Cultural considerations

p. 15

At Giza, the factors determining the differences and

similarities seen between the funerary structures,

including the three royal pyramids, are many and varied.

The reasons for the particular choice of locations for each pyramid, and the relative positions of them, have

remained a matter of enthusiastic speculation for many

centuries. It is only in the last few years that serious and

systematic efforts have been made to explain the

decisions taken by the Egyptian rulers and architects in a

more academic way, and with reference to their culture,

religion, technologies and traditions [Figure 16]. Aspects

of landscape archaeology have also become prominent

recently, and can be applied usefully at Giza, where

practical concerns due to the terrain available were

certainly influential, as will be discussed.

Nevertheless, ritual, symbolism and tradition also played

a major role in determining pyramid location choices on

the site. In fact, as one studies the factors that were

considered, it becomes apparent that many different

issues were of importance, and that the symbolic and

practical concerns relating to the site were all interrelated.

This sort of multi-layered symbolism is something that is

seen widely in early Egyptian material culture and

iconography, and in the culture as a whole. It is possible

that this multi-layering of ideas was in part a hangover

from pre- and proto-literate Egyptian society. In a

community without paper or records, preservation and

communication of information would have been carried

out through people’s living memories, and in conjunction

with the changing ritualised landscape and traditional

materials and myths, rather than as issues recorded on

paper in isolation from a wider context.

The way in which we subdivide, categorise and record

knowledge systematically today seems quite normal, but

in the past it may have been more usual to integrate

important knowledge with reference to existing

traditional symbolism. As a result of this older method of

information communication, older traditions heavily

influenced the iconography and theology of the new

dynastic Egypt, despite the importance of the new

technical developments and growing literacy.

p. 16

It is well known that the multi-layering of different ideas

enables them to be memorised more easily, so that it is

possible that the complexity of symbolism observed in

the Old Kingdom iconography was a characteristic of

pre-literate society.

The intertwining of practical and religious concerns is

one of the reasons that the Giza site, and other sites of

Old Kingdom Egypt, are so fascinating to study, and

difficult to interpret. This may also be the reason why

people today are so ready and able to project their own

technical and religious ideas back onto the site, adding

yet more layers to the multi-layered ideology associated

with this ancient project. Nevertheless, we now have to

hand enough evidence and data to finally synthesise the

architectural, archaeological, cultural and textual

evidence into one historical narrative.

The royal cubit was an integral part of the early state

development that assisted the expansion of industrial

scale agriculture, the growth of the administrative class of scribes [Figure 16], surveyors, tax collectors, overseers of surplus, and the evolution of monumental architecture.

The architecture that it enabled symbolically legitimised

the centralised pharaonic rule that kept the country

unified, and so underpinned the stability of the society.

Standardised measurement became part of the

monumental, architectural, pharaonic preservation

system.

As noted, there is no record of when or why the

standardised measurement system that was the royal cubit was subdivided into its curious 7 parts, but there are several natural characteristic of this setup that strongly suggest that the reason was linked to the cultural context in which it first developed, and to facilitating practical problem solving.

Figure 17 Basis for the 7-palm cubit: diagonals and

circles made easy

The important diagram above shows how the 7 palm

cubit is particularly well suited to measuring out square

diagonals as well as circular circumferences. Neither of

the approximations in the middle of the square is exact,

but the diagonal is very close to being exactly 10 palms

(only 1.02 % from being the true length of the diagonal),

whilst the quarter-circumference is almost exactly 11

palms (only a tiny 0.04% in error from being the true

length of the quarter circumference). This means that the

circumference of a full circle, swept out by a 7 palm

cubit, is very precisely 44 palms in length.

In fact, a 7-part subdivision of the cubit is the only

number of subdivisions (i.e. into 4 or 5 or 8 or 9 etc) of a

rule that can offer approximations of this total accuracy,

until we reach 14 subdivisions, which is simply the 7

doubled up again.

From textual evidence we know that the Egyptians were

indeed occupied with geometry related to square and

rectangular diagonals, and measuring square areas and

circular structures, so it is quite plausible that the 7 palm

subdivision was a conscious and deliberate choice based

on the useful approximations that fall naturally to this

setup. Calculations involving circular granary capacities

and cuboid block volumes, for example, are known from

the mathematic papyri.

Squares and square roots were certainly calculated by the

Egyptians by the time the Rhind Papyrus was written

(Gillings 1982: 214), and the diagonal of a square was

used so often that it was even allocated its own name

which was the ‘double remen’, the remen being the half

diagonal (Gillings 1982: 208).

From the simple diagram above [Figure 17], we can see

that the quarter circumference of a 7 palm cubit is almost

exactly 11 palms, when a right angle is swept out, and so

a full circumference is 44 palms. Given the widespread

use of the cubit and its application to geometric problems

including circular calculations, it seems highly likely that

the 7 palms were closely related to facilitating

approximations of circular circumferences and square

diagonals.

It is also interesting to note at this point the circular

symbol of the god Re which is almost always assigned to

the first digit of the royal cubits [Figure 18]. This was the

case when the symbols for the pantheon of Egyptian gods

were included alongside the digits on the rules as ‘finger

protectors’. The clear association of this circular symbol

for the major Egyptian solar god certainly fits with a

royal cubit system that originated with respect to circles

as well as linear measurement.

When we look at the pharaonic funerary architecture in

the following chapter, we will also find clear evidence of

circular proportions being applied into rectilinear

buildings. Not only that, but the relevant numerical

multiples of royal cubits associated with circular forms,

44, 22, 7 and 11, are measurable and observable within

the structures, to an extremely high degree of accuracy,

time and time again.

Figure 18 Symbol of the sun god Re from digit 1 of the

royal cubit

It was these characteristics of circular proportions and

their arithmetic relationships, first found in the Great

Pyramid, that first stimulated serious interest in the

geometry of the pharaonic monuments.

Nevertheless, it was not until 1883 when the first accurate

theodolite survey of the plateau was carried out, by the

grandfather of Egyptology, William Matthew Flinders

Petrie, that the ‘true facts of the matter’ started to become

apparent.

The next chapter outlines the facts of the matter, as they

have been uncovered from pharaonic funerary

architecture.