In this paper we will offer a few examples to illustrate the orientation of contemporary research in data analysis and we will investigate the corresponding role of mathematics. We argue that the modus operandi of data analysis is implicitly based on the belief that if we have collected enough and sufficiently diverse data, we will be able to answer most relevant questions concerning the phenomenon itself. This is a methodological paradigm strongly related, but not limited to, biology, and we label (...) it the microarray paradigm. In this new framework, mathematics provides powerful techniques and general ideas which generate new computational tools. But it is missing any explicit isomorphism between a mathematical structure and the phenomenon under consideration. This methodology used in data analysis suggests the possibility of forecasting and analyzing without a structured and general understanding. This is the perspective we propose to call agnostic science, and we argue that, rather than diminishing or flattening the role of mathematics in science, the lack of isomorphisms with phenomena liberates mathematics, paradoxically making more likely the practical use of some of its most sophisticated ideas. (shrink)

In this paper we argue that data science is a coherent and novel approach to empirical problems that, in its most general form, does not build understanding about phenomena. Within the new type of mathematization at work in data science, mathematical methods are not selected because of any relevance for a problem at hand; mathematical methods are applied to a specific problem only by `forcing’, i.e. on the basis of their ability to reorganize the data for further analysis and the (...) intrinsic richness of their mathematical structure. In particular, we argue that deep learning neural networks are best understood within the context of forcing optimization methods. We finally explore the broader question of the appropriateness of data science methods in solving problems. We argue that this question should not be interpreted as a search for a correspondence between phenomena and specific solutions found by data science methods; rather, it is the internal structure of data science methods that is open to precise forms of understanding. (shrink)

As a reply to the commentary (Humphreys in Found Sci, 2012), we explore the methodological implications of seeing artificial neural networks as generic classification tools, we show in which sense the use of descriptions and models in data analysis is not equivalent to the original empirical use of epicycles in describing planetary motion, and we argue that agnostic science is essentially related to the type of problems we ask about a phenomenon and to the processes used to find answers.

As a reply to the commentary (Lenhard in Found Sci, 2012), we stress here that structural understanding of data analysis techniques is the natural counterpart to the lack of understanding of phenomena in agnostic science. We suggest moreover that the dynamics of computational processes, and their parallels with the dynamics of natural processes, will increasingly be, possibly, the driving force of the development of data analysis.

We formalize the notion of isolated objects, and we build a consistent theory to describe their evolution and interaction. We further introduce a notion of indistinguishability of distinct spacetime paths of a unit, for which the evolution of the state variables of the unit is the same, and a generalization of the equivalence principle based on indistinguishability. Under a time reversal condition on the whole set of indistinguishable paths of a unit, we show that the quantization of motion of spinless (...) elementary particles in a general potential field can be derived in this framework, in the limiting case of weak fields and low velocities. Extrapolating this approach to include weak relativistic effects, we explore possible experimental consequences. We conclude by suggesting a primitive ontology for the theory of isolated objects. (shrink)

We argue that many optimization methods can be viewed as representatives of “forcing”, a methodological approach that attempts to bridge the gap between data and mathematics on the basis of an a priori trust in the power of a mathematical technique, even when detailed, credible models of a phenomenon are lacking or do not justify the use of this technique. In particular, we show that forcing is implied in particle swarms optimization methods, and in modeling image processing problems through optimization. (...) From these considerations, we extrapolate a principle for general data analysis methods, what we call ‘Brandt’s principle’, namely the assumption that an algorithm that approaches a steady state in its output has found a solution to a problem, or needs to be replaced. We finally propose that biological systems, and other phenomena that respect general rules of morphogenesis, are a natural setting for the application of this principle. (shrink)