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.