Why the Glove of Mathematics Fits the Hand of the Natural Sciences So Well :How Far Down the (Fibonacci) Rabbit Hole Goes

Why does the glove of mathematics fit the hand of the natural sciences so well? Is there a good reason for the good fit? Does it have anything to do with the mystery number of physics or the Fibonacci sequence and the golden proportion? Is there a connection between this mystery (golden) number and Leibniz’s general question, why is there something (one) rather than nothing (zero)? The acclaimed mathematician G.H. Hardy (1877-1947) once observed: “In great mathematics there is a very high degree of unexpectedness, combined with inevitability and economy.” Is this also true of great physics? If so, is there a simple “preestablished harmony” or linchpin between their respective ultimate foundations? The philosopher-mathematician, Gottfried Leibniz, who coined this phrase, believed that he had found that common foundation in calculus, a methodology he independently discovered along with Isaac Newton. But what is the source of the harmonic series of the natural log that is the basis of calculus and also Bernhard Riemann’s harmonic zeta function for prime numbers? On the occasion of the three-hundredth anniversary of Leibniz’s death and the one hundredth-fiftieth anniversary of the death of Bernhard Riemann, this essay is a tribute to Leibniz’s quest and questions in view of subsequent discoveries in mathematics and physics. (In the Journal of Interdisciplinary Mathematics, Dec. 2008 and Oct. 2010, I have already sympathetically discussed in detail Riemann’s hypothesis and the zeta function in relation to primes and the zeta zeros. Both papers were republished online in 2013 by Taylor and Francis Scientific Publishers Group.)

Natureza do espaço em Leibniz e a correspondência Leibniz-Clarke

http://dx.doi.org/10.5007/1808-1711.2015v19n2p297We study the Leibnizian conception of space based upon a critical analysis of the arguments developed throughout the Leibniz–Clarke correspondence. This study is done upon the content of the correspondence originally published by Clarke in 1717 and wholly republished by H. G. Alexander in 1956. Our main goal is to show how it is possible to unfold the Leibnizian concept of space in three distinct ontological structures, each one interconnected and strongly based in the principle of preestablished harmony. These three structures anticipate ideas that were partially, at least, retaken inside some modern perspectives in physics and its philosophy. The main points discussed are: (i) the contention against the newtonian atomism and absolute space; (ii) the ontological and physical implications of the Leibnizian metaphysical principles; (iii) the problem of the symmetry; (iv) the identification of a real property of spatial extension; (v) the conception of relative space as ideal structure and (vi) the emergency of a structure of relational space founded in the real structure of spatial extension.

Gottfried Wilhelm Leibniz

Gottfried Wilhelm Leibniz (b. 1646–d. 1716) was one of the greatest of the early modern “rationalist” philosophers. He is perhaps best known to students of philosophy as an advocate of the principle of sufficient reason, the preestablished harmony of mind and body, philosophical optimism, and the doctrine of monads. While many if not all of these ideas have fallen out of favor, it is nevertheless the case that Leibniz’s arguments are deep and important and worth taking very seriously. Leibniz was an eclectic philosopher; he sought to draw out views that he thought were close to the truth and combine them in new ways to arrive at the most plausible picture of the world. It is for this reason that, while he is sympathetic to parts of the “modern” philosophy of René Descartes (b. 1596–d. 1650), Thomas Hobbes (b. 1588–d. 1679), and Benedict (Baruch) de Spinoza (b. 1633–d. 1677), he offers criticisms of it at the same time through the language and ideas of ancient and medieval philosophy. He was not just a philosopher, however, but was also a mathematician, natural philosopher, engineer, historian, lawyer, and diplomat of the first rank. As this bibliography is intended principally for students of philosophy, his other work will largely be ignored, as well as scholarship on it.

Leibniz's theory of bodies: monadic aggregates, phenomena, or both?

Leibniz's conception of bodies seems to be a puzzling theory. Bodies are seen as aggregates of monads and as wellfounded phenomena. This has initiated controversy and unending discussions. The paper attempts to resolve the apparent inconsistencies by a new and formally spirited reconstruction of Leibniz's theory of monads and perception, on the one hand, and a (re-)formulation and precisation of his concept of preestablished harmony, on the other hand. Preestablished harmony is modelled basically as a covariation between the monadic and the ideal realm.