Natura non facit saltus
Encyclopedia
Natura non facit saltum (Latin for "nature does not make jumps") has been a principle of natural philosophy since at least Aristotle
's time. 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
, see Law of Continuity
. It is also an essential element of Charles Darwin
's treatment of natural selection in his Origin of Species. The phrase comes from Linnaeus
' Philosophia Botanica
.
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. 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
.
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
's time. It appears as an axiom in the works of Gottfried Leibniz
Gottfried Leibniz
Gottfried Wilhelm Leibniz was a German philosopher and mathematician. He wrote in different languages, primarily in Latin , French and German ....
(New Essays
New Essays on Human Understanding
New Essays on Human Understanding is a chapter-by-chapter rebuttal by Gottfried Leibniz of John Locke's major work, An Essay Concerning Human Understanding. It is one of only two full-length works by Leibniz...
, IV, 16) and Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
, the co-inventors of the infinitesimal calculus
Infinitesimal calculus
Infinitesimal calculus is the part of mathematics concerned with finding slope of curves, areas under curves, minima and maxima, and other geometric and analytic problems. It was independently developed by Gottfried Leibniz and Isaac Newton starting in the 1660s...
, see Law of Continuity
Law of Continuity
The Law of Continuity is a heuristic principle introduced by Leibniz based on earlier work by Nicholas of Cusa and Johannes Kepler. It is the principle that "whatever succeeds for the finite, also succeeds for the infinite"...
. It is also an essential element of Charles Darwin
Charles Darwin
Charles Robert Darwin FRS was an English naturalist. He established that all species of life have descended over time from common ancestry, and proposed the scientific theory that this branching pattern of evolution resulted from a process that he called natural selection.He published his theory...
's treatment of natural selection in his Origin of Species. The phrase comes from Linnaeus
Carolus Linnaeus
Carl Linnaeus , also known after his ennoblement as , was a Swedish botanist, physician, and zoologist, who laid the foundations for the modern scheme of binomial nomenclature. He is known as the father of modern taxonomy, and is also considered one of the fathers of modern ecology...
' Philosophia Botanica
Philosophia Botanica
Philosophia Botanica was published by the Swedish naturalist and physician Carolus Linnaeus who greatly influenced the development of botanical taxonomy and systematics in the 18th and 19th centuries. It is "the first textbook of descriptive systematic botany and botanical Latin"...
.
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
Continuous function
In mathematics, a continuous function is a function for which, intuitively, "small" changes in the input result in "small" changes in the output. Otherwise, a function is said to be "discontinuous". A continuous function with a continuous inverse function is called "bicontinuous".Continuity of...
, and also differentiable to some degree. Modern day quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
is sometimes seen as violating the principle, with its idea of a quantum leap. Erwin Schroedinger in his objections to quantum jumps supported the principle.
In the biological context, the principle was used by Charles Darwin
Charles Darwin
Charles Robert Darwin FRS was an English naturalist. He established that all species of life have descended over time from common ancestry, and proposed the scientific theory that this branching pattern of evolution resulted from a process that he called natural selection.He published his theory...
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
Genetic drift
Genetic drift or allelic drift is the change in the frequency of a gene variant in a population due to random sampling.The alleles in the offspring are a sample of those in the parents, and chance has a role in determining whether a given individual survives and reproduces...
, and discontinuous variation, such as mutation
Mutation
In molecular biology and genetics, mutations are changes in a genomic sequence: the DNA sequence of a cell's genome or the DNA or RNA sequence of a virus. They can be defined as sudden and spontaneous changes in the cell. Mutations are caused by radiation, viruses, transposons and mutagenic...
. However, as the basic structure of DNA
DNA
Deoxyribonucleic acid is a nucleic acid that contains the genetic instructions used in the development and functioning of all known living organisms . The DNA segments that carry this genetic information are called genes, but other DNA sequences have structural purposes, or are involved in...
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
Epigraph (literature)
In literature, an epigraph is a phrase, quotation, or poem that is set at the beginning of a document or component. The epigraph may serve as a preface, as a summary, as a counter-example, or to link the work to a wider literary canon, either to invite comparison or to enlist a conventional...
of Alfred Marshall
Alfred Marshall
Alfred Marshall was an Englishman and one of the most influential economists of his time. His book, Principles of Economics , was the dominant economic textbook in England for many years...
's Principles of Economics. An admirer of Herbert Spencer
Herbert Spencer
Herbert Spencer was an English philosopher, biologist, sociologist, and prominent classical liberal political theorist of the Victorian era....
, Marshall intended the epigraph both to proclaim his adherence to evolutionary thought and to justify his use of differential calculus
Differential calculus
In mathematics, differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus....
as an analytical tool—a use seen in all the seminal thinkers of neoclassical economics
Neoclassical economics
Neoclassical economics is a term variously used for approaches to economics focusing on the determination of prices, outputs, and income distributions in markets through supply and demand, often mediated through a hypothesized maximization of utility by income-constrained individuals and of profits...
.
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
Medieval Latin
Medieval Latin was the form of Latin used in the Middle Ages, primarily as a medium of scholarly exchange and as the liturgical language of the medieval Roman Catholic Church, but also as a language of science, literature, law, and administration. Despite the clerical origin of many of its authors,...
.
Variant forms
The principle is also variously referred to as:- "Natura in operationibus suis non facit saltum" — 1613 appearance of a similar quote.
- "Natura non saltum facit" (literally, "nature does not a jump make") — variant form used by Gottfried Leibniz
- "Die Natur macht keine Sprünge" — GermanGerman languageGerman is a West Germanic language, related to and classified alongside English and Dutch. With an estimated 90 – 98 million native speakers, German is one of the world's major languages and is the most widely-spoken first language in the European Union....
translation of the phrase.
See also
- In biologyBiologyBiology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...
- AnagenesisAnagenesisAnagenesis, also known as "phyletic change," is the evolution of species involving an entire population rather than a branching event, as in cladogenesis. When enough mutations have occurred and become stable in a population so that it is significantly differentiated from an ancestral population,...
- CladogenesisCladogenesisCladogenesis is an evolutionary splitting event in a species in which each branch and its smaller branches forms a "clade", an evolutionary mechanism and a process of adaptive evolution that leads to the development of a greater variety of sister species...
- Hopeful Monster
- Phyletic gradualismPhyletic gradualismPhyletic gradualism is a model of evolution which theorizes that most speciation is slow, uniform and gradual. When evolution occurs in this mode, it is usually by the steady transformation of a whole species into a new one...
- Punctuated equilibriumPunctuated equilibriumPunctuated equilibrium is a theory in evolutionary biology which proposes that most species will exhibit little net evolutionary change for most of their geological history, remaining in an extended state called stasis...
- Punctuated gradualismPunctuated gradualismPunctuated gradualism is a microevolutionary hypothesis that refers to a species that has "relative stasis over a considerable part of its total duration [and] underwent periodic, relatively rapid, morphologic change that did not lead to lineage branching"....
- Quantum evolutionQuantum evolutionQuantum evolution is a component of George Gaylord Simpson's multi-tempoed theory of evolutionary change, proposed to explain the rapid emergence of higher taxonomic groups. According to Simpson, evolutionary rates differ from group to group and even among closely related lineages...
- Stephen Jay GouldStephen Jay GouldStephen Jay Gould was an American paleontologist, evolutionary biologist, and historian of science. He was also one of the most influential and widely read writers of popular science of his generation....
- Anagenesis
- Continuous variation
- Continuum mechanicsContinuum mechanicsContinuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modelled as a continuous mass rather than as discrete particles...
- MathematicalMathematicsMathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
concepts of "not making jumps"- Continuous functionContinuous functionIn mathematics, a continuous function is a function for which, intuitively, "small" changes in the input result in "small" changes in the output. Otherwise, a function is said to be "discontinuous". A continuous function with a continuous inverse function is called "bicontinuous".Continuity of...
- Differentiable functionDifferentiable functionIn calculus , a differentiable function is a function whose derivative exists at each point in its domain. The graph of a differentiable function must have a non-vertical tangent line at each point in its domain...
- Discontinuous
- Discrete mathematicsDiscrete mathematicsDiscrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not...
vs mathematical analysisMathematical analysisMathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions... - Smooth functionSmooth functionIn mathematical analysis, a differentiability class is a classification of functions according to the properties of their derivatives. Higher order differentiability classes correspond to the existence of more derivatives. Functions that have derivatives of all orders are called smooth.Most of...
- Continuous function