TheInfoList

Daniel Bernoulli
FRS FRS may also refer to: Government and politics * Facility Registry System, a centrally managed Environmental Protection Agency database that identifies places of environmental interest in the United States * Family Resources Survey, a survey to c ...
(; – 27 March 1782) was a
Swiss Swiss may refer to: * the adjectival form of Switzerland , french: Suisse(sse), it, svizzero/svizzera or , rm, Svizzer/Svizra , government_type = Federalism, Federal semi-direct democracy under an assembly-independent Directorial ...
mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces ...

and
physicist A physicist is a scientist A scientist is a person who conducts scientific research The scientific method is an Empirical evidence, empirical method of acquiring knowledge that has characterized the development of science since at leas ...

and was one of the many prominent mathematicians in the
Bernoulli family The Bernoulli family () of Basel , french: link=no, Bâlois(e), it, Basilese , neighboring_municipalities= Allschwil (BL), Hégenheim (FR-68), Binningen, Switzerland, Binningen (BL), Birsfelden (BL), Bottmingen (BL), Huningue (FR-68), Münche ...
from Basel. He is particularly remembered for his applications of mathematics to mechanics, especially
fluid mechanics Fluid mechanics is the branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in o ...
, and for his pioneering work in
probability Probability is the branch of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained ...

and
statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a more technical sens ...

. His name is commemorated in the
Bernoulli's principle In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure, static pressure or a decrease in the fluid's potential energy. The principle is named after Daniel Bern ...
, a particular example of the
conservation of energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...
, which describes the mathematics of the mechanism underlying the operation of two important technologies of the 20th century: the
carburetor A carburetor (American English American English (AmE, AE, AmEng, USEng, en-US), sometimes called United States English or U.S. English, is the set of varieties of the English language native to the United States. Currently, American En ...

and the airplane
wing A wing is a type of fin A fin is a thin component or appendage attached to a larger body or structure. Fins typically function as foils that produce lift or thrust Thrust is a reaction (physics), reaction force (physics), force describ ...

.

# Early life

Daniel Bernoulli was born in
Groningen Groningen ( , , , ; gos, Grunn or ) is the capital city and main municipality of Groningen (province), Groningen province in the Netherlands. It is the largest city in the north of the Netherlands. As of December 2020, it had 233,218 inhabitan ...
, in the Netherlands, into a
family In human society A society is a Social group, group of individuals involved in persistent Social relation, social interaction, or a large social group sharing the same spatial or social territory, typically subject to the same Politic ...
of distinguished mathematicians.
Daniel Bernoulli and the Founding of Mathematical Economics
''
Mises Institute The Ludwig von Mises Institute for Austrian Economics, or Mises Institute, is a libertarian Libertarianism (from french: libertaire, "libertarian"; from la, libertas, "freedom") is a political philosophy Political philosophy or politi ...

'' (excerpted from ''
An Austrian Perspective on the History of Economic Thought ''An Austrian Perspective on the History of Economic Thought'' is two-volume non-fiction work written by Murray N. Rothbard. Rothbard said he originally intended to write a "standard Adam Smith-to-the-present moderately sized book"; but expanded ...
'')
The Bernoulli family came originally from Antwerp, at that time in the
Spanish Netherlands Spanish Netherlands es, Países Bajos Españoles; nl, Spaanse Nederlanden; french: Pays-Bas espagnols; german: Spanische Niederlande. (historically in Spanish: ''Flandes'', the name "Flanders" was used as a ''pars pro toto ''Pars pro toto'' (, ...

, but emigrated to escape the Spanish persecution of the
Protestant Protestantism is a form of that originated with the 16th-century , a movement against what its followers perceived to be in the . Protestants originating in the Reformation reject the Roman Catholic doctrine of , but disagree among themselves ...
s. After a brief period in Frankfurt the family moved to Basel, in Switzerland. Daniel was the son of
Johann Bernoulli Johann Bernoulli (also known as Jean or John; – 1 January 1748) was a Swiss Swiss may refer to: * the adjectival form of Switzerland , french: Suisse(sse), it, svizzero/svizzera or , rm, Svizzer/Svizra , government_type = ...

(one of the early developers of
calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations ...

) and a nephew of
Jacob Bernoulli Jacob Bernoulli (also known as James or Jacques; – 16 August 1705) was one of the many prominent mathematicians A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Ancient Greek, Greek: ) inclu ...
(an early researcher in
probability theory Probability theory is the branch of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are containe ...
and the discoverer of the mathematical constant e). He had two brothers, Niklaus and . Daniel Bernoulli was described by
W. W. Rouse Ball Walter William Rouse Ball (14 August 1850 – 4 April 1925), known as W. W. Rouse Ball, was a British mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Ancient Greek, Greek: ) ...
as "by far the ablest of the younger Bernoullis". He is said to have had a bad relationship with his father. Upon both of them entering and tying for first place in a scientific contest at the
University of Paris , image_name = Coat of arms of the University of Paris.svg , image_size = 150px , caption = , latin_name = Universitas magistrorum et scholarium Parisiensis , motto = ''Hic et ubique terrarum'' (Latin Latin (, or , ) is a classical ...
, Johann, unable to bear the "shame" of being compared Daniel's equal, banned Daniel from his house. Johann Bernoulli also plagiarized some key ideas from Daniel's book ''
Hydrodynamica ''Hydrodynamica'' (Latin for ''Hydrodynamics'') is a book published by Daniel Bernoulli in 1738.The book's full title is ''Hydrodynamica, sive de Viribus et Motibus Fluidorum Commentarii'' (Hydrodynamics, or commentaries on the forces and motio ...
'' in his own book ''Hydraulica'' which he backdated to before ''Hydrodynamica''. Despite Daniel's attempts at reconciliation, his father carried the grudge until his death. (1998) Around schooling age, his father, Johann Bernoulli, encouraged him to study business, there being poor rewards awaiting a mathematician. However, Daniel refused, because he wanted to study mathematics. He later gave in to his father's wish and studied business. His father then asked him to study in
medicine Medicine is the science Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity, awareness, or understanding of someone or something, such as facts ( descriptive knowledge), skills (proced ...

, and Daniel agreed under the condition that his father would teach him mathematics privately, which they continued for some time. Daniel studied medicine at
Basel , french: link=no, Bâlois(e), it, Basilese , neighboring_municipalities= Allschwil , neighboring_municipalities= Baselland (BL), Binningen, Switzerland, Binningen, Buschwiller (FR-68), Hégenheim (FR-68), Neuwiller (FR-68), Oberwil, Basel- ...
,
Heidelberg Heidelberg () is a university town in the German state The Federal Republic of Germany, as a federal state, consists of sixteen partly sovereign federated states (german: Land (state), plural (states); commonly informally / federated s ...

, and
Strasbourg Strasbourg (, , ; german: Straßburg ; gsw, label=Bas Rhin Bas-Rhin (; Alsatian: ''Unterelsàss'', ' or '; traditional german: links=no, Niederrhein; en, Lower Rhine) is a department Department may refer to: * Departmentalization, divi ...
, and earned a PhD in anatomy and botany in 1721. He was a contemporary and close friend of
Leonhard Euler Leonhard Euler ( ; ; 15 April 170718 September 1783) was a Swiss mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ) ...

. He went to

in 1724 as professor of mathematics, but was very unhappy there. A temporary illness together with the censorship by the
Russian Orthodox Church , native_name_lang = ru , image = Moscow July 2011-7a.jpg , imagewidth = , alt = , caption = Cathedral of Christ the Saviour The Cathedral of Christ the Saviour ( rus, Храм Хр ...

and disagreements over his salary gave him an excuse for leaving St. Petersburg in 1733. He returned to the
University of Basel The University of Basel (Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Latium. Through the power of ...
, where he successively held the chairs of
medicine Medicine is the science Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity, awareness, or understanding of someone or something, such as facts ( descriptive knowledge), skills (proced ...

,
metaphysics Metaphysics is the branch of philosophy that studies the first principles of being, identity and change, space and time, causality, necessity and possibility. It includes questions about the nature of consciousness and the relationship between ...

, and
natural philosophy Natural philosophy or philosophy of nature (from Latin ''philosophia naturalis'') was the philosophy, philosophical study of nature and the physical universe that was dominant before the development of modern science. From the ancient world, a ...
until his death. In May, 1750 he was elected a
Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a and the 's national . Found ...
.

# Mathematical work

His earliest mathematical work was the ''Exercitationes'' (''Mathematical Exercises''), published in 1724 with the help of Goldbach. Two years later he pointed out for the first time the frequent desirability of resolving a compound motion into motions of translation and motion of rotation. His chief work is ''Hydrodynamica'', published in 1738. It resembles
Joseph Louis Lagrange Joseph-Louis Lagrange (born Giuseppe Luigi Lagrangia
's ''Mécanique Analytique'' in being arranged so that all the results are consequences of a single principle, namely,
conservation of energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...
. This was followed by a memoir on the theory of the tides, to which, conjointly with the memoirs by Euler and
Colin Maclaurin Colin Maclaurin (; gd, Cailean MacLabhruinn; February 1698 – 14 June 1746) was a Scottish Scottish usually refers to something of, from, or related to Scotland, including: *Scottish Gaelic, a Celtic Goidelic language of the Indo-Europ ...
, a prize was awarded by the
French Academy French (french: français(e), link=no) may refer to: * Something of, from, or related to France France (), officially the French Republic (french: link=no, République française), is a transcontinental country This is a list of co ...
: these three memoirs contain all that was done on this subject between the publication of
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics a ...

's ''
Philosophiae Naturalis Principia Mathematica Philosophy (from , ) is the study of general and fundamental questions, such as those about existence Existence is the ability of an entity to interact with physical reality Reality is the sum or aggregate of all that is real or existen ...
'' and the investigations of
Pierre-Simon Laplace Pierre-Simon, marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French scholar A scholar is a person who pursues academic and intellectual activities, particularly those that develop expertise in an area of Studying, study. A ...

. Bernoulli also wrote a large number of papers on various mechanical questions, especially on problems connected with
vibrating strings in a string. The fundamental and the first 5 overtones in the harmonic series. A vibration in a string is a wave. Resonance causes a vibrating string to produce a sound In physics Physics (from grc, φυσική (ἐπιστή ...
s, and the solutions given by
Brook Taylor Brook Taylor (18 August 1685 – 29 December 1731) was an English mathematician best known for creating Taylor's theorem In calculus, Taylor's theorem gives an approximation of a ''k''-times differentiable function around a given poi ...
and by
Jean le Rond d'Alembert Jean-Baptiste le Rond d'Alembert (; ; 16 November 1717 – 29 October 1783) was a French mathematician, mechanician A mechanician is an engineer or a scientist working in the field of mechanics, or in a related or sub-field: engineering or com ...
. Together Bernoulli and Euler tried to discover more about the flow of fluids. In particular, they wanted to know about the relationship between the speed at which blood flows and its pressure. To investigate this, Daniel experimented by puncturing the wall of a pipe with a small open ended straw and noted that the height to which the fluid rose up the straw was related to fluid's pressure in the pipe. Soon physicians all over Europe were measuring patients' blood pressure by sticking point-ended glass tubes directly into their arteries. It was not until about 170 years later, in 1896 that an Italian doctor discovered which is still in use today. However, Bernoulli's method of measuring pressure is still used today in modern aircraft to measure the speed of the air passing the plane; that is its air speed. Taking his discoveries further, Daniel Bernoulli now returned to his earlier work on Conservation of Energy. It was known that a moving body exchanges its kinetic energy for potential energy when it gains height. Daniel realised that in a similar way, a moving fluid exchanges its specific kinetic energy for pressure, the former being the kinetic energy per unit volume. Mathematically this law is now written: : $\tfrac12 \rho u^2 + P = \text$ where P is pressure, ρ is the density of the fluid and u is its velocity.

# Economics and statistics

In his 1738 book ''Specimen theoriae novae de mensura sortis (Exposition of a New Theory on the Measurement of Risk)'', Bernoulli offered a solution to the St. Petersburg paradox as the basis of the economic theory of
risk aversion In economics Economics () is a social science Social science is the Branches of science, branch of science devoted to the study of society, societies and the Social relation, relationships among individuals within those societies ...

,
risk premium Overview A risk premium is a measure of excess return that is required by an individual to compensate them for being subjected to an increased level of risk. It is used widely in finance and economics with the general definition being the expec ...
, and
utility As a topic of economics Economics () is a social science Social science is the Branches of science, branch of science devoted to the study of society, societies and the Social relation, relationships among individuals within thos ...

. Bernoulli often noticed that when making decisions that involved some uncertainty, people did not always try to maximize their possible monetary gain, but rather tried to maximize "
utility As a topic of economics Economics () is a social science Social science is the Branches of science, branch of science devoted to the study of society, societies and the Social relation, relationships among individuals within thos ...

", an economic term encompassing their personal satisfaction and benefit. Bernoulli realized that for humans, there is a direct relationship between money gained and utility, but that it diminishes as the money gained increases. For example, to a person whose income is $10,000 per year, an additional$100 in income will provide more utility than it would to a person whose income is \$50,000 per year. One of the earliest attempts to analyze a statistical problem involving
censored dataIn statistics, censoring is a condition in which the Value (mathematics), value of a measurement or observation is only partially known. For example, suppose a study is conducted to measure the impact of a drug on mortality rate. In such a study, ...
was Bernoulli's 1766 analysis of
smallpox Smallpox was an infectious disease An infection is the invasion of an organism's body Tissue (biology), tissues by Pathogen, disease-causing agents, their multiplication, and the reaction of host (biology), host tissues to the infectious ...

morbidity A disease is a particular abnormal condition that negatively affects the structure A structure is an arrangement and organization of interrelated elements in a material object or system A system is a group of Interaction, interact ...
and
mortality Mortality is the state of being mortal, or susceptible to death; the opposite of immortality. Mortality may also refer to: * Fish mortality, a parameter used in fisheries population dynamics to account for the loss of fish in a fish stock throug ...
data to demonstrate the efficacy of
inoculation Inoculation is a set of methods of artificially inducing immunity against various infectious disease An infection is the invasion of an organism's body Tissue (biology), tissues by Pathogen, disease-causing agents, their multiplication, and ...

.

# Physics

In ''Hydrodynamica'' (1738) he laid the basis for the
kinetic theory of gases The kinetic theory of gases is a simple, historically significant classical Classical may refer to: European antiquity *Classical antiquity, a period of history from roughly the 7th or 8th century B.C.E. to the 5th century C.E. centered on the M ...

, and applied the idea to explain Boyle's law. He worked with Euler on
elasticity Elasticity often refers to: *Elasticity (physics), continuum mechanics of bodies that deform reversibly under stress Elasticity may also refer to: Information technology * Elasticity (data store), the flexibility of the data model and the clu ...
and the development of the Euler–Bernoulli beam equation.
Bernoulli's principle In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure, static pressure or a decrease in the fluid's potential energy. The principle is named after Daniel Bern ...
is of critical use in
aerodynamics Aerodynamics, from Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is appr ...
. non.(2001) "Daniel Bernoulli", ''
Encyclopædia Britannica The (Latin for "British Encyclopaedia") is a general knowledge English-language encyclopaedia which is now published exclusively as an online encyclopedia, online encyclopaedia. It was formerly published by Encyclopædia Britannica, Inc., ...
''
According to
Léon Brillouin Léon Nicolas Brillouin (; August 7, 1889 – October 4, 1969) was a French physicist A physicist is a scientist A scientist is a person who conducts scientific research The scientific method is an Empirical evidence, empirica ...
, the principle of superposition was first stated by Daniel Bernoulli in 1753: "The general motion of a vibrating system is given by a superposition of its proper vibrations."

*

# Legacy

In 2002, Bernoulli was inducted into the
International Air & Space Hall of Fame The International Air & Space Hall of Fame is an honor roll of people, groups, organizations, or things that have contributed significantly to the advancement of aerospace flight and technology, sponsored by the San Diego Air & Space Museum. Sin ...
at the
San Diego Air & Space Museum San Diego Air & Space Museum (SDASM, formerly the San Diego Aerospace Museum) is an aviation and space exploration museum in San Diego, California, San Diego, California, United States. The museum is located in Balboa Park, San Diego, California ...
.Sprekelmeyer, Linda, editor. ''These We Honor: The International Aerospace Hall of Fame''. Donning Co. Publishers, 2006. .

*
Bernoulli's principle In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure, static pressure or a decrease in the fluid's potential energy. The principle is named after Daniel Bern ...
* Euler–Bernoulli beam equation * St. Petersburg paradox *
Hydrodynamica ''Hydrodynamica'' (Latin for ''Hydrodynamics'') is a book published by Daniel Bernoulli in 1738.The book's full title is ''Hydrodynamica, sive de Viribus et Motibus Fluidorum Commentarii'' (Hydrodynamics, or commentaries on the forces and motio ...

# References

## Works cited

*(Original entry based on the
public domain The public domain consists of all the creative work A creative work is a manifestation of creativity, creative effort including Work of art, fine artwork (sculpture, paintings, drawing, Sketch (drawing), sketching, performance art), dance, wr ...

Rouse History of Mathematics Rouse may refer to: Places * Rouse, California, United States, a census-designated place * Rouse, Wisconsin, United States, an unincorporated community * Rouse Islands, Antarctica * Cape Rouse, Antarctica People * Rouse (surname) * Rouse Simmons ( ...
'') * * * * * *