Tag Archives: Quantum leaps

Arts, History, Philosophy, Science

Quantum Leaps: Plato

Portrait of Plato. Luni marble. Roman copy after a Greek original of Silanion. Inv. No. MC 1377. Rome, Capitoline Museums, Museum Montemartini.

Copy after the statue created by the renowned portrait-sculptor Silanion. The original, commissioned by Mithridates, was dedicated to the Muses in the Academy, seat of the philosophical school founded by Plato in Athens.

c. 427 – 347 BC

To understand how Plato came to the conclusions which have exercised such a profound impact on Western thinking, it is necessary to understand his own influences. Born in or around Athens at a time when the city-state was flourishing as one of the most dominant and culturally enlightened places on earth, he was strongly affected by the arguments of another great philosopher, Socrates, who also lived there. Socrates’ approach was to constantly strive for clearer definitions of words and people’s perceptions of those words in order to get nearer to ‘the truth’ that lay behind their often irritational and ill-thought-out use of them. This introduced to Plato the notion of ‘reality’ being distorted by human perceptions, which would become important in his approach to science and, in particular, metaphysics.

. Socrates’ Influence

Socrates’ was executed in 399 BC for allegedly ‘corrupting’ the youth of Athens with his ‘rebellious’ ideas. Reacting to this, Plato fled the city-state and began a tour of many countries which would last more than a decade. On his travels, he encountered a group of people who would become another major influence, the Pythagoreans. Begun by their founder Pythagoras, the school of disciples in Croton continued to promote their ‘all is number’ approach to everything.

. The Theory of Forms

The combination of these two major forces on Plato – plus, of course, his own work – brought him to his Theory of Forms, his main legacy to scientific thought. This consisted of an argument that nature, as seen through human eyes, was merely a flawed version of true ‘reality’ or ‘forms’; in an instructive metaphor, he compares humanity with cave dwellers, who live facing the back wall of the cave. What they perceive as reality, is merely the shadows thrown out by the sun. There is, therefore, little to be learnt from direct observation of them. For Plato, there had always existed an eternal, underlying mathematical form and order to the universe, and what humans saw were merely glimpses of it, usually corrupted by their own irrational perceptions and prejudices about the way things ‘are’.

Consequently, for Plato, like the Pythagoreans, the only valid approach to science was a rational, mathematical one which sought to establish universal truths irrespective of the human condition. This validation of the numerical method strongly impacted on science; disciples following in its tradition ‘made’ discoveries by mathematical prediction. For example, arithmetic calculations would suggest that future discoveries would have particular properties, in the case of unknown elements in Dmitry Mendeleev’s first periodic table for instance, and subsequent investigative work by scientists would prove the mathematics to be true. It is an approach still used by scientists today.

. The Academy

Plato also helped to influence scientific thought in a much more physical sense by founding an Academy on his return to Athens in 387 BC. Some commentators claim this institute to be the first European university, and certainly its founding principles as a school for the systematic search for scientific and philosophical knowledge were consistent with such an establishment. Plato’s influence was pervasive; it is said there was inscription over the entrance to the institute which read, ‘Let no one enter here who is ignorant of geometry.’ Over the subsequent centuries, the Athenian Academy became recognised as the leading authority in mathematics, astronomy, science and philosophy, amongst other subjects. It survived for nearly a thousand years until the Roman emperor Justinian shut it down in 529 AD, around the time the Dark Ages began.

. The Legacy of Plato

Plato is best remembered today as one of the greatest philosophers of the Western tradition. He might not, therefore, be an obvious candidate for inclusion in any compendium of famous or influential scientists. But in exactly the same way that the influence of Plato’s work stretched into many other academic areas such as education, literature, political thought, epistemology and aesthetics, so it is the case with his science.

Although Plato’s scientific and philosophical knowledge has undergone significant revival and reinterpretation over the course of history, his logical approach to science remains influential, standing testament to his far-reaching ideas.

‘Geometry existed before creation.’ – Plato

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Arts, History, Science, Society

Quantum Leaps: ‘Leonardo Da Vinci’

leonardo-da-vinci-the-art-of-science-2-638

1452 – 1519

It is something of an indulgence to include Leonardo Da Vinci in any study of scientists who changed the world, not least because most of his work remained unpublished and largely forgotten centuries after his death. His, however, was undoubtedly one of the most brilliant scientific minds of all time; arguably the biggest handicap preventing him from profoundly changing the world was the era in which he lived.

The genius of Leonardo’s designs for his inventions so far outstripped both his contemporaries’ intellectual grasp and contemporary technology that they were rendered literally inconceivable to anyone but him. If Leonardo could have teleported to Edison’s time, with his access to nineteenth century technology, one can only speculate how much more he may or may not have achieved than even Edison himself. But even in his own time, Leonardo’s achievements were notable:

. RENAISSANCE MAN

Leonardo is celebrated as the Renaissance artist who created such masterpieces as the Last Supper (1495 – 97) and the Mona Lisa (1503 – 06), yet much of his time was spent in scientific enquiry, often to the detriment of his art. The range of areas Leonardo examined was breathtaking. It included astronomy, geography, palaeontology, geology, botany, zoology, hydrodynamics, optics, aerodynamics and anatomy. In the later field, in particular, he undertook a number of human dissections, largely on stolen corpses, to make detailed sketches of the body. Irrespective of the breadth of his studies, however, perhaps 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?’ Next, 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.

. AERODYNAMICS

Moreover, in many instances he could then directly apply the results of his enquiries into nature to designs for inventions for human use. For example, his work in aerodynamics led him to make sketches for several flying machines – which, potentially, could have flown – including a primitive helicopter, some five hundred years before the invention became a reality. He even envisaged the need for his flying machines to have a retractable landing gear to improve their aerodynamics once airborne. In 1485 he designed a parachute, three hundred years before becoming an actuality, and included calculations for the necessary size of material to safely bring to ground an object with the same weight as a human. He also had an excellent understanding of the workings of levers and gears, enabling him to design bicycles and cranes.

. HYDRODYNAMICS

Leonardo’s studies in hydrodynamics led to numerous sketches on designs for waterwheels and water-powered machines centuries before the industrial revolution. In addition, he sketched humidity-measuring equipment as well as a number of primitive diving suits, mostly with long snorkel devices to provide a supply of air.

. MILITARY INVENTIONS

During his work for the Duke of Milan between 1482 and 1499, Leonardo prepared an array of designs for weaponry such as catapults and missiles. Even in this arena, however, he could not help but create sketches of weapons that lay way ahead of their time such as hand-grenades, mortars, machine-type guns, a primitive tank and, most audaciously, a submarine.

Leonardo’s Influence

Any list of scientists ‘who could’ have changed the world, then Leonardo Da Vinci would surely be at the top of the list. But although many of the designs for his potentially world-changing creations were never published, his methodical approach to science marks a significant and symbolic stepping-stone from the Dark Ages into the modern era.

Hoping to secure employment with the Duke of Milan, he wrote to him that his areas of expertise included: the construction of bridges and irrigation canals, the designing of military weapons and architecture, as well as painting and sculpture. To add to the list, Leonardo is also credited with being the first ever person to conceive of a bicycle.

Supplementary appendage:

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Leonardo Da Vinci painting: The Mona Lisa. An oil painting by the Italian Renaissance artist which was created in 1503.

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Arts, History, Science, Society

Quantum Leaps: Archimedes…

c. 287 – 212 BC

“Give me a place to stand on, and I will move the earth,” Archimedes is reputed to have declared to the people of Syracuse. The practicalities of an earth-bound life may have denied him that particular pedestal but arranging for his patron King Heiron to move a ship by pushing a small lever was considered only a slightly miraculous feat. With such audacious displays, along with his brilliance as an inventor, mechanical scientist and mathematician, it is no wonder Archimedes was so popular and highly regarded among his contemporaries.

The Mathematician

It was not only his peers, however, who benefited from Archimedes’ work. Many of his achievements are still with us today. First and foremost, Archimedes was an outstanding pure mathematician, “usually considered to be one of the greatest mathematicians of all time,’ according to the Oxford Dictionary of Scientists. He was, for example, the first to deduce that the volume of a sphere was 4πr³ x 3, where r is the radius. Other work in the same area, as outlined in his treatise On the Sphere and Cylinder, led him to deduce 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. He calculated pi to be approximately 22/7, a figure that was widely used for the next 1500 years.

The Archimedes Principle

Archimedes also discovered the principle that an object immersed in a liquid is buoyed or thrust upwards by a force equal to the weight of the fluid it displaces. The volume of the displaced liquid is the same as the volume of the immersed object. Legend has it that he discovered this when set a challenge by King Heiron to find out whether one of his crowns was made of pure gold or was a fake. While contemplating the problem Archimedes took a bath and noticed that the more he immersed his body in the water, the more the water overflowed from the tub. He realised that if he immersed the crown in a container of water and measured the water that overflowed he would know the volume of the crown. By obtaining a volume of pure gold equivalent to the volume of water displaced by the crown and then weighing both the crown and the gold, he could answer the King’s question. On making this realisation, Archimedes is said to have leapt from his tub and run naked along the street shouting ‘Eureka!’, ‘I have found it!’

Levers and Pulleys

Indeed, it was the practical consequences of Archimedes’ work which mattered more to his contemporaries and for which he became famous.

One such practical demonstration allowed King Heiron to move a ship with a single small lever – which in turn was connected to a series of other levers. Mathematically, he understood the relationship between the lever length, fulcrum position, the weight to be lifted and the force required to move the weight. This meant he could successfully predict outcomes for any number of levers and objects to be lifted.

Likewise he came to understand and explain the principles behind the compound pulley, windless, wedge and screw, as well as finding ways to determine the centre of gravity in objects.

Archimedes goes to war

Perhaps the most important inventions to his peers, however, were the devices created during the Roman siege of Syracuse in the second Punic War. The Romans eventually seized Syracuse, due to neglect of the defences, and Archimedes was killed by a Roman soldier while hard at work on mathematical diagrams. His last words are reputed to have been, ‘Fellow, do not disturb my circles!’

Further achievements

Inventions

. Archimedes’ Screw: a device used to pump water out of ships, and also to irrigate fields.

. Archimedes’ Claw: a huge war machine designed to sink ships by grasping the prow and tipping them over, used in the defence of Syracuse.

. Compound pulley systems: enabled the lifting of enormous weights at a minimal expenditure of energy.

. The method of exhaustion: an integral-like limiting process used to compute the area and volume of two dimensional lamina and three-dimensional solids.

Discoveries

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

. Known as the ‘father of integral calculus’, Archimedes’ reckonings were later used by, among others, Kepler, Fermat, Leibniz and Newton.

. Science Book

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