This granular life (1)

That the world is not solid but made up of tiny particles is a very ancient insight. Is atomic theory one of the most important ideas in human history?

According to tradition, in the year 450 BC, a man embarked on a 400-mile sea voyage from Miletus in Anatolia to Abdera in Thrace, fleeing a prosperous Greek city that was suddenly caught up in political turmoil. It was to be a crucial journey for the history of knowledge. The traveller’s name was Leucippus; little is known about his life, but his intellectual spirit proved indelible. He wrote the book The Great Cosmology, in which he advanced new ideas about the transient and permanent aspects of the world. On his arrival in Abdera, Leucippus founded a scientific and philosophical school, to which he soon affiliated a young disciple, Democritus, who cast a long shadow over the thought of all subsequent times.

Together, these two thinkers have built the majestic cathedral of ancient atomism. Leucippus was the teacher. Democritus, the great pupil who wrote dozens of works on every field of knowledge, was deeply venerated in antiquity, which was familiar with these works. “The most subtle of the Ancients”, Seneca called him. “Who is there whom we can compare with him for the greatness, not merely of his genius, but also of his spirit” asks Cicero.

What Leucippus and Democritus had understood was that the world can be comprehended using reason. They had become convinced that the variety of natural phenomena must be attributable to something simple, and had tried to understand what this something might be. They had conceived of a kind of elementary substance from which everything was made. Anaximenes of Miletus had imagined this substance could compress and rarefy, thus transforming from one to another of the elements from which the world is constituted. It was a first germ of physics, rough and elementary, but in the right direction. An idea was needed, a great idea, a grand vision, to grasp the hidden order of the world. Leucippus and Democritus came up with this idea.

The idea of Democritus’ system is extremely simple: the entire universe is made up of a boundless space in which innumerable atoms run. Space is without limits; it has neither an above nor a below; it is without a center or a boundary. Atoms have no qualities at all, apart from their shape. They have no weight, no color, no taste. “Sweetness is opinion, bitterness is opinion; heat, cold and color are opinion: in reality only atoms, and vacuum”, said Democritus. Atoms are indivisible; they are the elementary grains of reality, which cannot be further subdivided, and everything is made of them. They move freely in space, colliding with one another; they hook on to and push and pull one another. Similar atoms attract one another and join.

When atoms aggregate, the only thing that matters, the only thing that exists at the elementary level, is their shape, their arrangement, and the order in which they combine. Just as by combining letters of the alphabet in different ways we can obtain comedies or tragedies, ridiculous stories or epic poems, so elementary atoms combine to produce the world in its endless variety. The metaphor is Democritus’ own.

According to Democritus, our life is a combination of atoms, our thoughts are made up of thin atoms, our dreams are the products of atoms; our hopes and our emotions are written in a language formed by combinations of atoms; the light that we see is composed of atoms, which bring us images. The seas are made of atoms, as are our cities, and the stars. It’s an immense vision: boundless, incredibly simple, and incredibly powerful, on which the knowledge of a civilization would later be built.

On this foundation Democritus wrote dozens of books articulating a vast system, dealing with questions of physics, philosophy, ethics, politics and cosmology. He writes on the nature of language, on religion, on the origins of human societies, and on much else besides. All these books have been lost. We know of his thought only through the quotations and references made by other ancient authors, and by their summaries of his ideas. The thought that thus emerges is a kind of intense humanism, rationalist and materialist.

Democritus combines a keen attention to nature, illuminated by a naturalistic approach in which every residual system of mythic ideas is cleared away, with attention to humanity and a concern for life – anticipating by some 2,000 years the best aspects of the 18th-century Enlightenment. The ethical ideal of Democritus is that of a serenity of mind reached through moderation and balance, by trusting in reason and not allowing oneself to be overwhelmed by passions.

Plato and Aristotle were familiar with Democritus’ ideas, and fought against them. Both insisted on rejecting Democritus’ naturalistic explanations in favor of pursuing to understand the world in finalistic terms – believing that everything that happens has a purpose.

Aristotle speaks extensively about the ideas of Democritus, with respect. Plato never cites Democritus, but scholars suspect today that this was out of deliberate choice, and not for lack of knowledge of his works. Criticism of Democritus’ ideas is implicit in several of Plato’s texts, as in his critique of “physicists”, for example. In a passage in his Phaedo, Plato has Socrates articulate a reproach to all “physicists”. He complains that when physicists had explained that Earth was round, he rebelled because he wanted to know what good it was for Earth to be round; how its roundness would benefit it. 

The greatest physicist of the second half of the 20th century, Richard Feynman, wrote at the beginning of his introductory lectures on physics: “If, in some cataclysm, all scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis, or the atomic fact, or whatever you wish to call it, that all things are made of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence you will see an enormous amount of information about the world, if just a little imagination and thinking are applied.”

Without needing anything from modern physics, Democritus had already arrived at the idea that everything is made up of indivisible particles. He did it in part by marshalling arguments based upon observation; for example, he imagined, correctly, that the wearing down of a wheel, or the drying of clothes on a line, could be due to the slow flight of particles of wood or of water. But he also had arguments of a philosophical kind. Let’s dwell on these, because their potency reaches all the way to quantum gravity.

Democritus observed that matter could not be a continuous whole, because there is something contradictory in the proposition that it should be so. We know of Democritus’s reasoning because Aristotle reports it. Imagine, says Democritus, that matter is infinitely divisible, that is to say, that it can be broken down an infinite number of times. Imagine then that you break up a piece of matter ad infinitum. What would be left?

Could small particles of extended dimension remain? No, because if this were the case, the piece of matter would not yet be broken up to infinity. Therefore, only points without extension would remain. But now let us try to put together the piece of matter starting from these points: by putting together two points without extension, you cannot obtain a thing with extension, nor can you with three, or even with four. No matter how many you put together, in fact, you never have extension, because points have no extension. Therefore, we cannot think that matter is made of points without extension, because no matter how many of these we manage to put together, we never obtain something with an extended dimension. The only possibility, Democritus concludes, is that any piece of matter is made up of a finite number of discrete pieces that are indivisible, each one having finite size: the atoms.

The origin of this subtle mode of argumentation predates Democritus. It comes from the Cilento region in the south of Italy, from a town now called Velia, which in the fifth century BC was a flourishing Greek colony called Elea. This was home to Parmenides, the philosopher who had taken to the letter – perhaps too much – the rationalism of Miletus and its idea that reason can reveal to us how things can be other than they appear.

Parmenides had explored an avenue to truth via pure reason alone, which led him to declare that all appearances are illusory, thus opening the path that would progressively move toward metaphysics and distance itself from what would come to be known as “natural science”. His pupil Zeno, also from Elea, had brought subtle arguments to bear in support of this fundamentalist rationalism, which radically refutes the credibility of appearances. Among these arguments, there was a series of paradoxes that became known as “Zeno’s paradoxes”, and that seek to show how all appearance is illusory, arguing that the commonplace notion of motion is absurd.

The most famous of Zeno’s paradoxes is presented in the form of a brief fable: the tortoise challenges Achilles to a race, starting out with a 10-metre advantage. Will Achilles manage to catch up with the tortoise? Zeno argues that rigorous logic dictates that he will never be able to do so. Before catching up, in effect, Achilles needs to cover the 10 meters and, in order to do this, he will take a certain amount of time. During this time, the tortoise will have advanced a few centimeters. To cover these centimeters, Achilles will have to take a little more time, but meanwhile the tortoise will have advanced further, and so on, ad infinitum. Achilles therefore requires an infinite number of such times to reach the tortoise, and an infinite number of times, argues Zeno, is an infinite amount of time. Since, however, we do see the swift Achilles reaching and overtaking as many tortoises as he likes, it follows that what we see is irrational, and therefore illusory.

The string cannot be cut as many times as we want; matter is not continuous, it is made of individual atoms of a finite size.
Let’s be honest: this is hardly convincing. Where does the error lie? One possible answer is that Zeno is wrong because it is not true that, by accumulating an infinite number of things, one ends up with an infinite thing. Think of taking a piece of string, cutting it in half, and then again in half, and so on ad infinitum. At the end, you will obtain an infinite number of small pieces of string; the sum of these, however, will be finite, because they can add up only to the length of the original piece of string. Hence, an infinite number of strings can make a finite string; an infinite number of increasingly short times can make a finite time, and the hero, even if he will have to cover an infinite number of distances, ever smaller, will take a finite time to do so, and will end up catching the tortoise. In mathematics, we call this a converging series.

It seems that the paradox is resolved. The solution, that is, lies in the idea of the continuum – arbitrarily small times can exist, an infinite number of which make up a finite time. Aristotle is the first to intuit this possibility, subsequently developed by ancient and modern mathematics. But is this really the correct solution in the real world? Do arbitrarily short strings really exist? Can we really cut a piece of string an arbitrary number of times? Do infinitely small amounts of time exist? These are not just long-ago questions for Aristotle to ponder. They are precisely the problems that modern physicists face in trying to create a theory of quantum gravity, one that merges the large-scale rules of Albert Einstein’s general relativity with the tiny distances of quantum mechanics.

According to tradition, Zeno had met Leucippus and had become his teacher. Leucippus was therefore familiar with Zeno’s riddles. But he had devised a different way of resolving them. Maybe, Leucippus suggests, nothing arbitrarily small exists: there is a lower limit to divisibility. The universe is granular, not continuous. With infinitely small points, it would be impossible to ever construct extension – as in Democritus’ argument reported by Aristotle and mentioned previously. Therefore, the extension of the string must be formed by a finite number of finite objects with finite size. The string cannot be cut as many times as we want; matter is not continuous, it is made of individual atoms of a finite size.

Whether this abstract argument is correct or not, its conclusion – as we know today – contains a great deal of truth. Matter does indeed have an atomic structure. If we divide a drop of water in two, we obtain two drops of water. We can divide each one of these two drops again, and so on. But we cannot continue to infinity. At a certain point, we have only one molecule, and we are done. No drops of water exist smaller than a single molecule of water.

Read the second part of the article


January 10, 2018


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