Natura non facit saltus


Natura non facit saltus has been an important principle of natural philosophy. It appears as an axiom in the works of Gottfried Leibniz, one of the inventors of the infinitesimal calculus. It is also an essential element of Charles Darwin's treatment of natural selection in his Origin of Species. The Latin translation comes from Linnaeus' Philosophia Botanica.

Overview

The principle expresses the idea that natural things and properties change gradually, rather than suddenly. In a mathematical context, this allows one to assume that the solutions of the governing equations are continuous, and also does not preclude their being differentiable. Modern day quantum mechanics is sometimes seen as violating the principle, with its idea of a quantum leap. Erwin Schrödinger in his objections to quantum jumps supported the principle, and initially developed his wave mechanics in order to remove these jumps.
In the biological context, the principle was used by Charles Darwin and others to defend the evolutionary postulate that all species develop from earlier species through gradual and minute changes rather than through the sudden emergence of new forms. Modern evolutionary biology has terminology suggesting both continuous change, such as genetic drift, and discontinuous variation, such as mutation. However, as the basic structure of DNA is discrete, nature is now widely understood to make jumps at the biological level, if only on a very small scale.

Variant forms

The principle is also variously referred to as: