Alexander Baumgarten
Alexander Gottlieb Baumgarten (; ; 17 July 1714 – 27 MayJan LekschasBaumgarten Family'' 1762) was a German philosopher. He was a brother to theologian Siegmund Jakob Baumgarten (1706–1757).
Biography
Baumgarten was born in Berlin as the ...
, ''Metaphysics: A Critical Translation with Kant's Elucidations'', Translated and Edited by Courtney D. Fugate and John Hymers, Bloomsbury, 2013, "Preface of the Third Edition (1750)" p. 79 n. d " aumgartenmust also have in mind Leibniz's "''natura non facit saltus'' ature does not make leaps ( NE IV, 16)." Also see Gottfried Wilhelm Leibniz, '' Nouveaux essais sur l'entendement humain'', 1704, p. 5 /ref> (
Latin
Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through ...
for "nature does not make jumps") has been an important principle of
natural philosophy
Natural philosophy or philosophy of nature (from Latin ''philosophia naturalis'') is the philosophical study of physics, that is, nature and the physical universe. It was dominant before the development of modern science.
From the ancien ...
. It appears as an axiom in the works of
Gottfried Leibniz
Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathem ...
( ''New Essays'', IV, 16: ''"la nature ne fait jamais des sauts"'', "nature does not make jumps"), one of the inventors of the
infinitesimal calculus
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of ari ...
(see
Law of Continuity
The law of continuity is a heuristic principle introduced by Gottfried 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". Kepler used ...
). It is also an essential element of
Charles Darwin
Charles Robert Darwin ( ; 12 February 1809 – 19 April 1882) was an English naturalist, geologist, and biologist, widely known for his contributions to evolutionary biology. His proposition that all species of life have descended ...
's treatment of natural selection in his '' Origin of Species''. The Latin translation comes from
Linnaeus
Carl Linnaeus (; 23 May 1707 – 10 January 1778), also known after his ennoblement in 1761 as Carl von Linné Blunt (2004), p. 171. (), was a Swedish botanist, zoologist, taxonomist, and physician who formalised binomial nomenclature, the ...
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
Continuity or continuous may refer to:
Mathematics
* Continuity (mathematics), the opposing concept to discreteness; common examples include
** Continuous probability distribution or random variable in probability and statistics
** Continuous g ...
, and also does not preclude their being differentiable (differentiability implies continuity). Modern day
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
is sometimes seen as violating the principle, with its idea of a
quantum leap
''Quantum Leap'' is an American science fiction television series, created by Donald P. Bellisario, that premiered on NBC and aired for five seasons, from March 26, 1989, to May 5, 1993. The series stars Scott Bakula as Dr. Sam Beckett, a phys ...
.
Erwin Schrödinger
Erwin Rudolf Josef Alexander Schrödinger (, ; ; 12 August 1887 – 4 January 1961), sometimes written as or , was a Nobel Prize-winning Austrian physicist with Irish citizenship who developed a number of fundamental results in quantum theo ...
in his objections to quantum jumps supported the principle, and initially developed his
wave mechanics Wave mechanics may refer to:
* the mechanics of waves
* the ''wave equation'' in quantum physics, see Schrödinger equation
See also
* Quantum mechanics
* Wave equation
The (two-way) wave equation is a second-order linear partial different ...
in order to remove these jumps.
In the biological context, the principle was used by
Charles Darwin
Charles Robert Darwin ( ; 12 February 1809 – 19 April 1882) was an English naturalist, geologist, and biologist, widely known for his contributions to evolutionary biology. His proposition that all species of life have descended ...
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. In botany in particular, the
evolutionary biology
Evolutionary biology is the subfield of biology that studies the evolutionary processes (natural selection, common descent, speciation) that produced the diversity of life on Earth. It is also defined as the study of the history of life ...
has terminology suggesting both continuous change, such as
genetic drift
Genetic drift, also known as allelic drift or the Wright effect, is the change in the frequency of an existing gene variant (allele) in a population due to random chance.
Genetic drift may cause gene variants to disappear completely and there ...
, and discontinuous variation, such as
mutation
In biology, a mutation is an alteration in the nucleic acid sequence of the genome of an organism, virus, or extrachromosomal DNA. Viral genomes contain either DNA or RNA. Mutations result from errors during DNA or viral replication, m ...
. 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:
*''Natura in operationibus suis non facit saltum'' (transl.: "Nature in its operations doesn't make a (any) jump") — 1613 appearance of a similar expression.Texlog.de /ref>
*''Natura non faciat saltus, nec ab extremo ad extremum transeat nisi per medium'' (transl.: "Nature may not make jumps, nor may it pass from extreme to extreme except by way of a mean.") — John Ray (1682).
*''Natura non saltum facit'' (literally, "Nature does not make a jump") is a variant form, sometimes attributed to Gottfried Leibniz. ''Natura non facit saltum'' is also the epigraph of
Alfred Marshall
Alfred Marshall (26 July 1842 – 13 July 1924) was an English economist, and was one of the most influential economists of his time. His book '' Principles of Economics'' (1890) was the dominant economic textbook in England for many years. I ...
's 1890 ''Principles of Economics''. He most likely borrowed the phrase from Darwin's ''The Origin of Species''. An admirer of
Herbert Spencer
Herbert Spencer (27 April 1820 – 8 December 1903) was an English philosopher, psychologist, biologist, anthropologist, and sociologist famous for his hypothesis of social Darwinism. Spencer originated the expression " survival of the f ...
, Marshall intended the epigraph both to proclaim his adherence to evolutionary thought and to justify his use of
differential calculus
In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus—the study of the area beneath a curve ...
as an analytical tool—a use seen in all the seminal thinkers of
neoclassical economics
Neoclassical economics is an approach to economics in which the production, consumption and valuation (pricing) of goods and services are observed as driven by the supply and demand model. According to this line of thought, the value of a good ...
. The spelling variation (''saltus'' vs. ''saltum'') displays a mere numeral difference; because the Latin noun '' saltus'', meaning "leap", belongs to the 4th declension; so its singular accusative is ''saltum'' (leap), while the plural is ''saltus'' (leaps).
*''Die Natur macht keine Sprünge'' —
German
German(s) may refer to:
* Germany (of or related to)
**Germania (historical use)
* Germans, citizens of Germany, people of German ancestry, or native speakers of the German language
** For citizens of Germany, see also German nationality law
**Ge ...
translation of the phrase.
See also
*In biology
**
Anagenesis
Anagenesis is the gradual evolution of a species that continues to exist as an interbreeding population. This contrasts with cladogenesis, which occurs when there is branching or splitting, leading to two or more lineages and resulting in separate ...
**
Cladogenesis
Cladogenesis is an evolutionary splitting of a parent species into two distinct species, forming a clade.
This event usually occurs when a few organisms end up in new, often distant areas or when environmental changes cause several extinctions, ...
Punctuated equilibrium
In evolutionary biology, punctuated equilibrium (also called punctuated equilibria) is a theory that proposes that once a species appears in the fossil record, the population will become stable, showing little evolutionary change for most of ...
**
Punctuated gradualism
Punctuated gradualism is a microevolutionary hypothesis that refers to a species that has "relative stasis over a considerable part of its total duration ndunderwent periodic, relatively rapid, morphologic change that did not lead to lineage bran ...
Stephen Jay Gould
Stephen Jay Gould (; September 10, 1941 – May 20, 2002) was an American paleontologist, evolutionary biologist, and historian of science. He was one of the most influential and widely read authors of popular science of his generation. Goul ...
*
Continuous variation
In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there are no abrupt changes in valu ...
*
Continuum mechanics
Continuum mechanics is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such mo ...
*Mathematical concepts of "not making jumps":
**
Continuous function
In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there are no abrupt changes in val ...
**
Differentiable function
In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable function has a non- vertical tangent line at each interior point in ...
Discrete mathematics
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuou ...
vs
mathematical analysis
Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions.
These theories are usually studied ...
**
Smooth function
In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives it has over some domain, called ''differentiability class''. At the very minimum, a function could be considered smooth if ...