Jacob Bernoulli Deciphered

Elart von Collani


In 1655, the theologian, natural scientist and mathematician Jakob Bernoulli was born in Basel, and passed away in 1705, again in his hometown. The 50 years of Jakob Bernoulli’s life are full of outstanding achievements, which were crowned by the introduction of Stochastics. Unfortunately, his ideas were far ahead of his time and were not understood during his life. This contribution aims to demonstrate the significance of Jakob Bernoulli’s achievements and amend some of the many misunderstandings and errors with respect to his life and work.

1 Jakob Bernoulli’s Life

In 1582, Pope Gregor XIII released a decree, in which a new calendar was introduced because the mean year of the then used Julian calendar was too long and had caused the vernal equinox to drift backwards in the calendar year. In 1584, most of the Swiss cantons including the Canton Basel replaced the Julian calendar with the Gregorian calendar and 71 years later, on the 6th of January, 1655, Jakob Bernoulli was born as the fifth child of Margarethe Schönauer and the respectable Councilman of Basel, Nikolaus Bernoulli.

The date of birth is the first misunderstanding with respect to Jakob Bernoulli. In almost all biographies the “wrong” date of 27 December 1654 is stated 1, obtained by means of the obsolete Julian calendar, which was valid in the German protestant countries until 1700.

As reported in all his biographies, Jakob’s father wanted him to become a protestant clergymen and thus, Jakob studied philosophy and theology at the University of Basel and was educated in Latin, Greek and as reported in [15] especially in Scholastic Philosophy. In 1671, he earned the degree of Magister Artium in philosophy at the age of sixteen, and in 1676, he obtained the degree of Licentiate in theology. In [1] it is reported that his sermons in the German and French language were met with approval. During these years, he autodidacticly dealt with mathematics and at the early age of eighteen, he successfully solved a difficult problema chronologica according to [15, 8].

After his graduation in 1676, Jakob Bernoulli set out on a four-year journey through Switzerland and France. He first settled in Geneva as a tutor [8], where he taught a blind girl how to write in a self-developed Braille and then went on to France, where among others he started to study the works of Descartes.

Returning to Basel in 1680, he continued to study some of the mathematical and philosophical works of Descartes and Malebranche. Subsequently, the 25 year old theologian argued emphatically against these superior authorities, as is reported in [15] and in [8].

In 1981, Jakob wrote his first scientific treatise. It deals with the Kirch comet 2, claiming that comets are eternal bodies, whose course can be calculated. The treatise was published in 1681 under the title 3 Newly discovered Method of how the path of a Comet or Tailed Star can be reduced to certain fundamental laws, and its appearance predicted, (Basel 1681), see [12]. The young theologian Jakob Bernoulli’s first publication already shows his independent and critical way of thinking, as it contradicted the theological doctrine of his time that comets were used by God to give divine hints. The publication also proves Jakob Bernoulli’s fearlessness, as publishing such ideas was not at all safe at those times. Jakob Bernoulli predicted 4 the return of the comet for 17 May 1719. The treatise also includes (see [12]) a paragraph about astrology, condemning it and asserting that astrologers are shufflers and cheats!

Immediately after the publication, he started his second journey to the Netherlands and England, which he used to complete and improve his mathematical skills. In Amsterdam, he met, among others, the mathematician Johann Hudde, a disciple of Frans van Schooten and Bernhard Fullenius, who was a leading expert in dioptrical theory, at Franeken University.

However, probably the most important encounter was the meeting with Pierre Bayle in 1681, which is mentioned in [15]. Bayle had been professor at the protestant University of Sedan until 1681. When the protestants were suppressed in France and the University of Sedan abolished, Bayle left for the Netherlands and was appointed professor of philosophy and history at the newly founded Ecole Illustre in Rotterdam. Just as Jakob Bernoulli in Basel, Bayle had written a manuscript [2] on the Kirch comet, which was published in March 1682 anonymously under the title Lettre sur la comète de 1680 5. In his article, Bayle attacks superstition and argues that a society of atheists could endure, i.e., Christianity was not a necessary means for the survival of mankind, which was a shocking idea at the time and made him suspicious to both Catholics and Protestants.

Pierre Bayle and Jakob Bernoulli, two of the most clear-sighted persons of the 17th century, came together to work on the same topic with similar aims. Unfortunately, there is no record of this meeting. Probably in reaction to the pressure exerted upon him, Jakob Bernoulli issued, while still in Holland, a second Latin edition of his treatise on the Kirch comet published [12, 15] under the title Conamen novi systematis cometarum pro motu eorum sub calculum revocando de apparitionibus praecedendis adornatum (Amsterdam 1682). Maybe as a compromise to the church authorities, he states in this second issue that only the comet’s body is eternal and, hence, cannot constitute a divine sign, but that the tail, as something fortuitous, may be left to the theologians as a sign of divine wrath [8, 12].

He left Holland for England, where he met the astronomer John Flamsteed in Greenwich. Moreover, he got to know the Natural Scientist Robert Boyle and the Natural Philosopher Robert Hooke and attended a meeting of the Royal Society [12].

In 1683, he returned to Basel and instead of accepting an appointment as clergyman in Strasbourg, he offered a course on experimenta physico-mechanica at the University of Basel. In 1684, he married Judith Stupanus. The couple had two children, a daughter who married the merchant Nikolaus Ryhinerus, and a son named Nikolaus who became a painter and a town-councillor [12]. Finally, in February 1687, he was appointed to a professorship in mathematics at Basel University.

Jakob Bernoulli was a disputatious person who did not mince his words. In 1691, he delivered a report to the local (political) authorities on various malpractices within the university 6. Although or because the charge was well-founded, the university officials felt deeply offended, and in May 1691, they brought about a decision to deprive Jakob Bernoulli of the professorship. Only after he had apologized to the university rector, the decision was withdrawn in November 1691. In 1692, shortly after this incident, Jakob Bernoulli suffered from health problems which started with a dangerous cough, followed by gout, which finally resulted in a wasting fever, such that he passed away on 16 August 1705 [1]. It is possible that these health problems were accelerated by a fierce controversy between Jakob and his younger brother Johann, which started in 1692 and openly burst out in 1694 and probably reached a climax when Johann returned to Basel in 1705 in order to take the professorship in Greek [12]. At this occasion, Jakob wrote to Leibniz that Johann had not come for the Greek, but to take his own mathematical chair and, indeed, after Jakob had passed away in August, Johann became the chair holder.

After returning from his second journey, he started to work on a topic of utmost importance, namely uncertainty. The reasons why he turned to this subject, although it seems to be farthest from mathematics, are unknown. However, it is very likely that the discussions with Bayle, Hudde and Hooke redirected his attention to the main and most difficult problem of mankind, namely uncertainty, and the young theologian, mathematician and scientist readily met the challenge to scientifically solving the related problems. The results of his endeavours are contained in Jakob Bernoulli’s masterpiece, which was published eight years after he had passed away under the title Ars conjectandi.

2 The Title Ars conjectandi

Before we look closer at the contents of Jakob Bernoulli’s masterpiece, it is worthwhile to discuss the title. Hauser [11] expresses his opinion that by choosing the programmatic title, Bernoulli aimed at putting the work in a series with the artes liberals of scholastic science 7, which had been studied by Jakob Bernoulli as propaedeutic instruction for his studies of theology.

Hauser argues that Jakob Bernoulli especially wants to address rhetoric or the ars inveniendi from which he freely took vocabulary and concepts. The original meaning of ars inveniendi or heuristics is the Art of Findings/Inventions (see [13]) by means of which not only problems can be solved, but which also leads to new knowledge. Presumably, Jakob Bernoulli wanted to indicate that his proposal represented a new scientific discipline to be applied to all levels of human society, in politics, morals and economics (in civilibus, moralibus & oeconomicis) for gaining new knowledge and solving problems.

Hauser also suggests another noteworthy reason for Jakob Bernoulli to choose the title Ars conjectandi. In 1662, the book La Logique ou l’Art de Penser was published anonymously in Paris. The authors presumably are Antoine Arnauld and Pierre Nicole, two leading Jansenists, who worked together with Blaise Pascal. The Latin title of this book is Ars cogitandi, which according to Hacking [9] was “the most successful logic book of the time and cast the mould for generations of future treatises.” The Ars cogitandi consists of four books, with the fourth one being of interest to us. Hacking calls the corresponding chapters the probabilistic chapters and explains how they deal with decision-making under uncertainty by considering the analogy to gambling and introducing explicitly the concept of a quantified probability.

Of course, Jakob Bernoulli knew this influential book and he even cites it in his masterpiece. Thus, it is an obvious conclusion that by choosing the title Ars conjectandi, Jakob Bernoulli wanted to express that his book is a continuation and a fulfilment of what had been started in the fourth book of the Ars cogitandi.

There is another hint about Jakob Bernoulli’s visions and ambitions. During his first journey, he already started to write a diary about the advances in his research, which nowadays is a most valuable source in reconstructing the development of stochastics. Its title Meditationes might be chosen as an allusion on Descartes’s masterpiece Meditationes de prima philosophia, which was published in 1641 and became one of the most influential books in Europe. In fact, after his return from from France he adopted a rather critical attitude towards Descartes. Maybe, Jakob Bernoulli had already resolved at that time to develop something which would make Descartes’s ideas obsolete and wanted to express his purpose by choosing a programmatic title.

In summary, we conclude that the title Ars conjectandi has a more symbolic meaning and should not be taken literally. It shows the closeness to the liberal arts and it announces something very new and groundbreaking. Moreover, it recalls the L’Art de Penser because it is advocating a novel way of thinking itself, which becomes necessary if the handling of uncertainty proposed by Jakob Bernoulli is adopted. The true meaning of the title can only be assessed by looking at the results presented in the Ars conjectandi.

3 Significance of the Ars conjectandi

Jakob Bernoulli was a great mathematician. A list and an appraisal of his numerous important achievements in these fields can be found in almost any of his biographies and, therefore, is omitted here. We will concentrate on that part of Jakob Bernoulli’s scientific work which he himself judged as something much more outstanding than anything which could be derived in mathematics, namely his masterpiece Ars conjectandi, which nowadays is generally regarded as an important step in the development of the mathematical branch known as probability theory.

Bernoulli’s progress over time can be pursued by means of the Meditationes. According to [3], three working periods with respect to his “discovery” can be distinguished by aims and times. The first period, which lasts from 1684 to 1685, is devoted to the study of the problems regarding the games of chance posed by Christiaan Huygens; during the second period (1685-1686) the investigations are extended to cover processes where the probabilities are not known a priori, but have to be determined a posteriori. Finally, in the last period (1687-1689), the problem of measuring the probabilities is solved.

The above timetable shows that Jakob Bernoulli started his work on this new field almost immediately after the return from his second journey, during which he had met many mathematicians, in addition to Pierre Bayle, with his fundamental criticism of religion, postulates and dogma.

Although the Ars conjectandi had been more or less completed by 1690, he left it unfinished when he passed away 15 years later in 1705. This is a remarkable fact because Jakob Bernoulli was convinced that the Ars conjectandi was by far the most important of his works, with the importance not referring to the mathematical content, but rather to the foundation of science. It dealt with uncertainty and contained the key for the quantification of uncertainty. His findings would enable science to get rid of dogma and postulates and, thus, would lead to a better world. Probably, Jakob Bernoulli knew that his contemporaries were not able to follow his ideas and, therefore, he did not want to take the risk of publishing his discoveries without presenting a convincing example. To this end, he needed quantitative information in form of data. It is known (see [3]) that two years before his death, he desperately tried to get relevant data from Leibniz. In a letter dated 3 October 1703, he asked Leibniz to let him have a treatise of Johan de Witt about the calculation of annuities, which contained the desired data. Leibniz responded with a short description of de Witt’s paper, but did not send it. In the following two years up until 1705, when he passed away, Jakob pleaded repeatedly to Leibniz (for details see [4, 7]), however, Leibniz did not satisfy his request.

Jakob Bernoulli’s “discovery” refers to the revolutionary idea to develop a method to describe and handle uncertainty scientifically. In fact as will be shown later, Bernoulli’s ideas – if accepted – could have changed not only science, but humanity. Unfortunately, his ideas, which he presented in his masterpiece Ars conjectandi, were and are not understood until our times.

He notes [4]:

For me this discovery counts more than if I had completely found the quadrature of the circle; because even if the latter could be found, it would be of very little use.

Jakob’s widow and his children knew about the significance of the Ars conjectandi and feared that someone may steal Jakob’s intellectual property. Therefore, they did not dare to let anybody have it. Finally, in 1713 eight years after Jakob Bernoulli had passed away, the Ars conjectandi was published by Jakob’s nephew Nikolaus Bernoulli, after having taken parts word by word out of it for his own dissertation entitled De Usu Artis Conjectandi in Jure which was published already in 1709.

4 Content of the Ars conjectandi

Jakob Bernoulli aimed at developing a scientific method for providing a basis for decisions in all fields of human activities. Any decision refers to an activity with a certain purpose, and the problem with decisions is the uncertainty about the future development. Therefore, it is clear that Jakob Bernoulli aimed at developing methods for dealing scientifically with uncertainty about the future development.

Moreover, the only way of reducing uncertainty about the future development is to predict the future event. However, as Bernoulli recognized correctly, only a reliable prediction can be a sound basis for a decision. Therefore, two problems had to be solved:

Clearly, the two problems represent an incredible high level of difficulty, especially at the end of the 17th century with religion still being the measure of all things. This fact must be considered as it imposed a number of external but also internal limitations on Jakob Bernoulli.

Maybe, Bernoulli got the idea for dealing with uncertainty about the future development, when studying Huygens’s problems about gambling, where uncertainty refers to the outcome of a game. Another explanation could be the poor state of Europe as a result of religious and political decisions, which were based on dogma and intolerance and against which Pierre Bayle argued so fervently.

From the point of uncertainty, the advantage with gambling is the fact that the structure of uncertainty is a priori known by the symmetric construction of the games. Each outcome of a game has the same chance of actually occurring and, therefore, the ratio of the number of favourable outcomes and the total number of outcomes constitutes a reasonable quantification of uncertainty of an event. Presumably, by means of such thoughts Bernoulli solved the problem of quantification by introducing the probability of a future event. He explains:

The probability namely is the degree of certainty and differs from it as a part from the whole.

Relating this probability to a future event yields the following quantification: The probability of a future event is the degree of certainty of its occurrence. Unfortunately, Jakob Bernoulli did not explicitly state that a probability is necessarily a property of a future event, rather he repeatedly related the word with “what has been, what is and what will be‘”. In other words, Jakob Bernoulli did not distinguish between uncertainty about facts and uncertainty about future events. This omission led to many misinterpretations of his work, as will be explained below.

Having solved the problem of quantification of uncertainty, the even more difficult problem of developing a measurement procedure for the actual but unknown value of a probability of an event had to be developed. He states that this problem does not exist in the field of gambling because of the construction of the games.

However, it is a central problem in the general case, as it is not known whether a number of favourable cases as well as a total number of cases do exist and, if the numbers should exist, they can never be assessed. At this point, Jakob Bernoulli’s genius becomes evident. He notices in Chapter IV of Part IV about the unknown numbers:

Because these and similar things depend on completely hidden causes, which, moreover, continuously deceive our knowledge by the infinite variety of their interactions, it would make no sense at all to make an attempt to investigate them directly.

These words are remarkable because of two things:

Jakob Bernoulli did not stop here, but went on. He recognized that based on objective observation or experiments it would be possible to develop a measurement procedure for the unknown value of the probability of a future event. Note that the probability of an event in a certain situation is a fact and Jakob Bernoulli had the idea to measure it by means of the random results of experiments. This idea alone would make Jakob Bernoulli one of the greatest geniuses of mankind.

Next, Jakob Bernoulli developed the anticipated measurement procedure and proved at least theoretically that it works. The remarkable thing of his measurement procedure is the fact that it was again far ahead of his time and also ahead of our time with respect to the definition of the precision and reliability of a measurement procedure. Modern metrology seems to be antediluvian when compared with Bernoulli’s advances.

He derived a measurement procedure which allows one to specify the measurement reliability given as probability of obtaining a correct result. Because of this requirement, the measurement results are necessarily sets or in the one-dimensional case intervals instead of points. Jakob Bernoulli noticed about this important feature of any reliable measurement procedure:

To avoid misunderstanding, it is to be noticed, that we obtain the probability, which we aim to determine by the observations, not exactly (otherwise we would get the converse as the probability of having determined the exact value would get less with increasing number of observations) but only approximately namely between two bounds, which, however, can be arbitrary close to one another.

However, the more precision is demanded the higher the expense to be invested for the measurement procedure.

By the way, the extremely important observation that mankind is not able to detect the truth is already indicated in the introduction of Part II of the Ars conjectandi by the following programmatic words:

The infinite diversity which is manifest in the works of nature as well as in human activities and which constitutes the universe’s extraordinary beauty cannot have any other source than the diverse combination, mixture and grouping of its parts. The set of entities which interact in generating a phenomenon or event is often so big and varied that the exploration of all ways that may lead or not lead to its combination or mixture encounters the greatest difficulties.
Thus, it is not surprising that even the most intelligent and prudent persons commit no error more often than that which in logic is called insufficient enumeration of parts. Thus, I have no doubts to claim that this error is almost the only source of infinite many of the most severe mistakes, which we commit every day in our efforts to discover and utilize the things.

In other words, Jakob Bernoulli had realized that the wrong decisions which are made everywhere at every time are in their majority due to the fact that man tends to assume to have truth, although this is impossible. Jakob Bernoulli not only wanted to state this fact, but intended to replace the subjective traditional approach by an objective approach, which is provided without belief and opinion. Thus, finally we have found the aim of Jakob Bernoulli’s masterpiece Ars conjectandi, which he himself expressed in the following way, where the literal translation is replaced by taking into account the above elaborated aims and intentions of Jakob Bernoulli:

To predict something is to measure its probability. The Science of Prediction or Stochastics is therefore defined as the science of measuring as exactly as possible the probabilities of events so that in our decisions and actions we can always choose or follow that which seems to be better, more satisfactory, safer and more considered. In this alone consists all the wisdom of the Philosopher and the prudence of the Statesman.

Jakob Bernoulli intended to develop a Science of Prediction for providing mankind with better means in their decision-making processes. He states in the introduction of Part II that without the methods developed in the Ars conjectandi neither the wisdom of philosophers, nor the accuracy of the historians, nor the diagnosis of the physicians, nor the prudence of the politicians can persist.

5 Misinterpretations of the Ars conjectandi

There are many fundamental misunderstandings with respect to the Ars conjectandi. The first one refers to its aim. It is thought to be a decisive step towards the development of mathematics by laying the basis for the theory of probability. This wrong idea goes probably back to Jakob Bernoulli’s contemporaries, who considered him as one of the greatest mathematicians of his time. The idea became firmly established in 1865 when Isaac Todhunter published his book A History of the Mathematical Theory of Probability. Since then, it was not any more questioned, but taken as a proven fact.

The second misinterpretation concerns the concept of probability. Because Jakob Bernoulli fails to define it in a clear way, it is often looked upon as a measure of evidence. This results in two controversial interpretations of probability, a so-called objective one and a subjective one. The two interpretations led to the development of two different statistical sciences, namely the classical statistics following the frequency approach, and Bayes statistics following a subjective approach, both in opposition to each other similar to religious sects.

The most striking and most unjustified assertion, however, is the claim that Bernoulli’s measurement procedure represents the first limit theorem in probability theory. Bernoulli never aimed at deriving a limit theorem but, in fact, aimed at the exact opposite and this is expressed explicitly in the Ars conjectandi (see citation above).

Thus, none of the eminent results presented in the Ars conjectandi survived the death of Jakob Bernoulli. Instead of Jakob Bernoulli’s masterpiece, two other publications became relevant for the further development of the field dealing with uncertainty, namely Montmort’s Essay d’analyse sur les jeux de hazard, which appeared in 1708 and, especially, Abraham de Moivre’s treatise De mensura sortis: Seu de Probabilitate Eventuum in Ludis a Casu Fortuito Pendentibus of 1711 and its extended version The Doctrine of Chances: or, a Method of Calculating the Probability of Events in Play of 1718. The only item which Montmort and de Moivre took over from Jakob Bernoulli was the term probability, which in all the previous publications on gambling did not appear. In the preface of the first edition of de Moivre’s masterpiece The Doctrine of Chance, de Moivre expresses very clearly his thoughts about Jakob Bernoulli’s attempt to develop a science of prediction. De Moivre states:

Before I make an end of this Discourse, I think myself obliged to take Notice that some years after my Specimen was printed, there came out a Tract upon the Subject of Chance, being a posthumous Work of James Bernoully, wherein the Author has shown a great deal of Skill and Judgement, and perfectly answered the Character and great Reputation he hath so justly obtained. I wish I were capable of carrying on a Project he had begun, of applying the Doctrine of Chances to ‘Oeconomical’ and ‘Political’ Uses, to which I have been invited, together with Mr. de Montmort, by Mr. Nicholas Bernoully: I heartily thank that Gentleman for the good opinion he has of me; but I willingly resign my share of that task into better Hands, wishing that either he himself would prosecute that Design, he having formerly published some successful Essays of that Kind, or that his Uncle, Mr. John Bernoully, Brother of the Deceased, could be prevailed upon to bestow some of his Thought upon it; he being known to be perfectly well qualified in all Respects for such an Undertaking.

In the later editions of the Doctrine of Chance, even this short mentioning of Jakob Bernoulli is abandoned. Abraham de Moivre’s unambiguous refusal to carry on Jakob Bernoulli’s work clearly shows that Jakob’s ideas had passed away with him.

6 Summary

The 17th century was marked by religious wars and religious intolerance, founded on postulates and dogma. Pierre Bayle was one of the most ardent and eloquent fighters against dogma and in favour of tolerance. However Bayle, being a philosopher and theologian was not able to develop formal means for overcoming human subjectivity and human limitations. Jakob Bernoulli on the other hand was not only a philosopher and theologian, but additionally a mathematician. Maybe the short encounter of these two eminent men had made Jakob start to think of what had to be changed in order to guarantee better decisions. When he looked at the problems on gambling he almost immediately must have had the idea to extend the quantification from the trivial case of gambling to the general case of uncertainty. Subsequently, Jakob Bernoulli developed stochastics and hoped that it would help to improve the decision-making processes on all levels of human society and, thus, would lead the way out of the poor state of human societies. Since that time, the situation became worse and therefore it is high time to change from a subjective approach to an objective one as developed and proposed by Jakob Bernoulli.

Jakob Bernoulli had ‘reached for the stars’ and had success in sight when he met his fate. It is with foresight that he requested that Eadem Mutata Resurgo (Though changed I shall arise the same), should be engraved on his tombstone.

[1] Allgemeine Deutsche Biographie, Band 2, Leipzig, 1875.
[2] Bayle, Pierre (2005): A Philosophical Commentary of These Words of the Gospel, Luke 14.23, “Compel Them to Come In. That My House May be Full.” Edited, with an Introduction by John Kilcullen and Chandran Kukathas. Liberty Fund, Indianapolis.
[3] Bernoulli, Jakob (1975): Die Werke von Jakob Bernoulli. Herausgegeben von der Naturforschenden Gesellschaft in Basel. Band 3, Birkhäuser, Basel.
[4] Bernoulli, Jakob (1899): Wahrscheinlichkeitsrechnung. Übersetzt und herausgegeben von B. Haussner. Leipzig.
[5] v. Collani, Elart (Ed.) (2004): Defining the Science of Stochastics. Herdermann, Lemgo.
[6] v. Collani, Elart (2004): History, State of the Art and Future of Stochastics. In: History of the Mathematical Sciences. Eds. Ivor Grattan-Guinness and B.S. Yadav. Hindustan Book Agency, New Delhi.
[7] v. Collani, Elart (2005): 2005 - The Jakob Bernoulli Year, 350th Anniversary of Jakob’s Birth and 300th Anniversary of Jakob’s Death. Economic Quality Control 20, 155-169.
[8] de Fontenelle, Bernard (1705): Éloge de Jaques Bernoulli. Histoire de l’Académie royale des sciences, Paris.
[9] Hacking, Ian (1975): The Eemergence of Probability. Cambridge University Press, London.
[10] Hald, Anders (1990): A History of Probability and Statistics and their Applications before 1750. Wiley, New York.
[11] Hauser, Walter (1997): Die Wurzeln der Wahrscheinlichkeitsrechnung. Franz Steiner Verlag, Stuttgart.
[12] Pearson, Karl (1978): The History of Statistics in the 17th and 18th Century. Ed. by E.S. Pearson, Charles Griffin, London.
[13] Peckhaus, Volker (1999): Abduktion und Heuristik. In: Rationalität, Realismus, Revision. Vorträge des 3. Internationalen Kongresses der Gesellschaft für Analytische Philosophie ed. by Julian Nida-Rümelin. Walter de Gruyter: Berlin/New York, 833-841.
[14] Todhunter, Isaac (1865): A History of the Mathematical Theory of Probability. From the Time of Pascal to that of Laplace. Macmillan, Cambridge.
[15] Zedler, Johann Heinrich (Ed.) (1733): Großes Universal-Lexikon aller Wissenschaften und Künste, Band 4, Halle.

Elart von Collani
University of Würzburg
Sanderring 2
D-97070 Würzburg

1Maybe all the biographers took the date from Bernard de Fontenelle’s “ Éloge de Jacques Bernoulli” already published in 1705 in Histoire de l’Académie royale des sciences in Paris. The reason why Fontenelle stated a wrong date, although France had adopted the Gregorian calendar in 1582, is unknown to the author.

2This comet was discovered 14 November 1680 by the astronomer Gottfried Kirch in Coburg. It remained visible until 19 March 1681 and had an extraordinarily long tail and was looked upon as a sign of divine anger [12].

3The treatise was written in German and the complete title is as follows: “Neu-erfundene Anleitung, wie man den Lauff des Comet- oder Schwantz-Sternen in gewisse grundmässige Gesätze einrichten und ihre Erscheinung vorhersagen könne auß Anlaß des jüngst-entstandenen Cometens im Jahr 1680 und 1681 alles mit geometrischen Gründen dargethan und bewiesen, sampt angehencktem Prognostico”

4Voltaire notes sarcastically in his Letters on England, Letter XV On Attraction: “The guessing the course of comets began then to be very much in vogue. The celebrated Bernoulli concluded by his system that the famous comet of 1680 would appear again the 17th of May, 1719. Not a single astronomer in Europe went to bed that night. However, they needed not to have broke their rest, for the famous comet never appeared.”

5In 1683, an extended version was published under the title “Pensées diverses sur la comète de 1680.”

6Among others he complained [12, 1] about the corrupt way of appointments to the better paid university chairs and proposed that all professorships should be paid alike.

7The seven liberal arts comprised two groups, namely the trivium and the quadrivium. The trivium involved grammar, dialectic (logic), and rhetoric, while the quadrivium involved arithmetic, music, geometry, and astronomy. There were four faculties in medieval universities and the liberal arts were taught in the first one Facultas Artium. The other faculties (law, medicine and theology) were considered the scientific ones and had a higher status. The liberal arts originally represented the kinds of skills and general knowledge needed by the elite echelon of society.


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