Le spectacle de la Nature est un banquet où la soupe phénoménologique se doit d'être riche en modèles mathématiques variés
Où le blogueur essaie d'argumenter sur la nécessité de comparer les différents modèles mathématiques proposés par les physiciens pour comprendre et explorer plus avant la réalité, en le faisant à sa manière habituelle* c'est-à-dire par une citation de texte:
From the times of Niels Bohr, many physicists, mathematicians and biologists have been attentive to philosophical aspects of our doing. Most of us are convinced that the frontier situation of our research can point to aspects of some philosophical relevance - if only the professional philosophers would take the necessary time to become familiar with our thinking. Seldom, however, we read something of the philosophers which can inspire us. The US-American philosopher Charles Sanders Peirce (1839-1914) is an admirable exception. In his semiotics and pragmaticist (he avoids the word “pragmatic”) thinking, he provides a wealth of ideas, spread over an immense life work. It seems to me that many of his ideas, comments, and concepts can shed light on the why and how of mathematization...The quality of a mathematical model is not how similar it is to the segment of reality under consideration, but whether it provides a flexible and goal-oriented approach, opening for doubts and indicating ways for the removal of doubts (later trivialized by Popper’s falsification claim). More precisely, Peirce claims
- Be aware of differences between different approaches!
- Try to distinguish different goals (different priorities) of modelling as precise as possible!
- Investigate whether different goals are mutually compatible, i.e., can be reached simultaneously!
- Behave realistically! Don’t ask: How well does the model reflect a given segment of the world? But ask: Does this model of a given segment of the world support the wanted and possibly wider activities / goals better than other models?
I may add: we have to strike a balance between Abstraction vs. construction, Top-down vs. bottom-up, and Unification vs. specificity. We better keep aware of the variety of Modelling purposes and the multifaceted relations between Theory - model - experiment. Our admiration for the Power of mathematization, the Unreasonable effectiveness of mathematics (Wigner) should not blind us for the Staying and deepening limitations of mathematization opposite new tasks.
Bernhelm Booss-Bavnbek,
*Remarques transtextuelles (ou portrait du blogueur en métacognition)
Quelque part dans son Moi profond, le transcyberphysicien se rêve en soldat inconnu de la guerre épistémologique que se livrent les défenseurs des différents modèles scientifiques de la gravitation quantique (théories des supercordes, gravitation quantique à boucles, piste tensorielle, géométrie spectrale non commutative...); mais à travers son discours basé essentiellement sur un usage immodéré d'extraits de ses propres lectures, il se voit aussi comme une sorte de Sancho Panza: (son Ça en somme ;-) infidèle compagnon de route virtuel d'un célèbre blogueur de sciences polémiste (et parfois triste sire) dont il relate parfois les tribulations dans le métatexte de ce blog.
