Raw Competition (29)

Leibniz and Newton at each other's throats

Gottfried Wilhelm Leibniz (1646-1716), who was stunned and had his life upended, when Newton accused him of plagiarism.

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Science is based on competition. May many ideas sprout, a thousand flowers of them, and the best ones shine! That is its motto; peer verification is its method. It is like an Olympic game in its rewards, but its disciplines are huge in number and one can be prominent in one of the many rarified subfields without too much competition, even as some may become more glamorous, often within a fashion of the day.

But the methods of science and the mode of competition had to be established, and that happened in the founding Baroque period (neglecting Alexandria for the moment). Here I introduce Leibniz with an eye on what was special about this fecund time. For Leibniz it was the best of worlds until it turned to worst. He was on the way to become one of science’s immortals until a raw competition opened with Newton that brought him to a bitter old age.

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Establishing a method for determining a world view – scientific methods and traditions

Establishing methods for determining a world view through science was instrumental for any subsequent scientific quest. It provided the backbone out of which motivation could arise for new endeavors. And so, competition is also within the line of our story of the unfolding that led to understanding DNA. There was a time when knowing became important and the amassment of savvy a competitive quest. The case of acknowledgement was generally well handled (eg Pascal-Torricelli), even if at times it showed a rather raw nature as in this story.

The Baroque, celebrating the forms of seashells, functioned as the central trunk in developing the methods of basic knowledge creation from which the branches of our subsequent science sprouted. Yet the revolutionary step to this unfolding was already fully taken earlier, in Alexandria, but was then lost again. This essay is the first that has to cite Alexandria, in our case for precursors to the development of calculus. There was less need say with Faraday’s electricity but as we now go back in time, Alexandria will rise in importance. While this emphasis on Alexandria is not the common approach presently, I think that it will be important to visit when we will discuss more about the origins of science. We will have to orient ourselves on the pharos or light tower of Alexandria as it were.

On going back in history, here we are at a point of an explosive science unfolding and the questions of its own origin. But even here we will touch upon Archimedes as a precursor to understanding calculus with his method of exhaustion. If one were to proceed exclusively on the idea of science coming into being around 1600-1700 then one misses the essential aspect that there was a renaissance of antiquity that had triggered the movement. When you would have asked Galileo on what mission he saw himself, he would have expressed his desire to follow Archimedes above all. For him and us, looking back, it was as though aliens had spoken from somewhere lost in time to people lost in ignorance. It was as though paternal figures had taught in annunciatory ways to adolescents. And such situations may arise again when we may pick up communication with intelligence in space. We may yet become jolted, and not only by our own.

And we can follow this line of thought to a repeat of a loss of understanding the world at any time. With the world veering and swerving in uncertain ways, having problems like nuclear war unsolved, and presently resurfacing, we as humanity may lose our savvy sooner or later. It is then possible that surviving remnants of our libraries may seed a new interest in science down a long line. The new curiosity may then take our present existential savvy as a view of mental giants, alien almost to the devastated cultures, just as it has happened before.

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Gottfried Wilhelm Leibniz (1646-1716)

Gottfried Wilhelm Leibniz was a German polymath, and prominent in the field of mathematics and philosophy. Yet he was interested in a vast array of subjects with contributions as scattered in various learned journals and tens of thousands of letters and unpublished manuscripts. He wrote in several languages, primarily in Latin, French and German, but also in English, Italian and Dutch. Unfortunately, he is perhaps most remembered by his priority dispute with Newton over calculus. But increasingly he is also gaining historical importance for laying foundations of computer math. And he remains a mainstay of philosophy courses.

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Early Life – Leibniz at Leipzig

Leibniz was born in Leipzig, two years prior to the end of the Thirty Years War, which had ravaged central Europe. His family was Lutheran and belonged to the educated elite on both sides: his father, was a jurist and professor of Moral Philosophy at the University of Leipzig, and his mother, the daughter of a professor of Law.

Leibniz began his formal university education at the University of Leipzig in a chiefly Scholastic tradition, as the “modern” philosophy had not made a great impact in German-speaking lands. But he gained a great respect for ancient and medieval philosophy. Indeed, one of the leitmotifs of Leibniz's philosophical career was his desire to reconcile the modern philosophy with earlier ones. At the University of Altdorf, Leibniz published in 1666 the remarkably original Dissertation on the Art of Combinations, a work that sketched a plan for a logical calculus, a subject that would occupy him for much of the rest of his life. Leibniz then was sent on a mission to Paris for 4 years with trips to London that broadened his perspectives.

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Philosophy

Leibniz became one of the three great early modern rationalists. But unlike Descartes and Spinoza, the other two, Leibniz had a thorough university education in philosophy. He was influenced by his Leipzig professor, who also supervised his BA thesis in philosophy. Leibniz met Spinoza in 1676 and read some of his unpublished writings. In fact, he has since been suspected of questionably appropriating some of Spinoza's ideas. Leibniz admired Spinoza's intellect. But he was disappointed his conclusions were inconsistent with Christian orthodoxy.

Fitting the times as newly creative, not just imitative, Leibniz had his own philosophies; most notable perhaps is his notion that this world is the best possible of all worlds. It had to be, as God had created it. And this is also the reason that there is something instead of nothing. Isn’t he the father of all optimism even as he was to be often lampooned for this by others such as Voltaire? Isn’t he also the father of determinism with his saying that “nothing happens without a reason"?

Both Newton and Leibniz were afforded the grace to be born at a magnificent time that allowed the plucking of low hanging intellectual fruit. And in this sense, their science stories attract attention through time as they impart essential existential savvy, that tells compelling truths.

There is a touching entry in his Encyclopedia by the eighteenth-century French atheist and materialist Denis Diderot, whose views were very often enough at odds with those of Leibniz: “Perhaps never has a man read as much, studied as much, meditated more, and written more than Leibniz… What he has composed on the world, God, nature, and the soul is of the most sublime eloquence. If his ideas had been expressed with the flair of Plato, the philosopher of Leipzig would cede nothing to the philosopher of Athens”. Diderot was almost moved to despair in this piece: “When one compares the talents one has with those of a Leibniz, one is tempted to throw away one's books and go die quietly in the dark of some forgotten corner”. You note typical aspects of Baroque: a somewhat florid description and an attempt to give encyclopedic testimony.

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Calculators

Leibniz saw in binary arithmetic the image and proof of creation. Unity was God and zero was the void (notice that this is already beyond Aristotle’s horror vacui). According to Morris Kline* in Mathematics and the Physical World, this delighted Leibniz so much that he sent it to the Jesuit president of the Chinese tribunal for mathematics, to be used as an argument for the conversion of the Chinese emperor to Christianity. Though Leibniz had special reasons for considering base two, it took some time for it to develop beyond an intellectual amusement only. Neither this base nor any other had until recently been seriously considered as a substitute for base ten; that is until computers entered the scene.

Leibniz became one of the most prolific inventors in the field of mechanical calculators, taking up where Pascal left it. He was the first to describe a pinwheel calculator in 1685 and invented the Leibniz wheel, the first mass-produced mechanical calculator. In refining the binary number system, he placed the foundation of digital computers, including "the von Neumann machine". The latter is the standard of modern "computer architecture", followed from the second half of the 20th Century, and into the 21st. His calculus ratiocinator anticipated the universal Turing machine.

Leibniz, the great calculator, not only asked why there is something rather than nothing but also considered the basis of music: “Music is the hidden arithmetical exercise of a mind unconscious that it is calculating”. He has also been cited as saying: “It is rare to find learned men who are clean, do not stink and have a sense of humour… Nothing is more important than to see the sources of invention which are, in my opinion more interesting than the inventions themselves.”

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Differential calculus

Contrary to common perception integral calculus has a long history with the methods of exhaustion. Get the area of a circle by inscribing increasingly complex polygons in it (to exhaustion). Glimmers of insight appear deep in antiquity with earliest stirring in earnest, going back to Archimedes. Among the problems Archimedes tackled, are finding areas under parabolas and inside spirals or finding the volume of the sphere or derived parts of it. And perhaps most pertinent, Archimedes also showed how to compute the slope of a line tangent to a spiral. During Islam some of this work was further pursued. Galileo, Kepler, and others had then further pushed the idea of exhaustion as a preamble to calculus. The real storm of discovery happened though around 1666 with Newton and a little later, Leibniz.

In 1684 Leibniz published details of his differential calculus developed over some years. The paper contained the familiar d-notation (difference), the rules for computing the derivatives of powers, products, and quotients. Newton's 'method of fluxions' was written in 1671 but Newton didn’t attempt to get it published. It appeared in print only when John Colson produced an English translation in 1736.

This is another example of discoveries ripening to the point that it is only a matter of time until somebody plucks them. And here we have an especially pronounced problem with giving credit. Even as the waters haven’t cleared sufficiently, it has become commonly agreed that Newton discovered the method first but in a clumsy way and Leibniz discovered it independently and won the day in general applicability. Nevertheless, some vexing uncertainties remain. The two men never met but Leibniz may have been privy to some unpublished writing of Newton’s although his approach stayed rather independent. Leibniz had a habit of changing dates on documents though.

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Newton-Leibniz Calculus Controversy

The story of who amongst the two deserves the main credit is called the Newton-Leibniz Calculus Controversy. It was a late retrospective affair, in the early 1700s, instigated by people taking sides between English and Continental science joined by the two protagonists. It showed the growing pains of the nascent science and how it attempted to develop an ethical framework of acknowledgment.

Newton asserted that he had begun working on a form of calculus in 1666, at the age of 23. Newton circulated unpublished papers to his friends and used the technique discovered in his scientific works. This proved that these papers existed.

Leibniz devised his ideas in the mid-1670s and published his work in 1684 under the name: “A New Method for Maxima and Minima, as Well Tangents, Which is not Obstructed by Fractional or Irrational Quantities”. Even as the title of his paper is a little much, it can serve as a great summary of the basic idea of calculus.

Considering Leibniz's intellectual prowess, as demonstrated by his other accomplishments, he had more than the requisite ability to invent the calculus. He also went his own creative way about it. When Newton started to question the origin of Leibniz’s work, Johann Bernoulli, who used Leibniz's calculus to maximize functions, goaded Leibniz into defending himself from Newton.  But just as with the case of hate for Hooke, Newton stubbornly sought to destroy his opponent in a drawn-out proceeding. 

Within the unfolding controversy, Leibniz formulated principles of correct scientific behavior: "We know that respectable and modest people prefer it when they think of something that is consistent with what someone's done other discoveries, ascribe their own improvements and additions to the discoverer, so as not to arouse suspicions of intellectual dishonesty, and the desire for true generosity should pursue them, instead of the lying thirst for dishonest profit."

Newton's approach to this kind of priority problems can be illustrated by prior examples. One pertains to the discovery of the inverse square law concerning gravity. Hooke assumed that motion under planetary conditions should occur along orbits such as elliptical. But he couldn’t prove it. So, Hooke presented his ideas to Newton, who solved this problem, describing it in Principia without giving credit. The astronomer Haley insisted though that a phrase be inserted to the effect that the compliance of Kepler's first law with the law of inverse squares was "independently approved by Wren, Hooke and Halley."

In 1696, the position still looked potentially peaceful: Newton and Leibniz had each made limited acknowledgements of the other's work. But the case against Leibniz was promoted by Newton's friends, and summed up in the Commercium Epistolicum of 1712, which referenced all allegations. This document was thoroughly ironed by Newton. Leibniz never agreed to acknowledge Newton's priority in inventing calculus. He felt secure in his superior representation and understanding.

The question of acknowledgment is still sometimes a controversial one, although mechanisms for clarification are now better. An example is the relative contributions of US and French science in the unraveling of HIV.

But the controversy had a very negative effect on the life of Leibniz, who felt increasingly isolated and not appreciated. Even his patron left to become king of England. With Leibniz's death in 1716, the controversy subsided and gradually ceased to interest even Newton. After having sufficiently reduced his main competitors, Hooke and Leibniz, Newton felt he should return to his religious hatreds. And henceforth he occupied himself mainly with questions having to do with Trinity and an obscure historical bishop.

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General Ideas

Leibniz made himself a name by defining “space” and “time” as merely the vocabulary of relations between where objects are and when events take place. To Albert Einstein, though, space and time were the raw material of reality, even as the name of Relativity theory might suggest otherwise. There are still arguments raging on these points. But the idea underlying “a vocabulary of relations between where objects are and when events take place” has some appeal.

Leibniz's vis viva (Latin for "living force") is mv2, which is twice the modern kinetic energy. And from there he proceeded to postulate that the total energy would be conserved in mechanical systems. This gave rise to another regrettable nationalistic dispute, as it is rivaling Descartes and Newton’s conservation of momentum. Accordingly, Leibniz's ideas were promptly neglected in France and England, even as Germans admire their Newton as though he were their own, just like with Shakespeare. 

Leibniz proposed that the earth has a molten core, and so anticipated modern geology. He was a preformationist concerning embryos. And he also proposed that organisms are the outcome of a combination of an infinite number of possible microstructures.

Contrary to Newton, Leibniz was well traveled. He had visited London, Paris, or Vienna etc, but he had his employment in his later years in Hannover. He had actually hankered after a literary career. Through his life he was proud of his Latin poetry, and he boasted that he could recite the bulk of Virgil's "Aeneid" by heart. Like Newton and his religious interest, Leibniz had as one of his lifelong aims the reunification of the Christian Churches. He also took great interest in founding scientific societies.

Both, Leibniz and Newton were essential figures in the history of civilization who, in translating fundamental questions about the nature of the universe into the language of their own era, spoke for all time.

In E J Aiton*, Leibniz: A Biography, he is described as follows: “Leibniz was a man of medium height with a stoop, broad-shouldered but bandy-legged, as capable of thinking for several days sitting in the same chair as of travelling the roads of Europe summer and winter. He was an indefatigable worker, a universal letter writer (he had more than 600 correspondents), a patriot and cosmopolitan, a great scientist, and one of the most powerful spirits of Western civilisation.” There we see one of the first exponents of a world wide Web if still based on letters rather than electrons and liquid crystals.

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A world moored or unmoored?

In this time, within just a few generations, every fixed point that had anchored the world for thousands of years became unmoored. The discovery of America destroyed a purported complete geography, and astronomy did away with a “wholesome” universe and the earth as its pleasant center. One must realize the force of the spiritual torrent: Everything that educated people had accustomed themselves to, through long tradition, turned out to be a mistake or a lie. It is inviting to imagine what would be capable of producing a comparable effect on us today. The one thing that comes to mind would be the contact with a superior intelligence in space, with their anticipated mind-boggling pronouncements and formulations, just as it was then the contact with an earlier blossoming superior intelligence right here on earth amongst their fellow humans in their studiolos.

Yet even this intelligence in space is perhaps vaguely anticipated today, if not in detail. Our scientists know that relativity and quantum need to be joined and are open to the strangest notions about the future and past of the universe. But medieval Europeans could never have anticipated the existence of a New World in America, of experimental science or the loss of faith. This was utterly beyond their horizon. Even the time of Newton and Leibniz may l seem now like some distant eon when woolly mammoths roamed the Earth, and hopefully it will once be to people in the future, as carrying on this tradition. But as of now it is only some generations back and has influenced our lives immeasurably. I like to say that behaviorally we have become a new species because of it. As an electron, we are now expected to pop up in unlikely places, such as the moon or Antarctica (and return to tell!).

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The re-mooring of the world around 1666-1700 invites further thoughts about re-mooring’s origins. In the next essays I will depict more aspects of the times in the search for answers.

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