Delineation of buildings at Machu Picchu by Inca builders 31
situated on articial terraces on the hillside. The system
of terraces and the resulting plazas required considerable
interference with the natural landscape and prior plan-
ning of the use of individual areas within a single estab-
lishment. The technology for constructing the terraces
required engineering and construction skills, but also hy-
draulic skills that had already been developed by earlier
Andean cultures. However, it was not until Inca times
that projects of this type began to be realised on such
a scale. The Cuzco region, and in particular the Urubam-
ba river valley, has the most elaborate architecture of this
kind. The Incan architecture built in this area was mainly
located on terraces, less frequently on levelled grounds.
The planning and layout of the rebuilding of the cap-
ital of the Inca Empire at Cuzco, including the layout
of the Temple of the Sun, was described in the mid-16
th
century by a Spanish chronicler [2]. The historical de-
scription of the transformation of the centre of power is
attributed to Pachakuti Inqa Yupanka, who was said to
have personally drawn the plans for the buildings and,
with the help of imperial ocials, supervised the con-
struction. According to the description, the ruler used
a measuring tool in the form of a rope (quechua: ñañu
waska [3]). Its length is not known from chronicle de-
scriptions, nor has material evidence of its existence
been found. However, it can be surmised that if such
a physical standard of measurement existed then its
length was a multiple of a basic modulus – the deriva-
tive of one of the anthropometric measures.
Proving the existence of a unit of measurement or
a system of measurement units that the Incas used
should therefore take place on the basis of a metrologi-
cal analysis of the constructions considered to be impe-
rial projects. In the cosine quantogram method chosen
for the purpose of such analysis, the existence of a spe-
cic unit of measure is not assumed, but it is veried
whether, in the selected series of measurements, we can
proof the existence of a basic unit of measure (mod-
ule) – the quantum [4]–[7]. For Inca architecture, the
cosine quantogram method has so far only been used
at the urban scale. It has proven itself as a method in
the analysis of cultivated terraces located in the Sacred
Valley (Yukay-Urubamba Valley). According to a study
by I. Farrington, the estimated quantum value for about
400 measurements is 1.615 m [8]. This corresponds to
the value of the rikra, an Incan measure known from
Spanish colonial-era chronicles and quechua dictionar-
ies. A multiplication of this value is the waska (4 times
the rikra), a measure used to measure greater distances
with a rope. Here, we can expect the use of both famil-
iar measures such as rikra and waska on the outlines of
buildings, but also smaller units mentioned in histori-
cal sources, such as: half of the fathom (sikya), khococ
(cubit), chaqui (foot) [9].
The architecture of the Machu Picchu site, the con-
struction of which is historically identied with Pacha-
kuti Inqa Yupanki, the same ruler who was said to have
used a rope to measure buildings in Cuzco, seems to be
appropriate research material for the search for a basic
unit of measurement used as an architectural module.
Unlike other examples equally representative of metro-
logical studies, such as the temple of the Sun in Cuzco
itself (which, however, was largely a subject of recon-
struction), Machu Picchu represents an architecturally
homogeneous complex, constrained by the local topog-
raphy. Here we nd clear traces of conscious planning
evident, for example, in the articial landscaping in the
form of terraces and levelled ceremonial plazas. The
extent of the reconstruction of the architectural relics
of Machu Picchu since its rediscovery by H. Bingham
is also known [10].
Due to the fragmentary nature of the archaeological
research of the foundation of buildings in the area, it is
not possible to determine whether the priority for mark-
ing out the foundations of buildings was to prepare the
terraces on which the foundation of the building was
then laid out, or whether the building was laid out on
an incline and the area around the building was later
levelled to the appropriate height [11].
Testing quantum detection at different levels
available for measurement
Due to the non-invasive nature of the survey, archi-
tectural measurements from the 3D point cloud were
collected only above the current ground level, which in
only a few cases will correspond to the level at which
the building outline was measured by the former build-
ers. Due to the design of the walls, which are inclined
inwards at an angle of 3 to 6 degrees [12], [13], the re-
sults of the building outline measurements vary depend-
ing on the ground level available for measurement. The
quantum detection tests presented below are intended
to verify how dierent depths of the building arrange-
ment aects the value of the quantum estimation. The
basic assumption of this test is the existence of a level
or slope of the ground on which the building plans were
laid out according to a given unit of measurement.
Fig. 1. Schematic of quantum analysis for the different levels available
for measurement in relation to the theoretical foundation height on the
levelled terrain (elaborated by A. Kubicka-Sowińska)
Il. 1. Schemat analizy quantum dla różnych poziomów dostępnych
do pomiaru w stosunku do teoretycznej wysokości rozmierzania
obrysu na terenie zniwelowanym do poziomu
(oprac. A. Kubicka-Sowińska)
