Natura non facit saltus

Natura non facit saltum

Natura non facit saltum (Latin for "nature does not make jumps") has been a principle of natural philosophy since at least Aristotle's time.^[1] It appears as an axiom in the works of Gottfried Leibniz (New Essays, IV, 16) and Isaac Newton, the co-inventors of the infinitesimal calculus,^[2] see Law of Continuity. It is also an essential element of Charles Darwin's treatment of natural selection in his Origin of Species.^[3] The phrase comes from Linnaeus' Philosophia Botanica.^[4]

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 governing equations are continuous, and also differentiable to some degree. Modern day quantum mechanics is sometimes seen as violating the principle, with its idea of a quantum leap.^[5] Erwin Schroedinger in his objections to quantum jumps supported the principle.

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.

Natura non facit saltum is the epigraph of Alfred Marshall's Principles of Economics. An admirer of Herbert Spencer, Marshall intended the epigraph both to proclaim his adherence to evolutionary thought and to justify his use of differential calculus as an analytical tool—a use seen in all the seminal thinkers of neoclassical economics.

The spelling variation (saltus vs. saltum) is because the classical Latin noun saltus, meaning leap, was often written in the grammatically simpler neuter form saltum in medieval Latin.

Variant forms

The principle is also variously referred to as:

• "Natura in operationibus suis non facit saltum" — 1613 appearance of a similar quote.^[6]
• "Natura non saltum facit" (literally, "nature does not a jump make") — variant form used by Gottfried Leibniz
• "Die Natur macht keine Sprünge" — German translation of the phrase.^[6]

See also

• In biology
  • Anagenesis
  • Cladogenesis
  • Hopeful Monster
  • Phyletic gradualism
  • Punctuated equilibrium
  • Punctuated gradualism
  • Quantum evolution
  • Stephen Jay Gould
• Continuous variation
• Continuum mechanics
• Mathematical concepts of "not making jumps"
  • Continuous function
  • Differentiable function
  • Discontinuous
  • Discrete mathematics vs mathematical analysis
  • Smooth function

References

1. ^ Scienceblogs.com, Article "Nature makes no leaps..."
2. ^ Archimedes' use of infinitesimals
3. ^ Origin of Species, 1859, p. 194
4. ^ Quotes from Gottfried Leibniz on Wikiquote
5. ^ Marxists.org and Arizona.edu
6. ^ ^{a b} Texlog.de