08/05/2019

Philosophy and science have been intertwined since antiquity.

Henri Poincaré em 1905. Fotografia: Coleção Hulton-Deutsch/Corbis

Reproduction of Marcelo Viana's column in Folha de S.Paulo.

When I was in high school in Portugal in the late 1970s, the curriculum included two compulsory subjects for everyone: Portuguese and philosophy. I believe both are still compulsory there. They opened up horizons for me that I might not have reached otherwise.

One of my favorite subjects was the philosophy of science. That's how I learned about Poincaré and his ideas about the nature of mathematical reasoning. Mathematics is a remarkable science because it is both deductive (rigorous) and inductive (knowledge-creating): all facts are logical consequences of some fundamental statements, called axioms, but theorems, like Pythagoras' theorem, say things that go far beyond the axioms.

How is this possible, where does this knowledge come from?

It was in philosophy class, not math class, that I first heard about the marvelous objects that would later be called "fractals." The word was not yet known: Benoît Mandelbrot's book "Fractal Geometry of Nature," which coined and popularized the term, was only published (in English) a few years later. But fractals had already been puzzling mathematicians and philosophers since the 19th century.

Animação mostra formação de um floco de neve de Koch. Fonte: fractalnomics.com

How could anyone not be fascinated by Koch snowflakes, where every (!) point is a "corner" with no tangent line? Ten years later I had become a researcher, and the mathematics of fractals was already one of my greatest research interests, and it still is today.

How do we acquire knowledge, and what can we know: objective reality or a mere subjective representation? The questions of epistemology helped me, years later, to better understand the meaning of quantum mechanics.

The classes encouraged me to read more about philosophical topics, and that's how I discovered the excellent "History of Western Philosophy" by Bertrand Russell, one of the books mentioned when he won the Nobel Prize in Literature in 1950.

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