The Spheres from the Tower

The University of Pisa was situated close to the river Arno. The Medicis had built a fine rectangular building around an internal courtyard with a covered arcade, beneath which lecturers and students could stroll and argue in a dignified manner. The main subject for discussion, at least in the subjects concerned with natural philosophy, was Aristotle. His disciples had been called Peripatetics - those who walk about - because it was claimed that the master had taught in this way.

Aristotle's thoughts about the natural world had congealed into an unassailable system of instruction. In principle, his physics built on observation and the logical deductions arising from it. But the observations could be random and certainly were not systematised by means of controlled experiments. Emphasis was placed on the logical and philosophical conclusions - to such an extent that all the practical knowledge that had gradually accumulated, linked to technical advances in architecture and shipbuilding or the construction of clocks and the manufacture of spectacle lenses (to mention but a few), had barely impinged on university teaching of the fundamental physical questions concerning the natural world.

Many professors found greater academic prestige in interpreting an obscure passage of Aristotle than in observing for themselves. And academic discussion must adhere rigidly to the Master's pattern. It was still possible to hear, as a capping argument: Ipse dixit! - "He said so himself!" There were many, of course, who realised that not every answer to natural mysteries could be found in 1900-year old treatises, but nevertheless the Aristotelian framework of understanding limited their imagination and thought processes.

The very young Professor Galilei in occupying his chair at Pisa was not at all disconcerted that he had no degree himself. Thirty years later he was to write, comparing "good philosophers" to bad ones:

"I believe (...) that they fly, and that they fly alone like eagles, and not like starlings [storni]. It is true that because eagles are scarce they are a little seen and less heard, whereas birds that fly in flocks fill the sky with shrieks and cries wherever they settle, and befoul the earth beneath them."1

No one should doubt that Galileo considered himself to be one of the eagles. While his older, Aristotelian colleagues flocked round their Master's books, the 25-year old sought new paths.

But he, too, found inspiration in a Greek thinker. Galileo's declared model was Archimedes. In addition, he was virtually an Italian, as he had lived and worked in Syracuse, a Greek colony in Sicily. Archimedes combined observation with rigorous deduction and achieved practical results from this. The famous law that bears his name was the result of a knotty problem he was set by the despotic ruler of Syracuse: to calculate the ratio of gold to silver in the king's crown.

By contrast with the logical and speculative Aristotle, Archimedes began harnessing the powerful tool of mathematics to calculate and describe physical processes. Galileo was professor of mathematics. He clearly saw that a fundamental uprating of the subject would give qualitatively better natural science.

The establishment at Pisa was interested in the principles of movement, that branch of physics which would later be called kinematics. One of his elder colleagues had written a huge work, On Motion (De motu) which was circulating in manuscript form. The author was quite clear that Aristotle's doctrine of motion was wanting in certain respects, but even so he could not manage to free himself from tradition.

The young, newly appointed Galileo was not especially impressed with On Motion. But instead of going on the offensive against this entire massive bastion of physical theory, he decided to aim at a single, but very moot point, one where observations could easily be made: he would describe a "heavy body" in "natural motion" - what we today would call "free fall".

Aristotle made two fundamental errors in his description of falling objects. Firstly, he maintained that any falling object would achieve a certain fixed speed, and secondly, that such speed was proportional to the weight of the object. Or, to put it another way: every falling object falls with a definite, "in-built" speed, the heavier the object the higher the speed.

Galileo demonstrated the absurdity of this last contention with a simple mental experiment. One takes two stones of similar weight and ties them together - now, all at once, they will fall twice as fast as they would separately! It is also flies in the face of all experience that a sphere weighing one kilo falls one metre in the same time it takes a ten kilo sphere to fall ten metres.

Galileodecidetoinvestigate thematterfrombasic principles. Presumably he used - as his first biographer states - the obvious place for experiments in free fall: the famous detached, leaning belfry near the city's cathedral. In contrast to nearly everywhere else in Italy, the cathedral environs were not the city's main meeting place, but lay in peaceful seclusion by the north walls, so the chances of hitting passing townsfolk with falling iron balls was minimal.

He dropped wooden and iron balls, but the results of the experiments were far from conclusive. He could easily see that the balls fell at roughly the same speed, but that the iron ball hit the ground a little before the wooden one. He had no way of making precise observations, no clocks then were accurate enough to measure the fall times.

His observations were good enough to show that Aristotle's theories did not hold water, and Galileo tentatively launched his own. He concluded initially - and wrongly - that a body's falling speed is proportional to its mass density ("specific gravity"), a concept he had studied thoroughly in his work on Archimedes. He also realised that its speed was closely related to the medium it was falling through: an iron ball and a wooden ball might fall at roughly the same speed through air, but in water they behaved quite differently! Archimedes had taught him the concept of buoyancy, and this led him to reject yet another erroneous Aristotelian assumption: that bodies have an in-built "lightness" that operates in opposition to their "weight". The fact that wood floats in water is not due to its "lightness" lifting it up - it is simply that the material has a lower specific gravity than water.

However, for the time being he was saddled with the misconception that a falling body reaches a certain, stable speed of its own accord. It was then totally impossible, with the tools at his disposal, to measure the speed - far less the acceleration - of a sphere dropped from a tower.

Galileo did not only take Archimedes' point of view and argue for practical experiments to rebut Aristotle and inflexible academic thought, he also made sure he provoked his colleagues at Pisa on a more personal level.

Professorship brought with it the duty of donning a certain loose fitting official garb, based on the Roman toga. The young professor of mathematics had little time for the assumed and, to his mind, superficial dignity that this garment bestowed on its wearer. He penned a three-hundred-line lampoon2 on the toga in all its essence. Not only could one trip up on such a garment, but as he pointed out, it also swathes the body in an impractical way. All clothing ought to be designed so that men and women could readily obtain an idea of each other's physical attributes, indeed: "it would be best to go about naked"! But worse still was the way the toga's dignity prevented the professors from visiting the brothel. That forced them, quite literally, to take the matter into their own hands - a pastime that was every bit as sinful as visiting a bordello, but considerably less satisfying.

And so Galileo made his mark as an oppositional paradoxer. It was impossible for him, as yet, to give written vent to this same colourful lack of respect in his own subject. Galileo actually wrote his own version of On Motion, but he did not try to get it printed. His free fall experiments were spectacular, but deficient, and it is probably a myth that the other professors and students gathered admiringly at the foot of the tower. There was still too much he did not understand.

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