Book Review: God’s Philosophers by James Hannam

This was an epoch making book for me – it was the first book I read on a Kindle. I think the Kindle is great, especially for quote miners like myself. You can highlight passages, and then with the help of an Applescript (google it), one can download the highlighted passages to note taking software EverNote. Genius. If they handled PDFs and note-taking better, I’d be very tempted to dispense with printing papers altogether.

As for the book, it was very enjoyable reading. The topic of the book is the progress made towards understanding the natural world made during the Middle Ages, which are often portrayed as an intellectual dark age. Here are a couple of notable passages:

• I’ve heard some (usually not historians) claiming that the Medieval universe was small and pokey, obviously the product of small minds and blinkered imaginations. As far back as Boethius in 500 A.D., we see the opposite view: “It is well known and you have seen it demonstrated by astronomers, that beside the extent of the heavens, the circumference of the earth has the size of a point; that is to say, compared to the magnitude of the celestial sphere, it may be thought of as having no extent at all.”
• Similarly, Hannam addresses the idea that the Copernican revolution displaced Earth from its honorable place at the centre of the universe: “Another modern misconception about the medieval Christian worldview is that people thought the central position of the earth meant that it was somehow exalted. In fact, to the medieval mind, the reverse was the case. The universe was a hierarchy and the further from the earth you travelled, the closer to Heaven you came.”
• Why do experiments? Because there are many ways that the universe could have been, and the only way to find out is to go and see. The physical universe is not a logical necessity, and thus its properties cannot be deduced. It’s surprising how long it look for this idea to catch on: “For Aristotle, the iron shackles of logical necessity determined what the laws of nature had to be. They were not just the ones upon which God had deliberately decided, they were the only ones he could have used. Even if God had actually created the world, he would have had no choice about how it turned out.”
• A few years ago, Sydney University hosted a “comedy” debate about who was greater, Einstein or Newton. Physics (somewhat arbitrarily) defended Einstein against the mathematicians. Everyone’s favourite supervisor was heard to disparage the great Sir Isaac by saying that he ascribed gravity to “the occult”. It seems, however, that this was not a reference to witchcraft, but rather just the word associated with action at a distance: “Nowadays, the word ‘occult’ specifically means ‘magical’ or something connected to spiritualism. But it used to have a much wider sense, connoting any force or property that was hidden. Put bluntly, if you cannot see it, it could be classed as occult. Aristotle had little time for the concept and argued that all effects must be material. One thing, he said, can only affect another by touch.”
• A bit more myth debunking. Almost no one in the middle ages thought that the Earth was flat, and certainly no geographers were put on trial or opposed by the church for believing as such. Further, “The medieval logical conundrum that everybody knows is ‘How many angels can dance on the head of a pin?’ Sadly, this turns out to be the invention of a seventeenth-century Cambridge academic satirising the admittedly rather abstruse theology of Thomas Aquinas. If a medieval scholar had really asked this, he would have meant it as a joke.” Hannam also deals with “the persistent legend that certain individuals refused even to look through the telescope. In fact, we know of no one who definitely declined to do so. The argument was over what they would see once they had peered through it.”
• One of the most importance principles of modern physics is the equivalence principle: drop two different weights, and (ignoring wind resistance) they will hit the ground at the same time. I was always told that Galileo, armed with two shots and the leaning Tower to Pisa, was the first to notice this. However, “The earliest record we have of someone categorically rejecting this is from the work of John Philoponus back in the sixth century. He wrote: ‘If you let fall from the same height two weights, one of which is many times heavier than the other, you will see that the relative times required for their drop does not depend on their relative weights, but that the difference in the time taken is very small’.”
• Further, John Buridan (c. 1350) defends a set of ideas remarkably similar to inertia: “He realised that this led to a radical implication of his theory: ‘Impetus’, he said, ‘would last forever if it were not diminished and corrupted by an opposing resistance or a tendency to contrary motion.’ Therefore, if there is no air resistance, such as in a vacuum, then an object will continue moving forever. Looking to the heavens, Buridan suggested that this might be the case for the planets orbiting the earth.”

This is does not diminish the importance of the scientists who started the scientific revolution. These ideas are half formed, and without calculus (which, let’s remember, Newton invented) you couldn’t really form a complete theory of mechanics. However, the idea that the history of science goes: “Greeks, nothing, nothing, nothing, nothing, Copernicus, Kepler, Galileo, Newton” is simply not true.

As I’ve noted before, I’m no historian, and so I can’t vouch for the historical accuracy of the book. I was a bit confused by the physics of the following passage:

“A moving body will travel in an equal period of time, a distance exactly equal to that which it would travel if it were moving continuously as its mean speed.” [Quote from William Heytesbury, c. 1350.] This result, dubbed the mean speed theorem by historians, is central to physics because it describes the motion of an object, any object, falling under gravity. Note that it makes no mention of how much the object weighs. (Nor does it make allowances for air resistance, and so strictly speaking applies only to motion in a vacuum. That is why the feather and hammer fell at the same speed on the moon.)

If I’m interpreting this correctly, then Hannam’s discussion is at least misleading, if not mistaken. The mean speed theorem is a mathematical theorem. It is not a physical theory. I would state it as follows

If is a function from R to R, and , then , where u (v) is the initial (final) velocity.

This is a useful result because, as Hannam notes, a mass falling in a gravitational field (wih no other force) will have a constant acceleration. However, the mean speed theorem is not about gravity. It applies just as well where x is the price of goods and “acceleration” is the rate of change of inflation, or where x is a population and “acceleration” is the rate of change of the birth rate. It would apply in the presence of air resistance if another force acts to maintain a constant acceleration. It makes no reference to weight because it makes no reference to physical reality at all. The mean speed theorem is kinematics, not dynamics. Put another way, it is the mathematical solution to the equations of motion, but does not tell us about cause of the motion. The mean speed theorem is not why the feather and hammer fall at the same speed on the moon. The reason why is that gravitational acceleration does not depend on mass.

Proving the mean speed theorem takes a few lines of calculus; without calculus one needs a bit more cleverness. Perhaps the most important lesson is that if one plots velocity versus time then the distance travelled is the area under the curve. Galileo’s demonstration of the theorem is geometric (he was not the first to prove the theorem). As Alfred North Whitehead noted (somewhere – I’m moving so all my books are in a box), one of the keys for science moving beyond Aristotle was to reject the Philosopher’s advice to categorise, and instead measure. Quantifying motion, rather than just categorising motion into natural and violent, was an important step in the history of physics and the mean speed theorem is obviously a great help to this end.

All in all, I thoroughly recommend Hannam’s book.