Abstract
The sixteenth century in Europe began with an event that after two centuries would lead to a change in the way of conceiving things, and a desire on the part of the people to break the shackles of oppressive and impoverishing intolerances.
Lambert is an interesting case. A self-taught polymath, he took as his main line the application of mathematics to physics and even to metaphysics. As a philosopher he worked out an epistemology similar to Kant’s; as a physicist he sought effects linked by simple, general, and above all mathematical laws; as an experimentalist he advanced the quantitative study of photometry, pyrometry, hygrometry, and magnetism. He talked as an equal to Leonhard Euler and to Georg Brander, respectively the leading mathematician and the leading instrument maker in Germany. In a word, he was the perfect mathematical physicist: the mathematicians considered him an experimentalist with a ‘rare talent for applying calculation to experiments;’ the experimentalists thought him a mathematician with an unusual understanding of the behavior of instruments. All of which (we are told) he accomplished by working from five in the morning to twelve at night, with a two-hour break at noon.
—J. L. Heilbron, Elements of Early Modern Physics.
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Notes
- 1.
Although it is very likely that this was the case due to the testimonies we have from his collaborator Melanchthon and his secretary Georg Rörer, it is something that specialists still do not take for granted (see Roper (2017, pp. 11, 451 notes 2 and 3)).
- 2.
It should be noted that along with the revolt against the church there was also a peasants’ war, whom Luther initially supported, although he later retracted from this position cf. Roper (2017, Chap. 12). I am grateful to one of the anonymous reviewers for bringing this point to my attention.
- 3.
The origins of the Lambert family of Mulhouse are studied in Mieg (1939, pp. 27–30) by the historian and genealogist Philippe Mieg (if I have been able to consult this article it has been thanks to the kindness of Eliane Michelon from the Archives de Mulhouse who disinterestedly allowed me access to it); a summary can be found in Jaquel (1977, pp. 133–135). On the other hand, with regard to the historical context, I depended entirely on Parker (1997), Bergin (2001) and Oberle (1985).
- 4.
On the Holy Roman Empire see Stollberg-Rilinger (2018).
- 5.
The colony itself would be dissolved in 1623 with the arrival of Spanish troops.
- 6.
The so-called «Defenestration of Prague».
- 7.
Key step towards the Thirty Years’ War Parker (1997, p. 76).
- 8.
Oberle (1985, p. 12) who quotes Pfister, L’Alsace et l’Edit de Nantes in Revue historique, 1929 (pp. 217–240).
- 9.
It is possible that the tradition of placing the Lamberts as refugees from Lorraine (or more generally from France) comes from here, a tradition that Matthias Graf, pastor of Mülhausen and author of a reference biography on the Swiss published in 1829 on the occasion of the centenary of his birth (in Huber et al. (1829)), even situated within Lambert’s own family. An example is found in the biography of Formey on the occasion of his Eulogy on Lambert Sheynin (2010, p. 137), or in the article by Scriba (1973, p. 595) (to whom Sheynin (2010, p. 5) refers as Lambert’s modern biographer). Furthermore, the reader studying Lambert’s biography will notice how his family origins are usually placed among refugee Huguenots, although they were not really French. Philippe Mieg values this bibliographic tradition, finding in it some confirmation of what was already stated above to the effect that Lambert’s family had had contact with a Huguenot colony at Lambrecht (see Mieg (1939, pp. 26, 29)).
- 10.
In the Larousse dictionary: «In the Middle Ages and under the old regime, municipal magistrate [«magistrat», defined as «a character invested with important public functions»] in the cities of northern France, who assists the mayor [«maire», defined as «the first of those magistrates»]».
- 11.
- 12.
It will not be until 1787 that a measure of tolerance for them is restored in France (see Blanning (2000, pp. 135, 151)).
- 13.
Parker (1997, pp. 127, 128).
- 14.
Hermann (1988, p. 123).
- 15.
I use this term in a broad sense and without entering into terminological distinctions based on what place —France, England, Germany, etc.— one wants to focus on, as well as knowing that normally and without a clear consensus, it is framed in three different periods: «the long» (1688–1815), «the strict» (1700–1800) and «the short» (1715–1789) «Enlightenment» (the main source used for the historical period referred to has been Blanning (2000)).
- 16.
It must be said that the date of birth is not known for sure because at that time in Mülhausen there was no registration of birth, only of baptism (Lambert is baptized on August 29) (Jaquel 1973, p. 102). Although Jaquel says that the 26th is usually adopted as his date of birth, one finds in some biographies of the XVIII other accounts, such as the 29th in Barlow (1814), or the 28th (of April!) in Hutton (1815, p. 710). As for Lambert’s origins, in Lambertian historiography there is confusion about the nationality of the savant since on many occasions he is presented as French, German or Swiss. The Lamberts’ regions of origin were predominantly French-speaking, and they seem to have had contact with French communities in Lambrecht; furthermore, much of Alsace was dominated by the French (but not Mülhausen), it was completely French between 1798 and 1871 when it passed into German hands, and it was again from 1918, something frequently used to classify Lambert as French. On the other hand, on his father’s side he is of German origin, or at least until his great-grandfather arrived in Mülhausen from regions dominated by the Holy Roman Empire of the German Nation, and spent the last part of his life (12 years) in Germany, where he found his place (also between 1871 and 1918 Mülhausen came under German dominance, which also caused some to view Lambert as a German, in addition to the fact that his maternal language was Alsatian, a German dialect). The same would apply to the origin of his mother, her great-grandparents having been mainly Mulhousians and also Germans. Lastly, approximately the first 15 years of his life were spent in his hometown, at that time part of the Confederacy Helvetica (Switzerland). Jaquel (1973) analyzes the case in detail and comes to the conclusion that, although Mülhausen’s relationship with the Confederation was variable and the simplest and most rigorous at the same time would be to consider Lambert as Mulhousian, the most common and natural practice is to consider Mülhausen as a Swiss city. In this way, the most natural thing would also be to classify Lambert as Swiss. In this same line: Knobloch in Begehr et al. (1998, p. 5) considers Lambert Swiss, since Mülhausen in those days belonged to Switzerland until it was annexed to France; Rudolf Wolf (1816–1893) in his biography on Lambert translated from German in Sheynin (2010) adds (p. 150) that Lambert:
invariably considered himself a Swiss and until he earned any scientific title his contemporaries called him Mülhusino-Helvetus. I cannot therefore hesitate to describe that great thinker as a Swiss scientist.
Cajori (1927, p. 129 note 5) and Gray (2007, p. 84) present him as Swiss without further details; Calinger (2016) refers to him as Swiss-German (p. 643), although he clarifies that his hometown was in Switzerland (p. 427). In p. 558 note 22 he is clearer and speaks of him as Swiss.
- 17.
The data in Jaquel (1973, p. 102). In Klemme et al. (2016, p. 451) it is said that Lambert had four siblings, but it is also said (as elsewhere) that his family arrived at Mulhouse in 1635 as escaped refugees from Lorraine. By the way, and in line with what has just been said in the previous note, the title of this work shows the preference of the authors towards the German nationality of Lambert, although it would have to be said that considering him a German philosopher is a natural historiographic tendency since «he endeavored to develop a German philosophical language, and used only German in his impressive philosophical works» Jaquel (1973, p. 104).
- 18.
See Ferreirós (1995). These philosophical studies included history, mathematics, philosophy in the strict sense, physics, philology etc., of course, as they were understood at that time. To give just one example, in the eighteenth century physics was understood as «the science that teaches us the reasons and causes of all the effects that Nature produces» (Rohalt cited in Hankins (1985, pp. 10–11)), and so medicine, among others, was understood as part of physics. In fact, in the seventeenth century the physicist and the doctor were the same thing, and even today in certain languages such a connection can be traced in the designated words for a doctor (in English «physician» is defined in the Cambridge Dictionary as «a medical doctor, especially one who has general skill and is not a surgeon»).
- 19.
Sheynin (2010, p. 138). Texts referenced in Sheynin (2010) are: the Eulogy on Lambert (1780) by Johann Heinrich Samuel Formey (1711–1797), perpetual secretary of the Berlin Academy of Sciences among whose duties was to make the obituaries of the deceased members; and an 1860 biography of Johann Rudolf Wolf (1816–1893), professor of astronomy in Zurich. In what follows, and whenever appropriate, it will be made explicit which of the two is being referred to.
- 20.
Listed as a Great Comet, it was especially bright and spectacular, eventually developing a 6-tailed fan after reaching perihelion.
- 21.
Born in 1728, he studied law and philosophy at the Universities of Göttingen and Basel (he became professor of law at this latter university). A respected man, he was one of the founders of the Helvetic Society. He died in 1782 as a permanent member of the Berlin Academy.
- 22.
Wolf in Sheynin (2010, p. 151).
- 23.
Juan Arana in Lambert (1765/1767, p. 200).
- 24.
Here one can already see, as will be seen later, his intertwined vision of the different parts of science.
- 25.
He won’t marry either of them, so to speak, but in fact he will marry the two of them together (see Gray et al. (1978)).
- 26.
Lambert’s scientific diary was first edited by Karl Bopp in his Bopp (1915). Roger Jaquel, one of the great experts on Lambert, wrote in 1977 in connection with Lambert’s collected works that «the most urgent and appreciated service would consist of providing a translation, or at least a new edition of Lambert’s Monatsbuch» (Jaquel 1977, p. 95). One of Jaquel’s wishes was already fulfilled in a recent publication (Bokhove et al. 2020). It is more than desirable that an English translation be done.
- 27.
Lambert (1755). An exhaustive list of Lambert’s works can be consulted on the website Johann Heinrich Lambert (1728–1777) Collected Works—Sämtliche Werke Online written and designed by Maarten Bullynck: http://www.kuttaka.org/~JHL/Main.html. Also in the classic work by Max Steck Bibliographia Lambertiana (Steck 1970).
- 28.
The following section, and more generally the whole chapter, does not cover all of Lambert’s journeys. For a more detailed map I forward the interested reader to Jaquel (1979, pp. 52–53). Jaquel explains (pp. 50–51), that this map is a corrected version of Max Steck’s Topologische Karte der Reisen von J. H. Lambert (Topologic map of J. H. Lambert’s journeys), 1951.
- 29.
It is important to note, however, that this change was not immediate at all. In fact, up until mid-century the church was still gaining ground in some areas, and its dominance was strong in places such as France, Spain, Portugal and Hungary, making it difficult for innovative ideas to enter, whereas in other places they had already been introduced, such as in Great Britain, Holland or Prussia. Derek Beales in his chapter «Religion and culture» in Blanning (2000, pp. 131–177) makes it clear on page 133:
Among all the titles generally bestowed on the eighteenth century, ‘the Age of Religion’ and ‘the Christian Century’ are missing. They should not be, because at any rate in the first of my periods the churches were in many respects still gaining ground. But this achievement has been concealed, because historians have greatly exaggerated the immediate impact on religion of two developments of the late seventeenth century, first, the supposed ‘end of religious wars’ and, secondly, the ‘scientific revolution’ leading to what Paul Hazard entitled ‘the crisis of the European consciousness’ and dated to the years 1680 to 1715.
- 30.
Hankins (1985, p. 3). This is typical of voluntarist theology, an important view since the Middle Ages (and one opposed to rationalist theology, cf. Leibniz) (I thank J. Ferreirós for the comment).
- 31.
In fact, Lambert had already built experimental instruments to carry out his own observations, a habit that he was to maintain throughout his life.
- 32.
Foundations of differential calculus.
- 33.
The other two are: the two-volume treatise Introductio in analysin infinitorum (Introduction to the Analysis of the Infinite) in 1748, and the three-volume treatise which would arrive in 1768 Institutiones calculi integralis (Foundations of integral calculus).
- 34.
Quite a few parallels are to be noted between Mayer’s life and Lambert’s: financial difficulties (he grew up in poverty) and the loss of his father in his youth. He was also a self-taught man when learning mathematics and physics. One of the first things he excelled at before dedicating himself to astronomy was cartography, a field in which later Lambert would also make important contributions.
- 35.
Some lunar tables were of great practical interest as they made it possible to calculate longitude offshore, but it was a difficult task since, unlike the planets that are attracted to the sun, the moon is attracted also to the earth. This exercised the minds of such great savants of the day as Euler, d’Alembert and Clairaut, who faced this «Three-Body Problem», one of the three tests that Newton’s law of gravitation would have to pass for verification, together with the determination of the shape of the earth and the date of the return of Halley’s comet.
- 36.
Given the fundamental importance of Lambert’s investigations in this field, we will dedicate some lines to this issue in Appendix B.
- 37.
- 38.
Formey cited in Sheynin (2010, p. 142).
- 39.
Lambert (1758).
- 40.
Formey in Sheynin (2010, p. 142).
- 41.
Criticisms of mathematics as a useless and obscure discipline were not new. Petrus Ramus had already in 1569 published Scholarum Mathematicarum in which he examined the reason for the small esteem in which scholars held mathematics. He (like d’Alembert later on) would point to the structure and methodology of Euclid’s Elements —the classic text of mathematical instruction of the time— as the main problem (for more details see Schubring (2005, pp. 68–69) where the author claims this work by Ramus to be «the first methodological reflection on mathematics in print»). In relation to the dispute over the usefulness of mathematics around the figure of d’Alembert, see Richards (2006, pp. 702–704, 706).
- 42.
Diderot quoted in Richards (2006, p. 706).
- 43.
Richards (2006, p. 706).
- 44.
Preliminary Discourse.
- 45.
Hormigón (1994, p. 27).
- 46.
These impressions will be discussed more closely later in this chapter.
- 47.
- 48.
Lambert quoted by Wolf in Sheynin (2010, p. 153).
- 49.
The Churfürstliche Akademie der Wissenschaften (Sheynin 2010, p. 149 note 9).
- 50.
Lambert (1760). This work is usually referred as Photometry.
- 51.
Lambert (1761a).
- 52.
Olbers’ method is still used today.
- 53.
Lambert (1761b).
- 54.
In any case, although mechanism versus teleology was certainly the general trend (for example, in France they were very common ideas), it was not the only possibility. In Germany there was enormous influence from the ideas of Wolff, learned by Lambert in his first readings, and through this those of Leibniz, who argued that mechanism and teleology were not only not at odds, but that the source of mechanics were the final causes.
- 55.
Hankins (1985).
- 56.
Martín et al. (2007, p. 303).
- 57.
In letters reproduced in Sheynin (2010), comments can be found in relation to this work such as: «Lambert is Newton’s interpreter and rival» (p. 157) or « Lambert, one of the most astonishing geniuses of the 18th century» (p. 158). It is true, however, that some of those who flatter him have no qualms about criticizing him due to the lack of clarity that he shows in his writings (anyway there are divergent opinions).
- 58.
Cited by Wolf in Sheynin (2010, p. 159).
- 59.
Lambert (1764). Lambert’s philosophical work had an enormous impact, especially in Germany.
- 60.
As of July 12, 1762 Bopp (1924, p. 28). Thiébault II (1806a, p. 291) comes to say that Lambert decided to leave due to problems that had gotten him some envious rivals in the Academy. Euler seemed to be of the opinion that Lambert’s relation to the institution had worsened due to religious differences between the Protestant Swiss and the Jesuits Sheynin (2010, p. 172 note 22). The reference in Calinger (2016, p. 563 note 51) —«A Protestant, he [Lambert] could not work with the Bavarian Jesuits»— seems excessive.
- 61.
The symbols represent Mercury and the Sun respectively.
- 62.
They were modelled after the Royal Society of London (1662) and the Académie des Sciences de Paris (Parisian Academy of Sciences) (1666).
- 63.
The first to make room for other types of subjects apart from the classics that were already taught in the universities were the Pietists, who in their important educational reforms introduced novelties such as the teaching of geometry and mechanics (Blanning 2000, p. 136).
- 64.
- 65.
Calinger (2016, p. 177).
- 66.
Calinger (2016, p. 177).
- 67.
Thiébault II (1806a, p. 282).
- 68.
As of June 14, 1740 Preuss (1850, p. 391).
- 69.
Calinger (2016, p. 170). As can be seen, in some cases French escudos are mentioned —for example, in this letter or in another from Lagrange, which will be cited later— and in others, the thalers («reichsthaler») as in the case of Calinger, which is presumably the currency used for payment of salaries. Anyway, keep in mind that the equivalence at that time was 1 escudo \(=\) 1 thaler Kindleberger (2006, p. 475).
- 70.
See Calinger (2016, pp. 195, 196). Aarsleff (1989, p. 194) gives the data that around 1740, 20% of the population were Huguenots, a high percentage of whom had probably escaped from France by reason of religious persecutions —as commented at the beginning of the chapter— and had been welcomed by Frederick William I of Brandenburg, «the Grand Elector» (1620–1688), himself a Calvinist.
- 71.
His own education had been carried out by Huguenots Aarsleff (1989, p. 194).
- 72.
Quoted in Aarsleff (1989, p. 196).
- 73.
The transcript of this plenary session can be seen on the website of the Archive of the Berlin-Brandenburg Academy of Sciences and Humanities.
- 74.
Thiébault II (1806a, pp. 284–285).
- 75.
Aarsleff (1989, p. 198).
- 76.
In this regard see Cajori (1927).
- 77.
Begehr et al. (1998, pp. 1, 6).
- 78.
Calinger (2016, p. 428) writes:
In April 1761 Euler nominated Lambert to be a regular member of the Royal Academy of Sciences in Berlin, and he was unanimously elected. But late during the war Frederick, working to reestablish his control over the academy, withheld approval.
- 79.
This anecdote is reproduced in almost every biography of Lambert, so it would be interesting to see if it is possible to know of its authenticity. The closest you can get to proving it is by making use of the stories of those who had heard the opinions of the King at dinner that same day, in which he complained about Lambert’s mannerisms, or from some other member of the Academy who had heard something about the meeting. The version given here is the one reported by Dieudonne Thiébault in Thiébault II (1806a, p. 293), who by the way in Thiébault I (1806b, p. vi) says:
The first law which I prescribed to myself on entering upon this work, and from which I have never deviated even in thought, was to write with the strictest fidelity respecting the facts it should contain. I solemnly declare, no single word appears in it that has not my entire belief. Some readers will perhaps oppose to this assertion, the particular conversations which I have put into the mouths of the greater part of the persons who figure in my scene, such as Frederick, MariaTheresa, &c. As to this I can affirm that I have not only ascribed to my speakers no thoughts which were not really their own; but I can further take upon me to declare, that the very turn and way of presenting the thought is genuine and not of my own invention.
In Sheynin (2010, pp. 144, 172 note 30) other versions of the same interview can be read, the first of them by Formey in his Eulogy on Lambert —rather abbreviated— and the second by Graf, which is practically identical.
- 80.
See Cajori (1927, p. 127).
- 81.
Thiébault II (1806a, p. 290).
- 82.
It is not dated but is probably from January 1765 (Lalanne 1882, p. 142 note 1).
- 83.
As of March 1, 1765 (Holcroft 1789a, Vol. 11, pp. 20, 21).
- 84.
«It was probably also on d’Alembert’s recommendation to the king that Johann Heinrich Lambert was nominated».
- 85.
In fact, if he was not president, it was because he did not want to be, since after the death of Maupertuis in 1759, the King had offered and asked for him to be, both actively and passively.
- 86.
Such is the case of Euler who found it unacceptable (Calinger 2016, p. 431).
- 87.
As of June 16, 1769 (Lalanne 1882, p. 135).
- 88.
In any case, it must be kept in mind that a large part of Lambert’s works are written in German, which most likely diminished its reach and diffusion.
- 89.
As of July 15, 1769 (Lalanne 1882, p. 141).
- 90.
Discourse of reception by Mr. Lambert as a member of the Academy.
- 91.
Lambert (1765/1767, p. 215). This work will only appear after his death.
- 92.
Both this quote and the one to come, in Thiébault II (1806a, pp. 294–295).
- 93.
«A sort of playing cards, but marked differently from the common ones» (note by Thiébault).
- 94.
Sheynin opens a note here (included in Sheynin (2010, p. 173)) to try to throw a little light on this. The idea that can be extracted by reading the literature about it —without pretending to be better informed than Bernoulli himself— is that Lambert could have been just one more drop in a glass almost filled by a burned-out Euler. No matter how good a mathematician he was, for the king, Euler would never measure up to the like of d’Alembert or Voltaire, men with class and polished conversation. Furthermore, when Maupertuis began spending long stays outside of Berlin near the end of his life, and also since his death, Euler acted as president of the Academy, but he was never named as such despite d’Alembert’s recommendations, something that could have been felt to be a lack of recognition of their hard, brilliant and voluminous work. The king apparently distrusted the Swiss’s administrative skills, and should have blamed him for the high expenses of the Academy during war. After he ordered a commission to investigate why revenues had fallen so low —a commission led by Euler himself and in which Lambert was among its members— the tensions between them got worse. Lambert could have been a drop more, though (as pointed out by Sheynin in his note) would have been so without in the least intending to be. Calinger (2016, p. 442) says that «the idea that Lambert worked to drive Euler from Berlin is erroneous».
- 95.
As of October 11, 1766. Quoted by Wolf in Sheynin (2010, p. 164).
- 96.
Thiébault II (1806a, pp. 295, 296).
- 97.
As of August 7, 1769 (Lalanne 1882, p. 147).
- 98.
As of August 7, 1769 (Lalanne 1882, p. 147 note 1).
- 99.
As of September 14, 1769 (Lalanne 1882, p. 147 note 1).
- 100.
As of October 5, 1777 (Holcroft 1789b, Vol. 12, p. 107). The topic he proposed to discuss was the question of «whether it be useful to deceive the people», of which he said:
We have never dared to propose this great question to the French Academy, because the dissertations, sent for the prize, must, to the misfortune of reason, undergo censorship by two doctors of the Sorbonne; and because it would be impossible, with people like these, to write any thing rational. But your majesty has neither prejudices nor doctors of the Sorbonne. (as of September 22, 1777 (Holcroft 1789b, Vol. 12, p. 104))
- 101.
R. Wolf in Sheynin (2010, p. 168). These and other friends were the people closest to Lambert; he did not marry or have children.
- 102.
Formey in Sheynin (2010, p. 148).
- 103.
As of October 3, 1777 (Lalanne 1882, pp. 333–334).
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Dorrego López, E., Fuentes Guillén, E. (2024). Johann Heinrich Lambert: A Biography in Context. In: Irrationality, Transcendence and the Circle-Squaring Problem. Logic, Epistemology, and the Unity of Science, vol 58. Springer, Cham. https://doi.org/10.1007/978-3-031-52223-9_1
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