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Galileo's Thought Experiments

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Much of Galileo's most important work was in the form of imaginary experiments, not the result of ‘sensible’ (ahem) observations at all - although he was an effective exponent of the 'new technologies' of telescopes and so on too. In actual fact he 'borrowed' many findings - and theories - from other thinkers, and indeed, he is said to have been an insufferably arrogant and vain man. Nonetheless, the fact remains that amongst all the natural philosophers, he is one of the past masters of that much misunderstood technique: the thought experiment.

Galileo's Balls


One of the most famous but also most misunderstood experiments of them all was the one that involved Galileo Galilei (1564-1642), the celebrated astronomer, climbing the leaning tower of Pisa, leaning over the parapet and dropping two balls, a large heavy one and a smaller lighter one, and watching to see which hits the ground first.

Galileo was thinking of one of Aristotle's laws, to wit:

The question to be answered was which ball would hit the ground first - and at what speed - the large one or the small one?

For Aristotle at any rate, it still looks like the long walk up the tower steps is overdue. But Galileo did not need to carry out the experiment. Instead, he ran the process through in his mind. There are only three possibilities. The balls fall at the same speed, the heavier ball falls faster than the light one, or the light one falls faster than the heavy one.

Let's say heavy objects do fall faster than light ones. Then it seems the heavier weight will fall with the lighter weight acting, as it were, a bit like a parachute.

In that case, the two balls will together fall more slowly than the heavy weight would on its own.

On the other hand, once the two weights are tied together and held out over the parapet, they have effectively combined their weights, becoming one greater weight. Just holding the big weight, with the other dangling beneath, Galileo will feel this. When Galileo releases them, they must therefore fall even faster than the heavy weight would on its own. (Imagine the two are tied tightly together, for example, say by a single tight loop of string.)

It seems the two weights together must fall both faster and more slowly than before Galileo tied them together. And here is that thing philosophers love most of all: a contradiction. There is only one way to avoid it, and that is to assume that the heavy and light weights fall at the same speed.

Galileo describes the experiment as a conversation between two friends in Discorsi e Dimostrazioni Matematiche (1628):

This is justifiably seen as one of the great thought experiments.

It would even have been a ‘paradigm shift’ - except that the old ideas continued to live on. Indeed they still do.


Even nowadays, despite the experiment’s historical significance not all philosophers agree on what it shows, of course. For example, in an ingenious paper entitled 'Thought Experiments in Scientific Reasoning', the contemporary philosopher, Andrew Irvine, challenges Galileo's balls by denying that they can be really joined into one. Why, knots in the rope may come undone! "The lesson of course is that thought experiments, despite their power and versatility, are simply fallible", he continues before briskly concluding: "Thought experiments, despite their advantages, can never replace observation and actual experiment." Equally sadly, David Atkinson, a scientifically minded Dutch philosopher, concludes in his own paper on the subject, 'Experiments and Thought Experiments in Natural Science', that "the new Galilean dogma concerning free fall is itself a non sequitur". The conclusion does not follow from the premises. The roof is not attached to the walls...

This, for philosophers, is the worst possible insult. But Atkinson says that Galileo has brought it upon himself. He can be shown to be wrong and Aristotle vindicated by merely considering the possibility that, say, the leaning tower might have become submerged so that the balls being dropped were travelling through water and not through air. "The situation is even more complicated when the terminal velocity is reached in a condition of turbulent fluid flow, as is often the case in practice" he adds in a flourish.

That Galileo may not have been intending his experiment to apply to a situation in which the balls travelled through a liquid, but rather in conditions approximating to 'frictionless', is swept aside as "anything but self-evident". Instead, the Thought Experiment's findings are said to now be exposed as only in some cases empirically (sniff) true whilst in others empirically false. As for any notion that the thought experiment itself allows access to "a Platonic realm of truth", that is particularly misguided. "Galileo performed, and needed to perform, real experiments", Atkinson finishes loftily, thereby denying (like the Inquisition so many centuries before) the venerable astronomer even the right to philosophise.

So, does the experiment work? Yes, physicists know the principle that it established, that all bodies fall with the same acceleration irrespective of their mass and composition, as the Principle of Equivalence. It led directly to Einstein's General Theory of Relativity, which explains gravity by saying that when the Earth orbits the Sun, it is 'falling' through curved space-time.

Salvatius Ship

Another of Galileo’s great thought experiments, also a key contributor to modern notions of science, is equally simple in style and format, and equally profound. It appears in a charming work, in the manner of Plato, called the Dialogues Concerning the Two Chief World Systems ( 1632) . This time, Galileo's imaginary friend, Salvatius explains the experiment.

But what, we might wonder, are Salvatius' little fish supposed to prove?

The aim of Galilee's ship experiment was to explain why, if the world really is a sphere whizzing round on its axis in space, we are unaware of it. Back in 1632, the idea that we lived on rock hurtling around the Sun was still rather hard to swallow, and the now commonplace experience of smooth constant motion in one direction (for example, on a train, if not so much in a car) was still something of a rarity.

But 'the ship' illustrates that 'uniform horizontal motion' has no effect on the outcome of 'localised' experiments, which include the commonplace experiments of everyday sense perception. Only by stepping outside the local framework can measurements be made. To detect the motion of the ship, for example, we would have to look through the porthole at the receding cliffs, or the sun. To see the motion of the Earth itself, we must look at the night sky and the movement of the stars. (Of course, the cliffs might be shrinking, or the stars rotating on crystal spheres...)

Does it work?

The thought experiment has been resurrected in various similar forms subsequently by other physicists to make further useful intuitions about the nature of the universe. It threw light on deficiencies in another of Aristotle's faulty axioms, namely that of 'Absolute Rest', as well as undermining Newton's (later) pet nostrum of 'Absolute Space'. A more fruitful notion, the Principle of Equivalence was introduced to physics instead. Christian Huygens (1629-1695) later used it to improve his theory concerning the 'collisions of bodies', and in his novel, Sylvie and Bruno, Lewis Carroll (no less) described the difficulty of having tea inside a falling house, thereby anticipating by some years Einstein’s ‘falling box’ experiments which finally developed the concepts of 'inertial co-ordinate systems' and 'relative motion' into the first full-blown theory of relativity. (The ship's cabin is an inertial co-ordinate system, either when 'standing still', or proceeding "with any speed you like, so long as the motion is uniform", and provides points of reference.)

All that from just watching the fish!


These thought experiments and discussion are reproduced, slightly shortened, and amended, all with permission, from
Wittgenstein’s Beetle and Other Classic Thought Experiments (Martin Cohen, Blackwell 2005)

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