Lev Goldfarb,
ICPR, Aug. 2004

32

In mathematics, so far, we have been dealing with
various static (abstract) structures.

For example, in group theory, which does study the
subgroup lattice of a given
group, there are, quite naturally, no expectations that one subgroup is obtained by modifying
another one.

Even in a more “continuous” setting of a
topological space, there are again
no expectations that a
topological structure itself is evolving.

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In contrast, in ETS formalism, some
of the central building blocks of the
formal structure, the set of transformations, are being modified on the basis of the inductive experience.