by Mike Bennett
He went first to Padua, where he taught briefly, and applied unsuccessfully for the chair of mathematics, which was assigned instead to Galileo one year later. Bruno then moved to Venice in March 1592. For about two months he worked as an in-house tutor to Mocenigo. When Bruno announced his plan to leave Venice, his host, who was unhappy with the teachings he had received, denounced him to the Venetian Inquisition. They promptly had Bruno arrested.
Among the numerous charges of blasphemy and heresy brought against him in Venice based on Mocenigo’s denunciation was his belief in the plurality of worlds, as well as accusations of personal misconduct. Bruno defended himself skilfully, stressing the philosophical character of some of his positions, denying others and admitting that he had had doubts on some matters of dogma. The Inquisition however asked for his transferral to Rome. After several months and some quibbling the Venetian authorities reluctantly consented and Bruno was sent to Rome in 1593.
In Rome, Bruno’s trial lasted seven years during which time he was imprisoned, lastly in the Tower of Nona. Some important documents about the trial are lost, but others have been preserved, among them a summary of the proceedings that was rediscovered in 1940. The numerous charges against Bruno, based on some of his books as well as on witness accounts, included blasphemy, immoral conduct and heresy in matters of dogmatic theology, and involved some of the basic doctrines of his philosophy and cosmology. Luigi Firpo lists these charges made against Bruno by the Inquisition.
Bruno continued his defensive strategy, which consisted of bowing to the church’s dogmatic teachings, while trying to preserve the basis of his philosophy. In particular Bruno held firm to his belief in the plurality of worlds, although he was admonished to abandon it. His trial was overseen by the Inquisitor Cardinal Bellarmine, who demanded a full recantation, which Bruno eventually refused. On 20th January 1600, Pope Clement VIII declared Bruno a heretic and the Inquisition issued a sentence of death.
He was turned over to the secular authorities and, on 17th February 1600 in the Campo de’ Fiori, a central Roman market square, he was burned alive at the stake. His ashes were dumped into the River Tiber.
CHAPTER 4
Following the work of Brahe and Bruno, the next major steps in the field of scientific discovery were made by Galileo Galilei. Galileo was a physicist, mathematician, engineer and astronomer, born in Pisa, Italy in 1564. He discovered the Jovian moons Europa, Callisto, Ganymede and Io. His contribution to modern science was so significant that NASA named a space mission after him. The Galileo spacecraft was launched in 1989. It consisted of an orbiter and entry probe, and travelled to Jupiter to investigate the planet and its moons.
Galileo’s greatest achievements resulted from his improvements to the first telescope, and consequent astronomical observations and support for Copernicanism. Galileo has been called the father of modern observational astronomy, the father of modern physics, and the father of modern science. His contributions to observational astronomy include the telescopic confirmation of the phases of Venus, the discovery of the four largest satellites of Jupiter (named the Galilean moons in his honour), and the observation and analysis of sunspots. Galileo also worked in applied science and technology, inventing an improved military compass and other instruments.
Galileo’s championing of heliocentrism was controversial within his lifetime, when most subscribed to either geocentrism or the Tychonic system. He met with opposition from other astronomers, who doubted heliocentrism due to the absence of an observed stellar parallax. The matter was investigated by the Roman Inquisition in 1615, which concluded that heliocentrism was false and contrary to scripture, placing works advocating the Copernican system on the index of banned books and forbidding Galileo from advocating heliocentrism.
Galileo later defended his views in a subsequent book which appeared to attack Pope Urban VIII, thus alienating not only the Pope but also the Jesuits, who had both supported Galileo up until this point. He was tried by the Holy Office, then found to be vehemently suspect of heresy. He was forced to recant, and spent the rest of his life under house arrest. It was while Galileo was under house arrest that he wrote one of his finest works, Two New Sciences, in which he summarised the work he had done some forty years earlier on the two sciences now called kinematics and strength of materials.
Galileo’s father, Vincenzo Galilei, a lutenist and music theorist, had performed experiments establishing perhaps the oldest known non-linear relation in physics: for a stretched string, the pitch varies as the square root of the tension. These observations lay within the framework of the Pythagorean tradition of music, well known to instrument makers, which included the fact that subdividing a string by a whole number produces a harmonious scale. Thus, a limited amount of mathematics had long related music and physical science, and young Galileo could see his own father’s observations expand on that tradition.
Galileo was one of the first modern thinkers to clearly state that the laws of nature are mathematical. In The Assayer he wrote that philosophy is written in the language of mathematics, and its characters are triangles, circles and other geometric figures.
His mathematical analyses are a further development of a tradition employed by late scholastic natural philosophers, which Galileo learned when he studied philosophy. He displayed a peculiar ability to ignore established authorities, most notably Aristotelianism. In broader terms, his work marked another step towards the eventual separation of science from both philosophy and religion, which was a major development in human thought.
He was often willing to change his views in accordance with observation. In order to perform his experiments, Galileo had to set up standards of length and time, so that measurements made on different days and in different laboratories could be compared in a reproducible fashion. This provided a reliable foundation on which to confirm mathematical laws using inductive reasoning.
Galileo showed a remarkably modern appreciation for the proper relationship between mathematics, theoretical physics and experimental physics. He understood the parabola, both in terms of conic sections and in terms of the ordinate (y) varying as the square of the abscissa (x).
Galilei further asserted that the parabola was the theoretically ideal trajectory of a uniformly accelerated projectile in the absence of friction and other disturbances. He conceded that there are limits to the validity of this theory, noting on theoretical grounds that a projectile trajectory of a size comparable to that of the Earth could not possibly be a parabola, but he nevertheless maintained that for distances up to the range of the artillery of his day, the deviation of a projectile’s trajectory from a parabola would be only very slight.
Soon after Galileo was born, his great contemporary Johannes Kepler came onto the scene. He was born in Weil der Stadt, Germany in 1571. In common with Galileo, Kepler’s contribution to modern science is also considered to be so significant that NASA named one of its most famous space telescopes after him. The Kepler spacecraft was launched in 2009.
In October 1604, a bright new evening star appeared, but Kepler did not believe the rumours until he saw it himself. Kepler was a key figure in the 17th century scientific revolution. He is best known for his laws of planetary motion, which also provided one of the foundations for Isaac Newton’s theory of universal gravitation.
During his career, Kepler was a mathematics teacher at a seminary school in Graz, Austria, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to astronomer Tycho Brahe, and eventually the imperial mathematician to Emperor Rudolf II and his two successors.
He was also a mathematics teacher in Linz, Austria, and an advisor to General Wallenstein. Additionally, he did fundamental work in the field of optics, invented an improved version of the refracting telescope (the Keplerian Telescope), and made further telescopic developments following on from the work of his contemporary Galileo Galilei.
Kepler lived in an era when there was no clear distinction between astro
nomy and astrology, but there was a strong division between astronomy (a branch of mathematics within the liberal arts) and physics (a branch of natural philosophy).
Kepler described his new astronomy as celestial physics, and treated astronomy as part of a universal mathematical physics.
Kepler’s first major astronomical work was the first published in defence of the Copernican system. Kepler claimed to have had an epiphany in 1595, while teaching in Graz, demonstrating the periodic conjunction of Saturn and Jupiter in the zodiac. He realised that regular polygons bound one inscribed and one circumscribed circle at definite ratios, which he reasoned, might be the geometrical basis of the universe.
After failing to find a unique arrangement of polygons that fit known astronomical observations (even with extra planets added to the system), Kepler began experimenting with three-dimensional polyhedra. He found that each of the five Platonic solids could be uniquely inscribed and circumscribed by spherical orbs. Nesting these solids, each encased in a sphere, within one another would produce six layers, corresponding to the six known planets – Mercury, Venus, Earth, Mars, Jupiter and Saturn.
By ordering the solids correctly as the basic geometrical solids known as octahedron, icosahedron, dodecahedron, tetrahedron and cube, he found that the spheres could be placed at intervals corresponding (within the accuracy limits of available astronomical observations) to the relative sizes of each planet’s path. Kepler also found a formula relating the size of each planet’s orb to the length of its orbital period: from inner to outer planets, the ratio of increase in orbital period is twice the difference in orb radius. However, Kepler later rejected this formula, because it was not precise enough.
In terms of the impact of his published work, it can be seen as an important first step in modernising the theory proposed by Nicolaus Copernicus in his De Revolutionibus. Whilst Copernicus sought to advance a heliocentric system in this book, he resorted to epicycles and eccentric circles in order to explain the change in a planets’ orbital speed, and also continued to use as a point of reference the centre of the Earth’s orbit rather than that of the sun. Modern astronomy owes much to Kepler, despite some flaws in his deductions, since his work represents the first step in cleansing the Copernican system of the remnants of the Ptolemaic theory still clinging to it.
As the reader may be falling asleep by now from an overdose of science history, we will now take a look at Charles Darwin. Although he had absolutely nothing to do with physics, chemistry or gravity, he was a great man. He developed the theory of evolution, and his pioneering work is honoured by his marble statue that looks down over the main hall of the Natural History Museum in London.
For me, his greatest legacy is the annual award that bears his name. These awards are bestowed posthumously upon people who have excelled in improving the human gene pool.
I remember a few years ago this award was jointly bestowed on a brother and sister from Canada. They were impoverished students alone in their parents’ house over the weekend. They had told their friends that they could not go out one evening, as they had no money at all. The rest of the story was pieced together from the forensic examination of the scene, and was reported in the local press.
This hapless pair apparently ran out of alcohol that evening, and post mortems showed petrol and milk in their stomachs. It was concluded that they mixed petrol from the lawnmower with milk, and then sat down by the lounge fire to watch TV and enjoy their drinks. Soon thereafter, one or both of them threw up in the fireplace, and the resulting explosion and fire destroyed the house.
I have recently nominated a scrap-yard worker from Thailand for the Darwin Award this year following a story reported by BBC World News. A construction worker excavating the foundations for a building in Bangkok unearthed an unexploded 500-pound World War II bomb. Instead of calling the bomb squad, he sold it to a local scrapyard. Due to its size, they decided to cut it up with an oxyacetylene torch.
When the emergency services arrived on the scene, they found that the building had been completely demolished. There was a 3-metre crater in the ground and body parts were discovered over 100 metres away from the centre of the detonation. I doubt that anyone else this year will be more deserving of this award. The reader can obtain details of all previous Darwin Awards on the web.
CHAPTER 5
Follow the work of Galileo and Kepler, very major steps forward in physics and mathematics were made by Isaac Newton, who would soon be knighted in recognition of his work. Newton was born in Woolsthorpe-by-Colsterworth in the UK in 1643. He is considered by many to be the father of modern physics and kinematics.
His work laid the foundations for further developments in these areas for all future physicists. Today, the basic unit of force is named after him. One Newton is defined as the force required to accelerate a mass of one kilogram at a rate of one metre per second squared.
His book Mathematical Principles of Natural Philosophy, first published in 1687, laid the foundations for classical mechanics. Newton also made major contributions in the fields of optics and calculus.
This book formulated the laws of motion and universal gravitation, which dominated scientists’ view of the physical universe for the next three centuries. By deriving Kepler’s laws of planetary motion from his mathematical description of gravity, and then using the same principles to account for the trajectories of comets, the tides, the precession of the equinoxes and other phenomena, Newton removed the last doubts about the validity of the heliocentric model of the cosmos.
This work also demonstrated that the motion of objects on Earth and of celestial bodies could be described by the same principles. His prediction that the Earth should be shaped as an oblate spheroid was later vindicated by the measurements of Maupertuis La Condamine and others, which helped convince most Continental European scientists of the superiority of Newtonian mechanics over the earlier system of Descartes.
Newton was a fellow of Trinity College and the second Lucasian Professor of Mathematics at the University of Cambridge. Later in his life, Newton became president of the Royal Society. He also served the British government as Warden and Master of the Royal Mint.
Newton’s work is still taught to science students today, and his three laws of motion define kinematics. These laws state:
I. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.
II. The relationship between an object’s mass (m), its acceleration (a) and the applied force (F) is F=ma. Acceleration and force are vectors. In this law the direction of the force vector is the same as the direction of the acceleration vector.
III. For every action there is an equal and opposite reaction.
Newton also built the first practical reflecting telescope, and developed a theory of colour based on the observation that a prism decomposes white light into the many colours of the visible spectrum. He formulated an empirical law of cooling, studied the speed of sound and introduced the notion of a Newtonian fluid. In addition to his work on calculus, as a mathematician Newton contributed to the study of power series, generalised the binomial theorem to non-integer exponents and developed Newton’s method for approximating the roots of a function.
In 1679, Newton returned to his work on celestial mechanics by considering gravitation and its effect on the orbits of planets with reference to Kepler’s laws of planetary motion. This followed stimulation by a brief exchange of letters in 1679–80 with Hooke, who had been appointed to manage the Royal Society’s correspondence, and who opened a correspondence intended to elicit contributions from Newton to Royal Society transactions.
Newton’s reawakening interest in astronomical matters received further stimulus with the appearance of a comet in the winter of 1680–81, on which he corresponded with John Flamsteed. After the exchanges with Hooke, Newton worked out proof that the elliptical form of planetary orbits would result from a centripetal force inversely proportional to the s
quare of the radius vector. Newton communicated his results to Edmond Halley and to the Royal Society in a tract written on about nine sheets, which was copied into the Royal Society’s Register Book in December 1684.
Newton’s book The Principia was published on 5th July 1687 with encouragement and financial help from Edmond Halley. In this work, Newton stated his three universal laws of motion that contributed to many advances during the Industrial Revolution which soon followed, and were not to be improved upon for more than 200 years. Many of these advancements continue to be the underpinnings of non-relativistic technologies in the modern world. He used the Latin word gravitas (weight) for the effect that would come to be known as gravity, and defined the law of universal gravitation.
In the same work, Newton presented a calculus-like method of geometrical analysis using first and last ratios, and gave the first analytical determination (based on Boyle’s law) of the speed of sound in air. This inferred the oblateness of the spheroidal figure of the Earth, and accounted for the precession of the equinoxes as a result of the moon’s gravitational attraction on the Earth’s oblateness. This initiated the gravitational study of the irregularities in the motion of the moon, and provided a theory for the determination of the orbits of comets.
Newton made clear his heliocentric view of the Solar System. This was developed in a somewhat modern way, because already by the mid-1680s he recognised the deviation of the sun from the centre of gravity of the solar system. For Newton, it was not precisely the centre of the sun or any other body that could be considered at rest, but rather the common centre of gravity of the Earth, the sun and all of the planets. Newton observed that this centre of gravity either is at rest or moves uniformly forward.
