81477 - The contribution of the exceptions

N. Lygeros

When we have a general rule,
the exceptions look like problems.
They have something monstrous
for the normality.
We saw it in mathematics with the fractals
which were considered at the beginning
and I mean before the deep understanding
of Benoit Mandelbrot,
as monstrous functions.
At the end, after the revolution of fractals,
we realized that these exceptions
were in fact the elements
of a new nature.
In fact exceptions can be responsible
for exceptional discoveries.
I have in mind the moonshine in group theory
from the contribution of the sporadic groups
in the great classification.
By the way, if you choose
the root exception
to build the word exceptional
it has a reason.
Exceptions are singularities
and sometimes
they are the only relevant elements
to characterize a structure and its relations.
Exceptions belong to Mankind
because societies don’t want them.