The Encyclopedic tradition centered around the scientific human
being (l'homme scientifique) who it defined through language.
This tradition continued a line of progressive changes in
humankind's scientific experience. We can learn about these
changes by examining the language through which they are
expressed. The syncretic stage of human activity was dominated
by observations and short cycles of action- reaction. Incipient,
rudimentary science was not independent of the human being's
practical projection. Images and, later, names of plants,
animals, mountains, and lakes pertained to the beginning. Only
when the scope of observation broadened and, instead of the
immediate connection, a series of connections was accounted for,
did science become a praxis in itself.
Science was born together with the magical, and would continue to
develop in this symbiosis. Eventually, it joined religion in
opposing the magic. Observation and fear of the observed were
one. Names of stars testify to changes in the language in which
what we call astronomical science is embodied. Obviously there
was little awareness of the mechanics of the cosmos during the
time names changed. Mytho-magical terminology, followed by
zodiac signs of magic origin (in both cases with reference to
the practical activity of people during changing seasons), and by
the Christian names (after the establishment of Christianity),
is a line continued today in detailed catalogs encoding
positions, dynamics, and interrelations in numeric form.
In the experience of observing the sky and in deriving the notion
of duration (how long it took for celestial objects to change
position), humans projected their biological and cognitive
characteristics: seeing, association, comparison. Names were
given and observations were made, of position mainly, but also
of light intensity. With the emergent notion of time,
generalized from the notion of duration, stars were nolonger
related to divinities. Still, astronomical observation was used
to structure monastic life. Stars served as a nighttime clock.
At a time of reduced scientific inquiry (Europe from the 5th
century to the 10th), the observation of the skies, reflected in
maps of various constellations, prepared for future progress in
astronomy. Physical properties, such as intensity of light,
color, and brilliancy, later suggested better names because the
experience in which stars were recognized (navigation, in the
first place) required identification for successful performance.
Magic and science explained success in very different ways. This
was the time when planets were identified through properties
evident to all who needed the sky. The magic layer was projected
as a result of associations people made between qualities
characteristic of persons and the behavior of certain stars,
i.e., the perceived influence they had on events pertinent to
human existence. During the entire process, language served as
an instrument of integration and observation, as well as a means
for logical practice, such as deductions. Molding the experience
of time perception, storing the acquired knowledge, and further
shaping practical experiences of time, language acquired a very
powerful position in the human being's self-constitution in
time. This position would be strengthened by literacy, bound to
generalize distinctions in language and introduce them as
effective means of structuring new expectations. Only when
time-dependent practical requirements, such as those of
relativity, impossible to satisfy within literacy, became
critical was time freed from the captivity of verbal language.
A giant cognitive step bridged the immediacy of the
surroundings-where magic forces were rumored to exist, waiting
for humans to free them-and the notion of space. Geometry-which
literally means to measure land-is relevant as a practical
experience of human self-constitution that unites the concrete
task at hand (surveying, building, decorating, observing the
sky) and the generalization of distance. Measuring land ends up
not only in description of the land, but also in its
reconstitution in the abstract category of space. Language was
part of the process, and for as long as practical experiences in
the immediate surrounding were direct, geometric conventions
remained very close to their practical implications. Once
distinctions beyond direct relations in space were made possible
by the experience of navigation, by settled forms of social life
(leading to future cities), and by strategies for successful
securing and defense of land, the language of geometry changed.
Internally motivated developments, as well as those rooted in
forms of human praxis other than geometry, resulted in the
constitution of many geometric languages.
The languages of the foundations of geometry and of algebraic,
differential, or topological geometry are as different as the
practical experiences from which they are derived. In many
cases, literate language suffices for formulating geometric
problems, but breaks down in supporting the practice of
attempting solutions. Obviously enough, the intuitive visual
aspect of geometry is quite often better adapted to subjects such
as symmetry, higher order spaces, and convexity than is
literacy. Rigid spaces and elastic spaces behave differently
from spaces describable in language. Geometry frequently uses
notations whose referent is rather abstract. The freeing of time
and space from the captivity of language made an impact on the
condition of rationality, where scientific praxis is rooted, and
of reason, where philosophy originates.