Mathematics, Science and the Role of Data Analysis
(Freely translated by Fionn Murtagh from section 7,
Philosophy of Data Analysis, J.P. Benzecri,
L'avenir de l'analyse des donnees, Behaviormetrika, 10, 1-11, 1983).
In a "State of the Art Report", a collective work devoted to the
entirety of mathematical research in France, the authors note
as a self-evident epistemological truth that "mathematics are gifted
with a long time constant". Doubtlessly they intend by that, that
the more memorable mathematical works are not those that provide a
definitive solution to a given problem, but rather those that
uncover new perspectives that neither the cleverest of individuals,
nor the best coordinated of teams, have come up with over years of
work.
In data analysis, numerous disciplines have to collaborate. The
role of mathematics, while essential, is modest, in the sense that
classical theorems or elementary proof techniques are used almost
exclusively. But it is vital that certain abstract concepts
penetrate the mind-set of the users, the specialists who collect
the data and have to orientate the analysis in line with the
fundamental problems of their science. However the toolset of
computing develops at such a pace that research programmes that
were well nigh unachievable in the past have now come fully into the
orbit of the most accessible of computer devices or the web.
This very progress requires of data analysis to project, in
advance of the concrete work to be done, a vision of the
science as an indispensible motivation and justification.
This vision is philosophical. It is not a matter of translating
directly into mathematical terms the system of concepts of a
particular discipline, so as to link them in the model equations,
nor is it a matter of accepting the data as they manifest
themselves. Rather it is a matter of elaborating on the data,
in a deep-going and thorough synthesis, allowing new entities to be
discovered, and thereby simple relationship between these
new entities.
Through differential calculus, contexts that were admirably
dissected into simple components were then translated into so
many fundamental laws. We believe that it is reserved for
data analysis to express adequately the laws of that which is
complex in its very essence (living being, social body,
ecosystem) and cannot be dissected without changing its very nature.