Monday, December 07, 2009

Angels, Unmoved Movers and Impetus

‘It produces motion by being loved’

Aristotle (Metaphysics 12.7.1072b.3-4)

When a mover sets a body in motion he implants into it a certain impetus, that is, a certain force enabling a body to move in the direction in which the mover starts it, be it upwards, downwards, sidewards, or in a circle.

The implanted impetus increases in the same ratio as the velocity. It is because of this impetus that a stone moves on after the thrower has ceased moving it. But because of the resistance of the air (and also because of the gravity of the stone) which strives to move it in the opposite direction to the motion caused by the impetus, the latter will weaken all the time.

Therefore the motion of the stone will be gradually slower, and finally the impetus is so diminished or destroyed that the gravity of the stone prevails and moves the stone towards its natural place. In my opinion one can accept this explanation because the other explanations prove to be false whereas all phenomenaa agree with this one.

Jean Buridan's "Quaestiones on Aristotle's Physics":

In Medieval Europe, natural philosophy was significantly changed by an influx of Arabic and Greek works. These would mean that the system of astronomy in the Middle Ages would be basically Ptolemaic and Aristotelian. The first popularising text was one written by Al Farabi in the 9th century and translated by John of Seville in 1137. This gave the basics of the Ptolemaic system and long remained a standard text. It was in turn replaced and improved upon by a work called ‘The Sphere’ (In reference to the spherical cosmos) by Sacrobosco, whose real name was John of Holywood. John had taught at the University of Paris from 1230 to 1255 and had written ‘The Sphere’ when he was there in 1250. This work became a standard textbook on astronomy until the 17th century and went through numerous editions (High school textbook writers note; it discusses ‘the spherical earth’).

One of the things the Middle Ages had inherited from earlier cultures was a tension between Ptolemeic views of cosmology and Aristotelian physics. The basis of this was that Aristotle was really interested in the causes of motion and the ways in which the universe functions in a physical way. According to Aristotle, the earth has to be in the centre because that is the low point, the place to which heavy bodies naturally tend. Ptolemy on the other hand was preoccupied with getting the positions of the planets exactly right and having a predictive model that accounts for heavenly phenomena. The conflict came because, in order to do this, Ptolemy moved the earth from the centre of most of the celestial spheres. The spheres thereby orbit an eccentric, which is not coincident with the centre of the earth. This caused a lot of problems with Aristotelian physics. There was therefore a strong feeling against Ptolemy in Spain by Arabic authors; a good example being Muhammad Ibn Rushd (Averroes). His feeling was that Ptolemy should be rejected entirely in favour of a completely Aristotelian system regardless of what it would do to predictive astronomy. These controversies did not produce any workable solution.

One had been proposed by Ibn al-Haytham (AlHazen), (according to wikipedia; he was the discoverer of 'the scientific method' and inventor of every human discipline) which was to combine the two systems and make Aristotle's spheres so thick that the epicycles would run through them as through a channel. This would mean that the outside -the convex surface of each celestial sphere, and the interior concave surface of each celestial sphere- would actually be centred on the earth. The orbit of the planets would then run eccentrically through the think spheres, so both systems would be saved. This ‘solution’ was picked up by Roger Bacon and was praised by several other Franciscans; it then became a standard model for thinking about the universe. Once the thick spheres had been incorporated, attempts could be made to measure the distances to the planets and the thickness of the spheres. For example, if the spheres are nested together with no spaces in between them, then we can use the thickness of the spheres to calculate the sizes of the orbits.

Attempts to do this were made, the most famous by an Italian called Companus of Novara (although clearly not famous enough to get a wikipedia page). In the 1260 he wrote his ‘Theory of the Planets’ which attempted to give measurements for the size of the universe. He starts with the diameters of heavenly bodies, the sun being the largest with a radius of 17,850 miles. (modern calculations give it as 432000 miles; but nice try!). The moon is given as much smaller than the sun at a radius of under a 1000 miles (it’s really 2200 miles; but nice try!). He also tried to do the distances. For the moon he gave the inner surface of the moon sphere is 107,000 miles away. The outer surface is 209,198 miles away. He was actually quite close with that estimate, the moon is around 250,000 miles away on average. As he tries to calculate further and further away his estimates get more and more inaccurate. He says that Saturn for example is 73,383,747 miles away. The actual distance is more like 170,000,000 miles (not even close, but points for effort!). Nonetheless these were fairly reasonable attempts to judge how big the world actually was given the data and the instruments available. For someone living in the Medieval era, 73,000,000 miles is pretty damn big and so the Medieval universe was in no way small and comfortable.

Celestial spheres which carried the planets were accepted as real solid objects by essentially everyone in the Middle Ages. But what would make these objects move? The traditions of Aristotle were very important and, unfortunately, Aristotle was totally contradictory on this point. On the one hand he said in ‘On the Heavens’ that the heavenly spheres are made of the quintessence (the so called fifth element) and that the quintessence has a natural motion in a uniform circular direction. In ‘The physics’ and ‘The metaphysics’ the great philosopher says that unmoved movers –some kind of intelligences which are external to the orbs – cause them to move without being affected by them. In some places he says the spheres are en-souled and alive, thereby capable of moving themselves. How can these mysterious unmoved movers move the spheres? Aristotle doesn’t give a whole lot of help here, in fact he says that they cause the motion by ‘being loved’; which sounds great in a kind of namby pamby, new agey kind of sense but doesn’t really tell us a great deal (One of the forgotten legacies of Aristotle may be that he was the source of the phrase ‘love makes the world go round’, now a somewhat cheesy tag line for Valentines day cards and pop hits across the western world). Medieval philosophers generally were unsatisfied with this rather cryptic explanation so they tried to find other solutions.

God could be called in to be the single unmoved mover who causes the motion of the spheres, but that tended to violate the principle that god works through secondary causes (something that has also gone begging in the present day ‘Intelligent Design’ controversy). Some people instead proposed the idea that there were angels which had been created by God to cause the spheres to move. These were somewhat arbitrary supernatural entities, but at least they were secondary causes. This didn’t satisfy some people either because it violated the principle of naturalism which was so important. There have to be natural causes to things unless we cannot possibly avoid it! (yet another principle which seems to have been forgotten today; but I digress) As a result, some others like Robert Kilwardby (1215 –1279) and John Blund proposed that at creation God had implanted a natural motion in the spheres, which is similar to what Aristotle says in ‘On the Heavens’. Others argued that God had merely given a ‘push’ to the spheres to get them going and then they would keep moving for ever after.

One person who argued this was Jean Buridan, a master at the University of Paris. He invented the idea of impetus which is somewhat akin to our idea of momentum, an impressed force which keeps a moving body moving. This was also used to explain projectile motion. Since the heavenly spheres encounter no resistance and do not move through a medium (like a projectile through the air) the impetus shouldn’t be dissipated. This dealt a death blow to the angels; as Buridan puts it:

"one could imagine that it is unneccesary to posit intelligences as the movers of celestial bodies since the Holy Scriptures do not inform us that intelligences must be posited. For it could be said that when God created the celestial spheres, He began to move each of them as He wished, and they are still moved by the IMPETUS which He gave to them because, there being no resistance, the impetus is neither corrupted nor diminished."

Sadly – or fortunately depending on your point of view - his successors like Albert of Saxony followed him in dismissing the angels. Henry of Langenstein (d 1397) severely restricted their role and Nicolas of Cusa (d 1464) got rid of them altogether. As well of getting rid of the angels, impetus also dealt a blow to Aristotle. The traditional view held that the heavens and the earth were made of different stuff and performed differently. Now, with the unity of heavens and earth, the same theories for both could be devised.

Later Nicole Oresme would argue that the celestial spheres were constructed in such a way that they were like a clock which could be wound up under it’s own power (he did however retain the angels as a means of ensuring an inertia which would stop the celestial bodies from moving too fast) God might therefore have constructed a ‘clockwork’ structure, got it started and let it perpetuate it’s own motion. On the heavens he writes that:

‘he put into them motive qualities and powers just as he put weight and resistance against these motive powers in earthly things. These powers and resistances are different in nature and substance from any sensible things or quality here below. The powers against the resistances are moderated in such a way, so tempered and so harmonised that the movements are made without violence; thus, violence excepted, the situation is much like that of a man making a clock and letting it run and continue its own motion by itself’

This was part of a growing awareness throughout the thirteenth century and beyond, of a new concept of nature; a machine which acts according to quantitative laws. This would pave the way for conceptualising the world of physical science as something removed from direct observation and capable of mathematical expression.

Discuss this post at the Quodlibeta Forum


Matko said...

From where do you sap this information, Humphrey? You're a human library!

Humphrey said...

Got some notes from Lawrence Principe's lectures for the Faraday Institute as a starting point. Then various authorities on google books. Grant's Foundations of Science in the Middle Ages for Aristotle and the unmoved movers. E.G

Randomly found some very useful notes here:

Humphrey said...

Oh dear. That miniaturised link was supposed to go to part of 'Foundations of Science in the Middle Ages', instead it goes to a performance of 'Them Crooked Vultures' on the Friday night Jonathan Ross show.

Karl said...

Interesting as usual Humphrey. Unfortunately, I doubt the people who need to read it the most, the ones who still say the Medieval church and thinkers believed the world was flat or the universe was small, will do so. Try explaining to them how Ptolemy's Almagest was the definitive model before Copernicus and it explicitly states that the Earth is merely a point compared to the sphere of the fixed stars or when Ptolemy's Geographia resurfaced almost a hundred years before Columbus's voyage that its description of a spherical earth and map projections aroused no opposition among the nobility or the church you get some variation of 'what the hell are you talking about? Everybody knows the ancients believed the Earth was flat.' I don't know what to do about them.

Bjørn Are said...

Round them off!

Or flatten them.