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Chapter 1

Ancient Greeks

The beginning of The Feynman Lectures on Physics states the following:

“If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis. In that one sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied.”

The great American physicist Richard Feynman considered atomic theory to be the most important scientific achievement of human intelligence (see Fig. 1).

Modern physical science is an offspring of atomic theory, as noticed from Mendeleev’s periodic table from 150 years ago in 1869, culminating in current particle physics. We will discuss the current status of particle theory which has its roots in the natural philosophy of the classical Greek period. Roughly the first half of this book is devoted to the stories from the Greek period to WWII, and the second half to the establishment of the current particle theory in the last 70 years.

Let us start with Democritus, who is an important character in the theme of the book. Then, an opposite view is presented, that taken by Plato. These two are the ancient Greek counterparts to the two mentioned in our book title. However, they were influenced by philosophers who investigated the same topic, following the principle that there is a rational explanation to the physical world. Thus, various schools related to the topic (in Ionia, in Athens, in Magna Graecia, and in Alexandria) will be briefly mentioned (see Fig. 2).

Figure 1: Feynman’s blackboard.

The origin of atomism is credited to a remarkable Greek natural philosopher Democritus (460 BC–370 BC) of Abdera, Thrace. He was born in the 80th Olympiad (460 BC–457 BC) according to Apollodorus of Athens. He lived in the first classical period of the Greek tradition. Greek philosophy is said to have begun in 585 BC when Thales of Miletus predicted the eclipse of the Sun and ended when the Academy of Athens closed in 529 AD as a result of the East Roman Emperor Justinian’s stopping of its financial support. The period 2,500 years ago when Democritus worked was when the first problems were encountered. The first philosophers had the problem of defining the concepts, and Greek is accurate on this account compared to Latin and English. Science today has its jargon. For example, we use “flavour” and “colour” for properties of elementary particles, but we adopt these just for naming.

The first philosophers’ definition turns out to be consistent with later use. The noun kosmos derives from a verb meaning “to order”, “to arrange”, and “to marshal”. Thus, what the first Greek philosophers meant by kosmos was an orderly arrangement. Our use of the cosmos is the universe, the totality of things, but it is an ordered universe. The word physics derives from a verb “to grow”. Growing things, plants, animals, and moving planets, are different from stones at rest. Thus, physics meant study of nature in contrast to artificial items, and corresponds to the present-day science. A cause is needed for movement. The word arche cognates from a verb meaning “to begin”, “to commence”, “to rule”, and “to govern”. Writers on early Greek philosophy use arche to mean principle, which is not different from our current understanding. It is said that arche was first used by Anaximander. Nature is the principle and origin of growth.

Figure 2: A map of ancient Greek city states. Magna Graecia was the coastal areas of southern Italy, and Ionia included islands Chios and Samos and nearby four city states.

Gautama Buddha (624 BC–544 BC) was an enlightened teacher. The correct date of Buddha’s death was in dispute before 1956 AD, but it was declared officially in the sixth official meeting of Buddhist monks that that year was the 2,500 year anniversary of Buddha’s death. According to Buddha’s teaching, all beings come into being or cease to be, based on the causes and conditions which brought them into existence. In other words, they arise or cease only through interdependent relationships. The chief priest of the Buddhist temple Yakcheonsa, Sung Ku Kim (once an active quantum field theorist), says that the law of relationships or the theory of links — yeonkibeob in Korean — is the first principle of Buddhist philosophy. Without using the word creation, nothing exists on its own independent of anything else. Buddha’s teaching starts with brahman (meaning all in the universe in Sanskrit) and atman (real thing possessing the brahman). Around the same time when the first Greek philosophers (for example, Thales (624–623 BC to 548–545 BC)) anguished over defining the words including kosmos, Buddha taught his enlightenment to students in terms of brahman and atman, the self that possesses the faculties of feeling, understanding, will, and consciousness. Unlike the four elements of Plato, Buddhism does not allow creation of atman out of brahman. There are links only between atman.

The original writings on papyrus books of two and half millennia ago have not survived the time, largely due to the effects of climate and pests. The oldest writing on papyrus is the 4,500-year-old logbook Diary of Merer, recording transportation of casting stones to Giza from Tura, for Khufu’s Pyramid. It was found in a cave in Wadi al-Jarf on the dry Red Sea coast by archeologist Pierre Tallet in 2013. But, most books have not survived. Even if books from classical antiquity survived the perils of fire, raindrops from the library ceiling, or wear from excessive readings, they could not escape white-silver shiny bookworms. Aristotle presumed the existence of tiny bookworms, which were finally seen by Robert Hooke through a microscope in 1655. These worms are called “teeth of time” in The Swerve by Stephen Greenblatt. Writings in classical antiquity were on papyrus papers which are made from the 40-cm papyrus stems soaked in the Nile. The insect “teeth of time” finds this papyrus and nibbles away books like wood-eating ants destroying wooden structures over time. So, it was important that the writings of the first philosophers be copied for the next generations. When copied by scribes, there must have been errors or intended changes.

Between classical antiquity and now, the prodigious writer Simplicius of Sicily (c. 490–560) commented extensively on the works of Aristotle and others from which most of our information on the first philosophers is derived. Simplicius must have used copies of copies of copies of Lucretius’ copy of copies of Aristotle. The thoughts of the first philosophers were commented on by Aristotle and others in what are called “fragments” from which we understand the works of the first philosophers. Atomism of the classical antiquity arrives to us through Aristotle’s fragments, Simplicius’ translation, repeatedly copied by scribes in Christian monasteries in the Dark Ages dominated by Christianity, and Poggio’s discovery of Lucretius’ poems¹:

“Fear holds dominion over mortality

Only because seeing in land and sky

So much the course whereof no wise they knew,

· · · · · · · · · · · ·

But each might grow from any stock or limb

By chance and change, Indeed, and were there not For each its procreant atoms, could things have

· · · · · · · · · · · ·

But yet creation’s neither crammed nor blocked About by body: there’s in things a void–

· · · · · · · · · · · ·

Thus primal bodies are solid, without void.”

What Lucretius wrote is that the material of the universe is an infinite number of atoms moving randomly in the void (space). Now, most sources credit Democritus as the first atomist. His exact contributions are difficult to disentangle from those of his mentor Leucippus, as they are often mentioned together in texts. None of his writings have survived; only fragments are known from his vast body of work. Leucippus, the founder of atomism, was the greatest influence upon him. He and Democritus praise Anaxagoras. Most sources say that Democritus followed in the tradition of Leucippus and that they carried on the scientific rationalist philosophy associated with the school in Miletus. Both were thoroughly materialist, believing everything to be the result of natural laws. Unlike Aristotle or Plato, the atomists attempted to explain the world without reasoning as to purpose, prime mover,² or final cause. The atomists’ questions of physics should be answered with a purely mechanistic question, “What earlier circumstances caused this event?”, while their opponents search for “explanations” (logos), in addition to the material and mechanistic (see Fig. 3).

The atomistic void hypothesis was a response to the paradoxes of Parmenides and Zeno in Elea, the founders of metaphysical logic, who put forth arguments difficult to answer. To draw no movement in Democritus’ atomic theory, Parmenides and Zeno held that any movement would require a void — which is nothing — but a nothing cannot exist. The position of Eleatic school was “You say there is a void; therefore the void is not nothing; therefore there is not the void.”

The atomists agreed that motion required a void, but simply ignored the argument of the Eleatic school on the grounds that motion was an observable fact. Therefore, they asserted, there must be a void. This idea survived in a refined version as Newton’s theory of absolute space, which met the logical requirements of attributing reality to not being. Einstein’s theory of relativity provided a new answer to Parmenides and Zeno, with the insight that space by itself is relative and cannot be separated from time as part of a generally curved space–time manifold. Consequently, Newton’s refinement is now considered superfluous.

Figure 3: Democritus’ view with individual atoms.

Also, there was the Athenian school started by Socrates (470 BC–399 BC) and succeeded by Plato (430 BC to 348–347 BC) and Aristotle (384 BC–322 BC). Socrates’ philosophy is largely known by Plato’s dialogues. Plato established a school of thought where he taught students and held seminars. He also founded the Academy, the first institution of higher learning in the Western world. Based on ancient sources, most modern scholars believe that he was born in Athens or Aegina between 429 BC and 423 BC, not long after the start of the Peloponnesian War. According to Neanthes of Cyzicus, Plato was 6 years younger than politician Isocrates who was born in 436 BC. He is widely considered the pivotal figure in the history of Ancient Greek and Western philosophy, along with his teacher, Socrates, and his most famous student, Aristotle. Plato has also often been cited as one of the founders of Western religion and spirituality. The so-called Neoplatonism of philosophers like Plotinus and Porphyry influenced Saint Augustine and thus Christianity. Alfred North Whitehead once noted, “the safest general characterisation of the European philosophical tradition is that it consists of a series of footnotes to Plato.” Plato disliked Democritus, the founder of a competing philosophy, so much that he wished all of the latter’s books burned. Democritus was nevertheless well known to his fellow Northern-born philosopher Aristotle.

As a follower of Pythagorean teaching, Plato liked mathematical reasoning about Nature. So, he associated each of the four classical elements (fire, air, earth, and water) with a regular solid (tetrahedron, octahedron, cube, and icosahedron) due to their shapes, the so-called Platonic solids, and movements to golden ratios of numbers. He associated the fifth regular solid, the dodecahedron, to introducing time. Farmers in early civilisations needed to know the perfect time to plant their crops. Humans began to observe the Sun’s passage through a fixed point and this practice distinguished seasons. The Sun’s movement is time and hence the heavenly objects are related to time. These regular solids have fundamental faces, regular triangle, square, and regular pentagon. Even Werner Heisenberg mentioned³ the beauty (or symmetry) of Plato’s geometrical objects: “In Plato’s Timaeus, finally fundamental particles are not shapeless but mathematical objects.”

In Plato’s dialogues, Socrates and his company of disputants had something to say on many subjects, including several aspects of metaphysics. These include religion and science, human nature, love, and sexuality. More than one dialogue contrasts perception and reality, nature and custom, and body and soul. In the Timaeus (participants of the dialogue are Timaeus, Socrates, Hermocrates, and Critias), we find that Plato’s “the good (agathon in Greek)” becomes the principle in the creation of the universe. ‘Kosmos’ in Greek means “good, beautiful order”. Plato named the creator as dẽmiourgos, meaning craftsman-like carpenter. A carpenter exercises his best in making a table, and so does dẽmiourgos, realising agathon in the process of creating the universe. Dẽmiourgos in the dialogue Timaeus is the deified expression of Plato’s good and intelligence. Thus, Plato’s creation is both metaphysical and technical. The Timaeus was translated into Latin first by Marcus Tullius Cicero around 45 BC and later by Calcidius in the 4th century AD. Cicero’s fragmentary translation was highly influential in late antiquity, especially on Latin-speaking Church fathers such as Saint Augustine who did not appear to have access to the original Greek dialogue. Here, we follow a Korean translation from the Greek original by Korean experts on Plato’s dialogues.⁴

Timaeus narrates that Dẽmiourgos creates the universe based on his principle of the good and intelligence. Initially, the four elements (fire, air, earth, and water) were shapeless traces of them, mixed and in constant motion in the space (chòra). To relate to reality by observation, Plato reasoned that you cannot see anything without fire. Fire is the first element. Without earth, you cannot make solids. To have the continents, therefore, earth is the second element. To connect fire and earth, you need some flexible elements, which are air and water. Air and water are around the continent, and Fig. 4 places air and water around earth. In Fig. 4, the living creatures carrying the essence of these elements are inserted in the four regular solids. Then, Dẽmiourgos considered movements based on the patterns and the movement needed measuring time. For time, Plato related to the heavenly objects, Sun, Moon, planets, and stars. Out of these shapeless elements, Dẽmiourgos brought order and clarity, imitating (like a craftsman who follows a design) an unchanging and eternal model (idea or paradeigma). Timaeus travelled to Egypt and might have known Moses’ story, but his “shapeless” and the one in the first sentence of Genesis, “When in the beginning God created the heavens and the earth, the earth being untamed and shapeless, God said, Let there be light!” are different according to Chong-Hyun Park. The meaning in the Genesis is creation out of nothing (creatio ex nihilo in Latin introduced by Christian philosophers and clergy) and Greeks’ creation was “nothing is made out of nothing”(ex nihilo nihilo fit in Latin), namely, Dẽmiourgos’ creation was making shapes with the substance, technically using eidè (polygons) and arithmoi (numbers). As a carpenter, Dẽmiourgos had a purpose and designed his imitation based on the most ideal. The heavenly objects are placed in the dodecahedron⁵ with the Sun, the next important one beyond Earth, circling around it and others following the Sun or staying at one point, as shown in Fig. 5. The final shapes must be as beautiful (i.e., symmetric) as possible, ending up with five regular solids of Fig. 4.

Figure 4: Plato’s five regular solids and the corresponding elements.

Figure 5: Plato’s view of the universe in the dodecahedron.

•God’s design: Plato’s creation was a carpenter’s work following a principle (idea or paradeigma in Greek). Moses’ creation was out of nothing. In modern particle theory, the beauty and/or simplicity is frequently mentioned, which may be placed in Plato’s principle. So, we put Shakespeare’s ingenious design of the play in God’s design.

•Darwinism: The universe evolves according to the natural laws but the ingredients (particles) are put in the hot soup with certain initial conditions. Here, one does not need God’s hand of Fig. 1 in prologue. Even the initial conditions are better to be given by the natural laws. In this sense, basically Einstein’s God means creation via Darwinism.

Plato’s student Aristotle is considered to be the founder of the Peripatetic school of philosophy, opened in Lyceum in 335 BC, and Aristotelian tradition. Along with his teacher Plato, he has been called the ‘Father of Western Philosophy’. According to Chong-Hyun Park, Aristotle was trying to escape from the aura of Plato. Aristotle’s views on physical science written in Peri Physeos (On Nature) profoundly shaped medieval scholarship. Their influence extended from Late Antiquity and the Early Middle Ages into the Renaissance, and were not replaced systematically until the Enlightenment and theories such as classical mechanics. Aristotle considered one more element in addition to the four of Plato’s: ether. The Greek word for ether is pemtousia which means the fifth substance.

Historians in the 19th century invented the word “Neoplatonism” which applied to the tradition of Plato. The first Neoplatonist was Plotinus (c. 204–205 AD to 270 AD) in Hellenistic Roman Egypt. His writings Enneads have inspired centuries of Pagan, Jewish, Christian, Gnostic, and Islamic metaphysicians and mystics.

The atomic theory was applied in everyday living by Epicurus (341 BC–270 BC), who was born 7 years after the death of Plato on the island Samos to Athenian parents. He turned against the Platonism of his day and established his own school, known as “the Garden’, in Athens. His purpose of philosophy was to attain the happy, tranquil life, characterised by ataraxia (peace and freedom from fear) and aponia (the absence of pain) and by living a self-sufficient life surrounded by friends. He openly allowed women to join the school as a matter of policy. Epicurus and his followers were known for eating simple meals and discussing a wide range of philosophical subjects.

But, most knowledge of his teachings did not come from Greek originals but from the Latin written later by the Roman poet Titus Lucretius Carus or commonly Lucretius, the biographer Diogenes Laërtius, the statesman Cicero, and the philosophers Philodemus and Sextus Empiricus. He taught that death is the end of both the body and the soul and therefore should not be feared. Likewise, Epicurus taught that the gods, though they do exist, have no involvement in human affairs and do not punish or reward people for their actions. Nonetheless, he maintained that people should still behave ethically, not because of the ‘goodness’ mentioned by Plato but because of the burden of guilt which prevents them from attaining ataraxia.

Though popular, Epicurean teachings, pursuit of happiness, were controversial from the beginning in Athens which was the city of Plato. Epicureanism reached the height of its popularity during the late years of the Western Roman Republic, before declining as the rival school of Stoicism grew in popularity at its expense. It finally died out in late antiquity in the wake of early Christianity after Justinian’s edict of 529 AD. Epicurus himself was popularly, though inaccurately, remembered throughout the Middle Ages as a patron of drunkards, whoremongers, and gluttons.

Of course, there were many philosophers in the first classical period who influenced the atomic theory and Plato’s universe. The first person who thought deeply and deviated from the use of mythology to explain the world and the universe was Thales (624–623 BC to 548–545 BC) in the city state of Miletus in the ancient Greek Ionia. He is recognised as the first individual known to have entertained and engaged in scientific philosophy in Western civilisation, or more impressively the first since achieving cognitive faculty. He was one of the Seven Sages of Greece. The other Sages were politicians, Pittacus of Lesvos, Bias of Priene, Solon of Athens, Cleobulus of Lindos, Periander of Corinth, and Chilon of Sparta (Some cite Myson of Chenae and philosopher Anacharsis of Scythia, instead of Cleobulus and Periander). Thales was also a politician but is known better as the founder of the Ionian School. He proclaimed that the originating principle of nature and the nature of matter was a single material substance: water. Anaximander (610 BC–546 BC) succeeded Thales and became the second master of the Ionian School. Arguably, Pythagoras was one among his pupils. As mentioned before, Anaximander defined the word arche and is considered to be an early proponent of science and tried to observe and explain different aspects of the universe, with a particular interest in its origins, claiming that nature is ruled by laws.

Another ancient Ionian Greek philosopher who influenced philosophers of later times was Pythagoras who was the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced Plato, Aristotle, and through them Western philosophy. Pythagoras was credited with many mathematical and scientific discoveries, including the Pythagoras theorem, Pythagorean tuning, and the five regular solids, which were admired by Plato. It was said that he was the first man to call himself a philosopher (‘lover of wisdom’). Pythagorean ideas on mathematical perfection also impacted ancient Greek art. Pythagoras continued to be regarded as a great philosopher throughout the Middle Ages and his philosophy had a major impact on scientists such as Nicolaus Copernicus, Johannes Kepler, and Isaac Newton.

Diogenes Laërtius (3rd century AD) states that Pythagoras “did not indulge in the pleasures of love” and that he cautioned others to only have sex “whenever you are willing to be weaker than yourself”.

Parmenides and Zeno were born in Elea (560 BC–510 BC). Parmenides has been considered the founder of metaphysics or ontology and has influenced the whole history of Western philosophy. He was the founder of the Eleatic school of philosophy, which also included Zeno and Melissus of Samos. Zeno’s paradox was perhaps the first example of a method of proof called reductio ad absurdum, literally meaning to reduce to the absurd. Zeno’s paradoxes of motion were to defend Parmenides’ view. The single known work by Parmenides is a poem, On Nature, only fragments of which survive, containing the first sustained argument in the history of philosophy. In it, Parmenides prescribes two views of reality. In “the way of truth” (a part of the poem), he explains how all reality is one, change is impossible, and existence is timeless, uniform, and necessary. In the way of opinion, Parmenides explains the world of appearances, in which one’s sensory faculties lead to conceptions which are false and deceitful, yet he does offer a cosmology. Parmenides’ philosophy has been explained with the slogan “whatever is is, and what is not cannot be”. He is also credited with the phrase ex nihilo nihilo fit (out of nothing, nothing comes), commenting on Dẽmiourgos’ creation.

Before Democritus, Heraclitus (535 BC–475 BC) in Ephesus talked about the world in On Nature but he was uncertain where to place some words. So, he is nicknamed “The Obscure” or “The Riddler”. In Rhetoric, Aristotle described his style, “It is difficult to punctuate Heraclitus’ writings because it is unclear whether a word goes with what follows or with what precedes it. E.g. at the very beginning of his treatise, where he says: Of this account which holds forever men prove uncomprehending, it is unclear which ‘forever’ goes with.” He was author of On Nature which was dedicated to the great temple of Artemis, one of the Seven Wonders of the Ancient World. In Lives of the Philosophers, Diogenes Laërtius wrote, “They say that Euripides gave [Sokrates] a copy of Heraclitus’ book and asked him what he thought of it. He replied: ‘What I understand is splendid; and I think that what I don’t understand is so too — but it would take a Delian diver to get to the bottom of it.”’ Hippolytus presents a summary of Heraclitus’ main ideas in Refutation of All Heresies, “Heraclitus says that the universe is divisible and indivisible, generated and ungenerated, mortal and immortal, Word and Eternity, Father and Son, God and Justice.”

In Commentary on the Physics, Simplicius writes the following:

“In the first book of the Physics, Anaxagoras says that uniform stuffs, infinite in quantity, separate off from a single mixture, all things being present in all and each being characterized by what predominates. He makes this clear in the first book of the Physics at the beginning of which he says: Together were all things, infinite in quantity and in smallness. . .”

Here, Anaxagoras (510 BC–428 BC), born in Clazomenae and brought up in Athens, described the world as a mixture of primary imperishable ingredients, where material variation was never caused by an absolute presence of a particular ingredient, but rather by its relative preponderance over the other ingredients; in his words, “each one is ... most manifestly those things of which there are the most in it”. It is very similar to our understanding of chemical elements by Mendeleev’s table. But, he differs from Democritus’ atoms in introducing the concept of Nous (Cosmic Mind) as an ordering force, which moved and separated from the original mixture, which was homogeneous, or nearly so. He, being two generations before Democritus, might have influenced him. One generation before Democritus, Empedocles (490 BC–430 BC), a citizen of Akragas in Sicily, held the view that the four elements (fire, earth, breath, and rain written in Lucretius’ poem De Rerum Natura⁶) were those unchangeable fundamental realities. Plato had four elements, exactly the same as Empedocles’, changing breath to air and rain to water. Influenced by Pythagoras (died c. 495 BC) and the Pythagoreans, Empedocles challenged the practice of animal sacrifice and killing of animals for food. He developed a distinctive doctrine of reincarnation. Not only a scientific thinker and a forerunner to physicists, he was also a firm believer in Orphic mysteries. Aristotle mentions Empedocles among the Ionic philosophers, and he places him in very close relation to the atomist philosophers and to Anaxagoras.

Philosophers before Socrates (470 BC–399 BC), the first philosophers in the early antiquity, are customarily mentioned as pre-Socratic. Socrates was an Athenian philosopher credited as one of the founders of Western philosophy, and as being the first moral philosopher of the Western ethical tradition of thought. An enigmatic figure, he had no writings, and is known chiefly through the accounts of classical writers writing after his lifetime, particularly his students Plato and Xenophon. Plato’s dialogues are among the most comprehensive accounts of Socrates to survive from antiquity, from which Socrates has become renowned for his contributions to the fields of ethics and epistemology. It is this Platonic Socrates who lends his name to the concepts of Socratic irony and the Socratic method, or elenchus. However, questions remain regarding the distinction between the real-life Socrates and Plato’s portrayal of Socrates in his dialogues. Socrates exerted a strong influence on philosophers in later antiquity and in the modern era. Depictions of Socrates in art, literature, and popular culture have made him one of the most widely known figures in the Western philosophical tradition.

The statement “I know that I know nothing” is often attributed to Socrates, based on a statement in Plato’s Apology. The conventional interpretation of this is that Socrates’s wisdom was limited to an awareness of his own ignorance. Socrates believed the best way for people to live was to focus on the pursuit of virtue rather than the pursuit, for instance, of material wealth and happiness. He always invited others to try to concentrate more on friendships and a sense of true community, for Socrates felt this was the best way for people to grow together as a populace. His actions lived up to this standard: in the end, Socrates accepted his death sentence when his accusers thought he would simply leave Athens.

It is worthwhile to mention a few mathematicians after Plato who himself can be considered as one. In the Greek-speaking Alexandria, the capital of Ptolemy Kingdom,⁷ Euclid (325 BC–270 BC) wrote an encyclopedic treatise on all fields of mathematics, having written the integral knowledge of accumulated wisdom in Greece before. Being the best known among many, he may be regarded as the Father of Geometry. His remarkable book Elements provided an axiomatic logically coherent framework to discuss geometry on a two-dimensional flat plane involving parallel lines, similar and isosceles triangles. Euclid had the longest lasting impact of any ancient Greek mathematician as his textbook remained in use until the 20th century over 2,200 years later. Little is known about his life or how much of Elements was based on his own versus others’ discoveries.

It is remarkable that it was not until the 19th century that somebody discussed geometry on a curved surface such as on a sphere where parallel lines meet and that the angles of a triangle do not add to 180°, and so the Euclidean axioms fundamentally changed. This underlines just how simple and persuasive Euclid’s presentations were.

There was a mathematician physicist Archimedes (287 BC–212 BC) in Syracuse, Sicily. He was one of the leading scientists of classical antiquity and generally regarded as the greatest mathematician among the ancient Greeks. He partially anticipated modern calculus by the concept of sum of infinitesimals. He made an accurate estimate of π to two decimal places as π ≃ 3.14 and discovered that the area of a circle is given by πR², the volume of a sphere by 4πR³/3.

In order to determine whether the King’s crown had been made of pure gold, he enunciated the principle that weight is reduced under water by the weight of water displaced. He is alleged to have run naked into the street shouting “Eureka” after making this discovery while taking a bath, and went on to find that the crown-makers had indeed cheated the King.

Archimedes developed the idea of exponentiation to write large numbers. In mechanics, he contributed substantially to hydrostatics and to understanding the principles of levers. He invented a screw pump that is still used today. He designed a huge ship, Syracusia, the largest ship ever built at the time in which an Archimedean screw was used as the bilge pump.

Much more recently, Galileo described Archimedes’ accomplishments as ‘superhuman’ and the Fields Medal, the most prestigious prize in mathematics, is emblazoned with his image.

Despite protective orders by superiors, Archimedes was killed erroneously by a Roman soldier at the age of 75.

In Alexandria, Egypt, there were Hero (10 AD–70 AD) and Ptolemy (100 AD–170 AD). Hero was an engineer and mathematician. He invented an aelipile (or Hero engine), which is the precursor of the steam engine which prompted the field of thermodynamics in the 19th century AD. Hero is responsible for Hero’s formula in mathematics, which provides the area of a triangle from its side lengths. He also discovered methods for computing square roots and cube roots. Ptolemy was a mathematician, astronomer, and geographer. He wrote Almagest, the only surviving ancient treatise on astronomy. In it, he famously suggested a geocentric Ptolemaic Solar System, an idea which was generally accepted for 1,200 years until the work of Copernicus. He was certain that the Earth does not move, an idea firmly adopted by the Catholic church as Galileo found out to his peril. Ptolemy also contributed significantly to cartography, producing maps of Eurasia and Africa, which can be admired at the Royal Geographical Society in London. His maps are surprisingly good given their age, although not surprisingly they do contain entertaining mistakes when compared to any modern map.

To summarise Chapter 1, we started with the atomist Democritus and have described the accomplishments of over a dozen ancient Greeks, all with extraordinary intellects. The main achievements of antiquity were in philosophy including ethics, morals, and politics. These ideas remain a major influence in modern philosophy.

The overlap of science and modern ideas is necessarily less because the technology necessary to do useful experiments had not been developed since there were less data available. This is probably why the ancient Greeks depended more on philosophical speculations.

Nevertheless, modern physics has evolved in a Darwinian style from the atomism of Democritus and his school, who showed such remarkable prescience. Greeks admired Democritus, who was depicted on the 10-drachma coin before the switch to Euros. Of the ancient Greek mathematicans, Euclid and Archimedes founded the subject and set example for all later discoveries in mathematics.

Given all the intellectual progress between 600 BC and 100 BC, it can seem disappointing that only relatively small advances were made in the next 1,500 years.

__________________

¹T. L. Carus, On The Nature of Things (in English) (Enhanced EBooks Publishing, USA, 2015), Book I.

²Aristotle did not define the prime mover exactly and considered it as a general concept for the force that set the planets and universe in motion.

³W. Heisenberg, Physics and Philosophy: The Revolution in Modern Science (Penguin Books, New York, 1962), p. 71.

⁴C-h. Park and Y-k. Kim, Plato’s Timaeus in Korean (Seo Gwang Publishing Company, Seoul, Korea, 2000).

⁵Twelve is considered to be the number of heaven.

⁶S. Greenblatt, The Swerve: How the Renaissance Began (W.W. Norton & Company, New York, 2011).

⁷Even now there are more Greek speaking people in Alexandria than those in Greece.