Six Ages of the World: the Role of Faith in the Development of the Calculus

Would you like to read a paper I wrote for an advanced math class? I dropped it, because what kind of cruel professor makes you do math and also makes you write a research paper? Plus, he was a horrible old misogynist. Also, he was convinced that I am a religious fundamentalist, which I was never really sure how to deal with, or what even…anyway, nobody ever read it. Until you, now! Who doesn’t love math and history and intersectionality, am I right?

The foundations of the calculus were laid as early as the eleventh century, by a large and varied (geographically, historically and culturally) group of men. Surprisingly, a significant number of them were devoutly religious; Isaac Newton is as well known for his theological and philosophical writings as he is for his crucial role in the development of many mathematical theories. Similarly, famed Persian mathematician and physicist Alhazen, also known as Ibn al-Haytham, was a faithful Muslim who described his scientific work in spiritual terms, stating that “I constantly sought knowledge and truth, and it became my belief that for gaining access to the effulgence and closeness to God, there is no better way than that of searching for truth and knowledge.” (Plott, 465)

While the history books of the Western World attribute the development of calculus to Isaac Newton and Gottfried Liebniz in the seventeenth century, British professor Dr. George Gheverghese Joseph believes that they were beaten to the discovery by a quarter of a millennium by mathematicians at the Kerala School, in particular Madhava of Sangamagrama. His research team found that not only did Madhava and his students identify the “infinite series,” but that the work done in their university was very likely shown to Jesuit priests who had been sent by Pope Gregory XIII to Kerala to research modernizing the Julian calendar.

In a 2007 interview with Science Daily, Dr. Joseph explained, “There were many reasons why the contribution of the Kerala school has not been acknowledged – a prime reason is neglect of scientific ideas emanating from the Non-European world – a legacy of European colonialism and beyond. But there is also little knowledge of the medieval form of the local language of Kerala, Malayalam, in which some of most seminal texts, such as the Yuktibhasa, from much of the documentation of this remarkable mathematics is written.” Madhava, a devout Brahmin, wrote about the Newton power series hundreds of years before Newton’s birth; in fact, he referred to estimating an error term, which indicates that he understood the concept which would become known as the limit. (423)

While it is foreign to modern Western thought that faith and science could peacefully coexist, for most of human history it was a given. In earlier eras, science and religion were not considered distinct enterprises. The ancient Egyptians, Sumerians, Babylonians, and Greeks saw natural processes and events through a mythopoeic lens, viewing divine action and the natural world as one and the same. Storms at sea, for instance, were the expression of Poseidon’s rage. When later Greek culture separated supernatural agencies from their explanations of nature, it gave birth to an entirely new study of the natural world. If Zeus does not control the movement of the planets, then the patterns of the physical world must result from an entirely different set of dynamics. Merely asking that question – why? – rather than assuming it was the will of the gods set into motion an entirely new perspective.
Aristotle’s early studies of formal logic and natural sciences diverged from Plato, his mentor, in that he was more concerned with the actual substance of things rather than ideal Forms. Aristotle’s obsession with causation demonstrates the radical departure of his thought processes – God is no longer accepted as the cause. In Book 2 of “On the Soul,” Aristotle works through the question of what the soul consists of, and what it means to live, in an empirical fashion: “Living, that is, may mean thinking or perception or local movement and rest, or movement in the sense of nutrition, decay and growth. Hence we think of plants also as living, for they are observed to possess in themselves an originative power through which they increase or decrease in all spatial directions; they grow up and down, and everything that grows increases its bulk alike in both directions or indeed in all, and continues to live so long as it can absorb nutriment.” (Lawall, 831) Aristotle had clearly begun an entirely new, more naturalistic line of questioning about the state of being; however, he still considered metaphysics, or theologic science, as the “first philosophy.”

Europe, having lost the literary and scientific works of classical Greek and Roman civilizations, developed a strikingly different philosophical attitude. It was around 398 CE that the first signs of the “Great Divorce” in the Judeo-Christian world, between the faith-based inquiries of early scientists who sought to know more of God through study of the natural world and the coming post-Enlightenment rationalism, began to appear with the publication of St. Augustine’s “Confessions.” In his discussion of his boyhood, Augustine asserted that even the parts of his education that he most enjoyed, study of the classical Greek and Roman literature, had only served to lead him farther from God. Of his schooling, Augustine wrote,

“I loved not study, and hated to be forced to it. Yet I was forced; and this was well done towards me, but I did not well; for, unless forced, I had not learnt. But no one doth well against his will, even though what he doth, be well. Yet neither did they well who forced me, but what was well came to me from Thee, my God. For they were regardless how I should employ what they forced me to learn, except to satiate the insatiate desires of a wealthy beggary, and a shameful glory. But Thou, by whom the very hairs of our head are numbered, didst use for my good the error of all who urged me to learn; and my own, who would not learn, Thou didst use for my punishment- a fit penalty for one, so small a boy and so great a sinner.”

Augustine’s premise appears to be that all education is in essence a form of corruption that will lead inexorably to the sins of greed and pride, and a deepening entanglement with the degradation of the material world. (1116) As a subscriber to Plato’s Theory of Forms, Augustine argued that the natural, observable world was in all ways inferior to the world of pure spirit – the Platonic ideals of the Kingdom of Heaven were the true reality, while the physical world was merely full of shadows, a corruption of these pure abstractions. Developed in the third century of the Common Era by Plotinus, Neo-Platonic thought focused on transcendent religious ideals where God was the idea – the “One” which is the source of all being. What could be possibly be learned from a tree, the Neo-Platonists questioned, when the concept of Tree exists on an altogether separate plane, unclouded by the messy organic imperfections to be found in the realm of the sensual? Of his disdain for knowledge of the natural world, social critic Christopher Hitchens groused,

“Augustine was a self-centered fantasist and an earth-centered ignoramus: he was guiltily convinced that god cared about his trivial theft from some unimportant pear trees, and quite persuaded – by an analogous solipsism – that the sun revolved around the earth. He also fabricated the mad and cruel idea that the souls of unbaptized children were sent to ‘limbo.’ Who can guess the load of misery that this diseased ‘theory’ has placed on millions of Catholic parents down the years, until its shamefaced and only partial revision by the church in our own time?” (64)

For the Neo-Platonists, if primary causes are spiritual, then science becomes unnecessary; anagogical thinking would lead to epiphanies more surely than observation and measurement could lead to sound conclusions. Europe, hunkered down into a defensive posture from invading forces on all sides, had lost the original Greek and Roman texts on observation of the natural world, and had instead developed an obsession with cataloguing and organizing every aspect of existence as it related to the Great Chain of Being. This perspective would be profoundly challenged when contact with the Moors was re-established. Of the re-integration of Greek knowledge, Hitchens writes, “The scholastic obsessives of the Middle Ages were doing the best they could on the basis of hopelessly limited information, ever-present fear of death and judgment, very low life expectancy, and an audience of illiterates. …they had to work with pieces of Aristotle, many of whose writings were lost when the Christian emperor Justinian closed the schools of philosophy, but were preserved in Arabic translation in Baghdad and then re-transmitted to a benighted Christian Europe by way of Jewish and Muslim Andalusia. When they got hold of the material and reluctantly conceded that there had been intelligent discussion of ethics and morality before Jesus, they tried their hardest to square the circle.” (68). Ironically, in seeking to export Catholicism and retake the Holy Land from the Arabs, the Vatican accidentally imported a vast amount of knowledge that had been lost to the Western world for hundreds of years – technologies like the compass and astrolabe, but even more importantly, the works of the great Greek and Roman philosophers. The impact was immediate, and undeniable. A cultural revolution against modi antichi, or the “old ways” commenced.

The Neo-Platonists didn’t go down without a fight, however. Over the course of the next thousand or so years, the conflict between these two perspectives would intensify until the two belief systems – faith and science – came to be essentially antagonistic. However, before this split developed into its current bitterly divided entrenchments, many philosopher scientists continued to hold that knowledge of God and knowledge of the natural world could not be opposed. Erasmus argued in his classic satire “In Praise of Folly” that the Neo-Platonic Stoics were essentially creating their own “gardens of Tantalus,” a reference to the mythological character who was surrounded by delicious fruit which he could not eat (1926).

In fact, a number of modern people with allegiance to both science and faith have attempted to build or uncover the bridge between the two that Augustine began to chip away at in the fourth century. According to Professor Mary VandenBerg of the Calvin Theological Seminary in Michigan, “…the Reformed theological tradition tends to affirm scientific inquiry.” Introduced by French theologian John Calvin in the sixteenth century, the “Two Books” theory is often used by scientists with Christian beliefs to reconcile apparent differences between the two. This theory proposes that God reveals himself to mankind through two books; the Bible, or “Special Revelation,” and the book of “General Revelation,” or nature. Calvin asserted that these two “books,” both authored by God, could not contradict each other in any way. If they appear to do so, the cause must be human error in interpretation of one or the other. Thus, according to Reformists, a religious scientist need not feel conflicted between a geologist’s claim that the Earth is 4.5 billion years old and a biblical scholar’s claim that it is 6000 years old. One of them has simply interpreted the data incorrectly; and since the carbon-dating method is more accurate, the biblical expert is probably wrong. This need not mean that the Bible is wrong, however.

Religious historian Arthur McCalla referred to Isaac Newton specifically as an example of a scientist who believed in the two books theory so completely that his faith was the specific driver of his scientific inquiry. Of Newton, McCalla wrote: “Whatever knowledge God has revealed in the (uncorrupted) Book of Scripture is harmonious with what he has inscribed in the Book of Nature.” (17) Similarly, Stephen Jay Gould’s well-known theory of non-overlapping magisteria, or NOMA, argues that there is no inherent conflict between the domains of science and religion, because there is no overlap between their areas of expertise. Science governs the empirical constitution of the universe, Gould claims, while religion is defined by the search for proper ethical values and spiritual meaning. Not only do the domains of these individual magisterium (teaching authority) not overlap, but they are not the sole means of inquiry by which humans seek to understand the world; for instance, Gould cites art and the meaning of beauty as another magisterium altogether. “To cite the arch clichés,” he jokes, “we get the age of rocks, and religion retains the rock of ages; we study how the heavens go, and they determine how to go to heaven.” (4) Hitchens, of course, rejects this escape hatch while offering some sympathy to early scientists. “One must state it plainly. Religion comes from the period of human history where nobody – not even the mighty Democritus who concluded that all matter was made from atoms – had the smallest idea what was going on. It comes from the bawling and fearful infancy of our species, and is a babyish attempt to meet our inescapable demand for knowledge (as well as for comfort, reassurance, and other infantile needs).” (64)

For Isaac Newton, however, the question of whether scientific knowledge might be heretical was a moot point. He had his own secret religious heresies to worry about; as an anti-Trinitarian, he believed that worship of Jesus Christ and the Holy Spirit as equal deities to God was itself blasphemous within the context of monotheism. In fact, it was his Unitarianism that kept him from progressing beyond the prestigious Lucasian professorship at Cambridge, a position he was recommended for by his mentor, Isaac Barrow. Barrow had very nearly invented calculus himself; like his protégé, he held a keen interest in theology and left his position at the university to pursue his theological studies. Over the course of writing one of world’s great scientific works, Philosophiæ Naturalis Principia Mathematica, Newton described gravity, the Three Laws of Motion, and verified the accuracy of Kepler’s views on heliocentrism.

According to David Burton in The History of Mathematics, “Whereas Newton’s physical laws led some to view the universe as a self-sufficient mechanism, a gigantic piece of clockwork machinery, Newton himself insisted that the solar system was not a godless creation. This admirable ordering of the universe was precisely what confirmed in Newton his believe (sic) in a divine controller. The feeling that he was the man destined to unveil the ultimate truth about God’s creation led him to try his hand at theology and biblical studies.” (363). The depth of his faith, which consumed as much of his attention as had his mathematical studies, would lead Hitchens to later dismiss Newton as a “…spiritualist and alchemist of a particularly laughable kind…” in his anti-religion manifesto, “God is Not Great.” (65).

Professor Morris Kline proffers a very different perspective on the intersection of faith and genius in Newton’s life. “The Newtonian era created celestial mechanics but destroyed heaven…” he wrote. Kline described how Ptolemaic and Aristotelian philosophies, adopted by Christianity as a device to frame God, were gradually dismantled by successive scientific discoveries that curtailed the divine role in natural processes with each new observation. As rationalism replaced faith, the conflict between dogma and determinism intensified. “Each of the great intellects possessed a combination of mathematical or scientific genius and religious orthodoxy which today are regarded as incompatible and possible only in a period of transition….they attempted to reconcile their intellectual and spiritual affirmations. …[Newton] often justified the hard and, at times, dreary scientific work only because it supported religion by providing evidence of God’s order in the universe.” Kline also quotes Newton himself, who wrote in the second edition of Principles that “This most beautiful system of sun, planets, and comets could only proceed from the counsel and dominion of an intelligent and powerful Being.” (260)

Hitchens counters the example of Newton’s indisputable devoutness with the purely scientific viewpoint of another groundbreaking mathematician and astronomer, Pierre-Simon de Laplace. Laplace was the first astronomer to develop a concept of black holes, and revolutionized working models of solar systems by building them to be viewed from the outside. The French emperor, upon requesting and receiving his orrery, was confused; “…in his childish and demanding and imperious fashion, he wanted to know why the figure of god did not appear in Laplace’s mind-expanding calculations. And there came the cool, lofty, and considered response. ‘Je n’ai pas besoin de cette hypothese.’” (67) Hitchens is clearly impressed by Laplace’s assertion: “I do not need this assumption.”

German philosopher Gottfried Leibniz, Newton’s peer and the cofounder of calculus, was also a deeply religious man who wrote principally about beliefs systems, thought patterns and theology. Leibniz’s philosophical bent is noted for its optimal perspective – that the universe was created to be the best possible version of God’s vision. Without being aware of Calvin’s two books philosophy, Leibniz espoused the concept implicitly in his seminal work, “Theodicy” by stating that reason and faith are both gifts from God and thus cannot contradict each other.

It is not difficult to see how he would have thought of calculus as a metaphysical question rather than strictly one of hard science; arithmetic can tell us what to do with integers, but how to explain Zeno’s paradox of Achilles and the rabbit? As the distance is halved, neither can ever reach the finish line – for Leibniz, this was not a question of pure mathematics as it was understood at the time, but of the nature of the space between spaces. He was certain that metaphysical problems must have a pattern that could be revealed through logic; though they might appear unconnected on the surface, his work on calculus was based in the belief that spiritual laws must somehow correspond to natural laws.
Mathematician Paul du Bois-Reymond described this mindset: “As is well known, the theory of the maxima and minima of functions was indebted to him for the greatest progress through the discovery of the method of tangents. Well, he conceives God in the creation of the world like a mathematician who is solving a minimum problem, or rather, in our modern phraseology, a problem in the calculus of variations – the question being to determine among an infinite number of possible worlds, that for which the sum of necessary evil is a minimum.” (143)

While critics argue that the faith of the fathers of calculus is no more relevant to modern scientific endeavors than their affection for powdered wigs, Dr. Elaine Ecklund’s three-year study of 1700 scientists and their views on religion and spirituality produced some surprising results. She found that almost half of practicing American scientists identify with a religious label; even among the 30% who classified themselves as irreligious, “Many atheist and agnostic scientists even think key mysteries about the world can be best understood spiritually, and some attend houses of worship, completely comfortable with religion as moral training for their children and an alternative form of community.” In fact, Ecklund found 20% of atheists in her survey consider themselves to be “spiritual.” (156) Despite a particularly American strain of fundamentalist zealotry and a corresponding British strain of atheistic zealotry that seek to increase the perception of hostility between science and religion, the truth is, as it always has been, considerably less binary. Like Aristotle, Newton and Leibniz, many modern scientists continue to view their own personal faith as a motivation for seeking the truth, rather than a hindrance to its discovery.