Johann Heinrich Lambert

Johann Heinrich Lambert, or Jean-Henri Lambert (Mülhausen, August 26, 1728-Berlin, September 25, 1777), was a mathematician, physicist, German astronomer and philosopher of French origin. He showed that the number π is irrational, using the continued fraction development of tan x, which closed the possibility of being able to determine an "exact" expression (numeric fraction or quotient of two integers) for this number. He also made contributions to the development of hyperbolic geometry and astronomy, developing a method to calculate the orbits of comets and Lambert's theorem.

Life

Lambert came from a family of Huguenot refugees who had settled in Müllhausen (Alsace), a city that then belonged to the Swiss Confederation. The son of a tailor, he had six brothers. Despite the evident good school performance, the son already at the age of twelve had to drop out of school and work helping his father. But he continued his formation on his own with the help of all the books that were within his reach, studying in the afternoons. At fifteen he went to work in the steel industry and later as a bookkeeper. From 1746 he was the private secretary of the Swiss philosopher Isaak Iselin. in Basel, and, two years later, private teacher to Count Peter von Salis. in Chur. This job left him enough time to access the count's private library. It was at this time that he began in mathematical research.

Accompanying his sons, Lambert undertook various formative trips between 1756 and 1758, visiting the main intellectual centers of Europe and making contact with numerous scholars. Thus, he became a member of the Swiss Scientific Society (Société Scientifique). He published his first works in 1755.

In 1758, Lambert was living in Augsburg, where he had established himself as a publishing director. There he entered the circle of the founding members of the Electoral Academy of Sciences (Churfürstlichen Akademie der Wissenschaften), later renamed the Bavarian Academy of Sciences (Bayerische Akademie der Wissenschaften), where he entered in 1759 as a foreign member of Philosophy section. In 1764, at the proposal of the mathematician Leonhard Euler, he was made a member of the Berlin Academy of Sciences and received a highly endowed position as a Superstructure Councilor (Oberbaurat).

In the last decade of his life, he obtained the patronage of Frederick II of Prussia, and spent the rest of his life in reasonably comfortable fashion. He died in Berlin in 1777.

Scientific and philosophical work

Lambert belonged to the most outstanding mathematicians and logicians of his time. In 1959, the mathematician Georg Faber (1877-1966) wrote about Lambert:

Lambert war in Licht und Schatten das rechte Bild eines Gelehrten des 18. Jahrhunderts, der über Gott und die Welt alles mögliche schreibt, aber nicht von einem Katheder aus doziert. Unter den rund 2500 Mitgliedern, welche die [Münchner] Akademie in den zweihundert Jahren ihres Bestehens hatte, findet sich kein zweiter seinesgleichen.

Lambert was in good and bad the perfect portrait of a century scholarxviiiHe writes everything possible about God and the world, but does not teach from a Chair. Among the approximately 2500 members who were part of the [Munich] Academy in its two hundred years of existence, there is none equal to it.

Physics

Lambert established the doctrine of light intensity measurement as a science in his work Photometria, seu de mensura et gradibus luminis colorum et umbras (Augsburg, 1760). In this work he introduced the notion and the term "albedo".

He was the inventor of the first operational hygrometer and photometer. Furthermore, he researched the megaphone theory, having been hard of hearing himself since his birth.

In 1759 the first edition of his work Freye Perspective (Free Perspective) appeared, which made him widely known; the second edition appeared in 1774. This work prepared the later ones by Gaspard Monge and Jean-Victor Poncelet. He created a perspectograph named after him. Lambert's writings on perspective were edited in 1943 by Max Steck, accompanied by a detailed bibliography of all of Lambert's works.

Concerned with the representation of depth in paint and the representation of the transparency of air, Lambert discovered in 1760 the photometric law called the Beer-Lambert law, which relates light absorption to the properties of the material it passes through. He also formulated Lambert's law or Lambert's law of cosine in optics.

In 1772 he developed a special true-to-angle geographic projection, known as the Lambert conformal projection. Together with her, he developed further projections. In the same year he also published Lambert's color pyramid, which was the first three-dimensional color space.

Math

In 1761 (or else 1766),^{[citation needed]} Lambert proved the irrationality of the number π. Furthermore, he guessed that the number e and π were transcendental numbers.

He also made contributions to the development of hyperbolic geometry, being the first to introduce hyperbolic functions, in connection with the study of the theory of parallels and trigonometry. He also made conjectures (1786) about non-Euclidean space. Likewise, he formulated theorems on conic sections that simplified the calculation of the orbits of comets. He dabbled in cartography and actuarial mathematics.

The Lambert function W is named after him. Lambert first postulated it in 1758, although it was perfected by Leonhard Euler in 1783, and by George Pólya and Gábor Szegö in 1925.

Astronomy

In 1761, Lambert hypothesized that the stars near the sun were part of a group that traveled together through the Milky Way, and that there were many such groupings (star systems) throughout the galaxy. The former was later confirmed by William Herschel.

Also in 1761, taking Euler's results on the parabolic (zero-energy) trajectories of comets, he took them further by Lambert's theorem on elliptical orbits—three given positions allow one to determine the Keplerian motion of a satellite —. Numerous articles on spherical trigonomy (1770) are owed to him, although the notion of solid angle is not yet clearly defined.

In 1773, Lambert calculated the orbital coordinates of Neith, a satellite of Venus, whose observation had been validated by the community of astronomers; however, at the end of the 19th century it was proven that it did not exist.^{[citation needed]}

Lambert developed the generation theory of the universe that was similar to the nebular hypothesis that Immanuel Kant had recently published. Lambert had read The only possible foundation of a demonstration of the existence of God (1763), a work in which Kant briefly summarized his theory on the origin of the planets from a gaseous cloud. Kant's purpose was to illustrate the wisdom and purpose of God, and thus to support his existence. Initially, the philosopher had published an extended version of this theory in his General history of nature and theory about heaven (1755). Lambert was impressed by what he read in Kant's 1763 summary, and began a correspondence with Kant about the theory. Lambert soon published his own version of the protosolar nebula as a hypothesis for the origin of the Solar System.

In 1776 he founded the magazine Berliner Astronomisches Jahrbuch (Berlin Astronomical Yearbook).

Philosophy

Lambert also made important contributions to the theory of knowledge, to which he devoted his work Neues Organon, oder Gedanken über die Erforschung und Bezeichnung des Wahren (New Organon, or Thoughts on the investigation and designation of the true, 2 vols., Leipzig, 1764). The work is divided into four parts. In the first volume, there are dianology —or doctrine of the laws of thought— and alethiology —or doctrine of truth (from the Greek alétheia)—. In the second volume, semantics or semiotics —doctrine of signs— and, finally, phenomenology —a term introduced by Lambert, and by which he understands the doctrine of appearance— are dealt with. According to his own words in the "Introduction", the work would be especially inspired by Christian Wolff and John Locke, which is why in the first part, the dianoiology, he particularly sticks to the first; in fact, there are numerous similarities with Wolff's work, Vernünftige Gedanken von den Kräften des menschlichen Verstandes (Rational Thoughts on the Forces of Human Understanding, Halle, 1713). However, Lambert makes it clear that he has not limited himself to reproducing Wolff's ideas, but that he has also expanded them with his own conceptions. Part of his work was to create a new methodology for philosophy with the help of mathematics.

Lambert is considered a representative of rationalism —although he was critical of the ontology of Gottfried Leibniz and Wolff, taking Christian August Crusius's criticism even further— and an important predecessor of Kant, with whom he maintained a lively correspondence. He is also held as a forerunner of symbolic logic.

Literature

Illustration of De ichnographica campi vel regionis delineatione independenter ab omni basi perficienda (Acta Eruditorum1763).

Works by Lambert

• Remarquable propriétés de la route de la lumièreLa Haye, 1758.
• Photometria, sive de mensura et gradibus luminis, colorum et umbraeGotinga, 1760.
• Kosmologische Briefe über die Einrichtung des Weltbaues. Augsburg, 1761
• Insigniores orbitae cometarum proprietates. Gotinga, 1761.
• Neues Organon, oder Gedanken über die Erforschung und Bezeichnung des Wahren. 2 vols, Leipzig, 1764.
• Beschreibung und Gebrauch einer neuen und allgemeinen eccliptischen Tafel. Berlin, 1765.
• Beyträge zum Gebrauche der Mathematik und deren Anwendung, 2 vols, Berlin, 1765 (vol. 1) and 1770 (vol. 2).
• Anmerkungen über die Branderschen Mikrometer von Glase. Augsburg, 1769.
• Zusätze zu den logarithmischen und trigonometrischen Tabellen. Berlin, 1770.
• Anlage zur Architektonik, oder Theorie des Einfachen und Ersten in der philosophischen und mathematischen Erkenntnis. 2 vols. Riga, 1771.
• Beschreibung einer mit dem Calauschen Wachse ausgemalten Farbenpyramide. Berlin, 1772.
• Anmerkungen und Zusätze zur Entwerfung der Land- und Himmelscharten. 1772.
• Hygrometrie. Augsburg, 1774.
• Pyrometrie, oder vom Maaße des Feuers und der WÄrme. Berlin, 1779.
• Logische und philosophische Abhandlungen. Dessau, 1782-1787.
• Deutscher gelehrter Briefwechsel. Dessau, 1782-1784.
• Abhandlung über einige akustische Instrumente. Berlin, 1796 (German tradition of the original in French).
• Mémoire sur la résistance des fluides avec la solution du problème balistique (Mémoires de l'Acadèmie de Berlin pour l'année 1765). Edition of J. Corréard, Paris, 1846.

Editions

• Texte zur Systematologie und zur Theorie der wissenschaftlichen Erkenntnis. Geo Siegwart. Meiner, Hamburg, 1988 (ISBN 978-3-7873-0723-4)

Secondary literature

• A Short Account of the History of MathematicsW. W. Rouse Ball, 1908.
• Isaac Asimov, Asimov's Biographical Encyclopedia of Science and Technology, Doubleday " Co., Inc., 1972 (ISBN 0-385-17771-2).
• Ernst Cassirer, The problem of knowledge, vol. 2 (1907); Mexico D.F., FCE, 1956, 1986 (ISBN 968-16-2278-2), pp. 487-498. (Summary of the main contributions of Lambert in knowledge theory.)
• Athanase Papadopoulos and Guillaume Théret, « La théorie des parallèles de Johann Heinrich Lambert: Présentation, traduction et commentaires », Collection Sciences dans l'histoire, Librairie Albert Blanchard, Paris, 2014. ISBN 978-2-85367-266-5

Eponymy

• The Lambert, an Anglo-American luminance measurement unit.
• Lunar crater Lambert carries this name in his memory.
• Also, the Martian crater Lambert commemorates his name.
• Also called the asteroid (187) Lamberta, discovered in 1878.
• In the book City Permutation by Greg Egan is called Planet Lambert to a real world based simulation with simplified rules of physics.