GALILEO GALILEI (1564-1642)

1632 – Italy

‘Discounting air resistance, all bodies fall with the same motion; started together, they fall together. The motion is one with constant acceleration; the body gains speed at a steady rate’

From this idea we get the equations of accelerated motion:
v = at and s = 1/2at2
where v is the velocity, a is the acceleration and s is the distance traveled in time t

The Greek philosopher ARISTOTLE (384-322 BCE) was the first to speculate on the motion of bodies. He said that the heavier the body, the faster it fell.
It was not until 18 centuries later that this notion was challenged by Galileo.

The philosophers of ancient Greece had known about statics but were ignorant of the science of dynamics.
They could see that a cart moves because a horse pulls it, they could see that an arrow flies because of the power of the bow, but they had no explanation for why an arrow goes on flying through the air when there is nothing to pull it like the horse pulls the cart. Aristotle made the assumption that there must be a force to keep things moving. Galileo contradicted. He believed that something will keep moving at the same speed unless a force slows it down.

He contended that an arrow or a thrown stone had two forces acting upon it at the same time – ‘momentum’ pushes it horizontally and it only falls to the ground because the resistance of the air (a force) slows it down enough for it to be pulled to the ground by another force pushing downwards upon it; that which we now know as ‘gravity’.
This is the principle of inertia and led him to correctly predict that the path of a projectile is a parabola.

His insights were similar to the first two of the three laws of motion that Newton described 46 years later in ‘Principia’. Although he did not formulate laws with the clarity and mathematical certainty of Newton, he did lay the foundations of the modern understanding of how things move.

Galileo resisted the notion of gravity because he felt the idea of what seemed to be a mystical force seemed unconvincing, but he appreciated the concept of inertia and realized that there is no real difference between something that is moving at a steady speed and something that is not moving at all – both are unaffected by forces. To make an object go faster or slower, or begin to move, a force is needed.

Galileo would take a problem, break it down into a series of simple parts, experiment on those parts and then analyse the results until he could describe them in a series of mathematical expressions. His meticulous experiments (‘cimento‘) on inclined planes provided a study of the motion of falling bodies.

He correctly assumed that gravity would act on a ball rolling down a sloping wooden board that had a polished, parchment lined groove cut into it to act as a guide, in proportion to the angle of the slope. He discovered that whatever the angle of the slope, the time for the ball to travel along the first quarter of the track was the same as that required to complete the remaining three-quarters. The ball was constantly accelerating. He repeated his experiments hundreds of times, getting the same results. From these experiments he formulated his laws of falling bodies.
Mathematics provided the clue to the pattern – double the distance traveled and the ball will be traveling four times faster, treble it and the ball will be moving nine times faster. The speed increases as a square of the distance.
He found that the size of the ball made no difference to the timing and surmised that, neglecting friction, if the surface was horizontal – once a ball was pushed it would neither speed up nor slow down.

His findings were published in his book, ‘Dialogue Concerning the Two Chief World Systems’, which summarised his work on motion, acceleration and gravity.

His theory of uniform acceleration for falling bodies contended that in a vacuum all objects would accelerate at exactly the same rate towards the earth.

Legend has it that Galileo gave a demonstration, dropping a light object and a heavy one from the top of the leaning Tower of Pisa. Dropping two cannonballs of different sizes and weights he showed that they landed at the same time. The demonstration probably never happened, but in 1991 Apollo 15 astronauts re-performed Galileo’s experiment on the moon. Astronaut David Scott dropped a feather and a hammer from the same height. Both reached the surface at the same time, proving that Galileo was right.

Another myth has it that whilst sitting in Pisa cathedral he was distracted by a lantern that was swinging gently on the end of a chain. It seemed to swing with remarkable regularity and experimenting with pendulums, he discovered that a pendulum takes the same amount of time to swing from side to side – whether it is given a small push and it swings with a small amplitude, or it is given a large push. If something moves faster, he realised, then the rate at which it accelerates depends on the strength of the force that is moving it faster, and how heavy the object is. A large force accelerates a light object rapidly, while a small force accelerates a heavy object slowly. The way to vary the rate of swing is to either change the weight on the end of the arm or to alter the length of the supporting rope.
The practical outcome of these observations was the creation of a timing device that he called a ‘pulsilogium’.

Drawing by GALILEO of the surface of the moon

Galileo confirmed and advanced COPERNICUS’ sun centered system by observing the skies through his refracting telescope, which he constructed in 1609. Galileo is mistakenly credited with the invention of the telescope. He did, however, produce an instrument from a description of the Dutch spectacle maker Hans Lippershey’s earlier invention (patent 1608).

He discovered that Venus goes through phases, much like the phases of the Moon. From this he concluded that Venus must be orbiting the Sun. His findings, published in the ‘Sidereal Messenger‘ (1610) provided evidence to back his interpretation of the universe. He discovered that Jupiter has four moons, which rotate around it, directly contradicting the view that all celestial bodies orbited earth, ‘the centre of the universe’.

‘The Earth and the planets not only spin on their axes; they also revolve about the Sun in circular orbits. Dark ‘spots’ on the surface of the Sun appear to move; therefore, the Sun must also rotate’

1610 – Galileo appointed chief mathematician to Cosmo II, the Grand Duke of Tuscany, a move that took him out of Papal jurisdiction.

1613 – writes to Father Castelli, suggesting that biblical interpretation be reconciled with the new findings of science.

1615 – a copy of the letter is handed to the inquisition in Rome.

1616 – Galileo warned by the Pope to stop his heretical teachings or face imprisonment.

1632 – when Galileo published his masterpiece, ‘Dialogue Concerning the Two Chief World Systems’ – (Ptolemaic and Copernican) – which eloquently defended and extended the Copernican system, he was struggling against a society dominated by religious dogma, bent on suppressing his radical ideas – his theories were thought to contravene the teachings of the Catholic Church. He again attracted the attention of the Catholic Inquisition.
His book took the form of a discussion between three characters; the clever Sagredo (who argues for Copernicus), the dullard Simplicio (who argues hopelessly for Aristotle) and Salviati (who takes the apparently neutral line but is clearly for Sagredo).

In 1633 he was tried for heresy.

‘That thou heldest as true the false doctrine taught by many that the Sun was the centre of the universe and immoveable, and that the Earth moved, and had also a diurnal motion. That on this same matter thou didst hold a correspondence with certain German mathematicians.’
‘…a proposition absurd and false in philosophy and considered in theology ad minus erroneous in faith…’.

Threatened with torture, Galileo was forced to renounce his theories and deny that the Earth moves around the Sun. He was put under house arrest for the rest of his life.

After Galileo’s death in 1642 scientific thought gradually accepted the idea of the Sun-centered solar system. In 1992, after more than three and a half centuries, the Vatican officially reversed the verdict of Galileo’s trial.

Galileo’s thermoscope operated on the principle that liquids expand when their temperature increases. A thermoscope with a scale on it is basically a thermometer and in its construction Galileo was probably following directions given by Heron of Alexandria 1500 years earlier in ‘Pneumatics’. As with the telescope, Galileo is often incorrectly given credit for the invention of the thermometer.

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PYTHAGORAS (c.560 – c.480 BCE)

diagrammatic proof of Pythagoras' theoremSixth Century BCE – Greece

‘In a right-angled triangle, the square on the hypotenuse is the sum of the squares on the other two sides’

The Theorem may also be written as a general law:  a2 + b2 = c2  where c is the length of the hypotenuse of a right-angled triangle, and a and b the lengths of the other two sides. Pythagoras’ theorem is a starting point for trigonometry, which has many practical applications such as calculating the height of mountains and measuring distances.

c.525 BCE – Pythagoras taken prisoner by the Babylonians

c.518 BCE – establishes his own academy at Croton (now Crotone) in southern Italy

c.500 BCE – Pythagoras moves to Metapontum

Pythagoras was the first to prove the relationship between the sides of a right-angled triangle, but he did not discover it – it was known to Babylonians for nearly 1000 years before him.

His disciples, members of the semi-religious, philosophical school he founded, may have actually found many of the mathematical discoveries credited to Pythagoras. The inner circle of followers were known as mathematikoi and, unusually for the time, included women among its membership. An outer circle, the akousmatics, lived in their own homes and came in to the school by day.

Of the five key beliefs the Pythagoreans held, the idea that ‘all is number’ was dominant; the belief that reality at its fundamental level is mathematical and that all physical things like musical scales, or the spherical earth and its companions the stars and the universe, are mathematically related. Pythagoras was responsible for the widely held Greek belief that real knowledge had to be like mathematics – universal, permanent, obtained by pure thought and uncontaminated by the senses.

Because of the reverence with which the originator of the Pythagoreans was treated by his followers and biographers, it is difficult to discern legend from fact, such as the notion that he was the first to offer a three-part argument that the shape of the Earth is spherical:
The field of stars changes with the latitude of the observer; the mast of a ship comes into view before its hull as the ship approaches the shore from a distance; and the shadow of the Earth cast on the moon during a lunar eclipse is always round.

After Pythagoras, the idea of a ‘perfect’ mathematical interrelation between a globe moving in circles and the stars behaving similarly in a spherical universe inspired later Greek scholars, including ARISTOTLE, to seek and ultimately find physical and mathematical evidence to reinforce the theory of the world as an orb.

Attributed to the Pythagoreans is the discovery that simple whole number ratios of string lengths produce harmonious tones when plucked, probably the first time a physical law had been mathematically expressed.

Numerous other discoveries such as ‘the sum of a triangle’s angles is the equal to two right angles’ and ‘the sum of the interior angles in a polygon of n-sides is equal to 2n-4 right angles’ were made. They also discovered irrational numbers, from the realisation that the square root of two cannot be expressed as a perfect fraction. This was a major blow to the Pythagorean idea of perfection and according to some, attempts were made to try to conceal the discovery.

PLATONIC SOLIDS

To the Pythagoreans, the fifth polyhedron had monumental significance. Outnumbering by one the number of recognized elements, the dodecahedron was considered to represent the shape of the universe. 
A omerta, or code of silence, was imposed regarding the dodecahedron and divulging this secret to outsiders could mean a death penalty.

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ARISTOTLE (c.384 – c.322 BCE)

335 BCE – Athens

Bust of ARISTOTLE

ARISTOTLE

384 BCE – Born in the Greek colony of Stagira. The son of Nicomachus, court physician to the king of Macedonia
367 BCE – Enters Plato’s Academy in Athens
347 BCE – On Plato’s death Speusippus succeeds Plato as head of the Academy. Aristotle leaves the Academy for Lesbos
342 BCE – Becomes tutor to the young Alexander (the Great), son of Phillip of Macedon
335 BCE – Returns to Athens and founds the Lyceum
321 BCE – Accused of impiety, returns to Chalcis where he dies a year later

Aristotle reinforced the view espoused by PYTHAGORAS that the earth is spherical. The arc shaped shadow of the earth cast upon the moon during a lunar eclipse is consistent with this view. He also noted that when traveling north or south, stars ‘move’ on the horizon until some gradually disappear from view.

Proposing that there was no infinity and no void he accepted the notion of the earth at the centre of the universe, with the moon, planets, sun and stars all orbiting around it in perfect circles.
The universe existed as beautiful spheres surrounding the Earth, placed at the centre of the cosmos. This system was later refined by the Alexandrian astronomer Ptolemy and become the dominant philosophy in the Western world.

Explaining why the heavens rotate in perfect, uniform order, with none of the disturbances associated with earthly elements; he described the fifth element added to the traditional four, ‘Aether‘, as having a naturally circular motion. Everything beyond the moon was regulated by aether, explaining both its perfect movement and stability, while everything below it was subject to the laws of the four other elements.

Aristotle rejected the ideas of zero and infinity, hence he had explained away Zeno’s paradoxes – Achilles runs smoothly past the tortoise because the infinite points are simply a figment of Zeno’s imagination; infinity was just a construct of the human mind.
By rejecting zero and infinity, Aristotle denied the atomists’ idea of matter existing in an infinite vacuum, infinity and zero wrapped into one.
In contrast to the theory of atoms, like Plato, Aristotle believed that matter is composed of four elements ( Ignis, Aqua, Aer and Terra ) with differing qualities ( hot, wet, cold, dry )

[ Fire – hot + dry ; Water – cold + wet ; Air – hot + wet ; Earth – cold + dry ]

He believed that the qualities of heat, cold, wetness and dryness were the keys to transformation, each element being converted into another by changing one of these two qualities to its opposite.

Agreeing that things were composed of a single, primal substance (prote hyle) that was too remote and unknowable, he accepted EMPEDOCLES elements as intermediaries between the imponderable and the tangible world, concealing the complications behind a philosophy of matter.

The four elements always sought to return to their ‘natural place’. Thus a rock, for example, would drop to the earth as soon as any obstacles preventing it from doing so were removed – because ‘earth’ elements, being denser and heavier, would naturally seek to move downwards towards the centre of the planet. Water elements would float around the surface, air would rise above that and fire would seek to rise above them all, explaining the leaping, upward direction of flames.

Although the Aristotelian view of matter has been undermined as experiments proved that neither air nor water are indivisible; today, scientists define matter as existing in four phases, solid, liquid, gas and plasma.

MATTER (hyle); FORM (morphe); CAUSE; PURPOSE;

The place where his ideas converge with Plato’s is that for Aristotle, the pinnacle of the tower of superiority is the Good. According to Aristotle, all aims eventually lead to the Good, not necessarily of the individual but of humankind. Humans by nature are social and moral and everyone is part of a group, a family, village, town or city-state. There is no place for individualism or freethinkers, as without the happiness of the group then the individual cannot be happy.
The consequence of this emphasis on the community as opposed to the individual is hierarchy and subordination and as a result slavery was a very normal part of a well-ordered society.

  • Matter is itself only one component of the world – others being form and spirit. There are different sorts of living being in the world.
    Human beings possess immortal souls.
    He believed that there is in living creatures a fundamental vital principle, a ‘life force’, which distinguishes them from non-living material. The gods breathed this vital principle into living things, and thereby gave them their life – ( nous – spontaneous generation ).

The soul is governed by reason, spirit and appetite.
‘All human actions have one or more of these seven causes: chance, nature, compulsion, habit, reason, passion, and desire’ ( source )

  • Forms are incorporated in individual particulars as potentiality.
    All particular acorns possess the form of the potential oak tree.

Although Aristotle was a pupil at Plato’s Academy for almost twenty years, the two great thinkers were diametrically opposed on a number of subjects; he criticised Platonic forms for being impossibly transcendent and mystical.

Aristotle pursued his ideas unrestricted by Socratic theories that non-physical forms such as Truth and Beauty were the keys to understanding.

  • Four Causes – efficient, formal, material, final – (agent, form, matter, goal). – The ‘Timaeus’ – ( Plato’s work in which the chief speaker is encouraged to provide his account of the origins of the universe.)

  • ‘Action exists not in the agent but in the patient’
    To study a situation, or an action, Aristotle would categorise it into a series of subordinate and superior aims.

 

MOTION

  • Motion of Place – A to B

  • Motion of Quantity – change in amount

  • Motion of Quality – green apples turning red or from sour to sweet

 

Aristotle could explain why a rock, when thrown, would travel upwards through the air first before heading downwards, rather than straight down towards the earth. This was because the air, seeking to close the gap made by the invasion of the rock, would propel it along until it lost its horizontal speed and it tumbled to the ground.

Such notions made a lasting impact for the next two thousand years, if only by slowing down progress due to their unchallenged acceptance.

Some of Aristotle’s biology was faulty, such as defining the heart, not the brain as the seat of the mind.

 

Aristotle’s model of ‘the hydrologic cycle’ is uncannily close to the ideas we have today. The Sun’s heat changes water into air ( as defined as ‘elements’ by EMPEDOCLES ). Heat rises, so the heat in this air pulls the air up to the skies ( modern explanations of the nature of heat give a fuller understanding of the mechanisms involved ). The heat then leaves the vapour, which thus becomes progressively more watery again, and this process is marked by the formation of a cloud. The positive feedback of the increased ‘wateriness’ of the mixture in the cloud driving away its opposite ( the ‘heat’ ) and causing the cloud to become colder and shrink results in restoration of the true wateriness of the water, which falls as rain or, if the cloud is now cold enough, as hail or snow.

Aristotle was one of the first to attempt a methodical classification of animals; in ‘Generation of Animals’ he used means of reproduction to differentiate between those animals which give birth to live young and those which lay eggs, a system which is the forerunner of modern taxonomy. He noted that dolphins give birth to live young who were attached to their mothers by umbilical cords and so he classified dolphins as mammals.

Based on the Pythagorean universe, the Aristotelian cosmos had the planets moving in crystalline orbs.
Since there is no infinity, there cannot be an endless number of spheres; there must be a last one. There was no such thing as ‘beyond’ the final sphere and the universe ended with the outermost layer.
With no infinite and no void, the universe was contained within the sphere of fixed stars. The cosmos was finite in extent and entirely filled with matter.
The consequence of this line of reasoning, accounting for Aristotle’s philosophy enduring for two millennia was that this system proved the existence of God.

The heavenly spheres are slowly spinning in their places, making a divine music that suffuses the cosmos. The stationary earth cannot be the cause of that motion, so the innermost sphere must be moved by the next sphere out, which, in its turn must be moved by by its larger neighbour, and on and on. With a finite number of spheres, something must be the ultimate cause of motion of the final sphere of fixed stars. This is the Prime Mover.
Christianity came to rely on Aristotle’s view of the universe and this proof of God’s existence.
Atomism became associated with atheism.

The ideas of Aristotle were picked up by the twelfth century Andalusian philosopher Abu al-Walid Muhammad ibn Ahmed ibn Rushd (AVERROES) and were later adopted by the medieval philosopher THOMAS AQUINAS in the thirteenth century; whose concept of Natural Law is the basis of much thinking in the Christian world.

Aristotle had greater influence on medieval scholastic thought than Plato, whose rediscovery in the Italian renaissance influenced Petrarch, Erasmus, Thomas More and other scholars to question the dogmas of scholasticism.

Aristotle’s work in physics and cosmology dominated Western thought until the time of GALILEO and NEWTON, when much of it was subsequently refuted, though his work still underpins both Christian and Islāmic philosophy. His importance lies as much in his analytical method as in the conclusions he reached.

 

Aristotle expanded Plato’s concept of ‘virtue’ by dividing virtues into two groups, the 12 ‘moral’ and 9 ‘intellectual’ virtues, believing that each lay between the non-virtuous extremes of excess and deficiency.

Deficiency Virtue Excess
Cowardice Courage Rashness
Licentiousness (disregarding convention, unrestrained) Temperance (restraint or moderation) Insensibility (indifference)
Illiberality (meanness) Liberality (generosity) Prodigality (wasteful, extravagant)
Pettiness Magnificence Vulgarity
Humble-mindedness High-mindedness Vanity
Lack of ambition Proper ambition Over ambition
Irascibility (easily angered) Patience Lack of spirit
Understatement Truthfulness Boastfulness
Boorishness Wittiness Buffoonery
Cantankerousness Friendliness Obsequiousness
Shamelessness Modesty Shyness
Malicious enjoyment Righteous indignation Envy/spitefulness

His intellectual virtues consisted of :

art    scientific knowledge    prudence    intelligence    wisdom    resourcefulness    understanding    judgment    cleverness

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ASTROLOGY

– throughout the Middle Ages, astrology and astronomy were closely linked in both the Western and the Arabic worlds.
Although astrology was used for prediction, pre-modern astrology required a substantial command of mathematics and an informed astronomical knowledge.

PTOLEMY – ‘ The Almagest ’ how the planets move; ‘ Tetrabiblos ’ what effect the qualities of the planets (Mars – hot & dry, Moon – cold & wet [affect on the tides]) and their relative positions will have.

Belief that the influence of the planets may have an effect on earthly health and other matters (disease and character traits).

Tables of positions of planets became developed from the Babylonian originals in the Islāmic world.

Alphonsine tables produced for King Alphonso X of Castile in 1275.

Prognostication repeatedly condemned by the Church as influence of the planets denies the concept of free will.

Refutation of astrology is difficult owing to its complexity.

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CLAUDIUS PTOLEMY (c.90-168)

(NOT to be confused with the royal dynasty of the Ptolemys)

c.150 – Alexandria, Egypt

‘The Earth is at the centre of all the cosmos’

This erroneous belief dominated astronomy for 14 centuries.

‘The Earth does not rotate; it remains at the centre of things because this is its natural place – it has no tendency to go either one way or the other. Around it and in successively larger spheres revolve the Moon, Mercury, Venus, the Sun, Mars, Jupiter and Saturn, all of them deriving their motion from the immense and outermost spheres of fixed stars’. Ptolemy wrote in the thirteen-volume Almagest (Arabic for ‘The Greatest’), in which he synthesised the work of his predecessors. It provided a definitive compilation of all that was known and accepted in the field of astronomy up to that point.

Almagest’s eminence, importance and influence can only be compared with Euclid’s Elements. A major part of Almagest deals with the mathematics of planetary motion. Ptolemy explained the wandering of the planets by a complicated system of cycles and epicycles. Starting from the Aristotelian notion that the earth was at the centre of the universe, with the stars and the planets rotating in perfect circles around it, the Ptolemaic system argued for a system of ‘deferents’, or large circles, rotating around the earth, and eighty epicycles, or small circles, which circulated within the deferents. He also examined theories of ‘movable eccentrics’. These proposed just one circle of rotation, with its centre slightly offset from the earth, as well as ‘equants’ – imaginary points in space that helped define the focal point of the rotation of the celestial bodies. Ptolemy’s texts were written with such authority that later generations struggled for a thousand years to convincingly challenge his theories and they remained the cornerstone of Western and Arab astronomy until the sixteenth century.

Ptolemy’s theory was challenged by COPERNICUS and demolished by KEPLER. Ptolemy supported Eratosthenes’ view that the Earth is spherical.

Ptolemy’s other major text is his Tetrabiblos, a founding work on the then science of astrology.

Despite that Ptolemy’s ideas of a geocentric universe have been shown to be erroneous by modern researchers it must be remembered that at the time the observable phenomena would support this view of the cosmos. Without a more informed understanding of the mechanisms involved it can appear that heavenly bodies do in fact move according to the Ptolemaeic model and mathematical evidence was available to provide verification and vindication.

 Medieval Astronomy from Melk Abbey Credit: Paul Beck (Univ. Vienna), Georg Zotti (Vienna Inst. Arch. Science) Copyright: Library of Melk Abbey, Frag. 229  Explanation: Discovered by accident, this manuscript page provides graphical insight to astronomy in medieval times, before the Renaissance and the influence of Nicolaus Copernicus, Tycho de Brahe, Johannes Kepler, and Galileo. The intriguing page is from lecture notes on astronomy compiled by the monk Magister Wolfgang de Styria before the year 1490 at Melk Abbey in Austria. The top panels clearly illustrate the necessary geometry for a lunar (left) and solar eclipse in the Earth-centered Ptolemaic system. At lower left is a diagram of the Ptolemaic view of the solar system and at the lower right is a chart to calculate the date of Easter Sunday in the Julian calendar. Text at the upper right explains the movement of the planets according to the Ptolemaic system. The actual manuscript page is on view at historic Melk Abbey as part of a special exhibition during the International Year of Astronomy.

Library of Melk Abbey, Frag. 229

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THE MEDIEVAL ARAB SCIENTISTS

A great deal of what we know about the ancient world and its scientific ideas has come to us from documents which were translated from ancient Greek or other ancient languages into Arabic, and later from Arabic into European languages. The material reached the Arab world in many cases through the Roman empire in the East, Byzantium, which survived until 1453, almost a thousand years after the fall of Rome, during the period known in Europe as the Dark Ages.
During this time the consolidating influence of Islāmic religion saw Arab Muslims begin to build an empire that was to stretch across the Middle East and across North Africa into Spain. At the heart of the Islāmic world the caliphs ruled in Baghdad. Arab scientists sowed the seeds that would later be reaped in the scientific revolution of the seventeenth century, especially under the Abbasid dynasty during the caliphate of Harun al-Rashid and his son al-Mamun, and the Middle East became the intellectual hub of the World.

depiction of early islamic scholars at work at various scientific investigations

In the ninth century, at the House of Wisdom – a mixture of library, research institute and university – scholars worked to translate the great works of the GREEK thinkers. Muslim scholars of this golden age made important and original contributions to mathematics and astronomy, medicine and chemistry. They developed the ASTROLABE, which enabled astronomers to measure the position of the stars with unparalleled accuracy.Astrology & Astronomy in Iran and Ancient Mesopotamia: Astrolabe: An ancient astronomical instrument
In medicine they made the first serious studies of drugs and advanced surgery. A number of mathematicians, including Habash al-Hasib (‘he who calculates’), Abul’l-Wafa al-Buzjani, Abu Nasr al-Iraq and Ibn Yunus formulated trigonometry (including all six trig functions [ sin, cosec, cos, sec, tan, and cot ]) at a level far above that introduced by the Greek astronomer-mathematician HIPPARCHUS in the second century BCE.
It is largely through such efforts that Greek ideas were preserved through the DARK AGES.

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Eight hundred years before COPERNICUS, a model of the solar system was advanced with the Earth as a planet orbiting the Sun along with other planets.

A few centuries later this idea fell into disfavour with the early Christian Church, which placed mankind at the centre of the universe in a geo-centric model. The alternative teaching would be deemed heresy punishable by death and it would not be until the seventeenth century that the work of GALILEO, KEPLER and NEWTON gave credence to the ideas revitalized by Copernicus in 1543.

It is worth noting that even to-day at least half the named stars in the sky bear Arabic names (Aldebaran and Algol amongst others) and many terms used in astronomy, such as Nadir and Azimuth, are originally Arabic words.

 The Ulugh Beg Observatory in Samarkand, Uzbekistan

The elaborate observatory established by the Ulugh Begg in Samarkand in the fifteenth century appeared to function with a dictum meant to challenge PTOLEMY’s geocentric picture of the universe sanctioned by the Church in Europe. Arabic scholars had access to the early teachings of ARISTARCHUS, the astronomer from Samos of the third century BCE. (referred to by Copernicus in the forward of an early draft of De Revolutionibus, although omitted from the final copy)

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J’BIR IHBIN AYAM (722-804)

Around two thousand texts are attributed to this name; the founder of a Shi’ite sect. They were written over a hundred and fifty year period either side of the year 1000.

‘Sulfur and Mercury hypothesis’ (the idea that the glisten of mercury and the yellow of sulphur may somehow be combined in the form of gold).

An Alchemical theory: Accepting the Aristotelian ‘fundamental qualities’ of hot, cold, dry and moist, all metals are composed of two principles. Under the ground two fumes – one dry and smoky (sulfur), one wet and vaporous (mercury) – arising from the centre of the Earth, condense and combine to form metals.

This is said to explain the similarity of all metals; different metals contain different proportions of these two substances. In base metals the combination is impure, in silver and gold they co-exist in a higher state of purity.

The idea underpins the theory of transmutation, as all metals are composed of the same substances in differing proportions, and became the cornerstone of all chemical theory for the next eight hundred years.

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AL-KHWARIZMI (800-847)

820 – Baghdad, Iraq

Portrait of AL-KHWARIZMI

AL-KHWARIZMI

The man often credited with the introduction of ‘Arabic’ numerals was al-Khwarizmi, an Arabian mathematician, geographer and astronomer. Strictly speaking it was neither invented by al-Khwarizmi, nor was it Middle Eastern in origin.

786 – Harun al-Rashid came to power. Around this time al-Khwarizmi born in Khwarizm, now Khiva, in Uzbekistan.

813 – Caliph al-Ma’mun, the patron of al-Khwarizmi, begins his reign in Baghdad.

Arabic notation has its roots in India around 500 AD, thus the current naming as the ‘Hindu-Arabic’ system. al-Khwarizmi, a scholar in the Dar al-ulum (House of Wisdom) in Baghdad in the ninth century, is responsible for introducing the numerals to Europe. The method of using only the digits 0-9, with the value assigned to them determined by their position, as well as introducing a symbol for zero, revolutionised mathematics.

al-Khwarizmi explained how this system worked in his text ‘Calculation with Hindu numerals‘. He was clearly building upon the work of others before him, such as DIOPHANTUS and BRAHMAGUPTA, and on Babylonian sources that he accessed through Hebrew translations. By standardizing units, Arabic numerals made multiplication, division and every other form of mathematical calculation much simpler. His text ‘al-Kitab al-mukhtasar- fi hisab al-jabr w’al-muqabala’ (The Compendious Book on Calculating by Completion and Balancing) gives us the word algebra. In this treatise, al-Khwarizmi provides a practical guide to arithmetic.

In his introduction to the book he says the aim of the work is to introduce ‘what is easiest and most useful in mathematics, such as men constantly require in cases of inheritance, legacies, partition, lawsuits and trade, and in all their dealings with one another, or when measuring lands, digging canals and making geometrical calculations.’ He introduced quadratic equations, although he described them fully in words and did not use symbolic algebra.
It was in his way of handling equations that he created algebra.

The two key concepts were the ideas of completion and balancing of equations. Completion (al-jabr) is the method of expelling negatives from an equation by moving them to the opposite side

4x2 = 54x – 2x2  becomes  6x2 = 54x

Balancing (al-muqabala) meanwhile, is the reduction of common positive terms on both sides of the equation to their simplest forms

x2 + 3x + 22 = 7x + 12  becomes  x2 + 10 = 4x

Thus he was able to reduce every equation to simple, standard forms and then show a method of solving each, showing geometrical proofs for each of his methods – hence preparing the stage for the introduction of analytical geometry and calculus in the seventeenth century.

The name al-Khwarizmi also gives us the word algorithm meaning ‘a rule of calculation’, from the Latin title of the book, Algoritmi de numero Indorum.

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OMAR KHAYYAM (c.1048–1131)

In the service of the Kurdish-Turkish Sultan Salah al-Din ibn Ayyub (Saladin صلاح الدين يوسف بن أيوب‎ ), the nemesis of Richard the Lionheart during the second crusade, there was published a definitive treatise by Khayyām on algebra in which he classified algebraic equations up to the third degree and showed how geometric solutions to the equations could be obtained.

Image depicting OMAR KHAYYAM

Ironically, the source of Khayyām’s most enduring legacy is neither his mathematics nor his science but rather his poetry. The Rubaiyat, a translation, or recomposition, published initially in 1859 by the British poet Edward Fitzgerald, presents his work in a series of melancholic ruminations concerning the irreversibility of fate and the fleeting nature of life.

One explanation of the decline of science in Islāmic civilization, which began in the late fifteenth century, is the general fatalism that pervaded Islāmic culture, as revealed in the melancholia and pathos of Khayyām’s quatrains describing life continuing among the ruins of ancient grandeur.
Another explanation is the emergence in twelfth century Baghdad of an intellectual movement spearheaded by the fundamentalist al-Ghazali, which favoured faith and dogma over reason and direct evidence.

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THE DARK AGES

THE THIRTEENTH CENTURY

Ideas on ‘impetus’ and the motion of the heavenly spheres.

Diversity of opinion on what keeps the heavenly orbs moving.

The recipe literature – craft manuals outlining recipes for manufacture of alchemical materials. For example, glass production had died out in the Latin West, but remained important in the Arab world.

ROGER BACON suggests that alchemical power can surpass nature (human artifice may exceed nature, i.e. technology), compared with Aristotle, who suggests that artifice may only mimic nature, or complete that which nature has failed to finish.

Suma Perfectionis’, Gaber – Latin Franciscan text (passed off as Arabic). Underpinned by the sulfur-mercury theory and by Aristotle’s ‘minima naturalia’ (smallest of natural things)– the idea of a minimum amount of matter to hold a form – hence a smallest particle of any given substance. This differs from atomism but the ideas were not developed by Aristotle.

Thus, in the middle ages came the belief that metals are created by the coalescence of minima of the metals.
Particles may be tightly or lightly packed (density). Matter may be contaminated.
Noble metals (gold) are tightly packed small particles, unaffected by fire or corrosion.
Lead turns to powder (oxidised) in fire as it is composed of larger, less tightly packed particles.
Sublimation is explained by smaller, lighter particles being driven upward by fire, and so on.

THE FOURTEENTH CENTURY

Texts become more secret, written in code and disguised. Latin texts are written in such a style so as to appear to be derived from ARABIC.

1317 – The Pope outlaws transmutation.

Moral questions: ‘is alchemical gold as valuable as real gold?’

Quintessences’: the refined essences of metals.

The discovery that lead cannot be turned to gold has important consequences. It is a strong indication that some substances are truly permanent and indestructible.

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ALCHEMY

photo of an ancient document showing some of the symbols commonly used by alchemists

Alchemical symbols

Understanding of the alchemists is hampered by their predilection for making their writings incomprehensible ( instant knowledge was not to be available to the uninitiated ) and the popular view that their quest was simply to isolate the Philosophers’ Stone and to use it to transform base metals into gold. There was in fact a genuine search for mental and spiritual advance

Using a world-view totally unlike that recognised today, the alchemists’ ideas of ‘spirit’ and ‘matter’ were intermingled – the ability to use ‘spirit’ in their experiments was the difficult part.

alchemical symbol for gold

To transform copper to gold: – copper could be heated with sulphur to reduce it to its ‘basic form’ (a black mass which is in fact copper sulphide) – its ‘metallic form’ being ousted by the treatment. The idea of introducing the ‘form of gold’ to this mass by manipulating and mixing suitable quantities of spirit stymied alchemists for over fifteen centuries.

Whilst this transmutation of metals was the mainstream concern of alchemy, there emerged in the sixteenth century a school that brought the techniques and philosophies of alchemy to bear on the preparation of medicines, the main figures involved being PARACELSUS and JOHANN VAN HELMONT.

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cartoon of ALCHEMISTS AT WORK

ALCHEMISTS AT WORK

THE EIGHTEENTH CENTURY

COMBUSTION and PHLOGISTON

Noticing that burning a candle in an upturned container, the open end of which is submerged in water, causes the water to rise into the container, Philon of Byzantium inferred correctly that some of the air in the container had been used up in the combustion. However, he proposed that this is because this portion of the air had been converted into ‘fire particles’, which were smaller than ‘air particles’.

In 1700 the German physician Georg Ernst Stahl (1660-1734) invoked ‘phlogiston’ to explain what happens when things burn. He suggested that a burning substance was losing an undetectable elementary principle analogous to the ‘sulfur’ of J’BIR IHBIN AYAM, which he re-named ‘phlogiston’. This could explain why a log (rich in phlogiston) could seem to be heavier than its ashes (deficient in phlogiston). The air that is required for burning served to transport the phlogiston away.

The English chemist JOSEPH PRIESTLY (1733-1804), although a supporter of the phlogiston theory, ironically contributed to its downfall. He heated mercury in air to form red mercuric oxide and then applied concentrated heat to the oxide and noticed that it decomposed again to form mercury whilst giving off a strange gas in which things burnt brightly and vigorously. He concluded that this gas must be ‘phlogiston poor’.

Priestly combined this result with the work of the Scottish physician Daniel Rutherford (1749-1819), who had found that keeping a mouse in an enclosed airtight space resulted in its death (by suffocation) and that nothing could be burnt in the enclosed atmosphere; he formed the idea that the trapped air was so rich in phlogiston that it could accept no more. Rutherford called this ‘phlogisticated air’ and so Priestly called his own gas ‘dephlogisticated air’.

In 1774 Priestley visited the French chemist ANTOINE LAVOISIER (1743-1794).
Lavoisier repeated Priestly’s experiments with careful measurements.
Reasoning that air is made up of a combination of two gases – one that will support combustion and life, another that will not; what was important about Lavoisier’s experiments was not the observation – others had reached a similar conclusion – but the interpretation.

Lavoisier called Priestley’s ‘dephlogisticated air’, ‘oxygene’, meaning ‘acidifying principle’, believing at the time that the active principle was present in all acids (it is not). He called the remaining, ‘phlogisticated’, portion of normal air, ‘azote’, meaning ‘without life’

Oxygen is the mirror image of phlogiston. In burning and rusting (the two processes being essentially the same) a substance picks up one of the gases from the air. Oxygen is consumed, there is no expulsion of ‘phlogiston’.

Lavoisier had been left with almost pure nitrogen, which makes up about four fifths of the air we breath. We now know azote as nitrogen. Rutherford’s ‘mephitic air’ was carbon dioxide.

CALORIC

Like phlogiston, caloric was a weightless fluid, rather like elemental fire, a quality that could be transmitted from one substance to another, so that the first warmed the second up.

It was believed that all substances contained caloric and that when a kettle was being heated over a fire, the fuel gave up its caloric to the flame, which passed it into the metal, which passed it on to the water. Similarly, two pieces of wood rubbed together would give heat because abrasion was releasing caloric trapped within.

What is being transmitted is heat energy. It was the crucial distinction between the physical and the chemical nature of substances that confused the Ancients and led to their minimal elemental schemes.

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CHRISTIAN THEOLOGY & WESTERN SCIENCE

bust said to depict a likeness of Socrates

The speculative Greek philosophers, considering the great overarching principles that controlled the Cosmos, were handicapped by a reluctance to test their speculations by experimentation.
At the other end of the spectrum were the craftsmen who fired and glazed pottery, who forged weapons out of bronze and iron. They in turn were hindered by their reluctance to speculate about the principles that governed their craft.

WESTERN SCIENCE is often credited with discoveries and inventions that have been observed in other cultures in earlier centuries.
This can be due to a lack of reliable records, difficulty in discerning fact from legend, problems in pinning down a finding to an individual or group or simple ignorance.

The Romans were technologists and made little contribution to pure science and then from the fall of Rome to the Renaissance science regressed. Through this time, science and technology evolved independently and to a large extent one could have science without technology and technology without science.

Later, there developed a movement to ‘Christianise Platonism’ (Thierry of Chartres).

Platonism at its simplest is the study and debate of the various arguments put forward by the Greek philosopher PLATO (428/7-348/7 BCE).
The philosopher Plotinus is attributed with having founded neo-Platonism, linking Christian and Gnostic beliefs to debate various arguments within their doctrines. One strand of thought linked together three intellectual states of being: the Good (or the One), the Intelligence and the Soul. The neo-Platonic Academy in Greece was closed by the Emperor Justinian (CE 483-565) in CE 529.
During the early years of the Renaissance, texts on neo-platonism began to be reconsidered, translated and discoursed.

Aristotle’s four causes from the ‘Timaeus’ were attributed to the Christian God, who works through secondary causes (such as angels).

Efficient Cause – Creator – God the Father

Formal Cause – Secondary agent – God the Son

Material Cause – The four elements: earth, air, fire & water.
Because these four are only fundamental forms of the single type of matter, they cannot be related to any idea of ‘elements’ as understood by modern science – they could be transmuted into each other. Different substances, although composed of matter would have different properties due to the differing amounts of the qualities of form and spirit. Thus a lump of lead is made of the same type of matter (fundamental form) as a lump of gold, but has a different aggregation of constituents. Neither lead nor gold would contain much spirit – not as much as air, say, and certainly not as much as God, who is purely spiritual. ( ALCHEMY )

Final Cause – Holy Spirit

All other is ‘natural’ – underwritten by God in maintaining the laws of nature without recourse to the supernatural.
Science was the method for investigating the world. It involved carrying out careful experiments, with nature as the ultimate arbiter of which theories were right and which were wrong.

Robert Grosseteste (1168-1253) Bishop of Lincoln (Robert ‘Bighead’) – neo-platonic reading of Genesis – emanation of God’s goodness, like light, begins creation. Light is thus a vehicle of creation and likewise knowledge (hence ‘illumination’), a dimensionless point of matter with a dimensionless point of light superimposed upon it (dimensions are created by God). Spherical radiation of light carries matter with it until it is dissipated. Led to studies of optical phenomena (rainbow, refraction, reflection).

stained glass window depicting Robert Grosseteste (created 1896)

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LEONARDO FIBONACCI (c.1170-c.1250)

Also known as Leonardo Pisano. Published ‘Liber Abaci’ in 1202.

1202 – Italy

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FIBONACCI

Picture of a statue of Leonardo Pisano

FIBONACCI

‘A series of numbers in which each successive term is the sum of the preceding two’

For example:   1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , 34 , 55 , 89 , 144….

The series is known as the Fibonacci sequence and the numbers themselves as the Fibonacci numbers.

The Fibonacci sequence has other interesting mathematical properties – the ratio of successive terms ( larger to smaller;   1/1, 2/1, 3/2, 5/3, 8/5…. ) approaches the number 1.618
This is known as the golden ratio and is denoted by the Greek letter Phi.

Phi was known to ancient Greeks.
Greek architects used the ratio 1:Phi as part of their design, the most famous example of which is the Parthenon in Athens.

Fibonacci sequence in flower petals. flowers often have a Fibonacci number of petals - link to <http://pinterest.com/mcvjfly/fibonacci/>

Fibonacci sequence in flower petals

Phi also occurs in the natural world.
Flowers often have a Fibonacci number of petals.

      

During his travels in North Africa, Fibonacci learned of the decimal system of numbers that had evolved in India and had been taken up by the Arabs.
In his book Liber Abaci he re-introduced to Europe the Arabic numerals that we use today, adhering roughly to the recipe ‘the value represented must be proportional to the number of straight lines in the symbol’.

Following the Arabs, Fibonacci ( ‘son of the simpleton’ euph. or ‘son of the innocent’ ) introduced the place–value concept, with each position representing a different power of ten and these arranged in ascending order from right to left.

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ALBERTUS MAGNUS (c.1200- 80)

Graf von Bollstaadt – ‘The Universal Doctor’

Middle ages – Europe

‘The study of the natural world leads to a glorification of God’

portrait of Albertus Magnus

ALBERTUS MAGNUS

Bavarian philosopher, theologian and alchemist.
Wrote a paraphrase on ARISTOTLE and the Arabic comments on it. Responsible for a revival in Aristotelian thought.

Albert of Cologne was the eldest son of the Count of Bollsaadt. He studied in Padua and Paris, taught in Cologne and became a Dominican monk in 1223. He was made Bishop of Regensberg in 1260 but resigned two years later and spent the rest of his life teaching in Bavaria and the surrounding districts.
He died in 1280, was beatified in 1622, canonized as St. Albert the Great in 1931, and in 1941 was declared patron saint of all who cultivate the natural sciences.
His fame is due in part to the fact that he was the forerunner, guide and teacher of St.Thomas Aquinas; but Albert of Cologne was known as Albertus Magnus even in his own lifetime because of his prolific scientific writings and his great influence on the study of philosophy and theology.
His encyclopaedic compilation of all knowledge as understood at the time included his works Physica; Summa theologiae and De natura locorum and contained scientific treatises on alchemy, astronomy, mathematics, physiology, geography, economics, logic, rhetoric, ethics, politics, phrenology, metaphysics and all branches of natural science.

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Wrote on three realms of nature, De Animalibus, De Vegetablibus & De Mineralibus.
Concluded that fossils were phenomena or ‘games of nature’. Compiled a list of Aristotle’s errors.

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ROGER BACON (1214- 94)

(Doctor Mirabilis) ‘The Marvelous Doctor’

(Franciscan friar) Oxford – 1257

‘Mathematics (The first of the sciences, the alphabet of philosophy, door & key to the sciences), not Logic, should be the basis of all study’

Converted from Aristotelian to a neo-Platonist.

Etching of ROGER BACON Franciscan friar (1214- 94)

ROGER BACON

The Multiplication of Species; the means of causation (change) radiate from one object to another like the propagation of light.

‘An agent directs its effect to making the recipient similar to itself because the recipient is always potentially what the agent is in actuality.’

Thus heat radiating from a fire causes water placed near the fire,
but not in it, to become like the fire (hot). The quality of fire is multiplied in the water (multiplication of species).

All change may be analysed mathematically. Every multiplication is according to line, angles or figures. This thinking comes from the ninth century al-Kinde and his thoughts on rays and leads to a mathematical investigation into light.

Fear of the Mongols, Muslims and the Anti-Christ motivated the Franciscans. Franciscan neo-Platonism was based on Augustinian thought with a mathematical, Pythagorean, approach to nature. Bacon subscribed to this apocalyptical view, suffered trial and was imprisoned.
The Dominicans chose Aristotle – with a qualitative, non-mathematical approach to the world.

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THOMAS AQUINAS (1225- 74)

(Doctor Angelicus, Doctor Communis, Doctor Universalis)

St Thomas Aquinas

THOMAS AQUINAS

‘A theological need to explain a cause becomes the basis for a specific scientific explanation of the world’

Established by Christians and Muslims in order to confound the dualist philosophies coming out of Persia.

Thomas Aquinas was a Dominican priest, theologian, and philosopher. Called the Doctor Angelicus (the Angelic Doctor,) Aquinas is considered one the greatest Christian philosophers to have ever lived. Two of his most famous works, the Summa Theologiae and the Summa Contra Gentiles, are the finest examples of Christian philosophy.

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JOHANNES GUTENBERG (1395-1468)

Typographic resetting of Gutenberg's 42-line bible of 1452-55, using modern Fraktur and decorative initial in METAFONT by Yannis Haralambous. (Beginning of St. John's Gospel) from a LaTex advertising flyer.

1450 – Mainz, Germany

‘Movable type’

  

Hand-held block printing – a laborious process of carving whole pages of fixed text out of wooden slabs and reproducing copies using dies – had been used for many decades before the German inventor appeared. What Gutenberg mastered was the idea of placing individual metal letters – (his family background was in minting and metalworking, an ideal foundation for his training as an engraver and goldsmith. His skills enabled him to craft the first individual metal letter moulds) – into temporary mounts, which could then be dismantled or ‘moved’ once a page of text had been completed and reused to produce other pages.

In comparison to engraving and the single use of wooden blocks, the theoretically infinite number of sides which could be made out of a set of metal characters, together with the speed at which a template could be created, revolutionised printing and the spread of the printed word.

engraving of Johannes Gutenberg

Gutenberg printing press. Johannes Gutenberg (c. 13951468) invented the printing press sometime in the mid-fifteenth century. The moveable printing blocks it employed made it far simpler to operate than the complicated machinery of the Far East

Some sources credit the Chinese with inventing moveable type printing, using characters made of wood. What is notable is the quality of Gutenberg’s metal casts and press – they are almost as important as the idea of moveable type itself.

By the end of the fifteenth century tens of thousands of books and pamphlets were already in existence, giving academics the opportunity to share scientific knowledge widely and cheaply.

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LEONARDO DA VINCI (1452-1519)

1502 – Florence, Italy

‘In the Renaissance science was reinvented’

Image of the VITRUVIAN MAN

VITRUVIAN MAN

Leonardo is celebrated as the Renaissance artist who created the masterpieces ‘The Last Supper’ (1495-97) and ‘The Mona Lisa’ (1503-06). Much of his time was spent in scientific enquiry, although most of his work remained unpublished and largely forgotten centuries after his death. The genius of his designs so far outstripped contemporary technology that they were rendered literally inconceivable.

The range of his studies included astronomy, geography, palaeontology, geology, botany, zoölogy, hydrodynamics, optics, aerodynamics and anatomy. In the latter field he undertook a number of human dissections, largely on stolen corpses, to make detailed sketches of the body. He also dissected bears, cows, frogs, monkeys and birds to compare their anatomy with that of humans.

It is perhaps in his study of muscles where Leonardo’s blend of artistry and scientific analysis is best seen. In order to display the layers of the body, he developed the drawing technique of cross-sections and illustrated three-dimensional arrays of muscles and organs from different perspectives.

Leonardo’s superlative skill in illustration and his obsession with accuracy made his anatomical drawings the finest the world had ever seen. One of Leonardo’s special interests was the eye and he was fascinated by how the eye and brain worked together. He was probably the first anatomist to see how the optic nerve leaves the back of the eye and connects to the brain. He was probably the first, too, to realise how nerves link the brain to muscles. There had been no such idea in GALEN’s anatomy.

Possibly the most important contribution Leonardo made to science was the method of his enquiry, introducing a rational, systematic approach to the study of nature after a thousand years of superstition. He would begin by setting himself straightforward scientific queries such as ‘how does a bird fly?’ He would observe his subject in its natural environment, make notes on its behaviour, then repeat the observation over and over to ensure accuracy, before making sketches and ultimately drawing conclusions. In many instances he would directly apply the results of his enquiries into nature to designs for inventions for human use.

Self portrait of LEONARDO DA VINCI

LEONARDO DA VINCI

He wrote ‘Things of the mind left untested by the senses are useless’. This methodical approach to science marks a significant stepping-stone from the DARK AGES to the modern era.

1469 Leonardo apprenticed to the studio of Andrea Verrocchio in Florence

1482 -1499 Leonardo’s work for Ludovico Siorza, the Duke of Milan, included designs for weaponry such as catapults and missiles.
Pictor et iggeniarius ducalis ( painter and engineer of the Duke )’.
Work on architecture, military and hydraulic engineering, flying machines and anatomy.

1502 Returns to Florence to work for Pope Alexander VI’s son, Cesare Borgia, as his military engineer and architect.

1503 Begins to paint the ‘Mona Lisa’.

1505-07 Wrote about the flight of birds and filled his notebooks with ideas for flying machines, including a helicopter and a parachute. In drawing machines he was keen to show how individual components worked.

1508 Studies anatomy in Milan.

1509 Draws maps and geological surveys of Lombardy and Lake Isea.

1516 Journeys to France on invitation of Francis I.

1519 April 23 – Dies in Clos-Luce, near Amboise, France.

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PARACELSUS (1493-1541)

Europe – early sixteenth century

‘Added salt to the mercury/sulfur diad, making a trinity to match the holy trinity’

picture of philippus aureolus theophrastus_paracelsus

PARACELSUS

Elaborating his writings with occult mystery, Theophrastus von Hohenheim renamed himself Paracelsus and helped to reform medicine by making it chemical.
Many of his ideas were erroneous and his writings were deliberately obscure; he insisted that the ‘doctrine of signatures’ could reveal efficacious drugs for different organs. Proclaiming that specific therapies could counter a particular disease was a radically different approach to the Aristotelian attempts to rebalance an individual’s internal humors.

Paracelsus extended the ‘fundamental qualities’ of the four Aristotelian elements by adding a third ‘hydrostatic principle’ to the diad of J’BIR IHBIN AYAM – saying the material manifestation of the ancient elements ( ‘…everything that lies in the four elements’ ) may be reduced to mercury, sulfur and salt.

The first distillate of an organic substance would be the thin, volatile ‘mercury’, which acted in favour of youth and life while next came the ‘sulfur’, acting in favour of growth and increase. Finally, the dry mass left behind was the ‘salt’. The concept of these three principles was considered a slight advance upon that of the four elements.

These are not the same things as we recognize today, nor elements in their own right; the first two were components of metals, salt was a principle common to all living things.

The Royal physicians of Elizabeth I of England and Henry IV of France assimilated and adapted Paracelsus’s ideas and although his theories lost credibility, his chemical remedies entered mainstream medicine.

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NICOLAUS COPERNICUS (1473-1543)

1543 – Poland

‘The Sun is at the centre of the solar system, fixed and immobile, and planets orbit around it in perfect circles in the following order: Mercury, Venus, Earth with its moon, Mars, Jupiter and Saturn’

diagram of the heliocentric Copernican system

The heliocentric Copernican system

The Copernican system defied the dogma that the Earth stood still at the centre of the universe – a concept that dated back to ARISTOTLE, which had been given observational legitimacy by PTOLEMY and authority by Christendom – and set forth a new theory of a Sun centered universe. Why would God create a hugely complicated system of equants, epicycles and eccentrics, as Ptolemy had used to explain planetary motion around the Earth, when it would be much more simple and graceful to have them all revolving around the Sun?

“Eight hundred years before Copernicus, a model of the solar system was advanced with the Earth as a planet orbiting the Sun along with other planets”
A few centuries later this idea fell into disfavour with the early Christian Church, which placed mankind at the centre of the universe in a geo-centric model. The alternative teaching would be deemed heresy punishable by death and it would not be until the seventeenth century that the work of GALILEO, KEPLER and NEWTON gave credence to the ideas revitalized by Copernicus in 1543.

Not only did Copernicus place the Sun at the centre of the solar system, but he also gave detailed accounts of the motions of Earth, the Moon and those planets that were known at that time. Between 1510 and 1514 he drafted Commentariolus, his initial exposition of the theory. In order to have credence, the idea required that the Earth itself be not fixed in position. He said that the Earth revolves on its own axis once every twenty-four hours, which accounts for day and night and explains the apparent movement of the stars and Sun across the sky. Copernicus suggested in Commentariolus that the time taken for each planet to complete its cycle through the night sky might increase the further it is from the Sun.

Mercury’s cycle takes 88 days, which makes it the nearest planet to the Sun. Venus takes 225 days, Earth 1 year, Mars 1.9 years, Jupiter 12 years and Saturn 30 years. Thus Copernicus was able to work out the truth and attempted to establish the order of the planets.

He did not publish his findings because they were thought to contravene the teachings of the Catholic Church. Religious leaders of his time were against him. Martin Luther (founder of the Lutheran Church in Germany) denounced him as ‘a new astrologer…. the fool’ who wanted ‘to overturn the entire science of astronomy’. His book De Revolutionibus Orbium Coelestium (On the revolution of the celestial spheres) was published at the very end of his life, and a copy placed on his deathbed. Thus the greatest astronomer of his time died without seeing his book in print – the book as influential as Newton’s Principia and Darwin’s ‘On The Origin of Species’.

Portrait of Copernicus

The text was rejected by many academics; partially because the author had undermined the simplicity of his initial ideas by clinging to the Aristotelian belief that planetary motion took place in perfect circles. This meant Copernicus had been forced to introduce his own system of epicycles and other complex motions to fit in with observational evidence, thereby producing as equally complicated an explanation as the geocentric one he had initially rejected for its lack of simplicity.

It was not until Johannes Kepler offered the solution that the planets move in an elliptical, not circular, motion in 1609 that the simplicity that Copernicus had been seeking was offered and the rest of the model could be vindicated.

In fact, it was not until 1616 that the Church banned the text Copernicus eventually published for its ‘blasphemous’ content, although that sanction remained in place until 1835.

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