Revision 1106783036 of "Daniel Bernoulli" on enwiki

{{Short description|Swiss mathematician and physicist (1700–1782)}}
{{Use dmy dates|date=April 2017}}
{{Infobox scientist
| name              = Daniel Bernoulli
| image             = Porträt des Daniel Bernoulli - edit1.jpg
| caption           = Portrait of Daniel Bernoulli (1720-1725)
| birth_date        = 8 February 1700
| birth_place       = [[Groningen (city)|Groningen]], [[Dutch Republic]]
| death_date        = 27 March 1782 (aged 82)
| death_place       = [[Basel]], [[Old Swiss Confederacy|Republic of the Swiss]]
| residence         = 
| citizenship       =
| nationality       = Swiss
| ethnicity         =
| fields            = [[Mathematics]], [[physics]], [[medicine]]
| workplaces        =
| education         = [[University of Basel]] (M.D., 1721)<br />[[Heidelberg University]]<br/ >[[University of Strasbourg]]
| thesis_title      = Dissertatio physico-medica de respiratione (Dissertation on the medical physics of respiration)
| thesis_url        = https://books.google.com/books/about/Dissertatio_inauguralis_physico_medica_d.html?id=hxVbAAAAQAAJ&redir_esc=y
| thesis_year       = 1721 
| doctoral_advisor  =
| academic_advisors =
| doctoral_students =
| notable_students  =
| known_for         = [[Bernoulli's principle]]<br>Early [[kinetic theory of gases]]<br>[[Thermodynamics]]
| influences        =
| influenced        = Bernoulli University 
| prizes            =
| footnotes         =
| signature         = Daniel Bernoulli Signature.svg
}}

'''Daniel Bernoulli''' [[Fellows of the Royal Society|FRS]] ({{IPA-de|bɛʁˈnʊli|lang}};<ref>Mangold, Max (1990). ''Duden — Das Aussprachewörterbuch''. 3. Auflage. Mannheim/Wien/Zürich, Dudenverlag.</ref> {{OldStyleDate|8 February|1700|29 January}} – 27 March 1782<ref name="NNDB">{{Cite web|url=https://www.nndb.com/people/776/000159299/|title=Daniel Bernoulli|website=Notable Names Database|access-date=14 October 2019}}</ref>) was a [[Swiss people|Swiss]] [[mathematician]] and [[physicist]]<ref name="NNDB"/> and was one of the many prominent mathematicians in the [[Bernoulli family]] from Basel. He is particularly remembered for his applications of mathematics to mechanics, especially [[fluid mechanics]], and for his pioneering work in [[probability]] and [[statistics]]. His name is commemorated in the [[Bernoulli's principle]], a particular example of the [[conservation of energy]], which describes the mathematics of the mechanism underlying the operation of two important technologies of the 20th century: the [[carburetor]] and the airplane [[wing]].

==Early life==
[[File:HYDRODYNAMICA, Danielis Bernoulli.png|thumb|right|200px|Frontpage of ''[[Hydrodynamica]]'' (1738)]]
Daniel Bernoulli was born in [[Groningen (city)|Groningen]], in the Netherlands, into a [[Bernoulli family|family]] of distinguished mathematicians.<ref name=Rothbard>[[Murray Rothbard|Rothbard, Murray]]. [https://mises.org/daily/4941/Daniel-Bernoulli-and-the-Founding-of-Mathematical-Economics Daniel Bernoulli and the Founding of Mathematical Economics], ''[[Mises Institute]]'' (excerpted from ''[[An Austrian Perspective on the History of Economic Thought]]'')</ref> 
The Bernoulli family came originally from Antwerp, at that time in the [[Spanish Netherlands]], but emigrated to escape the Spanish persecution of the [[Protestant]]s. After a brief period in Frankfurt the family moved to Basel, in Switzerland.

Daniel was the son of [[Johann Bernoulli]] (one of the early developers of [[calculus]]) and a nephew of [[Jacob Bernoulli]] (an early researcher in [[probability theory]] and the discoverer of the mathematical constant [[E (mathematical constant)|e]]).<ref name=Rothbard/> He had two brothers, [[Nicolaus II Bernoulli|Niklaus]] and [[Johann II Bernoulli|Johann II]]. Daniel Bernoulli was described by [[W. W. Rouse Ball]] as "by far the ablest of the younger Bernoullis".<ref name="ball">{{cite book |last=Rouse Ball |first=W. W. |author-link=W. W. Rouse Ball |chapter=The Bernoullis |chapter-url=http://www.maths.tcd.ie/pub/HistMath/People/Bernoullis/RouseBall/RB_Bernoullis.html |title=A Short Account of the History of Mathematics |publisher=Dover |orig-year=1908 |year=2003 |isbn=0-486-20630-0 |edition=4th |url-access=registration |url=https://archive.org/details/shortaccountofhi0000ball }}</ref> 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]], 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]]'' 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.<ref name="mactutor">{{MacTutor Biography|id=Bernoulli_Daniel}} (1998)</ref>

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]], and Daniel agreed under the condition that his father would teach him mathematics privately, which they continued for some time.<ref name="mactutor"/>  Daniel studied medicine at [[University of Basel|Basel]], [[Heidelberg University|Heidelberg]], and [[University of Strasbourg|Strasbourg]], and earned a PhD in anatomy and botany in 1721.<ref name="andhist">{{cite book|last=Anderson, John David|title=A History of Aerodynamics and its Impact on Flying Machines|publisher=Cambridge University Press|year=1997|location=New York, NY|isbn=0-521-45435-2}}</ref>

He was a contemporary and close friend of [[Leonhard Euler]].<ref>{{Cite journal|last=Calinger|first=Ronald|date=1996|title=Leonhard Euler: The First St. Petersburg Years (1727–1741)|url=https://core.ac.uk/download/pdf/82068344.pdf|journal=Historia Mathematica|volume=23|issue=2|pages=121–166|doi=10.1006/hmat.1996.0015}}</ref> He went to [[Saint Petersburg|St. Petersburg]] in 1724 as professor of mathematics, but was very unhappy there. A temporary illness<ref name="mactutor"/> together with the censorship by the [[Russian Orthodox Church]]<ref>Calinger, Ronald (1996).p.127</ref> and disagreements over his salary gave him an excuse for leaving St. Petersburg in 1733.<ref>Calinger, Ronald (1996), pp.127–128</ref> He returned to the [[University of Basel]], where he successively held the chairs of [[medicine]], [[metaphysics]], and [[natural philosophy]] until his death.<ref name="eb"/>

In May, 1750 he was elected a [[Fellow of the Royal Society]].<ref>{{cite web|url=http://www2.royalsociety.org/DServe/dserve.exe?dsqIni=Dserve.ini&dsqApp=Archive&dsqCmd=Show.tcl&dsqDb=Persons&dsqPos=0&dsqSearch=%28Surname%3D%27bernoulli%27%29 |title=Library and Archive Catalogue |publisher=Royal Society |access-date=13 December 2010 }}{{dead link|date=December 2016|bot=InternetArchiveBot |fix-attempted=yes }}</ref>

==Mathematical work==
{{refimprove|section|date=February 2018}}<!--last 3 paragraphs are not cited-->
[[File:ETH-BIB-Bernoulli, Daniel (1700-1782)-Portrait-Portr 10971.tif (cropped).jpg|thumb|Daniel Bernoulli]]
His earliest mathematical work was the ''Exercitationes'' (''Mathematical Exercises''), published in 1724 with the help of [[Christian Goldbach|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]]'s ''Mécanique Analytique'' in being arranged so that all the results are consequences of a single principle, namely, [[conservation of energy]].  This was followed by a memoir on the theory of the tides, to which, conjointly with the memoirs by Euler and [[Colin Maclaurin]], a prize was awarded by the [[French Academy]]: these three memoirs contain all that was done on this subject between the publication of [[Isaac Newton]]'s ''[[Philosophiae Naturalis Principia Mathematica]]'' and the investigations of [[Pierre-Simon Laplace]].  Bernoulli also wrote a large number of papers on various mechanical questions, especially on problems connected with [[vibrating string]]s, and the solutions given by [[Brook Taylor]] and by [[Jean le Rond d'Alembert]].<ref name="ball"/>

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.<ref>The Turner Collection, Keele University, includes Bernoulli's diagram to illustrate how pressure is measured. See also part of Bernoulli's original Latin explanation.</ref>

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 [[Scipione Riva-Rocci|an Italian doctor]] discovered [[Sphygmomanometer|a less painful method]] 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:

: <math>\tfrac12 \rho u^2 + P = \text{constant} </math>

where P is pressure, ρ is the density of the fluid and u is its velocity.<gallery>
File:Hydrodynamica-2.jpg|alt=Outer spine of Bernoulli's Hydrodynamica|A 1738 copy of Bernoulli's ''Hydrodynamica''
File:Hydrodynamica-1.jpg|alt=|First page of the first section of a 1738 copy of ''Hydrodynamica''
</gallery>

==Economics and statistics==
In his 1738 book ''Specimen theoriae novae de mensura sortis (Exposition of a New Theory on the Measurement of Risk)'',<ref>English translation in {{cite journal|journal=Econometrica|volume=22|title=Exposition of a New Theory on the Measurement of Risk|year=1954|pages=23–36|url=http://www.econ.ucsb.edu/~tedb/Courses/GraduateTheoryUCSB/Bernoulli.pdf|jstor=1909829|doi=10.2307/1909829|last1=Bernoulli|first1=D.|issue=1 }}</ref> Bernoulli offered a solution to the [[St. Petersburg paradox]] as the basis of the economic theory of [[risk aversion]], [[risk premium]], and [[utility]].<ref>[[Stanford Encyclopedia of Philosophy]]: "[http://plato.stanford.edu/entries/paradox-stpetersburg/ The St. Petersburg Paradox] by R. M. Martin</ref>  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]]", 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.{{sfnp|Cooter|Ulen|2016|pp=44–45}}

One of the earliest attempts to analyze a statistical problem involving [[censoring (statistics)|censored data]] was Bernoulli's 1766 analysis of [[smallpox]] [[morbidity]] and [[Mortality rate|mortality]] data to demonstrate the efficacy of [[inoculation]].<ref>reprinted in {{cite journal|year=2004|pmid=15334536|url=http://www.semel.ucla.edu/biomedicalmodeling/pdf/Bernoulli&Blower.pdf|title=An attempt at a new analysis of the mortality caused by smallpox and of the advantages of inoculation to prevent it|last1=Blower|first1=S|last2=Bernoulli|first2=D|volume=14|issue=5|pages=275–88|doi=10.1002/rmv.443|journal=Reviews in Medical Virology|s2cid=8169180|url-status=dead|archive-url=https://web.archive.org/web/20070927032605/http://www.semel.ucla.edu/biomedicalmodeling/pdf/Bernoulli%26Blower.pdf|archive-date=27 September 2007|df=dmy-all}}</ref>

==Physics==
In ''Hydrodynamica'' (1738) he laid the basis for the [[kinetic theory of gases]], and applied the idea to explain [[Boyle's law]].<ref name="ball"/>

He worked with Euler on [[Elasticity (physics)|elasticity]] and the development of the [[Euler–Bernoulli beam equation]].<ref>{{cite book | title=History of Strength of Materials | author-link=Stephen Timoshenko | author=Timoshenko, S. P. | orig-year=1953 | year=1983 | isbn=0-486-61187-6 | location=New York | publisher=Dover |url=https://books.google.com/books?id=tkScQmyhsb8C}}</ref> [[Bernoulli's principle]] is of critical use in [[aerodynamics]].<ref name="eb">[Anon.] (2001) "Daniel Bernoulli", ''[[Encyclopædia Britannica]]''</ref>

According to [[Léon Brillouin]], the [[Superposition principle|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."<ref>[[Léon Brillouin|Brillouin, L.]] (1946). ''Wave propagation in Periodic Structures: Electric Filters and Crystal Lattices'', McGraw–Hill, New York, p. 2.</ref>

==Works==
[[File:Bernoulli, Daniel – Pieces qui ont remporté le Prix double de l'Academie royale des sciences en 1737, 1737 – BEIC 1285085.jpg|thumb|''Pieces qui ont remporté le Prix double de l'Academie royale des sciences en 1737'']]

* {{Cite book|title=Pieces qui ont remporté le Prix double de l'Academie royale des sciences en 1737|volume=|publisher=Imprimerie Royale|location=Paris|year=1737|language=fr|url=https://gutenberg.beic.it/webclient/DeliveryManager?pid=1285085}}

==Legacy==
In 2002, Bernoulli was inducted into the [[International Air & Space Hall of Fame]] at the [[San Diego Air & Space Museum]].<ref>Sprekelmeyer, Linda, editor. ''These We Honor: The International Aerospace Hall of Fame''. Donning Co. Publishers, 2006. {{ISBN|978-1-57864-397-4}}.</ref>

==See also==
* [[Bernoulli's principle]]
* [[Euler–Bernoulli beam theory|Euler–Bernoulli beam equation]]
* [[St. Petersburg paradox]]
* [[Hydrodynamica]]

==References==
===Footnotes===
{{reflist|25em}}

===Works cited===
{{refbegin|35em}}
*(Original entry based on the [[public domain]] [[Rouse History of Mathematics]]'')
*{{Cite EB1911 |wstitle=Bernoulli |display= Bernoulli § V. Daniel Bernoulli |volume=3 |page=805}}
*{{cite book | author=Cardwell, D.S.L. | title=From Watt to Clausius: The Rise of Thermodynamics in the Early Industrial Age | location=Heinemann | publisher=London | year=1971 | isbn=0-435-54150-1 }}
*{{cite book | first1 = Robert | last1 = Cooter | author-link = Robert Cooter | first2 = Thomas | last2 = Ulen | author-link2 = Thomas Ulen | title = Law & Economics | edition = 6th | year = 2016 | location = Berkeley | publisher = Addison-Wesley | series = Berkeley Law Books | url = http://scholarship.law.berkeley.edu/books/2/ | isbn = 978-0-13-254065-0 }}
*{{cite book |first=G.K. |last=Mikhailov |chapter=Hydrodynamica |chapter-url=https://books.google.com/books?id=UdGBy8iLpocC&pg=PA131 |editor1-first=Ivor |editor1-last=Grattan-Guinness |editor1-link=Ivor Grattan-Guinness |title=Landmark Writings in Western Mathematics 1640–1940 |url=https://books.google.com/books?id=UdGBy8iLpocC |year=2005 |publisher=Elsevier |isbn=978-0-08-045744-4 |pages=131–42 }}
*{{cite journal |last1=Pacey |first1=A. J. |last2=Fisher |first2=S. J. |title=Daniel Bernoulli and the ''vis viva'' of compressed air |journal=British Journal for the History of Science |volume=3 |issue= 4|pages=388–392 |date=December 1967 |doi=10.1017/S0007087400002934 |s2cid=145513749 |url=http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=2904748&fulltextType=XX&fileId=S0007087400002934}}
* {{cite encyclopedia | last =Straub | first =Hans | title =Bernoulli, Daniel | encyclopedia = [[Dictionary of Scientific Biography]] | volume = 2 | pages =36–46  | publisher = Charles Scribner's Sons | location = New York | year = 1970 | isbn = 0-684-10114-9}}
{{refend}}

==External links==
{{Commons category}}
{{Wikiquote}}
* {{cite web | url=http://www.mathematik.ch/mathematiker/daniel_bernoulli.php | title=Bernoulli Daniel | work=Mathematik.ch | access-date=2007-09-07 }}
* [[Murray Rothbard|Rothbard, Murray]]. [https://mises.org/daily/4941/Daniel-Bernoulli-and-the-Founding-of-Mathematical-Economics Daniel Bernoulli and the Founding of Mathematical Economics], ''[[Mises Institute]]'' (excerpted from ''[[An Austrian Perspective on the History of Economic Thought]]'')
* {{ScienceWorldBiography | urlname=BernoulliDaniel | title=Bernoulli, Daniel (1700–1782)}}
* {{Gutenberg author | id=Bernoulli,+Daniel | name=Daniel Bernoulli}}
* {{Internet Archive author |sname=Daniel Bernoulli}}

{{Bernoulli family}}
{{Authority control}}
{{DEFAULTSORT:Bernoulli, Daniel}}
[[Category:1700 births]]
[[Category:1782 deaths]]
[[Category:Bernoulli family|Daniel]]
[[Category:Heidelberg University alumni]]
[[Category:18th-century Swiss physicists]]
[[Category:18th-century Latin-language writers]]
[[Category:18th-century male writers]]
[[Category:18th-century Swiss mathematicians]]
[[Category:Swiss Calvinist and Reformed Christians]]
[[Category:Mathematical analysts]]
[[Category:Fluid dynamicists]]
[[Category:Probability theorists]]
[[Category:Fellows of the Royal Society]]
[[Category:Full members of the Saint Petersburg Academy of Sciences]]
[[Category:Swiss expatriates in the Dutch Republic]]
[[Category:Scientists from Groningen (city)]]
[[Category:Swiss expatriates in Germany]]