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.
Coherence and diversity
Science integrates the results of diversified experiences and
expresses the perceived human need to maintain a coherent
perspective of the whole. As a reaction to the establishment of
a permanent and universal language embodied in the practice of
literacy, partial languages of scientific focus emerged. Those
who knew from their own self-constitution in scientific practice
that global coherence, as preserved in language, and specialized
knowledge conflict, gave up the effort to harmonize the general
framework (of language) and the specialized perspective (of
science).
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