The human body is composed of certain elements but all the components and the body itself are built in rigorous order. Not only in their number, but in its dimensions and other characteristics. Architecture has the same elements and, as a technical discipline, it is more rigorous. Vernacular architecture, the product of simple, unschooled people, has much stricter order, not as a constraint but for simplification and to avoid mistakes. Both the human body and vernacular architecture are simple as a totality but complicated in details, for the best function. The methodology of the article consists of a technical survey of human body, its dimensions and possibilities in practice. Practice is extremely complicated because of differences in men’s heights.
Theory is based on mathematical expressions that are exact. Simple geometrical objects helped a lot: the trunk of a tree is circular, but a usable beam must be square - the common relation is the square root of two. Today we use mathematics, in the past simple but exact geometry was used. The result is a harmonising of interests. The best solution is nature itself: all its elements are built in accordance. Only harmonious composition can be beautiful. The conclusion is a very short recognition: beauty is the final goal of art and, if art is the ultimate conception in our built world, also in architecture.
The human body is composed of certain elements, but all the components and the body itself are built to a rigorous order. Not only in their number, but in their dimensions and other characteristics. Architecture has the same elements and, as a technical discipline, it is more rigorous. Vernacular architecture, as a product of simple, unschooled people, has much stricter order, not as a constraint, but for simplification and to avoid mistakes. Both the human body and vernacular architecture are simple in totality but complicated in detail, for the best function. Primeval man understood that order is very important. Order between quanta: in length, cross section and volume. He formulated the first measures by himself: finger (inch), fist, elbow (cubit), foot, step, reach. The problem was that no one foot or elbow were the same . The surface area in use in czarist Russia seems unlikely: ‘utro’ or ‘morning’ in English. This was the area that could be walked in one morning - but no step, speed or length of the morning was defined. It is no wonder that this ‘utro’ is no longer in use.
Precision is very important. This has been understood by some prominent scientists in history.
a. Pythagoras: Everything can be defined by numbers.
b. Karl Marx: Science will be perfect only with the use of mathematics.
c. Le Corbusier: The project net is a guarantee against the self-will of individuals.
d. Walter Gropius: Use of the golden section, modules in old Greece, triangulation in Gothic, are proof of the use of optical keys in the past .
Today’s measurements use the decimal system, for simplification. One meter is the 40,000,000st part of the meridian arc length . The decimal system is very simple, and the old systems were extremely complicated. Leigemann wrote how the ancient stadion fit into the ancient foot system, with a length of 600 feet, although Ptolemny used station as a length of 700 stadia . More interesting is the use of measures in Egyptian pyramids, with a length of baseline of 440 Cheops cubits. ‘The units of length of the pyramid builders were abandoned in Egypt during the middle dynasty, a new royal cubit was introduced then, which is the Egyptian Royal cubit with 2 gudea - units of 529.1 mm. There is one famous Greek exception: the stadium in Olympia was built very precisely according to 600 Herakles ‘pous’ . No measurement system is perfect.
The methodology of the article consists of a technical survey
of the human body, its dimensions, reach and possibilities and
its application in the measurement system. Man’s likeness can
be understood (every individual sees firstly himself), and this is
the main problem: no two people are alike. Formal dimensions
such as finger, fist, palm, foot, step or reach of a man depend on
one man only. It is thus no wonder an extremely large number
of different dimensions for the foot or elbow, the cubit, were
used. The metric system, with decimal numbers, is technically
the best solution, but it suppresses human harmony, closeness
to man. Practice is extremely complicated because of difference
in men’s heights. The most important man in a monarchy was
the king, and formal dimensions were often adapted to him.
Some emperors were tall, and some weren’t; they were ‘human’.
Dimensions were different but the relations between them were
fixed. Only relations between quanta can be used. And relations
are fixed. The human measurements system is close to the
human body. An individual likes his own body, he knows it: why
not use it for the simplification of his work? Of course, there are
exceptions, because of the different lengths of some elements
Anthropomorphic measures are close to a man’s body, from
the finger (some millimetres) to the reach of a man, more than
two metres in length. The English system uses inch, palm, span,
foot, cubit, yard, fathom, all dimensions that are close to the
body. A composition with anthropometric measurements can be
harmonized from details to the whole (Figure 2). There are three
important problems with anthropometric lengths:
The not understood and complicated system with fingers,
feet, steps is accommodated to man: but to which man and to a
man in which time? Medieval man was shorter than my father,
my father was shorter than me, and I am shorter than my son, at
least. One foot seems to be a very simple and suitable measure.
Is it really? There is not just one length of a foot (German: Schuh,
Slovene: cevelj) - the lengths are as follows:
The golden section cannot be written with the use of simple
numbers: it is a very sophisticated proportion, but hard to
express with numbers. It can be understood; it cannot be defined
without knowledge of mathematics. The facts are as follows:
The diagonal of a square according to Pythagoras is the
square root of two, if the baseline is equal to one. The diagonal
of two squares is the square root of five. The golden section can
be derived on the length of two squares (Figure 3) (with lengths
equal to two, and the diagonal equal to the square root of five).
The problem is using this system in vernacular architecture,
which was created by unschooled, simple masters. They saw
their own bodies and they used the system of golden section
(Figure 4). It was used not only in history, but also in recent
times. Women’s fashion in a skirt uses ‘new’ expressions such
as ‘mini, midi and maxi’ - even the automobile industry uses
them (Figure 5). Practical use of complex systems is surprisingly
Theory is based on mathematical expressions that are
certainly exact. This was a problem for masters of vernacular
architecture, who had no technical knowledge. Simple
geometrical objects helped a lot: the trunk of a tree is circular,
but a usable beam must be square - the common relation is the
square root of two. Vernacular architecture uses a circle, square
and triangle for composing fixed dimensions; in the case of the human body it is the golden section. Today we use mathematics,
in the past simple but exact geometry was used.
The golden section is the infinitive proportion of two sides,
in which the shorter side is in the same proportion to the longer
one as the longer one to the sum of both.
Infinitive means that we can prolong this expression
The diagonal of two squares (the sides of which are equal to
one) is equal to 5.
The whole length is equal to 2, and the height of the rectangle
The shorter side of the golden section is thus:
and the longer side:
The golden section does not apply only to the human body:
the palace of the United Nations Organisation in New York,
designed by Le Corbusier, is a very important realisation in
golden section. He advocated this proportion in Le Modulor.
Further realisations in this mode include Chandigar in India,
and a series of buildings in Europe, of which the most important
is Unite d’habitation in Marseille . Simplification starts with
use of the square root of two: but simple masters did not know
theory as we know it today. The trunk of a tree was the basic
element in felling timber. It is circular but is primarily used in
building in rectangular profiles. The most ‘eco’ idea is to use the
biggest possible rectangular profile from a circle: a square. The
relation between the baseline of this square and the diameter of
a trunk is:
where the circle’s diameter is equal to the diagonal of the
square (Figure 6). Practical use can be seen with the most
typical Slovene architecture: kozolec or hayrack. This is a stable,
vertical, wooden, covered but open object for drying and storing
on laths. Historically it was used for drying and storing cereals,
today only for hay. It is in use everywhere in Slovenia . John
May wrote: ‘Dr Borut Juvanec from Ljubljana University has said:
It is the only ethnic architecture I know’ . The construction
of a kozolec/hayrack consists of squares, and its composition is
surprisingly exact in all the typical objects (Figure 7).
The sacred well of Sant’Anastasia in Sardara, Sardinia
(Sardegna) is composed of a circular shaft, covered by a false
dome. Its diameter is of the same length as the width and length
of the construction with staircase.
When drawn, it shows two cubes. Scientific treatment shows
the possibility of a sunbeam, reflecting on the water surface and
returning to the surface of the earth as ‘the beam from inside
the Earth’. This is the ‘miracle’. It happens every April 21, on
the name day of the saint from the nearby church. The name Anastasia comes from Greek word ‘anastasos’ which means a
sort of resurrection (Figure 8).
The most common composition in drystone is corbelling.
This means placing the layers such that each subsequent course
overlaps the lower one, right up to the capstone. This can be
properly, technically executed only in split stone: the origin is
confirmed by the construction of more than six thousand years
old tombs. Tombs on the border of Yemen and Saudi Arabia are
from the fifth millennium BC, and nawamis from Sinai are from
the fourth . The construction is composed of corbelling in
cross section and a circle in ground plan. Corbelling is built with
the help of the square root of three divided by two (Figure 9).
The result is harmonising interests. The best solution is
nature itself: all its elements are built based on the construction,
use, function, maintenance, appearance. Only a harmonious
composition can be beautiful. Man is part of nature, he cannot be
in front of it, only in the first line. It is enough for survival. Man’s
survival in coarse nature is mostly matter of using the brain. All
his works, including in architecture, lead to a better environment,
safer and more cultural. Today we call it a ‘cultural landscape’.
There is no question of whether architecture is more theoretical
or more technical: the two elements, hand in hand, compose it.
The primeval builder made the first measures himself: with his
brain and his body. His thought developed culture and aesthetics
in theory, his hands developed certain skills, for practical use.
Both brain and hands developed specific methods. Today we
hardly believe they existed, but they certainly did. In architectural
action or architectural contemplation, people feel pleasure or
displeasure; they react . Primeval man understood that order
is most important, in his non-consciousness way. Order between
quanta: in length or in space (Figure 10).
Prime man formulated the first measures by himself: finger,
elbow, foot. The second problem was in the relation of quanta,
lengths mostly. Thousands of years before the first theoreticians
(Pythagoras, for instance) man used the ‘holy triangle’ (3,4,5 as
‘Egyptian’) and other physical orders, as well as an equilateral
triangle, square, cube etc. The golden section is widely used in
detail and in the whole composition. Order helps to co-ordinate
complicated elements. Order uses various ways and procedures
in settings planned, dedicated to facilitating the work or to
making it better. Order means restriction to people of narrow
vision. For open-minded people it provides new possibilities.
Practice in architectural order is very simple: starting with
orientations, planning, designing, building, putting to work.
This scheme cannot be changed and none of elements can be
neglected. ‘An important topic became the quest for potential
factors which determine the shape of architectural constructions
and which can explain the enormous diversity of house forms’
. Today we understand things with knowledge of science (in
proportion theory: mathematics, geometry). Yesterday it was
harder: Pythagoras knew more about geometry two thousand
years and more ago but use of his knowledge until, say 1800
with the introduction of the meter, was limited to some bright
people only (Figure 11).
Both compositions work, and the system and appearances
of the bridges are totally different. Understanding their
constructions is very simple. I have mentioned some theoretical
problems, but they must be explained in practical ways, because
they represent culture and incredible treasure of the heritage
received from our forefathers. A man or a human body is obviously
the key. Anthropology, as a scientific study of human beings and
their physical, social, material and cultural development ,
and especially anthropometry, are basic elements for scientific
treatment. Anthropometry is ‘the science of measurements as
applied to the physical varieties of man of all times and places.
Such characteristics as height and weight, the proportions of the
body, the rhythm of growth from before birth until death, are
measured with instruments and the results charted in statistical
tables for analysis and interpretations’ [10-15]. This thought fits
directly into architecture, especially vernacular architecture.
Nature is built in very strict order. Primeval man saw it all
in nature: order reigned in nature and what is against order
is condemned to collapse. Everything happens according to
tradition. Non-functioning in nature means simply the end of
an activity [16-23]. Nature is harmonized and man’s work in
it must be the same. Use of fixed dimensions in selected order
means calm composition of harmonious elements. Only a totally
harmonious composition can work perfectly and be beautiful.
The conclusion is a very short recognition: beauty is the final
goal of art - if art is the ultimate conception in our built world,
deriving from an architecture.