When Lejeune Dirichlet, at 23 years of age, worked with Alexander von Humboldt in making microscopic measurements of the motions of a suspended bar-magnet in a specially-built hut in Abraham Mendelssohn's garden, he could hear, nearby in the garden-house, the Mendelssohn youth movement working through the voicing of J. S. Bach's "St. Matthew's Passion." Felix and Fanny Mendelssohn, 19 and 23, were the leaders of a group of sixteen friends that would meet every Saturday night in 1828 to explore this `dead' work, unperformed since its debut a century earlier by Bach.[1]

The two simultaneous projects in the Mendelssohn garden at 3 Leipziger Strasse (in Berlin) are a beautiful example of Plato's classical education necessary for the leaders of a republic: The astronomer's eyes and the musician's ears worked in counterpoint for the higher purpose of uniquely posing to the human mind {how the mind itself worked}. As described in the {Republic}, Book 7, the paradoxes of each `field' - paradoxes (such as the 'diabolus') that, considered separately, tied up in knots the 'professionals' in each field - taken together would triangulate for the future statesman the type of problems uniquely designed to properly exercise the human mind. After all, such a mind would have to master more than astronomy and music, simply to bring before the mind the series of paradoxes, so as to be made capable for dealing with the much more complicated dealings of a human society. To oversimplify, since the mind does not come equipped with a training manual, the composer of the universe created the harmonies of the heavens and of music as, e.g., a mobile above a baby's crib.

In that hut, Dirichlet would have been making microscopic measurements as part of making a geo-magnetic map of the earth. The audacity in thinking that these miniscule motions of the suspended bar-magnet could capture such unseen properties, posed certain appropriate questions to Dirichlet. (Gauss' geodetic surveying a decade earlier was paradigmatic of the sort of project that mined such riches out of the ostensibly simple affair, e.g., of determining where one actually was! But this also applies to locating oneself in the process of a proper daily political-intelligence briefing.) Similarly, the sixteen youth working to solve amongst themselves the complicated inter-relationships of Bach's setting of the "Passion" story, as related by St. Matthew, would have forced their grappling with the scientific problem of ascertaining what our Maker would have in store for us, in their attempt to map their own souls. (Just for starters, regarding their `performance' questions: How does Jesus intone what he says? How does the chorus/audience respond to Jesus, and sometimes to each other? etc.) The following historical sketch is offered as a few measurements, but instead of using a suspended magnetic bar, we'll use a few years of Dirichlet's life, and thereby try to triangulate some of the important characteristics for a map of the culture that created the world that, today, we are challenged to master. Humboldts and Mendelssohns

Dirichlet's patron, Alexander von Humboldt, along with his brother Wilhelm, had studied in the 1780's with a host of pro-American Revolution leaders in Europe, notably including the Mendelssohn's famous grandfather, Moses. (These particular studies can be investigated by reading Moses Mendelssohn's Leibnizian work, {Morgenstunden}, or {Morning-Studies}, which describe the lessons that Moses gave to his son Joseph, and to the Humboldt youth.) Later, two of Moses' sons, Joseph and Abraham, ran the Mendelssohn Bank, which financed many of Alexander von Humboldt's scientific expeditions and projects. Abraham Mendelssohn, the father of Fanny, Felix, Rebecca and Paul, had set up, in his garden at 3 Leipziger Strasse, a special magnetically-neutral observation hut for Humboldt to measure minute magnetic fluctuations. Humboldt brought Dirichlet to Berlin in 1828, where he was one of the five or six who shared observational duties with Humboldt, in their mapping of the actual geo-magnetic shape and potential of the earth.

In 1827/8, Humboldt gave public lectures at the Singakademie Hall on physical geography - deliberately open to both men and women. Fanny Mendelssohn commented (in a letter to her friend Klingemann): "[T]he course is infinitely interesting. Gentlemen may laugh at us as much as they will; it is wonderful in this day and age for us to have an opportunity to hear something sensible, for once I must further inform you that we are attending a second lecture series, given by a foreigner on experimental physics. This course, too, is being attended mainly by women." Humboldt's presentations on his investigations of the earth were special public versions of his lecture-course at Berlin's famous Friedrich Wilhelm University (established in the previous decade by his brother, Wilhelm von Humboldt).

Felix Mendelssohn attended the University at the same time that a collaborator of Humboldt at the University, Phillip August Boeckh, the great philologist, lived as a tenant in the Mendelssohn home. (Years later, Felix would compose music for the staging of Boeckh's German translation of Sophocles' play, "Antigone.")

Humboldt also organized the Berlin scientific congress of August/September, 1828 - a conference that Metternich would find most dangerous. For the several weeks that Gauss stayed at Humboldt's home, they could discuss the implications of the geodetic and geo-magnetic projects. Finally, the representative from England, Charles Babbage, the noted promoter of Leibniz's analytic methods, found the conference to be historic, but found the highlight of Berlin to be the culturally-optimistic Mendelssohn household. It was at this time and in such circumstances that Dirichlet entered into the Mendelssohn youth movement. The Mendelssohn Youth Movement

Fanny's reports on the scene (in a 12/27/1828 letter to Klingemann): "Christmas-eve was most animated and pleasant. You know that in our house there must always be a sort of `jeune garde' ('young guard') and the presence of my brothers and the constant flow of young life exercise an ever attractive influence. I must mention Dirichlet, professor of mathematics, a very handsome and amiable man, as full of fun and spirits as a student, and very learned." Fanny's sister, and Dirichlet's future wife, Rebecca, was also at that Christmas party. We may assume that some or all of the sixteen-member `Saturday-night chorus' were there.

Also in attendance was Fanny's longtime love, Wilhelm Hensel, back in Berlin for two months now. He had just returned from five years of study of Renaissance art in Italy. Wilhelm, now 33, and a talented artist, had fought as a young man in the German Liberation Wars against Napoleon. Now, he had returned to Berlin to win Fanny as his wife (which somehow involved conquering Fanny's mother, Lea). A month later, the engagement was announced.

Fanny also mentions three of the suitors of Rebecca (who would all lose out to Dirichlet): * Professor Eduard Gans - "We see him very often, and he has a great friendship for Rebecca, upon whom he has even forced a Greek lesson, in which these two learned persons read Plato. It stands to reason that gossip will translate this Platonic union into a real one..." (Gans was the Jewish student of Hegel, covered in Steve Meyer's "Fidelio" article on the Haskalah.) Gans had been active in Jewish causes early on, but he converted in 1825 so that he could become a professor. * Johann Gustav Droysen, historian and philologist - Though only 19 years old, Fanny recognized in him "a pure, poetic spirit and a healthy amiable mind." Droysen published a translation of Aeschylus and the famous work on Alexander the Great, both before he was twenty-five. * Heinrich Heine, poet - "Heine is here... [H]is {Reisebilder} contain[s] delightful things; and though for ten times you may be inclined to despise him, the eleventh time you cannot help confessing that he is a poet, a true poet!" Once, he sent, via his close friend Droysen, his greetings to the 18-year-old Rebecca: "As for chubby Rebecka, yes, please greet her for me too, the dear child she is, so charming and kind, and every pound of her an angel." It seems that Heinrich Heine's brand of courtship of Rebecca was little different from his treatment of everything else in life. "St. Matthew's Passion"

Now picture Dirichlet in the observation hut in the garden at 3 Leipziger Strasse. Close by is the summer house, where Felix and Fanny worked out, with four hands at the piano, the voicing and composition of Bach's "St. Matthew's Passion" - left unperformed since Bach premiered it in 1729. In January, 1829, soon after Dirichlet had arrived on the scene in the Mendelssohn youth movement, Eduard Devrient and Felix Mendelssohn decided upon an historic March public performance, despite the discouragement of the music authorities. They knew that they had to defy the professional advice. As described years later by Fanny's son, the appropriately-named Sebastian Hensel: "Only just then the most intelligent musical people began to comprehend that something must be done to bring this treasure to daylight, and that this was in a musical point of view the greatest task of the period."

After hiring a hall, and with a performance six weeks away, the chorus swelled from 16 to 400 members, and the initial group had the 'Monge brigade' project of rapidly educating all the new-comers. Fanny described this rare and sublime process: "People were speechless with admiration, and faces grew long with astonishment at the idea that such a work could have existed unbeknownst to them... Once they grasped that fact, they began studying the work with warm and veritable interest. The enthusiasm of the singers, from the first rehearsal on - how they poured their heart and soul into the work; how everyone's love of this music and pleasure in performing it grew with each rehearsal - kept renewing the general wonder and astonishment." This process created "so lively and detailed an interest that all the tickets were sold the day after the announcement of the concert, and they had to refuse entrance to more than a thousand people... [At the concert itself,] I was sitting in the corner [of the massive chorus] so as to see Felix well, and I had arranged the strongest alto voices near me. The choruses were impassioned with extraordinary strength tempered with a touching tenderness, as I had never heard them before... [A] peculiar spirit and general higher interest pervaded the concert, that everybody did his duty to the utmost of his powers, and many did more..."

And, after the sublime, the ridiculous! At least one Berliner seemed to remain untouched: After the concert, at a celebratory dinner, Devrient's wife, Therese, sat between Felix and an obnoxious professor, who kept trying to get her drunk: "He clutched my wide lace sleeve in an unrelenting grip... to protect it, he said! And would every so often turn toward me; in short, he so plagued me with his gallantries that I leaned over to Felix and asked: `Tell me, who is this idiot beside me?' Felix held his handkerchief over his mouth for a moment - then he whispered: 'The idiot beside you is the celebrated philosopher Hegel!'"

Such were the circumstances of Dirichlet's first year in Berlin. By 1831, Dirichlet and Rebecca Mendelssohn were engaged, and by 1832, married. They were considered to be, in the extended Mendelssohn family discussions and debates, the most revolutionary. The couple had four children. Rebecca died late in 1858, age 47 (evidently of a similar type of stroke as had felled her older sister, 43, and brother, 39, a decade earlier). Dirichlet's compromised health declined further, and he followed her to the grave five months later, May 5, 1859. Dirichlet's Republican background and LaFayette's July 1830 Revolution As a youth of 17, Dirichlet was studying Gauss' {Disquisitione Arithmeticae), when he was sent to study in Paris. According to his nephew, Sebastian Hensel, Dirichlet was introduced there to General Foy by a republican associate of Dirichlet's parents, one Larchet de Charmont.[2] Foy employed Dirichlet as a tutor in his household from the summer of 1823 until Foy's death in November, 1825. Foy was in France's chamber of deputies, and was the leader of the opposition to the royalist restoration of the 1815 Congress of Vienna. Dirichlet thrived in this environment: "... [I]t was very important for his whole life that General Foy's house - frequented by the first notabilities in art and science as well as by the most illustrious members of the chambers - gave him an opportunity of looking on life in a larger field, and of hearing the great political questions discussed that led to the July Revolution of 1830, and created in him such a vivid interest." (Hensel's {The Mendelssohn Family}, Vol. I, page 312.)

The July Revolution of 1830 was led by LaFayette, and was at best a mixed affair. It overthrew the reactionary arrangements of the Congress of Vienna, and set up a tenuous arrangement whereby Louis Phillippe, the "Citizen King," would be a constitutional monarch. LaFayette gambled that this might work, as the "Citizen King" had pledged to be subservient to the written constitution. Two items of note reflect Foy's connections to the 1830 Revolution: In October, 1825, a few weeks before his death, Foy had troubled himself to write to LaFayette; and in 1823, Foy had sent from his care the 21-year-old Alexandre Dumas (three years Dirichlet's senior) to be Foy's agent in the household of Louis Phillippe. Later, in 1830, Dumas would serve as a captain in LaFayette's National Guard. Dumas had sought Foy's guidance, as Foy himself had earlier, in the 1790's, looked to Dumas' father, General Alexander Davy Dumas, as his military and political leader. General Dumas was first a hero of the French army, who then became an early opponent of Napoleon's imperial ambitions. He was part of the 1798 invasion of Egypt, but was imprisoned by Napoleon from 1799 to 1801 for publicly opposing Napoleon's imperial turn. (Similarly, Beethoven at this time also had hopes for Napoleon that he quickly recognized were greatly mistaken.) After the imprisonment, Napoleon's harsh treatment of General Dumas led to his early death at age 44 in 1806, leaving behind his four-year-old son.

After Foy died in November, 1825, there was a competition between Alexander Humboldt and Fourier for Dirichlet's services. Fourier, according to Hensel, "tried to avail himself of Larchet de Charmont's influence, to induce him [Dirichlet] to return to Paris, where he felt sure it was his vocation to occupy a high position at the Academy." Humboldt arranged for Dirichlet, then 21, to teach at Breslau, 1826-1828, and then brought him to Berlin in 1828, where he was the professor of Mathematics at the Berlin Military Academy, and where he joined the Mendelssohn youth movement. LaFayette, Dumas, Galois, Poe and Heine

Alexander von Humboldt returned to Paris in 1830 because of the ripened political situation. Cauchy - the Emperor of mathematics - had to flee Paris in July, 1830, when his King was deposed. For a short period, LaFayette thought that they could control the new "Citizen King." However, within a few months the financiers moved in and gained the upper hand in running the king, Louis Phillippe. In December, 1830, they succeeded in the arrest of the nineteen leaders of LaFayette's republican National Guard, the key defenders of the constitution. LaFayette testified at the March, 1831 trial; and the jury found them all not guilty.

At the celebratory dinner for the "19" were, among others, LaFayette, Dumas and another brilliant student of Gauss's work, Evariste Galois. (The latter had been, along with Neils Abel, a victim of Cauchy's ham-handed skullduggery at the head of the French Academy of Science.) At the dinner, Galois evidently made a notorious toast to Louis Phillippe's health, while putting his other hand on his sword, and adding that the king had better not fail in his duty to the constitution. Dumas reports that at that point, several of the attendees, including himself, jumped out of the windows of the hall, fearing, accurately, that the spies at the event would bring the police.[3] Galois was arrested, tried and released, when the jury refused to convict him.

He was re-arrested that summer, 1831, by the police prefect, Gisquet, for wearing a republican guard uniform in public. Gisquet avoided the path of the previously unsuccessful trials, and instead kept him in jail with no trial until the next spring - when his release, and the setup of his fatal `duel', fell hard one upon the other. When Galois' suspicious death roused a crowd to come to his funeral, and a public accounting was threatened, Gisquet carried out, the night before the funeral, pre-emptive arrests of Galois' friends.

Which of these events in Galois' last year, 1831/2, were witnessed by Edgar Allan Poe is unclear, but clearly Poe's "The Purloined Letter" skewers Gisquet (the "prefect G -"), and, by inference, celebrates the "poet-mathematician," Galois. While Poe does also refer, and explicitly so, to the mathematician, Charles Auguste Dupin (the historical figure that was, literally, a member of the Monge brigade, having been taught by Monge), Poe's "poet-mathematician" image does not need to be `reduced' to one individual. However, the politically-sensitive case of Galois at the time of Poe's visit to Paris, and the reference to the "prefect G-", makes it clear that the Galois case would have been understood by astute readers of Poe's time. Regardless, Poe's "poet-mathematician" image would appropriately apply to any of the leading (1820's) students of Gauss: Galois, Abel or Dirichlet. Poe's "poet-mathematician" would have been fully at home in the Mendelssohn garden at 3 Leipziger Strasse. Finally, Heine, upon the news of the July Revolution, decided to leave Berlin for Paris. He would have been there, with Alexander von Humboldt, during these events. His early work in Paris during this period may be examined in his {The Romantic School}, where he diagnosed for the French and the Germans, the evil medievalism of the cultural string-pullers that had deliberately set out to murder the Germany of Moses Mendelssohn, Lessing and Schiller. No successful European revolution could proceed without dealing with these skeletons. And none did.

The rapid sketch, above, is only a beginning suggestion as to the interplay of: Gauss's {Disquisitiones Arithmeticae}; the healthy benefits of opposing evil (e.g., the imperial beastman, Napoleon); the children and grandchildren both of Moses Mendelssohn and of the American Revolution in Europe; and the passion of magnetic measurements and the revival of Bach's "St. Matthew's Passion." Much more can, and should be, covered in this specific period, regarding the activities of J. F. Cooper, J. Q. Adams, LaFayette, Friedrich List, Poe, etc. But this abbreviated historic sketch, centered around Dirichlet, should take us back to the Gauss/Dirichlet/Riemann dialogue somewhat refreshed.

[1] J.S. Bach had composed and performed this work in Leipzig, 1729. The manuscript was given to Felix by his aunt Sarah Itzig Levy, a proponent of Bach. (Otherwise, one could say that it was fortunate that Felix Mendelssohn had exactly sixteen friends to cover the four quartets of soprano/alto/tenor/bass - but it were more likely that the orbit defined the planet; that is, the Bach project cemented the potential friendships.)

[2] Larchet is unknown to this author. Since it is thought that Dirichlet's parents were active republicans who had to leave Napoleonic France years before, and since Larchet de Charmont was a friend both of Foy and of Dirichlet's parents, it were likely that they shared their anti-Napoleonic republicanism.

[3] Recall that Dumas is also the one who made the knowing allusion, as part of Dumas' typically `factitious' fiction, to Poe's stay in Paris. This is the reference that Allen Salisbury reported on years ago in his "Campaigner" article on Poe.