First Thoughts On the Determination of the Orbit of Carl F. Gauss

By Tarrajna Dorsey

Bernardo.              Last night of all,

                                when yon same star that’s westward from the pole

                                Had made his course to illume that part of heaven

                                Where it now burns, Marcellus and myself,

                                The bell then beating one, -

Enter Ghost.

Marcellus.             Peace, break thee off; look, where it comes again!

Bernardo.              In the same figure, like the king that’s dead.

Marcellus.             Thou art a scholar, speak to it, Horatio.

Bernardo.              Looks it not like the king?  mark it, Horatio.

Horatio.                 Most like: it harrows me with fear and wonder.

Bernardo.              It would be spoke to.

Marcellus.             Question it, Horatio.

Horatio.                 What art thou that usurp’st this time of night,

                                Together with that fair and warlike form

                                In which the majesty of buried Denmark

                                Did sometimes march? by heaven I charge thee, speak!

Marcellus.             It is offended.

Bernardo.              See, it stalks away!

Horatio.                 Stay! speak, speak!  I charge thee, speak!

Exit Ghost

Marcellus.             ‘Tis gone, and will not answer.

________________________

The year is 1799.  The dusk of the century hangs in the air, and all of Europe awaits with bated breath the dawn of the new century:  what answers may it hold?   Several questions have already been made their reply: the American Revolution, the shining daughter of the best of European culture, now ripens beneath a distant sun, while the French Revolution, intended as her twin, lies forsaken in the dust. In France , Napoleon Bonaparte leads a coup d’etat in the French government, and assumes power on November 9^th. The young naturalist, Alexander von Humboldt, sets off from Paris on his five year journey through the Americas .  In the small town of Brunswick, in Germany , the young Carl Friederich Gauss submits his first work and dissertation on the “Fundamental Theorem of Algebra” to Göttingen University. There, “the leading adornment of Göttingen,” in Gauss’s words, Georg Christoph Lichtenberg, collaborator of Abraham Kaestner and physicist, dies.  Kaestner follows several months later, and with him,  the height of the great classical period of Germany is interred. On December 16^th, Gauss writes to his good friend Wolfgang Bolyai,

This letter will hardly reach you this year; tell me in your next one when you received it; the last day of December will at least be the last day which we call seventeen hundred (if micrological exegets[1] now postpone the end of the century one more year), and will be especially sacred to me.  Note that when it is midnight here for us, midnight is already an hour past with you.  On such festive occasions my mind passes into a loftier mood, into another spiritual world; the partitions of the room disappear, our filthy, paltry world with everything that appears so big to us, makes us so happy and so unhappy, disappears, and I am an immortal pure spirit united with all the good and noble who adorned our planet and whose bodies space or time separated from mine, and I enjoy the higher life of those greater joys which an impenetrable veil conceals from our eyes until death…

The Dilemma

When the eager soul, who has heeded the advice of statesman Lyndon LaRouche[2] and taken to the investigation of the development of physical science from Johannes Kepler through Gauss and Bernhard Riemann, arrives at the threshold of Gauss’s investigations, they will undoubtedly open to the preface of the Theory of the Motions of Heavenly Bodies Moving About the Sun in Conic Sections and find written the following words: 

Several astronomers wished me to publish the methods employed in these calculations immediately after the second discovery of Ceres; but many things- other occupations, the desire of treating the subject more fully at some subsequent period, and, especially, the hope of a further prosecution of this investigation would raise various parts of the solution to a greater degree of generality, simplicity, and elegance,- prevented my complying at the time with these friendly solicitations. I was not disappointed in this expectation, and have no cause to regret the delay.  For, the methods first employed have undergone so many and such great changes, that scarcely any trace of resemblance remains between the method in which the orbit of Ceres was first computed, and the form given in this work.[emphasis added]

Thus, the eager soul finds themselves presented with an entirely new problem: to rediscover, independently of any aid from Gauss himself, Gauss’s discovery.  Perhaps this eager soul will wonder at the elusiveness of Gauss.  While Kepler is effusive, exuberant about everything, and eager to impart his every thought, Gauss appears as the man behind the smokescreen, remaining ever quiet and removed.  He does not lay out his mind, transparent, before the reader- in fact he even throws up false signals at times to throw them off the trail! What pedagogy, or what trickery is this?!

The intent of this author, is not to make any excuses for Gauss, who needs none, but to portray for the eager soul the cultural processes which shaped, and to some extent limited, the actions of Gauss, so that they might find their own answers.  As will be seen, no insight into the answer to this general question will be found in searching for some ‘tragic flaw’ of Gauss in and of himself.  The answer will be sought in the fabric and the culture of the time, which underlay the actions of him and his contemporaries.

Universal History

Had our eager soul been a young student in the late 18^th century, attending Jena university, they would have had the opportunity of gleaning an insight into the answer to this question from Friedrich Schiller, the great German thinker and poet, himself, during his first lecture as professor of universal history, delivered May 26^th 1789, two months before the French Revolution broke out in France (July 14^th 1789).  After a great procession of the students to find a larger auditorium, as the original one could not hold the hundreds of students who were eager to hear a lecture from Friedrich Schiller, he remarked,

Even that we found ourselves together here at this moment, found ourselves together with this degree of national culture, with this language, these manners, these civil benefits, this degree of freedom of conscience, is the result perhaps of all previous events in the world: The entirety of world history, at least, were necessary to explain this single moment.

Although the entirety of human history is hardly a subject that could be covered in the scope of the present discussion, there is a specific unfolding of events beginning with the end of the German classical period, and extending through the 1814-1815 Congress of Vienna and the 1819 Carlsbad Decrees, that must be illustrated here if we are to gain any insights at all.  Yet one more crucial lesson from our teacher of universal history must be noted here.

Recall any institutional education concerning the subject of history that you have been exposed to over the course of development of your existence: of what relevance was it to you?  What do you remember of it, if anything at all? (the funny quirks of your teacher and the number of spots on the wall that look like animals do not count).  For the reason that we have largely been robbed of a true, living sense of history in which we play a decisive role, we must again become students of another time, where this concept was better understood.  As was clearly known and taught by Schiller in his lectures on universal history that same year[3], the essence underlying the specific events of any particular period of history, is the battle over what the view of mankind is that will govern the society, and whether or not man will be allowed to develop his creative mental powers, in order to increase his happiness, i.e. knowledge of the universe in which he exists.  From the ancient battle of Prometheus and Zeus [4], to the constitution of Athens as contrasted with Sparta, to the American Revolution, to the fight for the development of nuclear power today, this has always been the essential pivot-point of history.  Are human beings inherently destructive, selfish, arrogant, and foolish beings- even worse than animals?  Do we exist according to the doctrine of “the survival of the fittest”?  Or do we exist as a species which transcends the law of the jungle; a species which is subject to a higher law of morality based upon reason, and our likeness to the creator? Here lies the stage upon which the entirety of the events and characters of the following discussion will appear.

Enter Ghost.

Carl F. Gauss is born in the year 1777 – a time when the eyes of millions of people throughout the world still sparkle with optimism at the prospects of the American Revolution.  After centuries of war and oppression, the possibility of a better existence for a greater portion of mankind is no longer a myth, or a far off dream, but a tantalizing and attainable idea.  Conceptions which had long lain dormant, are now closer than ever to actually being realized politically.  The talk in the humanist circles across Europe is giddy with expectation. Dr. Benjamin Franklin meets with French statesman Jean-Sylvain Bailly in Paris. Wolfgang Amadeus Mozart is there as well, meeting with the circles which end up facilitating the production of his Le Nozze di Figaro, first performed before Viennese nobility in 1786, three years before the French revolution begins.  Among these circles is Pierre de Beaumarchais, author of the Le Nozze di Figaro, and a generous contributor of cannon to the American revolutionary army.  The Courier de l’Europe, directly subsidized by the French government, publishes the Declaration of Independence, and extracts from Thomas Paine’s Common Sense are published in periodicals and journals across Europe. The excitement is infectious.

Like the runner who, nearing the goal after a long race, hears the footsteps of their competitor still close behind, and yet draws new strength from the prospect of victory close at hand and bursts forward across the finish line- so the founding fathers of the true age of reason in Europe continued their work, in hopes of achieving a twin victory.

Chief among these men were Gotthold Ephraim Lessing (1729-1781), Moses Mendelssohn (1729-1786), and Abraham Kaestner (1719-1800). From their earlier collaboration to defend against the attacks on the universal genius Gottfried Wilhelm Leibniz[5] at the Berlin Academy, to their work to create a classical renaissance in the literature, art, and language culture of Germany, these great men were driven by a passion and love for the reasoning capacity of mankind.  As the poet Heinrich Heine (1797-1856) later put the role of Lessing so well,

…we Germans modeled our clumsy temple of art after the bepowdered Olympus of Versailles…  Lessing was the literary Arminius[6] who emancipated our theatre from that foreign rule…  But not only by his criticism, but also through his own works of art, did he become the founder of modern German original literature.  All the paths of the intellect, all the phases of life, did this man pursue with disinterested enthusiasm.  Art, theology, antiquarianism, poetry, dramatic criticism, history,- he studied these all with the same zeal and with the same aim.  In all his works breathes the same grand social idea, the same progressive humanity, the same religion of reason, whose John he was, and whose Messiah we still await.

A painting of the scene from the Phaedon, by the famous German painter, sculptor, and contemporary of Gauss, Johann Gottfried Schadow (1764-1850), with one more guest added in: Moses Mendelssohn.

The same could be said of Kaestner, as well as Mendelssohn. Mendelssohn had grown up in a Jewish ghetto in Dessau, a town near Berlin, in a family which cherished, and later preserved, the music of Bach.[7]  In his team-up with Lessing, he provided the sharp wit needed to shame into silence the cynicism and spreading disease of Voltaire, Euler, and Maupertuis (the chief anti-humanist/anti-Leibnizians of the time).  Kaestner had grown up in the city of Leipzig, where the presence of Leibniz, one of its most distinguished inhabitants, and where the music of Johann Sebastian Bach, permeated the atmosphere- a testimony to the cultural activity of the city in general.  After he had accepted the professorship of mathematics at Göttingen in 1756, he taught geometry, physics, and astronomy, among many other things, while at the same time writing a tremendous work on the foundations of mathematics- which reviews the works of Nicholas of Cusa and Johannes Kepler extensively, among others, as part of a larger project on the entire history and development of science.[8] On top of this, he pens a wealth of beautiful as well as biting poems[9], and heads up the work at the observatory.  More will be developed concerning the environment at Göttingen leading up to 1795, the year of Gauss’s arrival.  Here, it suffices to call upon the words of Heine once again, himself a student at Göttingen many years later, in order to capture the fighting essence of this humanist triumvirate[10]:

[Lessing] was a whole man, who, while with his polemics waging destructive battle against the old, at the same time created something newer and better. ‘He resembled,’ says a German author, ‘those pious Jews, who, at the second building of the temple, were often disturbed by the attacks of their enemies, and with one hand they would fight against the foe, while with the other hand they continued to work at the house of God.’  This is not the place to discuss Lessing more fully, but I cannot refrain from saying that, in the whole range of literary history, he is the author whom I most love.

A Great Moment?

And what became of the life’s work of these great men? What became of the hopeful expectations of Europe? What became of the much anticipated twin Revolution?  The year of 1789 best illustrates the case.  On April 30^th, Gauss’s twelfth birthday, George Washington delivers his first inaugural address as the first President of the Constitutional Republic of the United States of America : 

…there is no truth more thoroughly established than that there exists in the economy and course of nature an indissoluble union between virtue and happiness; between duty and advantage; between the genuine maxims of an honest and magnanimous policy and the solid rewards of public prosperity and felicity; since we ought to be no less persuaded that the propitious smiles of Heaven can never be expected on a nation that disregards the eternal rules of order and right which Heaven itself has ordained; and since the preservation of the sacred fire of liberty and the destiny of the republican model of government are justly considered, perhaps, as deeply, as finally, staked on the experiment entrusted to the hands of the American people.

On June 17^th, in France , which had been a great supporter of the American Revolution, a national assembly is convened, where the intention to usher in a constitutional monarchy is introduced.  An oath swearing commitment to this intent, the famous “Tennis Court Oath,” is taken on June 20^th.[11]  The high pressure environment surrounding Paris and Versailles is seemingly quiet, but tense—foreboding quite the storm.  Essentially, two factions are at work to gain the support of the King, Louis the XVI: the collaborators of Bailly, President of the National Assembly convening in Versailles, including the vice president and American Revolution veteran the Marquis de Lafayette, and Lazare Carnot, military leader and head of the educational ministry, versus the collaborators of Jacques Necker, finance minister to the King, including his accomplices the Duke of Orleans (a.k.a. Phillipe Egalitè), the pawn of the head of the British Foreign Office Jeremy Bentham (which reveals the true interests at hand), and their lackeys Danton and Robespierre, leaders of the “leftist” Jacobin mob. While Bailly’s National Assembly deliberates over a constitution, and gathers a militia in order to gain defense, Necker sends in tens of thousands of the National Guard which serve