Agnostic Science. Towards a Philosophy of Data Analysis

Abstract

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.

Is Big Data Enough? A Reflection on the Changing Role of Mathematics in Applications

“…By using short and evocative labels, we could say that these motifs concern, respectively, the microarray paradigm, the preeminence of historical phenomena, the conceptualization of developmental processes, and the principle of forcing, which we have introduced and partially expanded upon in [23], [24], [25], also in response to some acute commentaries in [14], [20]. Here we would like to simply focus on their rationale and potential significance in clarifying the underlying trends of quantitative, data-driven science.…”

“…Thus in [23] we have spoken of the microarray paradigm to indicate how much modern data analysis is supported by the belief that sufficiently large data collected from a phenomenon will allow…”

“…As we can see from these examples, within the microarray paradigm answers are found through a process of automatic fitting of the data to models that do not carry any structural understanding beyond the actual solution of the problem itself. This is a distinctive lack of knowledge that we wanted to emphasize in [23] by speaking of "agnostic science". The overly optimistic belief in the assumptions of the microarray paradigm was popularized in a recent cover article in Scientific American [32], where the author discusses how the collection of unprecedented amounts of data could allow the construction of a computing model to predict the future, and even earlier in the opinion piece of Chris Anderson in Wired magazine [1] which envisioned a future of atheoretical, automatic science.…”

“…Our objective in [23] was less concerned with stating that such a paradigm has gained ground or why this has happened than in uncovering its structure, and the assumptions it depends upon. Indeed, physicists often work and approach their science from a very different point of view.…”

“…But here we want to discuss a more general organizational motif: the principle of forcing, 1 which we introduced in [23]. In that paper we suggested that several disparate techniques developed to apply sophisticated mathematics to empirical problems can be brought together under a common methodological viewpoint: the idea of forcing mathematical ideas and methods on the data.…”