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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ARCHIMEDES (c.287 – c.212 BCE)

Third Century BCE – Syracuse (a Greek city in Sicily)

‘Archimedes’ Screw – a device used to pump water out of ships and to irrigate fields’

Archimedes investigated the principles of static mechanics and pycnometry (the measurement of the volume or density of an object). He was responsible for the science of hydrostatics, the study of the displacement of bodies in water.

Archimedes’ Principle

Buoyancy – ‘A body fully or partially immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body’
The upthrust (upward force) on a floating object such as a ship is the same as the weight of water it displaces. The volume of the displaced liquid is the same as the volume of the immersed object. This is why an object will float. When an object is immersed in water, its weight pulls it down, but the water, as Archimedes realised, pushes back up with a force that is equal to the weight of water the object pushes out-of-the-way. The object sinks until its weight is equal to the upthrust of the water, at which point it floats.
Objects that weigh less than the water displaced will float and objects that weigh more will sink. Archimedes showed this to be a precise and easily calculated mathematical principle.

 
 

Syracuse’s King Hiero, suspecting that the goldsmith had not made his crown of pure gold as instructed, asked Archimedes to find out the truth without damaging the crown.

Archimedes first immersed in water a piece of gold that weighed the same as the crown and pointed out the subsequent rise in water level. He then immersed the crown and showed that the water level was higher than before. This meant that the crown must have a greater volume than the gold, even though it was the same weight. Therefore it could not be pure gold and Archimedes thus concluded that the goldsmith had substituted some gold with a metal of lesser density such as silver. The fraudulent goldsmith was executed.

Archimedes came to understand and explain the principles behind the compound pulley, windlass, wedge and screw, as well as finding ways to determine the centre of gravity of objects.
He showed that the ratio of weights to one another on each end of a balance goes down in exact mathematical proportion to the distance from the pivot of the balance.

Perhaps the most important inventions to his peers were the devices created during the Roman siege of Syracuse in the second Punic war.

He was killed by a Roman soldier during the sack of the city.

 
 
 
 

(image source)

Π The Greek symbol pi (enclosed in a picture of an apple) - Pi is a name given to the ratio of the circumference of a circle to the diameterPi

‘All circles are similar and the ratio of the circumference to the diameter of a circle is always the same number, known as the constant, Pi’

Pi-unrolled-720.gif

 
 

The Greek tradition disdained the practical.  Following PLATO the Greeks believed pure mathematics was the key to the perfect truth that lay behind the imperfect real world, so that anything that could not be completely worked out with a ruler and compass and elegant calculations was not true.

In the eighteenth century CE the Swiss mathematician LEONHARD EULER was the first person to use the letter  Π , the initial letter of the Greek word for perimeter, to represent this ratio.

The earliest reference to the ratio of the circumference of a circle to the diameter is an Egyptian papyrus written in 1650 BCE, but Archimedes first calculated the most accurate value.

He calculated Pi to be 22/7, a figure which was widely used for the next 1500 years. His value lies between 3 1/2 and 3 10/71, or between 3.142 and 3.141 accurate to two decimal places.

 

‘The Method of Exhaustion – an integral-like limiting process used to compute the area and volume of two-dimensional lamina and three-dimensional solids’

Archimedes realised how much could be achieved through practical approximations, or, as the Greeks called them, mechanics. He was able to calculate the approximate area of a circle by first working out the area of the biggest hexagon that would fit inside it and then the area of the smallest that would fit around it, with the idea in mind that the area of the circle must lie approximately halfway between.

By going from hexagons to polygons with 96 sides, he could narrow the margin for error considerably. In the same way he worked out the approximate area contained by all kinds of different curves from the area of rectangles fitted into the curve. The smaller and more numerous the rectangles, the closer to the right figure the approximation became.

This is the basis of what thousands of years later came to be called integral calculus.
Archimedes’ reckonings were later used by Kepler, Fermat, Leibniz and Newton.

In his treatise ‘On the Sphere and the Cylinder’, Archimedes was the first to deduce that the volume of a sphere is 4/3 Pi r3  where r  is the radius.
He also deduced that a sphere’s surface area can be worked out by multiplying that of its greatest circle by four; or, similarly, a sphere’s volume is two-thirds that of its circumscribing cylinder.

Like the square and cube roots of 2, Pi is an irrational number; it takes a never-ending string of digits to express Pi as a number. It is impossible to find the exact value of Pi – however, the value can be calculated to any required degree of accuracy.
In 2002 Yasumasa Kanada (b.1949) of Tokyo University used a supercomputer with a memory of 1024GB to compute the value to 124,100,000,000 decimal places. It took 602 hours to perform the calculation.

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GALEN OF PERGAMUM (130-201)

161 – Rome, Italy

Bust of GALEN

GALEN

‘A body of work consisting 129 volumes. Some of the deductions were wrong’

Born in Pergamum (now Bergama in Turkey) in the reign of the Emperor Hadrian (76-138AD)
Studied in Corinth and Alexandria
157 – became surgeon to the Pergamum gladiators
161 – became physician to the emperors Marcus Aurielius and Commodus

Famous for the sheer volume of medical thought which he presented. He summarized his observations in books such as ‘On The Usefulness of Parts of The Body’. His works on medical science became accepted as the only authority on the subject for the following 1400 years. One explanation is that Galen not only incorporated the results of his own findings in his texts, but also compiled the best of all other medical knowledge that had gone before him into a single collection, such as that of Hippocrates.
In particular, Galen adopted Hippocrates’ ‘four humors’ approach to the body. This resulted from a desire to see in bodily conditions the attributes of the four Aristotelian elements. Thus earth was reflected in the body as black bile or melancholy; air as yellow bile or choler; fire as blood and water as phlegm.

After the move to Rome in 161 Galen became physician to emperors Marcus Aurelius, Lucius Verus, Commodus and Septimus Severus. This position allowed him the freedom to undertake dissection in the quest for improved knowledge.
Galen was not permitted to scrutinise human cadavers, so he dissected animals and Barbary apes. His most important conclusions concerned the central operation of the human body. Sadly they were only influential in that they limited the search for accurate information for the next millennia and a half.

Many people visited the shrine of Asklepios, the god of healing in Galen’s hometown, to seek cures for ailments and Galen observed first-hand the symptoms and treatment of diseases. After spells in Smyrna (now Izmir), Corinth and Alexandria studying philosophy and medicine and incorporating work on the dissection of animals, he returned to Pergamum in 157, where he took a position as physician to gladiators, giving him further first-hand experience in practical anatomical medicine. He realized that there were two types of blood flow from wounds. In one the blood was bright red and came spurting out, and in the other it was dark blue and flowed out in a steady stream. These observations convinced him these were two different types of blood. He also believed there was a third form of blood that flowed along nerves.

Galen believed that blood was formulated in the liver, the source of ‘natural spirit’. In turn this organ was nourished by the contents of the stomach that was transported to it. Veins from the liver carried blood to the extremes of the body where it was turned into flesh and used up, thus requiring more food on a daily basis to be converted into blood. Some of this blood passed through the heart’s right ventricle, then seeped through to the left ventricle and mixed with air from the lungs, providing ‘vital spirit’ which then passed into the body through the arteries and regulated the body’s heat. A portion of this blood was transported to the brain where it blended with ‘animal spirit’, which was passed through the body by the nerves. This created movement and the senses. The combination of these three spirits managed the body and contributed to the make-up of the soul. It was not until 1628 that WILLIAM HARVEY‘s system of blood circulation conclusively proved the idea of a single, integrated system.

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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

image of statue of Leonardo Fibonacci ©

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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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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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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ANDREAS VESALIUS (1514- 64)

1543 – Padua, Italy

‘In spite of his premature death, Vesalius left behind a revolutionary legacy to anatomy students’

Portrait of Vesalius &copy:

VESALIUS

By his reasoned, critical approach to GALEN he broke the reverence ascribed to the former master and created a model for independent, rational investigation in the development of medical science.

 

In 1543, Vesalius published ‘De Humani Corporis Fabrica Libri Septem‘ (The Seven Books on the Structure of the Human Body). Book One reveals Vesalius’s understanding of the importance of the skeleton. Book Two is about muscles; Book Three – Veins and Arteries; Book Four – The Nervous System. Book Five concerns the Main Body Organs; Book Six – The Heart & Lungs; Book Seven – The Brain.

 

At 42cm tall and 28cm wide with over 700 densely packed pages, it was impressive in size alone. It contained 200 illustrations, was the first definitive work on human anatomy actually based on the results of methodical dissections of humans and was the most accurate work on the subject ever written. Galen himself had never dissected a human body as this had been forbidden by Roman religious laws.

Anatomical Study Illustration from De Humani Corporis Fabrica 1543Anatomical Study Illustration from De Humani Corporis Fabrica 1543

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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’

Portrait of GALILEO GALILEI ©

GALILEO GALILEI

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 Hiero 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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EVANGELISTA TORICELLI (1608- 47)

1640 – Italy

‘Together with VINCENZO VIVIANI (1622-1703) realised that the weight of air pushing on a reservoir of mercury can force the liquid to rise into a tube that contains no air; that is, a vacuüm’

In 1650 OTTO VON GUERICKE (1602-1686) invented an air pump and showed that if you remove the air from the centre of two hemispheres that are resting together, the pressure of the outside air is sufficient to prevent a team of horses from pulling them apart.

1657 – Formed the Accademia del Cimento with eight other Florentines to build their own apparatus and conduct experiments to advance the pursuit of knowledge. Disbanded after ten years as a condition of its patron Leopoldo de Medici’s appointment as cardinal, its dissolution followed Galileo’s trial by the Catholic Church and marked the decline of free scientific research in Italy.

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BLAISE PASCAL (1623- 62)

1647 – France

Portrait of BLAISE PASCAL

BLAISE PASCAL

‘When pressure is applied anywhere to an enclosed fluid, it is transmitted uniformly in all directions’

EVANGELISTA TORICELLI (1608-47) had argued that air pressure falls at higher altitudes.

Using a mercury barometer, Pascal proved this on the summit of the 1200m high Puy de Dome in 1647. His studies in this area led to the development of PASCAL’S PRINCIPLE, the law that has practical applications in devices such as the car jack and hydraulic brakes. This is because the small force created by moving a lever such as the jacking handle in a sizable sweep equates to a large amount of pressure sufficient to move the jack head a few centimetres.
The unit of pressure is now termed the pascal.

‘The study of the likelihood of an event’

Together with PIERRE DE FERMAT, Pascal developed the theory of probabilities (1654) using the now famous PASCAL’S TRIANGLE.

Chance is something that happens in an unpredictable way. Probability is the mathematical concept that deals with the chances of an event happening.

Probability theory can help you understand everything from your chances of winning a lottery to your chances of being struck by lightning. You can find the probability of an event by simply dividing the number of ways the event can happen by the total number of possible outcomes.
The probability of drawing an ace from a full pack of cards is 4/52 or 0.077.

Probability ranges from 1 (100%) – Absolutely certain, through Very Likely 0.9 (90%) and Quite Likely 0.7 (70%), Evens (Equally Likely) 0.5 (50%), Not Likely 0.3 (30%) and Not Very Likely 0.2 (20%), to Never – Probability 0 (0%).

Picture of the 'Pascaline'. The French mathematician Blaise Pascal invented the a mechanical calculation machine. He called it the Pascaline. The Pascaline was made out of clock gears and levers and could solve basic mathematical problems like addition and subtraction.

 
 

The computer language Pascal is named in recognition of his invention in 1644 of a mechanical calculating machine that could add and subtract.

 
 
 

Like many of his contemporaries, Pascal did not separate philosophy from science; in his book ‘Pensees’ he applies his mathematical probability theory to the problem of the existence of God. In the absence of evidence for or against God’s existence, says Pascal, the wise man will choose to believe, since if he is correct he will gain his reward, and if he is incorrect he stands to lose nothing.

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LUIGI GALVANI (1737- 98) ALESSANDRO VOLTA (1745-1827)

1791 & 1799 – Italy

‘Galvani: An electric current is produced when an animal tissue comes into contact with two different metals.

Volta: An electric current is not dependent on an animal tissue and can be produced by chemicals’

Galvani was wrong and Volta was right.

Galvani had found that by touching a dead frog’s legs with two different metal implements, the muscles in the frog’s legs would twitch. Galvani wrongly concluded it was the animal tissue that was storing the electricity, releasing it when touched by the metals. He felt he had discovered the very force of life – ‘animal electricity’ – that animated flesh and bone.

portrait of LUIGI GALVANI ©

GALVANI

Soon dozens of scientists were trying to bring corpses back to life by electrifying them. Volta was not convinced the animal muscle was the important factor in the production of the current.

He repeated Galvani’s experiments and concluded, controversially at the time, the different metals were the important factor.

A bitter dispute arose as to whose interpretation was correct. Volta began putting together different combinations of metals to see if they produced any current; later he produced a wet battery of fluid and metals.
Volta’s method of producing electric current involved using discs of silver and zinc dipped in a bowl of salt solution. He reasoned that a much larger charge could be produced by stacking several discs separated by cards soaked in salt water – by attaching copper wires to each end of the ‘pile’ he successfully obtained a steady current.

The ‘voltaic pile’ was the first battery in history (1800). Napoleon Bonaparte, who at the time controlled the territory in which Volta lived, was so impressed he made him a Count and awarded him the Legion d’Honour.

portrait of ALESSANDRO VOLTA ©

VOLTA

Volt, the SI unit of electric potential, honours Volta.

Although Galvani’s theory on ‘animal electricity’ was not of any major importance, he has also achieved nominal immortality; like ‘volt’, the words ‘galvanic’ (sudden and dramatic), ‘galvanised’ (iron or steel coated with zinc) and ‘galvanometer’ (an instrument for detecting small currents) have become part of everyday language.

A volt is defined as the potential difference between two points on a conductor carrying one ampere current when the power dissipated between the points is one watt.

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AMEDEO AVOGADRO (1776-1856)

1811 – Italy

‘Equal volumes of all gases at the same temperature and pressure contain the same number of molecules’

In 1811, when Avogadro proposed his HYPOTHESIS, very little was known about atoms and molecules. Avogadro claimed that the same volume of any gas under identical conditions would always contain the same number of fundamental particles, or molecules. A litre of hydrogen would contain exactly the same number of molecules as a litre of oxygen or a litre of carbon dioxide.

Drawing of AVOGADRO ©

In 1814 ANDRE AMPERE was credited with discovering that if a gas consisted of a single element, its atoms could clump in pairs. The molecules of oxygen consisted of pairs of oxygen atoms, and the molecules of chlorine, pairs of chlorine atoms.
Diatomic gases possess a total of six degrees of simple freedom per molecule that are related to atomic motion.

This provides a way of comparing the weights of different molecules. It was only necessary to weigh equal volumes of different gases and compare them. This would be exactly the same as comparing the weights of the individual molecules of each gas.

Avogadro realised that GAY-LUSSAC‘s law provided a way of proving that an atom and a molecule are not the same. He suggested that the particles (molecules) of which nitrogen gas is composed consist of two atoms, thus the molecule of nitrogen is N2. When one volume (one molecule) of nitrogen combines with three volumes (three molecules) of hydrogen, two volumes (two molecules) of ammonia, NH3, are produced.

N2 + 3H2 ↔ 2NH3

However, the idea of a molecule consisting of two or more atoms bound together was not understood at that time.

Avogadro’s law was forgotten until 1860 when the Italian chemist STANISLAO CANNIZZARO (1826-1910) explained the necessity of distinguishing between atoms and molecules.

Avogadro’s constant
From Avogadro’s law it can be deduced that the same number of molecules of all gases at the same temperature and pressure should have the same volume. This number has been determined experimentally: it’s value is 6.022 1367(36) × 1023AVOGADRO’S NUMBER

Avogadro's_number_in_e_notation

That at the same temperature and pressure, equal volumes of all gases have the same number of molecules allows a simple calculation for the combining ratios of all gases – by measuring their percentages by volume in any compound. This in turn facilitates simple calculation of the relative atomic masses of the elements of which it is composed.

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GUGLIELMO MARCONI (1874-1937)

1897 – Bristol, England

photograph of GUGLIELMO MARCONI (1874-1937). © Marchese Guglielmo Marconi was a brilliant manipulator of other scientist’s findings, especially those of RUDOLPH HERTZ’s (1857-94) breakthrough discovery of radio waves in 1888.

GUGLIELMO MARCONI (1874-1937)

Marchese Guglielmo Marconi was a brilliant manipulator of other scientist’s findings, especially those of RUDOLPH HERTZ’s breakthrough discovery of radio waves in 1888. Hertz had died shortly afterwards in 1894.

After moving from his large family estate in Italy to England, where his experiments with radio waves generated much interest, he set up the Marconi Wireless Company Limited in 1900.
The event which made him world-famous was the two thousand mile transmission of Morse code across the Atlantic in 1901.

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ENRICO FERMI (1901- 54)

1942 – USA

Fermi established his reputation with his concept of radioactive beta decay, the theory that a proton could be created from a neutron via the shedding of an electron (a beta particle) and an antineutrino.

The Joliot-Curies had announced their discovery that radioactive isotopes could be generated artificially by showering certain elements with alpha particles in 1934. Fermi realised that the newly discovered neutrons would be even better suited to this purpose as their lack of charge would allow them to slip into elements’ nuclei without resistance.

Fission chain reaction

Fission chain reaction

Fermi established the concept of ‘slow-neutrons’ by placing a piece of solid paraffin in front of the target element during bombardment. Working his way through the elements he created a number of new radioactive isotopes.

He was awarded the 1938 Nobel Prize for physics and later the significance of his work when applied to uranium was realised. Using his neutron-bombarding technique in a series of experiments with 235uranium, Fermi and NIELS BOHR confirmed that a nuclear chain reaction could almost certainly be created as the basis of an atomic bomb.

By Dec 2 1942 his team had created an ‘atomic pile’ of graphite blocks, drilled with uranium, which went on to produce a self-sustaining chain reaction for nearly half an hour.

picture of the Nobel medal - link to nobelprize.org

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