the language of mathematics. The first one is imprecise and fuzzy while the
other one is precise and exact. It would have been rather puzzling if these
two were to register and be controlled by the same area of the brain and in
the same manner. Because then it would have been hard to understand as to
how the same area of the brain could produce imprecise and fuzzy language
at the same time that it was producing another independent language which
was precise and exact. It shows consistency of the ideas presented here
that Varley et al found that indeed the two languages arise intrinsically in a
different manner within the human brain.
If these two modes of languages register differently in the human brain,
then it is possible that they arose at different periods of time during human
evolution, due to different requirements of adaptation needed for them to be-
come essential for survival. The first, the spoken language, arose as a result
of social interaction and as a result of demands of survival for food etc. While
the second, the language of mathematics, arose as a result of man’s inter-
action with nature. As man spends more time with nature than with other
human beings, the second language must be more naturally acquired than
the first one. This point is also supported by the fact that other creatures
have been interacting with nature for a longer period of time than what we
humans have been doing. Do they have a language of mathematics? Indeed
they do. When a bird needing to feed two chicks in its nest, actually brings
back two insects to feed them, then indeed it has acquired the rudiments
of mathematics. Hence it is clear that humans in the course of evolution
must have learnt elements of the language of nature well before they learnt
to speak. Therefore, it may come as a surprise to some, but mathematics
as a language of nature, albeit in a more elementary form, must have been
available to species other than homo sapiens. Indeed current research shows
that acquisition of spoken language may be a much later development in
human evolution. In fact, the growth of the human brain and the faculty of
(spoken) language acquisition may have been simultaneous ( Deacon (1992)
)■
Mistakes are an inherent part of mathematics. Do these mistakes oc-
cur accidentally or are they basic to mathematics itself? Rene Descartes
thought mistakes by mathematics were inadvertent. Charles Peirce thought
that these were due to lapse of memory. Ludwig Wittgenstein stated that ac-
tually mathematics was a subject in which it was possible to make mistakes.
In fact in mathematics it is impossible not to make mistakes. Riemann used
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