Why do we need theories?

Abstract

Theories organize knowledge and construct objectivity by framing observations and experiments. The elaboration of theoretical principles is examined in the light of the rich interactions between physics and mathematics. These two disciplines share common principles of construction of concepts and of the proper objects of inquiry. Theory construction in physics relies on mathematical symmetries that preserve the key invariants observed and proposed by such theory; these invariants buttress the idea that the objects of physics are generic and thus interchangeable and they move along specific trajectories which are uniquely determined, in classical and relativistic physics. In contrast to physics, biology is a historical science that centers on the changes that organisms experience while undergoing ontogenesis and phylogenesis. Biological objects, namely organisms, are not generic but specific; they are individuals. The incessant changes they undergo represent the breaking of symmetries, and thus the opposite of symmetry conservation, a central component of physical theories. This instability corresponds to the changes of the environment and the phenotypes. Inspired by Galileo's principle of inertia, the "default state" of inert matter, we propose a "default state" for biological dynamics following Darwin's first principle, "descent with modification" that we transform into "proliferation with variation and motility" as a property that spans life, including cells in an organism. These dissimilarities between theories of the inert and of biology also apply to causality: biological causality is to be understood in relation to the distinctive role that constraints assume in this discipline. Consequently, the notion of cause will be reframed in a context where constraints to activity are seen as the core component of biological analyses. Finally, we assert that the radical materiality of life rules out distinctions such as "software vs. hardware."

Keywords: Biological organization; Default state; Mathematical symmetries; Phase space.

Fig. 1

Lorenzetti, Ambrogio, L’Annonciation, 1344. Pinacoteca Nazionale, – Wikipedia.org, CC-PD-Art. A column, solid near the ground is attenuated towards the top where it overlaps and hides the vanishing axis of perspective at infinity, an explicit reference to God. In 1344, this was an extraordinary innovation: a rigorously drawn projective space. And then, by the effect of the geometry of this floor that goes from man to God, a new space is deployed: God is present in the story being told, albeit hidden, far away at infinity. The Madonna has a new human dimension: her solid, three-dimensional body accompanies the expression of a nascent humanism. Perspective introduces God as the actual limit, at infinity, therefore as the limit of a space which encompasses everything, including the human spaces which are Renewed. All of the first paintings with “prospettiva” will be annunciations, this unique locus of the meeting between infinitude and finitude according to Catholic theology (From (Longo, 2011)).