Law and mechanism in the cosmos
We have reached an interesting moment in our journey to understand the origin and development of inequality and prejudice. If we look backwards, we find Platonic solids and a mathematical and geometrical structure of the universe, tied to the model of the Great Chain of Being and to plenitude and continuity from the Timaeus. If we look forward, we see the idea of the bounded universe of concentric circles dissolving, and the discovery of laws of nature in the universe that will replace emanation as the explanation of nature. Looking both backwards and forwards is the famous astronomer and mathematician Johannes Kepler (1571-1630).
In looking forwards, he discovered three laws, known as Kepler’s three laws.
The first two were published in his New Astronomy of 1609.
The first law says that the orbit of a planet is not a circle but is elliptical. This avoids the need for epicycles, and it places the center of the solar system where the sun is, and not at the center of the earth’s orbit. It was not clear to Kepler what force would steer a planet at the correct speed along an elliptical curve.
The second law said that planets do not orbit at a uniform speed but go more quickly when they are nearer the sun (perihelion) and slower when further away from the sun (aphelion).
The third law―perhaps the most important―stated that there is a mathematical law that determines the distance a planet is from the sun and the time it takes to complete an orbit. It is called the law of inverse square. And it is this: the square of the orbital periods of the planets goes up in step with the whole of their distances from the sun. So, for example, a planet that is four times (22) as far as another planet from the sun takes 8 times (23) as long to complete an orbit.
Remember that in the past such things had been explained by emanation, angels, and gods. Now Kepler was explaining the motion of the planets by means of mathematical laws. And for Kepler, this meant that God was a mathematician, and that the universe was ordered or systematic.
To employ this new-found order, Kepler looked backwards to Plato and to the Platonic solids, to provide us with perhaps the most ingenious and beautiful structure of the old cosmos using modern mathematical sensibilities. He devised a model of the Harmonices mundi or Harmony of the World (1619) (which included his third law of motion). It was the beauty of the mathematics of his new cosmos that now gave the cosmos its harmony, its harmonious order, and its ratio and proportion. He found the ratios between the planets to correspond to musical ratios. He then set out to answer the question as to why there were six planets. He speculated that the beauty of the mathematics in the universe was carried by the five Platonic solids which held each planet in relation to the others. Each Platonic solid, or regular shape, was therefore placed within the next one until he achieved this famous diagram of the harmony of the universe.
(see Kepler’s solar system from his Mysterium Cosmographicum, 1596 via Wikimedia Commons and Kepler’s Platonic solid model of the Solar System from Mysterium Cosmographicum.)
With Kepler then we get the beginning of laws of motion tied to the ancient idea of Platonic solids. It was to the laws that science would turn its attention.
Next, we turn to Galileo Galilei (1564-1642). His achievements are remarkable, and here is a list that mentions them all too briefly. I have divided them into three groups; those that support acentrism; those that contribute new laws; and the famous story of his trial.
With regard to the growing awareness of acentrism that was undermining the Aristotelian universe, in 1604 Galileo proved that a new star was much further from the earth than the model of concentric circles allowed. And a new star proved that the heavens were after all changeable. This offended the logic of mastery and identity which held that what was absolutely true was also absolutely unchangeable. Tycho Brahe (1564-1601) has also discovered a new star in 1572.
By 1609 Galileo heard reports of a new instrument called the telescope. He built his own refractory telescope, magnifying natural vision by 1000x larger and 30x nearer. He described what he saw in his book Sidereus nuncius, or The Sidereal [Starry] Messenger (1610). It changed forever the view of the universe.
UNFOLDING GREAT AND MARVELLOUS SIGHTS,
AND PROPOSING THEM TO THE ATTENTION OF EVERY ONE,
BUT ESPECIALLY PHILOSOPHERS AND ASTRONOMERS,
BEING SUCH AS HAVE BEEN OBSERVED BY GALILEO GALILEI, A GENTLEMAN OF FLORENCE, PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF PADUA, WITH THE AID OF A TELESCOPE LATELY INVENTED BY HIM.
Respecting the Moon’s Surface, an innumerable Number of Fixed Stars, the Milky Way, and Nebulous Stars, but especially respecting Four Planets which revolve around the Planet Jupiter at different distances and in different periodic times, with amazing velocity, and which, after remaining unknown to every one up to this day, the Author recently discovered, and determined to name the MEDICEAN STARS.
He showed that the moon’s surface was not smooth (it had been thought to be smooth like a pearl);
Of the moon he stated that
‘I feel sure that the surface of the Moon is not perfectly smooth, free from inequalities and exactly spherical, as a large school of philosophers considers with regard to the Moon and the other heavenly bodies, but that, on the contrary, it is full of inequalities, uneven, full of hollows and protuberances, just like the surface of the Earth itself, which is varied everywhere by lofty mountains and deep valleys.’
He also measured the height of some of the moon’s mountains, measurements are still agreed with today.
Cohen says that in order to see how the moon was thought about up to this point, one could look at Dante’s Divine Comedy here, in Book 2 of Paradiso, Dante ascends with Beatrice, towards Paradise, first reaching the moon, the first of the heavenly bodies. Dante the pilgrim asks Beatrice to explain why from the earth there appear to be dark spots when, having arrived at the moon, it is smooth and flawless, or an ‘eternal celestial pearl … as brilliant, hard, and polished as a diamond struck by a ray of sunlight.’ Beatrice’s answers that it is another example of how, even when he uses his own senses, man frequently demonstrates the weaknesses of mortal or human reasoning.
Dorothy L Sayers notes here that the term ‘eternal celestial pearl’, meaning the moon, in the original Italian is l’eterna margarita’ (not the pizza). Margarita, meaning pearl, comes from Persian and Sanskrit, and Sayers says here that the translation of margarita as onion―which she uses in her translation―is very appropriate because the word onion, according to Pliny, means an exceptionally large pearly which is single and undivided.
Shakespeare uses onion in this same sense in Hamlet:
And in the cup an onion shall he throw
Richer than that which four successive kings
In Denmark ‘s crown have worn (Hamlet v.ii.)
He measured the heights of some of the moon’s mountains―if the moon resembled the Earth, then again this lent weight to the idea that the earth was not unique in the heavens (remember that in Revolutions Copernicus had suggested that the earth was just another of the ‘wandering stars’). Galileo also refuted the idea that the earth was at the bottom of the cosmos. He conceived of ‘earthshine’ in contrast to moonshine, arguing that the moon was not lit by an internal luminosity as had been believed, but by light from the sun reflected by the earth. If all the planets did this, then, he said, perhaps they all orbit the sun.
Based on his observations of stars in his telescope he argued that the stars must be much further away than the Aristotelian system allowed for. The Milky Way, he said, ‘is nothing else but a mass of innumerable stars planted together in clusters’ (Galileo, 1880, 42).
But the really big news in the book, the one that most contributed to acentrism, was the discovery of four planets never seen before: the moons of Jupiter. Galileo called them the Medicean stars in honor of Grand Duke Cosimo of the House of Medici, but history now shows that two other people, Thomas Harriot in England, and Simon Marius in Germany, may well have seen these before Galileo. Marius may have built his own telescope and seen the moons of Jupiter in 1609. But he did not begin making his notes until the day after Galileo first described them in a letter. Galileo accused Marius of plagiarism, but Marius has left his mark here. In 1609 he called the moons Io, Europa, Ganymede and Callista, and these are the names by which they are still known today.
The Sidereal Messenger proved that the universe had no one single center, and since Jupiter was the center of the orbit of its four moons, perhaps there were many such centers. This struck a fatal blow to the Aristotelian system. It questioned the Great Chain of Being in regard to the hierarchy of continuity and the process of its implementation by emanation. It also questioned the logic of mastery and identity by suggesting that the unchangeable heavens are changeable, or, as we might say today, fluid. Might we go as far as to say that Galileo’s discoveries ‘queered’ the cosmos? New worlds gave additional incentive to believe not just that there are other worlds, but that there might also be other kinds of life on other worlds. John Milton, who visited Galileo while the latter was under house arrest, said in Paradise Lost
Of amplitude almost immense, with stars
Numerous, and every star perhaps a world
Of destined habitation
(Book VII. 620-3)
There is another way in which Galileo undermined the picture of the universe with an unmoving earth at its center. Remember that Aristotle had argued that the earth must be at rest since an object thrown straight into the air returns back to the hand that threw it. If the earth moved, then the object would get left behind. But something was in play that Aristotle did not recognize. Objects behave the same if they are travelling at a constant speed or if they are at rest. You can’t tell them apart. Think of being on a train and throwing a ball in the air. If the train is traveling at a constant speed, then the ball will fall back to you, just as it would do if the train were sitting in the station. Throwing an object in the air does not show whether the train, or the earth, is moving at constant speed or at rest.
On its own, then, this kind of Galilean relativity undermined the centrism of the old universe and the immobility of the Earth. But the logic of truth had not changed. What had changed was that the picture of the cosmos no longer conformed to the logic of truth. Remember we saw that truth had to be something ‘in-itself’, resistant to infinite regression, simple, and not dependent upon anything else, irreducible to anything else, and maintained by its own necessity. Into the gap left by the demise of the Aristotelian universe stepped something that still met these same requirements of the logic of truth, something that was its own mastery and identity: mechanics, or the laws of motion in nature.
The universe may have changed, but the logic of truth had not. The structure of truth was the same, but something new was needed that would now replace the old truths. Truth needed a new version of identity and mastery for its old logic. The new universe would not be Aristotelian, but the logic of its truth would remain so. In our next lectures we will look at how this developed in natural philosophy, and in future lectures we will look at how it played out in terms of inequality in the social and political world.
Galileo himself made dramatic contributions to mechanics with his three laws of motion.
- The law of uniform motion―distance travelled is proportional to the speed travelled and the time taken
- The law of acceleration of falling bodies. Gravity speeds up the acceleration of a falling object by a mathematical ratio: the distance travelled is the square of the time taken (e.g., 1 second = I meter, 2 seconds = 4 meters, 3 seconds = 9 meters). As such, a feather and a hammer, with no resistance, would fall at the same rate and hit the ground together if dropped together from the same height. Aristotle had said that the speed of the descent of an object would depend on its weight (we now know that the acceleration of free-falling body is 9.8 m/s/s or the rate of acceleration of gravity).
So, to sum up these two laws,
- Natural horizontal motion is motion at a constant velocity
- Natural vertical motion is falling at a constant acceleration
- The third law of motion concerns the motion of a projectile. The ball thrown into the air on the train travels in a parabola back to the hand. Things don’t drop straight down because horizontal motion is combined with vertical motion to form a curved path. (Bombs dropped from a plane don’t fall straight down. With the vertical speed of gravity and the horizontal speed of the plane they drop in a curved path.)
Why is this important? Because when a projectile lands, say, on a table, its vertical motion is stopped (gravity) but its horizontal motion is unaffected. Thus Galileo showed Aristotle to be wrong again. Aristotle believed the natural state of an object was to come to rest. Galileo argued that an object would keep moving, possibly eternally. With this he paves the way for Newton’s first law of motion later in the same century.
So far then ..
Galileo has undermined Aristotle’s concentric universe and his physics. Mechanics is replacing the emanationist universe of the Great Chain of Being. So, will mechanics now become the new shape of the logic of mastery?
But before we look at this question, it is worth looking at Galileo’s trial as an example of how hard the old shape of mastery as prepared to defend against itself against the new shapes.
In 1633 Galileo stood trial in Rome before the Inquisition for heresy in his all-too Copernican book Dialogue Concerning the Two Chief World Systems (1632). Despite previous warnings he was found guilty of heresy for supporting the idea that the earth moves and is not the center of the universe. The logic of mastery sentenced him to life imprisonment.
Galileo is reported to have dropped to his knees, holding the Bible, and offered his abjuration (his renunciation of these heresies) in Latin. He said, ‘I also swear and promise to adopt and preserve entirely all the penances which have been or may be by this Holy Office imposed on me.’ Yet, legend has it, as he rose to his feet he uttered under his breath ‘Eppur si muove’ (And yet, it moves). His life sentence was served as house arrest in Sienna where, despite what he had said to the Inquisition, he worked on another publication Dialogues Concerning Two New Sciences (1638). Finally, he moved to the hills above Florence. He died, blind, in 1642.
Only in 1992 did the Pope agree that Galileo should not have been condemned.
Copernicus, N. (2002) On The Revolutions of the Heavenly Spheres, Philadelphia, Running Press.
Galileo Galilei, (1880) The Sidereal Messenger, trans. Edward Stafford Carlos, London, Rivingtons.
 Galileo Galilei, (1880) The Sidereal Messenger, trans. Edward Stafford Carlos, London, Rivingtons, p. 15.
 Paradiso, II. 31-4.
 The root of onion in Latin is unionem, a single pearl or onion.
 Book 1.9., Copernicus, 2002, p. 19.