practice—surveying. Just as optics developed from
attempts to reproduce visual space, geometry was
discovered through efforts to model physical space
in survey documents. Representation of space has
been a critical element of urban civilization since it
first emerged, and archaic documents show that
Sumerian surveyors first applied the principles of
geometry over 6,000 years ago.
The distinction between geometric and optical
science might best be described as the contrast
between the vertical (or aerial) and horizontal per-
spective. When a viewing station is situated directly
above a field, that is, when the viewpoint is parallel
to the field, objects present a geometrically accurate
appearance. Their size, shape, and distance from
one another appear in the mathematically correct
ratio. When objects are viewed horizontally, that is
at a 90-degree angle to the viewing field, then per-
spectival effects occur. Near objects appear rela-
tively larger than distant objects, elements of
objects are foreshortened, and distances are dis-
torted. The philosopher Plato used these effects to
criticize empirical knowledge, but he did not realize
that perspectival effects could be defined mathema-
tically. Only a few generations later, Euclid was able
to systematize optics, creating one of the early suc-
cesses of rational science.
Thanks to optics we can produce rigorous des-
criptions of visual space that can be translated into
geometric terms. In other words, we can mathema-
tically account for the apparent distortions of
vision, and we can even work backwards to the
geometrically correct description of an object. Our
brains do this automatically, for instance when we
perceive an irregular hexagon as a cube or realize
that a nearby house is smaller than a distant moun-
tain. Optical algorithms can be embedded into
machinery, which is precisely what happens in pho-
tography. When stated as an algorithm, focusing a
camera is an act of measurement, which is why the
focus ring of a manual camera states the distance
between the film plane and the subject of the shot.
Classical optics has long been superseded by mod-
ern sciences of light and vision, but its influence
remains in the ubiquitous technologies of photogra-
phy, cinema, and video. And it is even apparent in
the new technologies of virtual reality, since its prin-
ciples play a strong role in generating realistic spaces
for games, flight training, and other simulated envir-
onments. It is almost redundant to say that the
primary expression of optics lies within the camera,
which is by definition an optical device. Photo-
graphic cameras evolved from the camera obscura,
a device that originated in medieval laboratories.
Scientists in the Middle Ages revived Classical learn-
ing, but they contributed an empiricism that was
previously absent. The development of the camera
is a consequence of an empirical approach where
observation and instrumentation complemented the-
oretic speculation on visual phenomena.
In its simplest form the camera obscura is a shut-
tered room with a narrow aperture that admits
light. The first recorded use of the camera obscura
is in an optical treatise written by the ninth century
scientist al-Kindi, who constructed a special room
to investigate the nature of light. At this point the
image-forming abilities of the camera were of little
interest. Al-Kindi and his tenth century successor
Abu Ali al-Hasan Ibn al-Haytham built camera
obscuras to investigate the propagation of light.
Euclid had assumed that light propagated in a recti-
linear fashion, and the camera obscura was used to
provide physical evidence for that statement. Opti-
cal texts by al-Kindi and Ibn al-Haytham became
standard university fare, and through them knowl-
edge of the camera spread to centers of learning in
the Islamic world and Europe.
The camera obscura remained rudimentary and
relatively unknown until the Italian Renaissance,
when interest in naturalist representation accompa-
nied a revival of Classical culture. Naturalism was
expressed in the painting and reliefs of the Renais-
sance, prime examples of which were drawn in per-
spective. The term perspective comes from the
Latin word for optics, and so-called Renaissance
painting is simply painting done within the frame-
work of optics. While the exact origins of Renais-
sance perspective were not documented, it is likely
that perspectival method arose from a combination
of trial and error, notably in the work of Giotto,
combined with medieval optics and the discovery of
theGeographyof Claudius Ptolemy by Florentine
scholars. The latter work contains the only defini-
tive record of classical perspective, adapted for the
representation of the Earth’s surface, and it could
have inspired the inventors of Renaissance perspec-
tive, Bruno Brunelleschi and Leon Battiste Alberti,
to develop the technique.
The training and tools of perspectival painters
were in keeping with the geometric origins of optics.
In the introduction toOn Painting, the first known
handbook on artistic perspective, Alberti calls on
painters to learn geometry and become mathemati-
cians. Perspectival method adapted surveying tools
like compasses, rulers, and measuring cords to the
canvas, which is not surprising since many Renais-
sance artists were also accomplished engineers, ar-
chitects, and urban designers.
Once again the conditions for progress in optics
were in place, this time within a culture that wasOPTICS