Philolaus of Tarentum

Philolaus was a Greek Pythagorean and Pre-Socratic philosopher. It was a number of reports tat indicate that Philolaus was born some time before 440 BC.

Pythagoras is said to have retired to Metapontum toward the end of his life and to have died there about 500 BC. Tradition holds that he left no written works, but his ideas were carried on by a large number of eager disciples. Philolaus of Tarentum is one of his disciples is said to have written the account of Pythagoreanism.

Philolaus had studied with some of the expelled Pythagoreans, and he was interested in number magic and mysticism. Philolaus is generally credited with being the first Pythagorean to set the school’s teachings down in writing,

He put forward a theory of metaphysics that posited two fundamental principles, the unlimited and the limiting, which were the source of everything else.

Philolaus considers harmony as a necessary for creation of the cosmos. Otherwise only a disorderly and incoherently woven whole would arise, not the cosmos.

He is said to have thought in Thebes after leaving Italy when the Pythagorean school in Croton was disbanded. He may have returned to Tarentum to teach in his old age.
Philolaus of Tarentum

Heracleitus of Ephesus

Amongst the great Ionian who concerned themselves exclusively with philosophy was Heracleitus of Ephesus. He was the son of Blyson, or as some say, of Heraceon.

Almost nothing is known of Heracleitus’ life. He was aid lived during the period spanning the end of the sixth century and the beginning of the fifth century BC.

He grew up in one of the richest and most splendid cities in Asia Minor, Ephesus, at a time when it flourished under Persian rule. The city was founded about 1000 BC by colonists from Athens, it prospered by tapping the trade of both the Cayster and the Maeander.

He is specially remembered for his view that ‘everything is in a state of flux’. Fire, the most changeful of elements, is the origin and image of all things. Living creatures are formed of a mixture of the changeful essences of which fire and are types.

Heracleitus had definite ideas as to the question of diet, for he lived on herbs and abstained from meat. When he suffered from dropsy for instance, and held a consultation with most important physician in Ephesus, he suggested to them that his condition was like one after a heavy rain and a drought was needed to disperse the accumulation of water.
Heracleitus of Ephesus

Calendar in ancient culture

Calendars are manmade tools used to track time. They have become almost indispensible tools of human civilization.

Ancient cultures develop calendars to keep track of longer stretches of time that coincide with the four seasons.

Calendars are based upon astronomical observations, marking the passage of time using the phases of the moon and movement of the Sun. Civilizations from Asia to the Americas develop calendars based upon the phases of the moon.

Early calendars were usually for agriculture, financial, religious and political uses and often did not include a year count. The first historians to use calendar date systems for relating events were the Greek historians.

Ancient Greek calendars go back to early Antiquity but evidence of how they were structures and reckoned begins only in the sixth century BC. In general the calendars of Greece were lunar, but their lunar character could be disrupt by deliberate interference or tempering.

The main Athenian calendar is often called ‘archontic’ or ‘festival calendar’ - although its use went far beyond the determination of festival dates – to distinguish it from the so-called ‘prytanic calendar’, peculiar to Athens, that was used at Athens alongside it.

It wasn’t until Rome was fully under the rule of Augustus Caesar that calendars were used to refer to particular year names or numbers and month and day dates.
Calendar in ancient culture

Democedes of Cnidus: physician and adventurer

The peninsula of Cnidus was the seat of the most ancient medical school. Democedes was born in Croton, southern Italy in 560 or 555 BC. After travelling widely in Greek lands, Democedes became the medical attendant of the Persian monarch. Later he was employed as a spy to explore the coasts of Greece.

He escape from this service, however and settled in the Greek colony of Corto0n, in the instep of Italy. Here he devoted himself to writing a treatise in medicine. Croton became an important scientific center. The man who first made it famous in the world was Democedes.

Democedes left Croton and went to Aegina unequipped, without the tools of his craft, but his skill was such that within a year he surpassed the most famous physicians.

In the second year the Aeginetans appointed his state physician and paid him an annual salary of one talent, about $1200. In the third year the Athenians hired him for a hundred minae, and Polycrates in the next for two talent.

Herodotus records that Democedes was the physician of Polycrates of Samos, who perished in 522 BC and then of Darius, the King of Persia, from whom he was able to escape and return to his birthplace, Croton in 518 BC which toward the end of his life he had to leave again because of political difficulties.
Democedes of Cnidus: physician and adventurer

Ancient timekeeping device: Gnomon

The timekeeping devices used by different cultures are remarkably similar. The early inventions of the ancient civilizations of Egypt, Mesopotamian and Greece were crude and merely measured the amount of daylight versus nighttime hours.

The first of these devices is the gnomon, an early sundial. Sundials are considered to be the oldest form of timekeeping, although not in the form in the modern-day design.

The gnomon is essential a large stick place in direct sunlight. The time of day is determined by following the position of the shadow cast by the gnomon.

When the sun roses in the east, the pole will cast a long shadow to the west as the sun is shining directly onto the eastern-facing side of the pole.

As the sun rises in the sky, the shadow will slowly move to the northeast, finally pointing north at noon when the sun is at its highest in the sky, then gradually moving to the southeast as the sun sets, before ending in exactly the opposite position from its position at sunrise as the sun sinks beneath horizon.

The Babylonians and Egyptians divided the day into 12 units, six for sunrise to noon and six from noon to sunset.

Gnomons are used in Egypt in timekeeping for thousands of years. According to hieroglyphics texts, the measurement of time was central to the daily life of ancient Egyptians as early as the Old and the Middle Empires.

Greek astronomers of the Hellenistic period (around 550 BC) used the gnomon, a pole placed in the ground in an open field or area.
Ancient timekeeping device: Gnomon 

Cleostratus of Tenedos astronomical calendar

Greek astronomer, Cleostratus of Tenedos (520-432 BC) who lived rather outside the Ionian zone, made two important contributions to astronomy.

One was an improvement in the calendar, involving a better measure of the solar year. Together with Eudoxus, Cleostratus is credited with trying an 8-year cycle to commensurate the lunar and solar calendars.

Cleostratus proposed in the course of the eight years, to insert three intercalary months, of 30 days each, at the end of the third, fifth and eighth years respectively. He thus got a period of 2922 days, comprising 99 lunar revolutions.

The other was the knowledge of the signs of the zodiac and constellations in it which he introduced from Mesopotamia.

Zodiacal signs are frequently encountered upon Mesopotamia boundary stones and indicate the time of year at which the stones were erected.
Cleostratus of Tenedos astronomical calendar

Anaximander of Miletus

Anaximander (611-547 BC), Miletan pupils of Thales took much interest in geography. Anaximander is generally regarded as the second philosopher in the western philosophical tradition after Thales.

Anaximander also can be called the West’s first astronomer and geographer. He was the first among the Greeks to represent the details of the surface of the earth by maps. The idea of map-making was known in Egypt where plans of particular districts or objects as mines, houses and temples were being drawn up as early as 1400 BC. Anaximander, however, sought to convey a concrete picture of the surface of the earth as a whole.

From Babylon also he introduced the sun-dial. It consisted in essence of a gnomon, a fixed upright rod, the direction and length of the shadow of which can be measured hour by hour.

Anaximander was the first to speculate on the size and distance of the heavenly bodies. Departing from the Homeric view that the earth was a flat plate or disk, Anaximander characterized earth as a drum shaped cylinder suspended in midair. This idea looks remarkably like a guess at the celestial law of gravity.

This placement strongly suggested that the heavenly bodies passed through the sky and then under the Earth to reappear again the next day, thereby superseding earlier cosmological tendencies that limited the movement of heavenly bodies only to the sky above.

Anaximander seems to have guessed at the biological process of evolution. He is recorded as having believed that humankind originally emerged from fishes to step forth onto land.
Anaximander of Miletus 

Ancient history of calculus

Calculus comes from the Latin word for ‘pebble’ the primitive method of counting whose influence is also visible in the English word ‘calculation’.

The calculus had its origin in the logical difficulties encountered by the ancient Greek mathematicians in their attempt to express their intuitive ideas on the ratios or proportionalities of lines, which they vaguely recognized as continuous, in terms of numbers, which they regarded as discrete.

Archimedes (287 BC – 212 BC) developed a significant part of the calculus. The fundamental notion of the calculus - that of a limit - was well understood by Archimedes, although he did not call it by name.

The first known definition of continuity according to Aristotle (383-322 BC): A thing is continuous when of any two successive parts the limits at which they touch are one and the same and are, as the word implies, held together.

Indian mathematicians produced a number of works with some ideas of calculus. The formula for sum of the curve was first written by Aryabhata in 500 AD, order to find the volume of a cube, which was an important step in the development of integral calculus.

Indian astronomers also came very close to creating what now call calculus. They had advanced to the point where they could apply ideas from both integral and deferential calculus to derive the infinites series expansion of the sine, cosine and arctangent functions.

Early applications for calculus included the study of gravity and planetary motion, fluid flow and ship design and geometric curves and bridge engineering.
Ancient history of calculus

The history of Greek science

The birth of Greek science and philosophy did not occur in what is now Greek itself but in the city of Miletus and their Hellenic colonies on the Aegean coasts of Asia Minor.

It is certain that Greek science in its origin was dependent on traditions that came from more ancient civilizations, notably from Egypt and Mesopotamia.

Herodotus was the first to suggest that the Greeks obtained their knowledge of astronomy from Egypt and Mesopotamia.

Greek sciences period can be divided into four main chronological divisions:
*Pre-Socratic period (600 BC – 400 BC)
*The century of Plato and Aristotle later the creation of the Epicurean and Stoic philosophies.
*Hellenistic period (300-100 BC)
*Greco-Roman period, from about 100 BC to 600 AD

One of the major features of Greek science is that most of its practitioners were autodidacts. Even those who studied under a philosophical giant seem, with very few exceptions, not to have been content to follow a path laid down by a predecessor.

They wished to carve out their own path, citing predecessors’ view when it suited them, and ignoring them likewise.

In medicine, to early Greeks, it had seemed as if there were differing forces or powers within their bodies, to which they gave a variety of names, Plato describes three competing ‘souls’ one located in the liver, one located in the heart and one located in the head.

Most other early Greek thinkers located most or all of the human soul in the heart, as did Aristotle and Zenon, and it remain part of the collection of ideas.

The Greek since was bound to decline because of the lack of balance between reason and experience, because of its organicist setting, or because of its functioning in a slave society, or it happened to decline with the advent of the Romans and of Christianity.
The history of Greek science

Measure speed of light by Empedocles

The speed of light is one of the mysteries that has intrigued scientists for centuries. The ancient Greeks had the hypothesis that human vision was an active event initiated by the eye.

From this hypothesis they concluded that the speed of light was infinite, as one could see arbitrarily distant objects the moment the eyelids are opened.

As early as 429 BC, the Greek thinker, Empedocles believed that light travels at a finite speed though it seems to arrive instantaneously. He drew the logical conclusion that light takes a certain amount of time to travel from the source to the surface showing the shadow.

Empedocles thus stated that the speed of light is finite. He was, though, a notable exception among the ancient thinkers, for most agreed with Aristotle that the speed of light was infinite.

The first attempt to challenge this assumption and measure the speed of light was made by Galileo in 1667 using a very primitive method. Galileo, with his firm belief in the experimental approach, was one of the first 17th century scientists to attempt to calculate the speed of light.

The first precise measurement of the speed of light was made in 1849 by the French physicist Hippolyte. His value was only 5% greater than modern one.
Measure speed of light by Empedocles

Archimedes of Syracuse

Archimedes of Syracuse
He was Greek engineer who made the first measurement of specific gravity.

He studied in Alexandria, after which he returned to Syracuse where he spent most of the rest of the life.

He made many mathematical discoveries, including the most accurate calculation of pi made up to that time.

In engineering he was the founder of the science of hydrostatics. He is well known for the discovery of ‘Archimedes Law’ that a body wholly or partly immersed in a fluid loses weight equal to the weight of the fluid displaced.

He thus made the first measurement of specific gravity.

Archimedes also proved the law of the lever and developed the theory of mechanical advantage boasting to his cousin Hieron, ‘Give me a place to stand on and with a lever I will move the whole world.’

To prove his point, he launched one of the biggest ships built up to that date.
During his time in Egypt he devised the ‘Archimedean Screw’, still used today in Middle Eastern countries for pumping water.

He also built an astronomical instrument to demonstrate the movements of the heavenly bodies, a form of orrery.

He was General of Ordnance to Heiron and when the Romans besieged Syracuse, a legionary came across Archimedes geometrical diagrams in he sand.

Archimedes immediately told him to ‘Keep off’ and the soldier killed him.

He also experimented with burning glasses and mirrors or setting for to wooden ships.
Archimedes of Syracuse