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Chapter 2

God’s Plan

Immediately following the ancient Greeks, we should discuss Titus Lucretius Carus (99 BC–55 BC) who is considered to be the intellectual heir to Epicurus. He was a Greek Epicurean at the time of Julius Caesar (100 BC–44 BC) and the author of the remarkable, long poem De Rerum Natura (On the Nature of Things) written in Latin. Lucretius must have admired the atomism judging from his beautiful sentence, “the elements are like the letters of the alphabet where with 24 letters you can construct thousands of words.” The original Latin De Rerum Natura written on papyrus consisted of 7,400 lines filling six books and must have been copied tens of times though papyrus survived impressively long. But, it was thought to have been lost to posterity until a copy from copies of copies of Simplicius of the 6th century AD was found in a German monastery in 1417 by Poggio Bracciolini (1380–1459).

A cultural hero Lucretius was a Prometheus in Greek mythology, and in the 20th century Robert Oppenheimer was called a modern Prometheus.¹ There must have been many admirers of Prometheus during the time of Caesar as the famous Roman statesman and orator Marcus Tullius Cicero (106 BC–43 BC) praised De Rerum Natura as “Poetry of Lucretius is rich in brilliant genius, yet highly artistic.” The greatest Roman poet Virgil (70 BC–19 BC) was about 15 years old when Lucretius died and he must have read De Rerum Natura, judging from his youngster-style acclamation, “Blessed is he who has succeeded in finding out the cause of things”.

The influence of the ancient Greeks at that time can be seen everywhere in Italy. The current name of Naples arises from Nea Polis (new city in Greek) due to Gordon Semenoff’s interpretation, showing that Greek influenced so much in this region. From the remains in Pompei, archeologists find the influence of Greek philosophers in Rome. Lucretius belonged to the school of Epicurus, although Greenblatt’s 2019 book The Swerve² cites that Philodemus (a Greek invited to Rome since Greek classicism was admired there) stayed in Rome at the time of Lucretius. So, the Epicurus school seems to be a Greek school at the time of Greek supremacy, specialising in Natural Laws.

The original Latin poem must have been admirable to Romans in the classical period even as the English translation with 7–9 words in a line muses beautifully:

“Whilst human kind

Throughout the lands lay miserably crushed

Before all eyes beneath Religion–who

Would show her head along the region skies

Glowering on mortals with her hideous face–

A Greek it was who first opposing dared

Raise mortal eyes that terror to withstand,

Whom nor the fame of Gods nor lightning’s stroke

Nor threatening thunder of the ominous sky

Abashed; but rather chafed to angry zest

His dauntless heart to be the first to rend

The crossbars at the gates of Nature old.”

It is not known to what extent actually Lucretius intended to convey the philosophy of Epicurus because this poem is through the 6th-century prodigeous pagan writer Simplicius. Still, Democritus was a generation earlier than Epicurus. This poem was given much publicity and importance in the book The Swerve by Steven Greenblatt published in 2011 and winner of a 2012 Pulitzer prize. Greenblatt suggested that the De Rerum Natura played a significant role in seeding the Renaissance. Whether true or not, the poem does contain in Lines 113–140 of Book II a truly remarkable atomistic description of Brownian motion, which was understood only two millennia later by Boltzmann (1872) and Einstein (1905), and which Lucretius regarded as proof of the existence of atoms.

Not surprisingly, his other scientific musings were less accurate. Although he suggested the idea that Nature experiments across aeons and that organisms have the best chance of survival when they best adapt in terms of strength, speed, and intellect, he did not anticipate what we now know as evolution. He did not recognise the superiority of humans to animals, which is a strong motive among God’s plan of the universe.

Poggio’s discovery of De Rerum Natura was made toward the end of Dark Ages or it may be better to say that it ended the Dark Ages. The reason that it was hidden so long was because Epicureanism was regarded as pagan by Christian leaders. For the book De Rerum Natura to be known to the masses, it must have been copied to a great extent. If purchase of De Rerum Natura were allowed, merchants must have copied it to get profit with whatever its cost. But, forbidden by Church elders, it was copied only in isolated monasteries in the Dark Ages. Copying it was not given preference in the isolated monasteries and there must have been some errors or puported corrections by scribes in the monasteries. In The Swerve, Stephen Greenblatt imagines a possible scene in a monastery scriptorium:

“The monastery was a place of rules, but in the scriptorium there were rules within rules. Access was denied to all non-scribes. Absolute silence reigned. Scribes were not allowed to choose the particular books that they copied or to break the dead silence by requesting aloud from the librarian such books as they might wish to consult in order to complete the task that had been assigned them. An elaborate gestural language was invented in order to facilitate such requests as were permitted. If a scribe wanted to consult a psalter, he made the general sign for a book–extending his hands turning over imaginary pages–and then, by putting his hand on his hand in the shape of a crown, the specific sign for the Psalm of King David. If he was asking for a pagan book, he began, after making the general sign, to scratch behind his ear, like a dog scratching his fleas. And if he wished to have what the Church regarded as a particularly offensive or dangerous pagan book, he could put two fingers into his mouth, as if he were gagging.”

In the middle of the Dark Ages, it must have not been possible for scribes to copy De Rerum Natura with ease, as only a few remaining ones today testify. In the early Roman Empire, alternatively called the late classical period, “paganism” was used for practicing polytheism, with gods of Jupiter, Neptune, Venus, etc. The early Christians in the 4th century practiced polytheism because it was practiced in rural and provincial areas compared to the Christian population in the big cities. In the late classical period, Christians used to judge one as a pagan if he practiced a ritual sacrifice as in the carnivals.

A pivotal Emperor leading to the Dark Ages was Constantine the Great (272–337), who legalised Christianity in February 313 as a compromise with the rival Emperor Licinius (263–325), authoring the Edict of Milan. The Edict stated that Christians should be allowed to follow their faith without oppression along with all other religions/cults in the Roman Empire. He chose the Greek city Byzantium (later known as Constantinople) as the Capital of the Empire and opened the millenium-lasting Byzantine Empire. Since then, the city was the capital of the East Roman Empire (better known as Byzantium) and the Ottoman Empire, now called Istanbul. The Emperor must have favoured Greece out of all the candidates for the capital. As Yannis Rizos commented, Istanbul in Greek means “To the City”, saying that his mother always said ‘istanbul’ when she went out to Corfu city. Istanbul was The City in the Byzantine Empire.

The Edict of Milan, allowing pagans the same rights as Christians, was allegedly reneged by Licinius, not favouring Christians, in the year 320, and Licinius was made a private man in the great civil war of 324. So, the Christian-prone Constantine convened the first Council of Nicaea in 325, declaring the Nicene Creed, God the Trinity, and the statement of Christian belief. In contrast to Trinity, the non-trinitarian doctrine Arianism, proposed by Arius (c. 256–336) of Alexandria in Egypt, was made illegal. Since then, Constantine the Great heavily promoted the Christian Church, which even seeded in the High Middle Ages the Papal claim to temporal power based on the forged Donation of Constantine. Constantine ordered Old Saint Peter’s Basilica to be built, which took over 30 years to complete. For this, he went to great lengths to erect the basilica on top of St. Peter’s resting place, even allowing changes of the initial design of the basilica. He became the patron of Christianity with Licinius absent.

Even before becoming the only Emperor of the whole Roman Empire, Constantine dealt a blow to Donatists, whose doctrine derives the name from the North African bishop Donatus (?–c. 355). Donatism had flourished during the fourth and fifth centuries. It had its roots in the Christian community of the Roman African province (now Algeria and Tunisia), which was ruled by Constantine in 311. Donatism was a heresy leading to a schism in the Church of Carthage from the 4th to the 6th centuries. The Roman governor of North African, lenient to the large Christian minority under his rule throughout the persecutions, was satisfied with Christians handing over their scriptures as a token repudiation of faith. But, when the persecution ended, Christians who handed the holy things over were called traitors by their critic Donatists (who were mainly from the poorer classes). Donatists argued that Christian clergy must be faultless for their ministry to be effective, and their prayers and sacraments to be valid. The Donatists were rigourists, saying that the church must be a church of ‘saints’ but not ‘sinners’. Caecilianus, on the opposite side of Donatists, was archdeacon and then Bishop of Carthage in 313–316. His appointment as Bishop led to the Donatist Controversy of the Late Roman Empire. There were Christian bishops ordained by Donatus during 313 and 316 against the bishops of the Caecilianus party. The North African bishops could not come to terms with this, and the Donatists asked Constantine to act as a judge in the dispute. Three regional Church councils, and another trial before Constantine, all ruled against Donatus and the Donatism movement in North Africa. In 317, Constantine issued an edict to confiscate Donatist church property and to send Donatist clergy into exile.

Even before the Council of Nicaea, Donatists were crushed by Constantine. So, the Nicene Creed dealt mostly with Arianism, a name originating from the Christian presbyterian Arius. Arianism is a non-Trinitarian Christological doctrine which asserts the belief that Jesus Christ is the Son of God who was begotten by God the Father at a point in time, a creature distinct from the Father and is therefore subordinate to him, but the Son is also God, i.e. called God the Son.

Also, he enforced the Nicaea Council’s recommendation on prohibiting the celebration of the Lord’s Supper on the day before the Jewish Passover, which marked a definite break of Christianity from the Jewish tradition. But, Jews were not considered pagans by his laws. Even though it was made illegal if Christians were affected by Jewish, such as by seeking converts, by attacking other Jews who had converted to Christianity, by owning Christian slaves, or by circumcising their slaves, Jewish clergies were given the same exemptions as Christian clergies.

Even with these strong Evicts of Constantine the Great, Epicureanism had permeated deeply in the public in the late classical period, chiefly because of the Epicurean motive of the pursuit of happiness. So, there was a strong need to suppress the pagan belief of Epicureanism.

In the early Byzantine Empire in Alexandria, three or four generations after Constantine, there was an influential and beautiful Hellenistic, Neoplatonist philosopher Hypatia (350–370 ?–415) whose father Theon (c. 335–405) was a mathematician. She used to ride a chariot in the city in a philosopher’s cloak tribon. In her own lifetime, Hypatia was renowned as a great teacher and a wise counsellor, and many came to her to learn the works of Plato and Aristotle.

As recently as 1996, there was big news about Wiles’s proof of Fermat’s last theorem that x³ + y³ = z³ does not have integer solutions. This equation is a Diophantine equation discussed in Arithmetica authored by Diophantinus (201–215 to 285–299) of Alexandria, about one and half centuries before Hypatia. In 1637, Pierre de Fermat wrote in the margin of a copy of Arithmetica that he found a truly marvellous proof of his last theorem, but that the proof was too large to fit in the margin. Hypatia is known to have written a commentary on Diophantus’s 13-volume Arithmetica. This item alone can show that the Neoplatonist Hypatia was an influential mathematician, astronomer, and philosopher. But, in her lifetime, Neoplatonism was not embraced by Christianity. During the religious feud in Alexandria, four generations after the Nicene Creed, Serapeon (the temple of Greek–Egyptian Jupiter as a means to unify the Greeks and Egyptians) was destroyed. The Serapeon in Alexandria had the second-best collection compared to the Museum of Alexandria, containing a half million papyrus rolls in its peak. With the Serapeon gone, the written pagan knowledge also disappeared. During this chaos, Hypatia was murdered by a mob of Christians led by a lector named Peter in March 415. Hypatia’s murder shocked the Empire and transformed her into a “martyr for philosophy”, and her father’s student Damascius became increasingly fervent in his opposition to Christianity. Damascius (c. 458–after 538), born in Damascus of Syria and known as “the last of the Neoplatonists,” was the last scholar of the School of Athens. He was one of the pagan philosophers persecuted by Emperor Justinian I in the early 6th century. Among the disciples of Damascius, the most important are Simplicius who was mentioned as the celebrated commentator on Aristotle in Chapter 1. Some modern scholars consider that the legend of Saint Catherine of Alexandria was probably based on the life and murder of Hypatia, with reversed roles of Christians and pagans after embracing Platonism in Christianity in the Middle Ages. But, Neoplatonists in Alexandria at that time were pagans. In any case, our information on the Greeks’ atom has a lineage Democritus–Epicurus–Aristotle–Lucretius–Hypatia–Simplicius.

The downfall of the statue of Serapis at Serapeon of Alexandria in 415 was lamented by poet Palladas as the end of way of life in the Epicurean ‘Gardens’, and the murder of the intellectual Hypatia was a precursor of the death knell for the whole pagan tradition, which was finally terminated by Emperor Justinian in 429. With the Eviction, other paganisms, including Stoicism and Scepticism, were also driven out. Stoicism was started by Zeno of Citium (c. 334 BC–c. 262 BC) in Athens in the early 3rd century BC, and the Stoics were taught that “virtue is the only good” for human beings, and that external thing — such as health, wealth, and pleasure — were not good or bad in themselves. According to Stoicism, the path to happiness for humans is found in accepting the moment as it presents itself, by not allowing oneself to be controlled by the desire for pleasure or fear of pain, exactly the opposite way of Epicureanism. As Neoplatonism was evicted, so was Stoicism. The virtue of Stoicism is similar to that of Platonism, and the stoic attitude was installed in the monasteries in the Middle Age. Scepticism is an attitude where one shows doubt whether something is true or useful. Radical forms of scepticism deny that knowledge or rational belief is possible, and urge us to suspend judgment on many or all controversial matters. More moderate forms of skepticism claim only that nothing can be known with certainty, or that we can know little or nothing about the big question in life, such as whether God exists or whether there is an afterlife. Religious scepticism is “doubt concerning basic religious principles such as immortality, providence, and revelation”. The 13th-century saint Thomas Aquinas (1225–1274) stated on the creation in Genesis: “With respect to the origin of the world, there is one point that is of the substance of the faith, viz. to know that it began by creation,” and the Roman Catholic Catechism³ published in 1566 placed “belief” in the first place. Scepticism was evicted along with the other paganisms in 429.

Along with Epicureanism, Neoplatonism, Stoicism, and Scepticism, Totemism and Animism also belonged to the evicted paganisms. Along with Animism, Totemism was the earliest form of belief worshipping a sacred object, or symbol that served as an emblem of a group of people, such as a family, clan, lineage, or tribe. Animism derived from Latin anima (meaning breath, spirit, and life) is the religious belief that objects, places, and creatures all possess a distinct spiritual essence. There is some common ground in Totemism and Animism.

By the early 5th century, what mattered most were the logical philosophies from the classical Greek period. Stoicism was practiced by monks in the monasteries sprawling after the Justinian Evict. Thus, as in most cases — Heaven and Hell, Sun and Moon, North and South, plus and minus, good and bad, love and hate, freedom vs. equality, Republican vs. Democrat, particle and wave — there remain two dominating pagans from Greek philosophies: Epicureanism and Neoplatonism. As John Vergados commented, Romans the excellent soldiers wanted some philosophy from Ancient Greeks.

Epicureanism aims at the pursuit of happiness, and Neoplatonism aims at the pursuit of virtue. Which was chosen by Romans?

Cicero’s epigram nihil est virtute pulchrius (there is nothing more beautiful than virtue) morally resonates in our ears, and Thomas Jefferson’s insertion “pursuit of happiness” in the Declaration of Independence is recited over and over again. It must have been difficult to favour one over the other. To Christians, both were pagans. Then, they looked for a possibility of changing the way of practicing. To Epicureans, all were materialistic and God was not acceptable by definition. They did not view the world in the way of Empedocles that even if gods existed they do not interfere the humans. Epicureans were useless to Christians.

In the 5th century, the greatest Christian Father Saint Augustine (354–430) adopted a very non-literal approach for the ‘6 days’ of creation (Hexahemeron in Greek) of Genesis, saying that it was not a temporal succession, but all things were produced simultaneously by God in the single instant and subsequently underwent some natural process of development.⁴ The 13th century book Summa by Saint Thomas Aquinas of the classics of the history of philosophy stated that St. Clement (c. 150–216) and Origen (c. 185–254) had held the same view.⁵ This view held that the universe underwent some natural process of development. But, hexahemeron at an instant is not reconcilable with the swerve (little by little) of atomistic creation mused by Lucretius. Platonic creation by Dẽmiourgos narrated by Timaeus is not the interpretation of Augustine, but there is a possibility to change the Neoplatonists’ minds because they were not 100% materialist. They had the virtue which can be God’s will instead of materialistic happiness. They can be transformed to Christians. So, through Saint Augustine, Christian Fathers adopted one philosophy of Ancient Greeks, Neoplatonism.

Independently from Saint Augustine, Saint Ambrosius (340–397), Archbishop of Milan, authored the Hexahemeron. Hexahemeron was first presented in Lenten lectures by Saint Basil (329–330 to 379), the bishop of Caesarea Mazaca in Cappadocia (modern-day Turkey). Saint Ambrosius was exchanging letters with Basil and must have been influenced by Basil, and he was notable for his influence on Augustine of Hippo. The hexahemeron must have been an issue in the beginning of the 5th century.

There was no place to talk about Epicureanism after 429. And, Epicureanism was forgotten together with the Lucretius poem De Rerum Natura.

Scientifically, the Latin numerals are not helpful in developing science by estimating the magnitude of some number. In a sense, the Dark Ages helped in importing the so-called Arabic numerals into Europe in the Islamic era, which began in 622 when Islamic armies started to conquer Arabia, Egypt, and Mesopotamia. In a century, Islam had reached the area of present-day Portugal in the west and Central Asia in the east. The spread of Islam across Western Asia and North Africa encouraged an unprecedented growth in trade and travel by land and sea as far away as Southeast Asia and China. Its Golden Age was roughly between 786 and 1258 (the year Baghdad fell to the Mongols) with stable political structures and flourishing trade. In this Golden age, of course astronomy was useful for determining the Qibla, the direction that should be faced towards Mecca in which to pray. Arabian merchants traded merchandise all over the world to India, to Indonesia, and even to the Far East. During this period, Catholic Europeans got the Oriental spices and also the Indian numerals through Arabian merchants.

Richard Bulliet, Pamela Crossley, Daniel Headrick, Steven Hirsch, and Lyman Johnson state, “Indian mathematicians invented the concept of zero and developed the ‘Arabic’ numerals and system of place-value notation used in most parts of the world today”.⁶ The development to the currently used numerals was gradual, and the Arabian merchants used it for trading during the third Islamic caliphate, the Abbasid Caliphate (Capital Bagdad, 750–1258), and most Europeans must have thus learned the Arabic numerals.

According to the ancient Indian mathematical text found in 1881 in the village of Bakhshali, Mardan (near Peshawar in present-day Pakistan), the Indian numerals was used around 385 and 465, the estimate given by the carbon dating of Maan Singh.⁷ The Bakhshali manuscript, Fig. 1(a), contains the “placing symbol” (a bullet) in the second line from the bottom. In Fig. 1(b), the “placing symbol” is written as 0. Here, two aspects are of concern in mathematics. First of all the beautiful Arabic numeral itself is not important. The important thing is that it is just one connected letter. As shown in Fig. 1(b), some original Indian numeral forms survive until now but the important aspect of it is just one unit. It is not so in Chinese and in Latin. The second is the placing mark, the bullet in Fig. 1. The placing mark is very useful in the present-day decimal system. It is also useful in binary numbering or in any other numbering system. If we used the duodecimal numbering system, we must have used two more one-unit characters for 10 and 11. The placing can still be the bullet. Today, the decimal-system numerals 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 are used more often than the Roman alphabets. The book On the Calculation with Hindu Numerals by al-Khwarizmi (c. 780–850) written about 820 and the book On the Use of the Indian Numerals by al-Kindi (801–873) were principally responsible for spreading the Hindu–Arabic numeral system throughout the Middle East and Europe.

Figure 1: The Bakhshali manuscript marked on birch bark (a), and the Indian numerals (b).

In particular, al-Kindi was an Arab Muslim philosopher, deeply affected by the Greek Neoplatonist, and one of his lifelong efforts was to make the Greek thought acceptable to a Muslim audience, which was carried out at the House of Wisdom in Baghdad, an institute of translation and learning patronised by the Abbasid Caliphs. Like Simplicius, he was a prodigious writer, writing at least 260 books on geometry (32 books), medicine and philosophy (22 books each), logic (nine books), and physics (12 books).

While Christians in Europe were blocked from the knowledge of the ancient Greeks, al-Kindi spread the Greek view of the solar system from Ptolemy, who placed the Earth at the centre of a series of concentric spheres, in which the known heavenly bodies (the Moon, Mercury, Venus, the Sun, Mars, Jupiter, and the stars) are embedded, which would be changed by Copernicus after the Dark Ages of the Europe. Al-Kindi must have been influenced by Saint Augustine (354–430) in attempting to demonstrate the compatibility between philosophy and natural theology, and had successfully incorporated Aristotelian and (especially) Neoplatonist thought into an Islamic philosophical framework as the first philosopher writing in the Arabic language. Most medieval Islamic mathematicians wrote in Arabic with some others writing in Persian.

In al-Kindi’s view, the knowledge of God is the goal of meta-physics, but later the most influential Islamic philosopher al-Farabi (c. 872 to 950–951) strongly disagreed with him on this issue, saying that metaphysics is actually concerned with the first principle, and as such, the nature of God is purely incidental. A first principle is a basic proposition or assumption that cannot be deduced from any other proposition or assumption. In philosophy, first principles are from First Cause attitudes taught by Aristotelians. In mathematics, first principles are referred to as axioms or postulates. In physics, theoretical work is said to be from first principles or ab initio, if it does not make assumptions such as an empirical model and a parameter fitting. In the West, several centuries after al-Farabi, René Descartes (1596–1650) described the concept of a first principle in the preface to the “Principles of Philosophy: Now these principles must possess two conditions: in the first place, they must be so clear and evident that the human mind, when it attentively considers them, cannot doubt of their truth; in the second place, the knowledge of other things must be so dependent on them as that though the principles themselves may indeed be known apart from what depends on them, the latter cannot nevertheless be known apart from the former.” Central to al-Kindi’s understanding of metaphysics is God’s absolute oneness, which he considered an attribute uniquely associated with God. In addition to absolute oneness, al-Kindi also described God as the Creator or an active agent. Of God as the agent, all other intermediary agencies are contingent upon Him. The key idea here is that God ‘acts’ through created intermediaries, which in turn ‘act’ on one another — through a chain of cause and effect — to produce the desired result. In reality, these intermediary agents do not ‘act’ at all; they are merely a conduit for God’s own action.

In contrast to al-Kindi, who considered the subject of meta-physics to be God, al-Farabi believed that it is related to God only to the extent that God is a principle of absolute being. Al-Kindi’s view was, however, a common misconception regarding Greek philosophy among Muslim intellectuals at his time in Baghdad, and it was for this reason that Avicenna (c. 980–1037) remarked that he did not understand Aristotle’s metaphysics properly until he had read a prolegomenon written by al-Farabi. Neoplatonism was started in the Platonic tradition by Plotinus (c. 204–205 to 270) in Hellenistic Roman Egypt. Hypatia mentioned earlier was a Neoplatonist. His six Enneads were edited and compiled by his student Porphyry (c. 234–305) around 270. Through Augustine of Hippo (354–430), an early Christian theologian, the Cappadocian Fathers, Pseudo-Dionysius the Areopagite (a Christian theologian and philosopher of the late 5th to early 6th century), and several subsequent Christian and Muslim thinkers, Enneads greatly influenced Western and Near-Eastern thought. Neoplatonism influenced mainstream theological concepts within religions, such as the work on duality of the one in two metaphysical states that laid the foundation for Christian notions of Jesus being both god and man, a foundational idea in Christian theology.

Al-Farabi’s cosmology is essentially based upon three pillars: Aristotelian metaphysics of causation, highly developed Plotinian cosmology, and the Ptolemaic astronomy. In his model, the universe is viewed as a number of concentric circles: the outermost sphere or ‘first heaven’, the sphere of fixed stars, Saturn, Jupiter, Mars, the Sun, Venus, Mercury, and finally the Moon. The centre of these concentric circles inside the Moon’s orbit contains the material world. It is a more elaborate form of Fig. 5 in Chapter 1.

In the Dark Ages, both Christian Fathers and Muslim philosophers were concerned about the role of God and the creation of the universe, and accepted the concept of “duality”. Contemporary physicists also use that word: wave–particle duality in Bohr’s quantum mechanics, “triality” as an extended form in the heyday of the eight-fold way, and T–S duality and ADS/CFT correspondence in string theory. Among these usages, the most profound one is the wave–particle duality that is discussed in Chapter 5.

In the Islamic world, some aspects of fundamentals of mechanics were also studied, which is however dwarfed by Newtonian mechanics and universal gravitation. In the 6th century, John Philoponus (c. 490–570) rejected the Aristotelian view of motion. However, unlike Galileo, Philoponus did not have the unfortunate peril of sitting in front of inquisitors. He argued instead that an object acquires an inclination to move when it has a motive power impressed on it. More interesting is the statement of Ibn Sina (980–1037) that a moving object has “force” which is dissipated by external agents like air resistance. Ibn Sina distinguished between ‘force’ and ‘inclination’ (mayl); he claimed that an object gained mayl when the object is in opposition to its natural motion. His mayl is potential energy under current understanding. But, he did not invent an appropriate device to prove his statement.

In the Islamic world, there was great progress in practical applications, e.g. in geology, astronomy, and engineering. As mentioned above, astronomy became a major discipline within Islamic science. Another was astrology, predicting events with the best knowledge for going to war or founding a city. Al-Battani (850–922) accurately determined the length of the solar year. He contributed to the Tables of Toledo, used by astronomers to predict the movements of the Sun, Moon, and planets. Six centuries later, Copernicus (1473–1543) used these astronomic tables. Al-Zarqali (1028–1087) developed a more accurate astrolabe, used for centuries afterward. He constructed a water clock in Toledo, and discovered that the Sun’s apogee moves slowly relative to the fixed stars, and obtained a good estimate of its motion by its rate of change. Nasir al-Din Tusi (1201–1274) in Persia wrote an important revision to Ptolemy’s 2nd-century celestial model. When Tusi became Helagu’s astrologer, he was given an observatory and gained access to Chinese techniques and observations. He developed trigonometry as a separate field, and compiled the most accurate astronomical tables available at that time.

But, the historian of science Bertrand Russell took the view⁸ that Islamic science lacked the intellectual energy required for innovation, and was chiefly important for preserving ancient knowledge and handing it on to medieval Europe, while admirable in many technical ways. Transfer of Indian/Arabic numerals to medieval Europe may be his basis of judgement, but al-Farabi’s understanding of Aristotle is a fundamental intellectual understanding. So, recently, there has been a revisionist view, exemplified by theoretical physicist Nobel Laureate Abdus Salam,⁹ George Saliba,¹⁰ and John M. Hobson,¹¹ that a Muslim scientific revolution occurred during the Middle Ages. Scholars such as Donald Routledge Hill¹² and Ahmad Y. Hassan¹³ argue that Islam was the driving force behind these scientific achievements. Here, it is worthwhile to cite Gustavo Branco’s comment¹⁴ that in recent years physics in the Mediterranean region was not as progressive as that in the Nothern Europe because of the influence of the Catholicism forbidding free thinking. In a sense, Hill and Hassan point out that in the Islamic world there was not that much prohibition of free thinking.

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¹K. Bird and M. J. Sherwin, American Prometheus: The Triumph and Tragedy of J. Robert Oppenheimer (Vintage Book Company, 2006).

²S. Greenblatt, The Swerve: How the Renaissance Began (W.W. Norton & Company, New York, 2011).

³S. M. Barr, Modern Physics and Ancient Faith (University of Notre Dame Press, Notre Dame, IN, 2003).

⁴S. M. Barr, Modern Physics and Ancient Faith (University of Notre Dame Press, Notre Dame, IN, 2003).

⁵The views of the church fathers of Hexahemeron are reviewed in Appendix 7 of Volume X of the Blackfriars edition of The Summa Theologiae of St. Thomas Aquinas (Eyre and Spottiswoode, Ltd., London, 1967), pp. 203–204.

⁶R. Bulliet, P. Crossley, D. Headrick, S. Hirsch, and L. Johnson, The Earth and Its Peoples: A Global History, 3rd Ed. (Houghton Mufflin, Boston, 2005), Chapter 6 “India and Southwest Asia”, p. 163, ISBN 0-618-42770-8.

⁷M. Singh, Subandhu (Sahitya Akademi, 1993), pp. 9–11, ISBN 81-7201-509-7.

⁸B. Russell, History of Western Philosophy (Simon and Shuster, US, 1945), Book 2, Part 2, Chapter X.

⁹A. Salam, H. R. Dalafi, and M. Hassan (1994). Renaissance of Sciences in Islamic Countries (World Scientific, Singapore, 1994), p. 162, ISBN 9971-5-0713-7.

¹⁰G. Saliba, A History of Arabic Astronomy: Planetary Theories During the Golden Age of Islam (New York University Press, 1994), ISBN 978-0-8147-8023-7.

¹¹J. M. Hobson, The Eastern Origins of Western Civilisation (Cambridge University Press, 2004, ISBN 978-0-521-54724-6).

¹²D. R. Hill, Islamic Science and Engineering (Edinburgh University Press, 1993), ISBN 978-0-7486-0455-5.

¹³A. Y. Hassan and D. R. Hill, Islamic Technology: An Illustrated History (Cambridge University Press, 1986), p. 282.

¹⁴A private comment at Corfu, Summer 2019.