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## The Christian inspiration of the science of nature

Ignacio Sols

lecture delivered on September 16, 2022

I congress of the Spanish section of the Society of Catholic Scientists

Pamplona, Spain, September 15-17, 2022

I will develop this topic: *Christianity has been to physics what Greece was to mathematics*. Not only the cultural matrix in which it developed, but its own worldview inspired the birth of that science. Let's start with mathematics.

Mathematics begins the moment there is a demonstration. Therefore, the previous civilizations - Babylonian, Indian, Chinese, Egyptian - that worked with numbers and geometric forms, did not do mathematics properly speaking, since they did not provide demonstrations but only formulas as a recipe, although it was certainly the prehistory of mathematics, without which this science would not have been possible.

By reducing the Pythagorean Philosophy all reality to issue, it reduced to issue, in particular, geometric forms, and thus arose the first demonstrations of arithmetical formulas by geometric arrangements, for example, the demonstration that the sum of the first n odd numbers is the square of n. (Thus, 1+3+5 is the square of 3). They demonstrated this by filling a square with n L-shaped lines with an odd, increasing issue of points. By demonstrating that, if the side of a square is a issue, then its diagonal cannot be - the ratio of the two is not a fraction - they found, in traumatic contradiction to their own Philosophy, that geometry and arithmetic are not equivalent, opting then for geometry^{1}. In that development, the Greeks discovered what today we call scientific theory, as a logical deduction of some axioms that are postulated, in this case plane geometry deduced from the five postulates of Euclid^{2}.

It is said with ignorance that the Christians destroyed ancient science, although the science of nature, literally physics (physis=nature) had not yet been born in Greek antiquity. As for mathematical science, it was only developed in Alexandria as a scientific or research activity, and was not destroyed by anyone, but became the science of Islam, when Alexandria was taken in 640 by an army of the third caliph Otman. (In Athens, after the transfer of the scientific activity to Alexandria at the end of the 4th century B.C., only commentators, or teachers, remained, a tradition that had its golden chain of Christian commentators in Byzantium - with cultural focus in the Library Services of Constantinople - until its fall in 1453).^{3}.

In the fair half of the seventh century, the century following the capture of Alexandria, science shifted its capital to the capital of the Abbasid caliphate, Baghdad, flourishing as the science of Islam, from the beginning of the ninth century, in The House of Wisdom, which came to surpass the ancient Library Services of Alexandria in issue of volumes. Most of its initial intellectuals - thirty-seven - were Christian Arabs. This fulfilled the rule that the victors -Muslims- end up recognizing the cultural superiority of the vanquished -Christians- until being educated by them, after a work of translation of the culture of the vanquished: the first translators, such as Yahyah, his disciple Hunayn ben Ishac, or his son, Ishac ben Hunayn, were Christian Arabs. But the leading mathematician Al-Guarizmi was already a Muslim. He created algebra, whose formulas he demonstrated with Euclid's geometry, and popularized the Indian numeration introduced in the Arab world in 662 by the Syrian bishop Severus Sebockt, to which in that same 9th century the zero would be added, a numeration with which it was already possible to calculate (impossible with Greek or Roman numerals). Other Arab creations followed, such as spherical trigonometry, useful for astronomy and the science of navigation.

Less fortunate than Byzantium, the Christian West was heir to the culture of Rome, rich in humanistic aspects, but without scientific activity, i.e. research. However, the Christian Boethius, from the 6th century, wrote a brief summary of mathematical science with four ways: arithmetic, geometry, astronomy, music, which was taught in the high ages average as mathematical quadrivium in monastic and cathedral schools, thus preserving the faint Roman flame. Master of the cathedral school of Reims was the mathematician Gerbert of Aurillac, future pope Sylvester II - the pope of the year 1000 - who introduced the Arabic numerals in the Christian world (although they would not be popularized until the work of Leonardo of Pisa, son of Bonacci - Fibonacci -, already in the 13th century). He formed a group of disciples giving rise to a first intellectual renaissance that made it possible that, when Toledo was reconquered from the Almoravids, definitively at the beginning of the following 12th century, a school of translators of Arabic science was created there, which nourished the nascent universities with philosophical and mathematical knowledge at the end of that century and the beginning of the following 13th century. In that same 13th century, the Dominican Jordanus Nemorarius and the pope's chaplain, Campanus, expanded Euclid's geometry. From Jordanus, for example, is the law of the inclined plane. And in the 14th century, Nicolas d'Oresme, bishop of Lisieux, scientific light of the age average, will introduce the coordinates of the plane - longitude and latitude - in his work *De latitudine formarum and *added for the first time two convergent series, showing others to be divergent. This new flowering of mathematics benefited from the translations from Greek, in the 16th century, of mathematical works of greater depth. The Sicilian priest Francesco Maurolico translated Apollonius' book of conics, which in 1637 was to give birth to coordinate geometry, into the works of Pierre de Fermat and René Descartes; and he also translated Pappus' fourth-century Synagoge, probably the first Christian mathematician, in which he solved various problems of maxima and minima. Pierre de Fermat, in the same year 1637, in a two-page letter sent to the *Republic of Letters*, the first internet managed by the minimal priest Marin Mersenne, unified Pappus' methods in which a maximum or a minimum is produced when a certain value is annulled, which he defined precisely, and which today we call derivative!

The so-called *invention of calculus*, half a century later, did not consist then in the definition of the derivative, but in the finding that the integral (or calculus of quadratures) is the inverse operation of the derivative (or calculus of tangents, since Fermat). This reduced the difficulty of integration, in which the Jesuit Bonaventura Cavalieri had made essential contributions (with the principle that bears his name), to the automatism of the derivative, in which the Jesuit Gregoire de Saint Vincent had made progress** **(with his method of *infinitesimals*, with which he found the derivative of the logarithm). The Frenchman Blaise Pascal (Voltaire will not forgive him for not finishing it) and the Italian Evangelista Torricelli (who in fact invented it, but died without publishing his work) were on the verge of inventing calculus. Parallel lives: both with work also in physics, in fact related. Both died at the age of 39, and both Catholics, deeply religious. Calculus was to be invented by Isaac Newton in the 1670s, closely following the method of calculus of the tangent of the Anglican priest Isaac Barrow. Gottfried Leibniz came later to this same invention, but published it before, in 1682 and 1684, in the *certificate *Eruditorum, German imitator of the *Journal des savants*, first scientific magazine created in continuation of the *Republique des lettres*.

The Christians contributed, then, in a decisive way, to the development and extension of mathematics. But *there is no reason why their Christian worldview influenced this noble activity *. In my opinion,* *was a Christian science, but not a Christian science, but a continuation of the science born of the Greek spirit, in which, once born, anyone can enter, independent of their worldview. And I say this despite the fact that its protagonists were Christians, many of them deeply religious. This is the case of Pierre de Fermat, for example, whose two daughters, among his three sons, embraced the religious state; or René Descartes, who converted the Queen of Sweden to Catholicism, or Isaac Newton, who wrote theological works -a kind of Arianism-; or also, Gottfried Leibniz who made great efforts, although ineffectively, to reunite his Lutheran confession with Catholicism.

And this will be the case of the mathematicians of the following 18th century, the Calvinist Leonhard Euler - also with theological work - and Jean Louis Lagrange, a Catholic, whose generalized coordinates, inspired by the polar coordinates of the medieval member of the clergy John Buridan, will make the infinitesimal calculus more easily applicable. But, in this same 18th century, Bishop George Berkeley, a connoisseur of this calculus, accused of the lack of rigor with which the infinitesimals are divided in it, making two falsehoods a truth. With the sting of this accurate criticism, Augustin Cauchy will initiate the rigorization of the calculus in the following 19th century, in an exciting adventure that will culminate in the work of Bernard Riemann (as the Cauchy integral and the Riemann integral recall). But this required a proof of our intuitive notions about the real numbers, in which the German priest Bernard Bolzano will participate with several theorems, including the one that bears his name. In fact, it was Bolzano who first proposed a foundation of mathematics in logic and who first used the term set ("Menge") to distinguish finite sets from infinite sets, just as Cantor would later do. But George Cantor will also distinguish between different types of infinity (by showing that the infinity of numbers is different from that of real numbers), which gave rise to his transfinite mathematics. To support this mathematics, he created set theory, which was soon to be understood as the *formalization of all mathematics*. Half a century later, in 1930, Kurt Gödel demonstrated the impossibility of proving its consistency, although no one doubts that mathematics is consistent, that is, that it does not contain any contradictions^{4}. But as far as our topic is concerned, let us say that these protagonists of the rigorization of mathematics, Cauchy, Riemann, Bolzano, Cantor, Gödel were all deeply Christian. Riemann, in fact, was a Lutheran pastor, although he never became a pastor because of panicus fori; as was his teacher Karl Friederich Gauss, the *princeps mathematicorum* to whom a good part of contemporary mathematics is heir. A science in which a multitude of Christians participated, but which was born in the Greek cultural matrix and inspired by the Pythagorean Philosophy .

Something similar happened to physics with Christianity. It begins with the conversion of John Philopon from paganism, which leads him to reject the belief in the divinity of the stars, and to say that they are not made of subject different from that of the earth, so we will understand their movements when we know the movements on earth. Responding to two questions of Aristotle about the movement, he wrote around the year 530 about the natural movement or free fall: "if you drop a body and another several times heavier you will find that they fall to the ground at about the same time". About violent movement, or movement produced by a driving force, Philopon said that this gives the mobile a momentum - what we call today inertia - by which it no longer needs any force to continue moving. From there follows the medieval prehistory of physics - as a theory of movement or momentum - when it was taken up again by the Persian Avicenna, 11th century. In the 12th century Avempace of Saragossa will say that the speed in the movement is produced by the difference between driving force and resistance to the movement (which was still resistance of the medium, they still did not have the idea of resistance of the mobile, or inert mass). And he will erroneously say that this comparison is the difference between force and resistance; but later, in the same century, it will be Averroes of Cordoba who will say, correctly, that it is the quotient. When the theory of motion passed to the Christian universities of the 13th century, after the translations in Toledo in the 12th century, St. Albert the Great and Peter Gil of Rome (Bishop of Bourges) will follow the correct line of Averroes; while Roger Bacon, St. Thomas and Duns Scotus follow in parallel the mistaken line of Avempace. But what is important here is that this theory of momentum, born of a Christian, has passed again, through the mediation of Islam, to the Christian world, until producing in the 14th century the first concepts that we call scientific today -*uniform* motion*, uniformly accelerated motion, speed average-* that is to say universals that have not been abstracted by observation of nature (who has seen the speed average?) but have been constructed by means of a definition.

After the impasse of the plague, the Hundred Years' War and the War of the Three Roses, the theory of motion was still preserved at the beginning of the 16th century at teaching in Paris. There studied the Segovian Dominican Domingo de Soto, the first to apply the notion of uniformly accelerated motion to the free fall of bodies, which will be experimental in the following century, in the work of Galileo. And it is also he who places the resistance to motion not in the medium but mainly as *internal resistance* of the mobile: its inert *mass *. Galileo will take up this concept, which will allow Descartes to *construct*the concept of quantity of motion (mass x velocity) as a conserved quantity in the absence of forces. This will lead Newton, in 1687, to establish this principle as the basis of his mechanics: if a force is applied, it equals the variation, or time derivative, of the quantity of motion. Thus physics was born, and it was born as a commission from Edmund Halley to Isaac Newton to deduce the three laws of the planets that Johannes Kepler -using the system introduced by Copernicus, canon of the cathedral of Frauenburg- had observed experimentally. Kepler had earlier written (in *Harmonices mundi*): "God wanted us to recognize them [the laws] by creating us after his own image, so that we could participate in his very thoughts".

Physics, then, began its prehistory with the change of worldview from the ancient world to the Christian world -paradigmatic in the conversion of John of Philopon-, was gestated in the bosom of Philosophy medieval scholasticism, and was born of the conviction that the world is the work of a God, supreme intelligence, who "arranged everything from agreement to measure, issue and weight", that is to say that he left laws of mathematical form; laws, therefore, that the intelligence of man - his image and likeness - should be able to recognize with the use of mathematics. This quotation of the book of Wisdom was in vogue among the intellectuals of that time in which Kepler writes "God always geometrizes"*(Harmonices mundi*). Thus, physics was not only gestated and born in the work of Christians, but* physics was born inspired by the Judeo-Christian worldview *. This is how Alfred Northcott Whitehead puts it: "Faith in the possibility of science derived from medieval theology".

Once the train of physics was set in motion, anyone, believers or non-believers, could get on it, so it is less important the undoubted fact that there were many Christian believers in its development; let us take for example the case of electromagnetism, in which it is possible to experiment when Alexander Volta, who was a catechist, invented the electric battery to create direct currents. Both Ampere and Biot were also Catholic converts; and Joule and Oersted were an Anglican and a Lutheran who both wrote in terms similar to those of Kepler; and electromagnetism passed from its prehistory to its history, in the work of Michel Faraday and James Clerk Maxwell, both deeply Christian. This theory predicts the electromagnetic waves that a Lutheran, Heinrich Rudolf Hertz, managed to produce, and that at the turn of the century the Italian Guglielmo Marconi, also a deeply religious Catholic, would use for radio. At higher frequencies, this theory connects with the wave theory of light of Christian Huygens and Augustin Fresnel, predicting the speed previously measured by Hippolyte Fizeau, three names of Christian confession, and whose corpuscular nature was also demonstrated by the experience of another Christian: the Compton effect.

Coming to the more modern quantum theory, this arose as an explanation of the experience of two Anglicans Rayleigh and Jeans, the latter with apologetic work. Its founder Max Planck was a Lutheran who found in his Christian faith strength and consolation for the death of his two wives and, in adulthood, of his two daughters and three sons, two in the First World War and the third hanged for his participation in the attempt against Hitler. When his quantum theory was applied to an atomic theory arising from the experiences of Joseph John Thomson, discoverer of the electron, and Ernest Rutherford, discoverer of the atomic nucleus -both Anglicans-, it would lead to quantum mechanics whose starting shot in 1925 was the thesis of Louis de Broglie, a French Catholic, and whose final understanding came in 1927 with the uncertainty principle of Werner Heisenberg, a Lutheran. This crowned two years of research in which other Christian believers such as Pascual Jordan and Wolfgang Pauli collaborated.

None of these was member of the clergy, but there are even founders in other branches of physics: René Juste Haüy, who was co-founder with the Anglican Bragg, of crystallography; or George Lemaïtre, founder of the Big-Bang theory. In fact, there are entire areas of science that have a priest as founder, such as stratigraphy, founded by Blessed Nicholas Steno, or Genetics, founded by Gregor Mendel.

We can end by asking ourselves: what is the difference between mathematics and physics, for which the latter had to wait for the Christian worldview? The answer may be that the verification of the truth of mathematical propositions does not require experimentation, but the truth of physical propositions requires the observation of nature, and cannot be deduced, since the world is not necessary but contingent - it may not be, or may be, contingent.^{5}The answer may be that the verification of the truth of mathematical propositions does not require experimentation, but the truth of physical propositions requires observation of nature, and cannot be deduced, since the world is not necessary but contingent - it may not be, or may be otherwise - a concept that the Greeks did not have.

That is why the affirmation of the contingency of the world in the condemnation by the Bishop of Paris, Étienne Tempier, 1277, of the Averroist thesis that saw the world as necessary, has been called the magna carta of science by Pierre Duhem. In fact, this important document was the backing for the call for experimentation in the work of the Franciscans Robert Grosseteste and Roger Bacon, who ten years earlier had written in his famous *Opus tertium*: "Experimental science can perform multiple and unsuspected inventions. It can produce marvelous effects and machines that improve the conditions of human life, such as: fire or perpetual lamps, weapons that can destroy the enemy without the necessity of physically wounding him with the sword, antidotes against dangerous poisons, explosives, ships without oars or sails, cars that move by themselves, flying machines, elevating machines, submersible machines, bridges without pillars, etc. There are many things that have very strange powers and properties that we do not yet know about because of negligence in conducting experiments." Written in the 13th century!

I would like to end by quoting, in support of this thesis that physical science was born with a religious inspiration, the great creators of quantum theory and the theory of relativity.

Max Planck: "There can never be a true civil service examination between science and religion. Any serious and thoughtful person realizes, I believe, the necessity of recognizing and cultivating the religious aspect present in his own nature, if he wants all the forces of the human soul to act together in perfect balance and harmony. And it is really *no accident* that the greatest thinkers of all ages were deeply religious souls, even if they did not publicly display their feelings in this regard" (Planck, *The Mystery of Our Being*, art. in Wilber, 1988, p. 210).

Albert Einstein: "Science can only be created by those who are deeply imbued with a yearning for truth and understanding. The source of these feelings comes, however, from the religious sphere. To it belongs also the faith in the possibility that the rules governing the world of the existent are rational, that is, attainable by means of reason. I cannot conceive of a true scientist who lacks this deep faith. All this can be expressed in an image: science without religion is lame, and religion without science is blind" (Albert Einstein, Ideas and Opinions, art. in Wilber, p. 166).

1 For example, the first demonstration that has come down to us literally is the squaring, by Hippocrates of Chio, of two moons, 5th century B.C. A moon is the difference between a circle and another of greater radius, and its squaring means the possibility of constructing by ruler and compass the side of a square of equal radius area. He then conjectured the quadrature of the circle, a problem that, like the doubling of the cube and the trisection of the angle, stimulated Greek mathematics for centuries in search of a solution. These three conjectures received a negative answer in the 19th century.

2 Euclid probably took the idea of postulate, as something that is not demonstrated but serves to demonstrate, from the very recent postulate of exhaustion of the brilliant mathematician Eudoxus, a generation earlier: if a magnitude -length, area or volume- is subtracted from more than its half, and what remains is subtracted from more than its half, etc., it becomes smaller than any magnitude (epsilon, we would say now) given a priori.

3 The 6th century commentators, Eutotius, Anthemius of Tralles and Isidore of Miletus were the architects of Hagia Sophia, 6th century, and great figures followed in later centuries, such as Michael Constantine Psellus in the 11th century, or Pachymeres and Maximus Planudes in the 13th century.

4 Gödel conjectured - guided, as he declares, by his platonicism, against formalism and logicism that pretended to reduce mathematics to pure logic - a negative answer to a conjecture of Hilbert about mathematics: the decidability of arithmetic (equivalent to the decidability of set theory, that is, of all mathematics). This means that Hilbert proposed to prove the existence of an oracle algorithm that could decide whether or not a given proposition follows from its axioms. When Alan Turing became aware of this, he created the theory of machines, to show that the problem of his paradox - the so-called Halt Problem - is unsolvable by an algorithm or machine. This proved Gödel's negative conjecture, and gave rise - as a consolation award ! - to cybernetics, when Von Neumann in 1946, at the Princeton EDVAC project , and Turing in 1950 at the British ACE project , built the first computers. (Computer science was born, like so many other technological revolutions, from a theoretical problem - let us take a good grade- without any use internship ). But as far as our topic is concerned, let us say that Turing was an atheist, and that Von Neumann was a convert to Catholicism (with his ideas and comings and goings, but he died a Catholic); and that the so-called "father of computers", the British Charles Babbage, who a century earlier had designed his programmable "analytical machine" (in fact, programmable with punched cards, like the ones we used in the seventies), was also a Christian, deeply believing. But its construction remained unfinished, although it inspired implementations in the following century.

5 In fact, only physics, and not mathematics, is science in Wittgenstein's strict sense, since the propositions of mathematics have no sense. Indeed, the meaning of a proposition is, in Wittgenstein's famous Tractatus, what it says about nature, and therefore propositions that can only be false or can only be true are meaningless, the latter being the case of mathematical propositions. They affirm nothing about the world -although they say a lot about ideas to those of us who are Platonists-. For the opposite side, the logicist -in retreat after the theorems of a Gödel who found inspiration in his platonicism- mathematics only affirms what we all agree on agreement: that what is contained in our mathematical libraries is deducible in first-order logic from the ten axioms of Zermelo-Fraenkel. On the other hand, physical propositions can be true or false, and to find out it is necessary to observe the world.