De los principios matemáticos de Galileo a los fractales. Un enfoque desde el nuevo realismo - Carhuancho Pezo, Eder Alberto (2025)
This essay analyzes the transition from the mathematical principles of Galileo Galilei to Benoit Mandelbrot’s fractal theory, based on the approach of Markus Gabriel. For Galileo, the universe is written in the mathematical language of Euclidean geometry, reflecting a rational divine design, but he was unable to model complex phenomena such as biological systems. Fractals, coined by Mandelbrot in 1975, introduce the notion of self-similarity. From a new realist perspective, Markus Gabriel interprets reality as multiple “fields of meaning,” where fractals operate in the mathematical-aesthetic realm, but not in ethical or theological matters. The essay explores how fractals overcome Euclidean limitations, offering a new geometry of nature, and proposes a “fractal pluralism.” For Kant, fractals are synthetic a priori constructions; for Gabriel, they are real objects in their domain, but not universal. This interdisciplinary dialogue connects mathematics, philosophy and theology, showing that reality, although plural, is intelligible through its multiple domains, where order and chaos coexist.