Linearity and nonlinearity between physics and mathematics before Poincaré.
Journal title EPISTEMOLOGIA
Author/s Angelo Marinucci
Publishing Year 2012 Issue 2012/2 Language Italian
Pages 19 P. 299-317 File size 620 KB
DOI 10.3280/EPIS2012-002009
DOI is like a bar code for intellectual property: to have more infomation
click here
Below, you can see the article first page
If you want to buy this article in PDF format, you can do it, following the instructions to buy download credits
FrancoAngeli is member of Publishers International Linking Association, Inc (PILA), a not-for-profit association which run the CrossRef service enabling links to and from online scholarly content.
The article explains why before Poincaré scientists never considered chaos, although since XVIII cent. Appeared mathematical tools and physical problems giving rise to it. The answer is in the relationship between linearity and nonlinearity concerning solutions of nonlinear and nonintegrable differential equations. Marinucci always sticks to the three body problem, showing that from Newton to Poincaré a reductionistic method lead to the two body problem plus one perturbation. He also underlines how physics and mathematics are entangled: the exactness of mathematical procedures and the physical certitude of mathematical results allowed to reach a true knowledge. Under this perspective physical reality warranted an essential linearity of nonlinear and nonintegrable differential equations. Linearity was not only a mathematical concept, but the translation of two philosophical concepts: simplicity and order in nature. In the age of algebraic analysis, differential equation was the standard of recognizability of a scientific knowledge.
Keywords: Determinism, linearity, three body problem, algebraic analysis, differential equations, reductionism.
Angelo Marinucci, Linearità e non linearità tra fisica e matematica prima di Poincaré in "EPISTEMOLOGIA" 2/2012, pp 299-317, DOI: 10.3280/EPIS2012-002009