grand gallery (to store
plugs and portcullis doors), several chambers to support
different stellar-related ceremonies.
+ Build mud-brick model of Pyramid, using different coloured
bricks.
+ See how sloping shafts & chambers pierce each layer and
sloping band of core.
+ Experiment with different layouts for false chambers,
robber-defeating plugs, etc.
+ Choose design, mark each mud brick, use as master plan for
project management control. Locate building materials - bulk
of material to be as near as possible (Giza plateau).
+ White Tura limestone for facing to be brought by boat during
Inundation.
+ Granite blocks and sarcophagi to be brought down river from
Aswan.
+ Design landing stage and hauling avenue as precursors to
Valley Temple and Causeway respectively.

Start
_________________________________________________________________

Behaviour Diagram for Khufu's Pyramid

Behaviour Diagram

Typical Behaviour Diagram for Planning Khufu's Pyramid

Organization

* Men organized in gangs/crews of 800-1000
* Crew names painted on blocks:-
+ The crew, Khufu excites love
+ The crew, The White Crown of Khufu is Powerful
+ The crew, Menkaure is drunk(!)
* Other marks painted on blocks:-
+ This side up
+ To be taken away
+ For the Royal Tomb
* Crews, in teams of 25, headed by a soldier
* Teams put their own marks on stones, and competed with each other
* Team graffiti:-
+ Khufu's cartouche in Great Pyramid
* Progress - completed King's chamber in Year 17. (Confirms
Herodotus' estimate of 20 years for Great Pyramid, 10 years for
Causeway)

What's at the end of the Ventilation Shaft, Khufu's Pyramid, Queen's Chamber
South?

Well, I don't know, of course. But guessing is anybody's game. My
guess goes like this:-

* Hemon would have to build a model of the pyramid to understand the
construction process, to manage progress and to illustrate the
whole project to Pharaoh Khufu
* Once built, it would be dismantled layer by layer and then used as
a master plan, with each model brick being replaced on the model
as the real stone blocks were placed on the pyramid.
* Once the pyramid and the model were fully assembled, what to do
with the model?
+ it contained all the "secrets of the many chambers of Thoth"
+ its discovery would help tomb robbers
* Two answers:-
1. Destroy the model, even though after 20 years, it had
probably taken on a reverence of its own
2. Hide the model - but where?
* One ultimately logical place to hide the model would be in the
Pyramid. Then, anyone who found the model must already have
penetrated the secrets

Start

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Last updated: Feb 2000