Aristotle the Scientist
October 19, 2015
Do objects of different weight fall at the same speed? At school we are told that, by letting balls drop from the Tower of Pisa, Galileo Galilei had demonstrated that the correct answer is yes. For the preceding two millennia, on the other hand, everyone had been blinded to the fact by the dogma of Aristotle, according to which the heavier the object, the faster it falls. Curiously, according to this story, it seems never to have occurred to anyone to test whether this was actually true before Francis Bacon and his contemporaries began observing nature and freed themselves from the straitjacket of Aristotelian dogmatism.
It's a good story, but there's a problem with it. Try dropping a glass marble and a paper cup from a balcony. Contrary to what this beautiful story says, it is not at all true that they hit the ground at the same time: the heavier marble falls much faster, just as Aristotle says.
No doubt at this point someone will object that this happens because of air, the medium through which the things fall. True, but Aristotle did not write that things would fall at different speeds if we took out all the air. He wrote that things fall at different speeds in our world, where there is air. He was not wrong. He observed nature attentively. Better than generations of teachers and students who are prone to take things on trust, without testing them for themselves.
Aristotle's physics has had a lot of bad press. It has come to be thought of as built upon a priori assumptions, disengaged from observation, patently wrongheaded. This is substantially unjust. Aristotle's physics remained a reference point for Mediterranean civilization for so long not because it was dogmatic, but because it actually works. It provides a good description of reality, and a conceptual framework so effective that no one was able to better it for two thousand years.
The essence of the theory is the idea that, in the absence of other influences, every object moves toward its "natural place": lower down for earth, a little higher for water, higher again for air, and higher still for fire; the speed of "natural movement" increases with weight and decreases according to the density of the medium in which the object is immersed. It's a simple, comprehensive theory that provides an elegant account of a great variety of phenomena—why smoke rises, for instance, and why a piece of wood drops down in air but floats upward in water. As a theory it is obviously not perfect, but then we should remember that nothing in modern science is perfect either.
The bad reputation that has become attached to Aristotle's physics is partly the fault of Galileo, who in his writings launches a scathing all-out attack upon Aristotelian theory, portraying its adherents as fools. He did so for rhetorical reasons. But the bad reputation of Aristotle's physics is also due to the silly gulf that has opened up between scientific culture and humanist-philosophical discourse. Those who study Aristotle generally know little about physics, and those who are engaged in physics have little interest in Aristotle. The scientific brilliance of books by Aristotle such as his On the Heavens and Physics—the work from which the very discipline derives its name—is all too readily overlooked.
There is also another, more significant factor that explains our blindness to his scientific brilliance: the idea that it is impossible to compare the thought produced by cultural universes so distant from each other as those of Aristotle and of modern physics, and that therefore we should not even try. Many historians today express horror at the idea of seeing Aristotelian physics as an approximation of Newtonian physics. To understand the original Aristotle, they argue, we must study him in the light of his context, and not through the conceptual frameworks of subsequent centuries. This may be true if we want to improve our understanding of Aristotle, but if we are interested in understanding today's knowledge, how it emerged from the past, it is precisely the relations between distant worlds that counts.
Philosophers and historians of science such as Karl Popper and Thomas Kuhn, who have had a strong influence on contemporary thought, have emphasized the importance of points of rupture in the course of the development of knowledge. Examples of such "scientific revolutions," where an old theory is abandoned, include the move from Aristotle to Newton, and from Newton to Einstein. According to Kuhn, in the course of such passages a radical restructuring of thought takes place, to such a degree that the preceding ideas become irrelevant, incomprehensible even. They are "incommensurable" with the subsequent theory, according to Kuhn. Popper and Kuhn deserve credit for having focused on this evolutive aspect of science and the importance of breaks, but their influence has also led to an absurd devaluation of the cumulative aspects of knowledge. Worse still is the failure to recognize the logical and historical relations between theories prior to and after every significant step forward. Newton's physics is perfectly recognizable as an approximation of Einstein's general relativity; Aristotle's theory is perfectly recognizable as an approximation contained within the theory of Newton.
This is not all, for within Newton's theory it is possible to recognize features of Aristotelian physics. For instance, the great idea of distinguishing the "natural" motion of a body from that which has been "forced" remains intact in Newtonian physics, as it does later in Einstein's theory. What changes is the role of gravity: it is the cause of forced motion in Newton (where natural motion is uniformly rectilinear), while it is an aspect of natural motion in Aristotle as well as, curiously, in Einstein (where natural motion, termed "geodesic," returns to being that of an object in free fall, as in Aristotle). Scientists do not advance either as a result of mere accumulation of knowledge or by means of absolute revolutions in which everything is thrown out and we begin again from zero. They advance instead, as in a wonderful analogy first made by Otto Neurath and frequently cited by Quine, "like sailors who must rebuild their ship on the open sea, never able to start afresh from the bottom. Where a beam is taken away a new one must at once be put there, and for this the rest of the ship is used as support. In this way the ship can be shaped entirely anew, but only by gradual reconstruction." In the great ship of modern physics we can still recognize its ancient structures—such as the distinction between natural and forced motion—as first laid out in the old ship of Aristotelian thought.
Let's go back to bodies falling through air or water and see what actually happens. The fall is neither at a constant speed and dependent on weight, as Aristotle maintained, nor at constant acceleration and independent of weight, as Galileo argued (not even if we ignore friction!). When an object falls, it goes through an initial stage during which it accelerates, then stabilizes at a constant speed which is greater for heavier bodies. This second stage is well described by Aristotle. The first stage, on the other hand, is usually very brief, difficult to observe, and as a result of this had escaped his notice. The existence of this initial stage had already been noted in antiquity: in the third century bce, for example, Strato of Lampsacus observed that a falling stream of water breaks into drops, indicating that the drops accelerate on falling, just like a line of traffic that breaks up as the vehicles accelerate.
To study this initial phase, which is difficult to observe because everything happens so quickly, Galileo devises a brilliant stratagem. Instead of observing falling bodies, he looks at balls rolling down a slight incline. His intuition, difficult to justify at the time but well-founded, is that the "rolling fall" of the balls reproduces that of bodies falling freely. In this way Galileo manages to record that at the beginning of the fall it is acceleration that remains constant, not speed. Galileo succeeded in uncovering the detail almost imperceptible to our senses where Aristotle's physics fails. It is like the observation used by Einstein at the beginning of the twentieth century in order to go beyond Newton: the movement of the planet Mercury, looked at closely, does not follow exactly the orbits calculated by Newton. In both cases, the devil is in the detail.
Einstein does to Newton what Galileo and Newton did to Aristotle: he shows that, for all its effectiveness, his version of physics is good only as a first approximation. Today we know that even Einstein's physics is not perfect: it fails when quantum physics enters into the equation. Einstein's physics needs to be improved upon as well. We are still not sure how.
Galileo did not build his new physics by rebelling against a dogma, or by forgetting Aristotle. On the contrary, having learned deeply from him, he worked out how to modify aspects of the Aristotelian conceptual cathedral: between himself and Aristotle there is not incommensurability but dialogue.
I believe this is also the case at the borders between different cultures, individuals and peoples. It is not true, as today we love to repeat, that different cultural worlds are mutually impermeable and untranslatable. The opposite is true: the borders between theories, disciplines, eras, cultures, peoples and individuals are remarkably porous, and our knowledge is fed by the exchanges across this highly permeable spectrum. Our knowledge is the result of a continuous development of this dense web of exchanges. What interests us most is precisely this exchange: to compare, to exchange ideas, to learn and to build from difference. To mix, not to keep things separate.
There's quite some distance between Athens in the fourth century bce and seventeenth-century Florence. But there is no radical rupture, and no misunderstanding. It is because Galileo knows how to enter into dialogue with Aristotle, and to penetrate into the heart of his physics, that he finds the narrow opening through which it can be corrected and improved. He puts this beautifully himself, in a letter written in later life: "I am certain that if Aristotle were to return to Earth he would receive me amongst his followers, in virtue of my very few contradictions of his doctrine."
Lolita and the Blue Icarus
February 8, 2015
Passing through the Natural History Museum in Milan recently, I came across an old cabinet containing a collection of blue butterflies, together with what for me was an unexpected name in a context such as this: Vladimir Nabokov.
The same Nabokov, that is, who was the author of such dazzlingly written novels as Lolita:
"Lo-lee-ta: the tip of the tongue taking a trip of three steps down the palate to tap, at three, on the teeth. Lo. Lee. Ta.
She was Lo, plain Lo, in the morning, standing four feet ten in one sock. She was Lola in slacks. She was Dolly at school. She was Dolores on the dotted line. But in my arms she was always Lolita."
He is perhaps one of the greatest novelists of the twentieth century. As an article in the literary supplement of The New York Times recently reminded us, "in academic circles Nabokov is increasingly mentioned in the company of such lights as Marcel Proust and James Joyce."
And yet Nabokov sought, by his own account, a very different kind of renown. One of his poems, "On Discovering a Butterfly," begins like this: "I found it and I named it, being versed / in taxonomic Latin; thus became / godfather to an insect and its first / describer-and I want no other fame." Butterflies were his passion. Lolita was written during one of the trips he made west every year in the United States, avidly searching for butterflies.
In that serene pantheon where the souls of great writers dwell, I can imagine Nabokov smiling: a few years ago in the Proceedings of the Royal Society of London, one of the most authoritative scientific journals, an article was published announcing that his most audacious scientific theory had been confirmed. His name will remain forever in the annals of science: he was the first to understand the migration of the Blue Icarus (Polyommatus icarus), the enchanting blue butterfly that can be admired in the museum in Milan. This was the kind of fame he was looking for: to be "the godfather of an insect."
Nabokov's theory was about the mode of migration of these butterflies on the continent of America. In 1945 he published the hypothesis that they had evolved in Asia and had arrived in the United States by crossing the Bering Strait in five successive waves, during the course of ten million years. No one took him seriously. It was difficult to imagine that butterflies living in warm climates could push so far north. And yet Nabokov was right: modern DNA sequencing techniques have made it possible to reconstruct the genealogy of the species and to confirm his hypothesis exactly. In addition, the reconstruction of changes in climate over time has shown that the Bering Strait underwent phases of sufficiently warm climate to make it possible for the passage of such waves of butterflies, precisely in the periods that Nabokov had suggested.
Nabokov was the curator of the Lepidoptera section in the Harvard University Museum of Comparative Zoology. He published detailed descriptions of hundreds of species. He used to collect butterflies in his childhood, the happy descendant of an extremely wealthy family of the Russian aristocracy. When he was eight years old, his father was imprisoned for political reasons: the young Vladimir carried a butterfly to his cell. With his father murdered and the family fortune lost in the Revolution, he escaped to Europe, where he eventually used the earnings from his second novel to pay for a butterfly-hunting expedition in the Pyrenees.
He was forced to flee from Europe too, after the Nazis came to power, and continued to cultivate his passion for entomology in the United States. He was regarded as a skillful amateur, capable of describing the different species of butterfly, being himself one of the last specimens of a type nearing extinction: nineteenth-century aristocrats who collected Lepidoptera as a pastime. But a decade after his death in 1977, various entomologists began to take his scientific work seriously. His classifications turn out to be astute. One of the butterflies he described is named Nabokovia cuzquenha in his honor. A book published in 1999, Nabokov's Blues, tells the story of the rediscovery of Nabokov's classifications. But another ten years elapsed before the spectacular proof arrived of his hypothesis about butterflies crossing the Bering Strait, and with it the recognition of his status as a scientist of real worth.
Is there a connection between Nabokov's science and his literary work? It is hard to resist the temptation of associating Lolita with butterflies, especially the Lolita seen through the lens of Humbert Humbert's desperate love. But this is probably too facile. The issue is discussed in an essay by Stephen Jay Gould with the suggestive title "No Science without Fancy, No Art without Facts: The Lepidoptery of Vladimir Nabokov," in which he argues that Nabokov's acute focus, his almost obsessive concern for observation and detail, is at the root of both his success as a butterfly collector and his technique as a novelist. Which is probably true. Nabokov himself has written: "A writer should have the precision of a poet and the imagination of a scientist."
Aristotle the Scientist
October 19, 2015
Do objects of different weight fall at the same speed? At school we are told that, by letting balls drop from the Tower of Pisa, Galileo Galilei had demonstrated that the correct answer is yes. For the preceding two millennia, on the other hand, everyone had been blinded to the fact by the dogma of Aristotle, according to which the heavier the object, the faster it falls. Curiously, according to this story, it seems never to have occurred to anyone to test whether this was actually true before Francis Bacon and his contemporaries began observing nature and freed themselves from the straitjacket of Aristotelian dogmatism.
It's a good story, but there's a problem with it. Try dropping a glass marble and a paper cup from a balcony. Contrary to what this beautiful story says, it is not at all true that they hit the ground at the same time: the heavier marble falls much faster, just as Aristotle says.
No doubt at this point someone will object that this happens because of air, the medium through which the things fall. True, but Aristotle did not write that things would fall at different speeds if we took out all the air. He wrote that things fall at different speeds in our world, where there is air. He was not wrong. He observed nature attentively. Better than generations of teachers and students who are prone to take things on trust, without testing them for themselves.
Aristotle's physics has had a lot of bad press. It has come to be thought of as built upon a priori assumptions, disengaged from observation, patently wrongheaded. This is substantially unjust. Aristotle's physics remained a reference point for Mediterranean civilization for so long not because it was dogmatic, but because it actually works. It provides a good description of reality, and a conceptual framework so effective that no one was able to better it for two thousand years.
The essence of the theory is the idea that, in the absence of other influences, every object moves toward its "natural place": lower down for earth, a little higher for water, higher again for air, and higher still for fire; the speed of "natural movement" increases with weight and decreases according to the density of the medium in which the object is immersed. It's a simple, comprehensive theory that provides an elegant account of a great variety of phenomena—why smoke rises, for instance, and why a piece of wood drops down in air but floats upward in water. As a theory it is obviously not perfect, but then we should remember that nothing in modern science is perfect either.
The bad reputation that has become attached to Aristotle's physics is partly the fault of Galileo, who in his writings launches a scathing all-out attack upon Aristotelian theory, portraying its adherents as fools. He did so for rhetorical reasons. But the bad reputation of Aristotle's physics is also due to the silly gulf that has opened up between scientific culture and humanist-philosophical discourse. Those who study Aristotle generally know little about physics, and those who are engaged in physics have little interest in Aristotle. The scientific brilliance of books by Aristotle such as his On the Heavens and Physics—the work from which the very discipline derives its name—is all too readily overlooked.
There is also another, more significant factor that explains our blindness to his scientific brilliance: the idea that it is impossible to compare the thought produced by cultural universes so distant from each other as those of Aristotle and of modern physics, and that therefore we should not even try. Many historians today express horror at the idea of seeing Aristotelian physics as an approximation of Newtonian physics. To understand the original Aristotle, they argue, we must study him in the light of his context, and not through the conceptual frameworks of subsequent centuries. This may be true if we want to improve our understanding of Aristotle, but if we are interested in understanding today's knowledge, how it emerged from the past, it is precisely the relations between distant worlds that counts.
Philosophers and historians of science such as Karl Popper and Thomas Kuhn, who have had a strong influence on contemporary thought, have emphasized the importance of points of rupture in the course of the development of knowledge. Examples of such "scientific revolutions," where an old theory is abandoned, include the move from Aristotle to Newton, and from Newton to Einstein. According to Kuhn, in the course of such passages a radical restructuring of thought takes place, to such a degree that the preceding ideas become irrelevant, incomprehensible even. They are "incommensurable" with the subsequent theory, according to Kuhn. Popper and Kuhn deserve credit for having focused on this evolutive aspect of science and the importance of breaks, but their influence has also led to an absurd devaluation of the cumulative aspects of knowledge. Worse still is the failure to recognize the logical and historical relations between theories prior to and after every significant step forward. Newton's physics is perfectly recognizable as an approximation of Einstein's general relativity; Aristotle's theory is perfectly recognizable as an approximation contained within the theory of Newton.
This is not all, for within Newton's theory it is possible to recognize features of Aristotelian physics. For instance, the great idea of distinguishing the "natural" motion of a body from that which has been "forced" remains intact in Newtonian physics, as it does later in Einstein's theory. What changes is the role of gravity: it is the cause of forced motion in Newton (where natural motion is uniformly rectilinear), while it is an aspect of natural motion in Aristotle as well as, curiously, in Einstein (where natural motion, termed "geodesic," returns to being that of an object in free fall, as in Aristotle). Scientists do not advance either as a result of mere accumulation of knowledge or by means of absolute revolutions in which everything is thrown out and we begin again from zero. They advance instead, as in a wonderful analogy first made by Otto Neurath and frequently cited by Quine, "like sailors who must rebuild their ship on the open sea, never able to start afresh from the bottom. Where a beam is taken away a new one must at once be put there, and for this the rest of the ship is used as support. In this way the ship can be shaped entirely anew, but only by gradual reconstruction." In the great ship of modern physics we can still recognize its ancient structures—such as the distinction between natural and forced motion—as first laid out in the old ship of Aristotelian thought.
Let's go back to bodies falling through air or water and see what actually happens. The fall is neither at a constant speed and dependent on weight, as Aristotle maintained, nor at constant acceleration and independent of weight, as Galileo argued (not even if we ignore friction!). When an object falls, it goes through an initial stage during which it accelerates, then stabilizes at a constant speed which is greater for heavier bodies. This second stage is well described by Aristotle. The first stage, on the other hand, is usually very brief, difficult to observe, and as a result of this had escaped his notice. The existence of this initial stage had already been noted in antiquity: in the third century bce, for example, Strato of Lampsacus observed that a falling stream of water breaks into drops, indicating that the drops accelerate on falling, just like a line of traffic that breaks up as the vehicles accelerate.
To study this initial phase, which is difficult to observe because everything happens so quickly, Galileo devises a brilliant stratagem. Instead of observing falling bodies, he looks at balls rolling down a slight incline. His intuition, difficult to justify at the time but well-founded, is that the "rolling fall" of the balls reproduces that of bodies falling freely. In this way Galileo manages to record that at the beginning of the fall it is acceleration that remains constant, not speed. Galileo succeeded in uncovering the detail almost imperceptible to our senses where Aristotle's physics fails. It is like the observation used by Einstein at the beginning of the twentieth century in order to go beyond Newton: the movement of the planet Mercury, looked at closely, does not follow exactly the orbits calculated by Newton. In both cases, the devil is in the detail.
Einstein does to Newton what Galileo and Newton did to Aristotle: he shows that, for all its effectiveness, his version of physics is good only as a first approximation. Today we know that even Einstein's physics is not perfect: it fails when quantum physics enters into the equation. Einstein's physics needs to be improved upon as well. We are still not sure how.
Galileo did not build his new physics by rebelling against a dogma, or by forgetting Aristotle. On the contrary, having learned deeply from him, he worked out how to modify aspects of the Aristotelian conceptual cathedral: between himself and Aristotle there is not incommensurability but dialogue.
I believe this is also the case at the borders between different cultures, individuals and peoples. It is not true, as today we love to repeat, that different cultural worlds are mutually impermeable and untranslatable. The opposite is true: the borders between theories, disciplines, eras, cultures, peoples and individuals are remarkably porous, and our knowledge is fed by the exchanges across this highly permeable spectrum. Our knowledge is the result of a continuous development of this dense web of exchanges. What interests us most is precisely this exchange: to compare, to exchange ideas, to learn and to build from difference. To mix, not to keep things separate.
There's quite some distance between Athens in the fourth century bce and seventeenth-century Florence. But there is no radical rupture, and no misunderstanding. It is because Galileo knows how to enter into dialogue with Aristotle, and to penetrate into the heart of his physics, that he finds the narrow opening through which it can be corrected and improved. He puts this beautifully himself, in a letter written in later life: "I am certain that if Aristotle were to return to Earth he would receive me amongst his followers, in virtue of my very few contradictions of his doctrine."
Lolita and the Blue Icarus
February 8, 2015
Passing through the Natural History Museum in Milan recently, I came across an old cabinet containing a collection of blue butterflies, together with what for me was an unexpected name in a context such as this: Vladimir Nabokov.
The same Nabokov, that is, who was the author of such dazzlingly written novels as Lolita:
"Lo-lee-ta: the tip of the tongue taking a trip of three steps down the palate to tap, at three, on the teeth. Lo. Lee. Ta.
She was Lo, plain Lo, in the morning, standing four feet ten in one sock. She was Lola in slacks. She was Dolly at school. She was Dolores on the dotted line. But in my arms she was always Lolita."
He is perhaps one of the greatest novelists of the twentieth century. As an article in the literary supplement of The New York Times recently reminded us, "in academic circles Nabokov is increasingly mentioned in the company of such lights as Marcel Proust and James Joyce."
And yet Nabokov sought, by his own account, a very different kind of renown. One of his poems, "On Discovering a Butterfly," begins like this: "I found it and I named it, being versed / in taxonomic Latin; thus became / godfather to an insect and its first / describer-and I want no other fame." Butterflies were his passion. Lolita was written during one of the trips he made west every year in the United States, avidly searching for butterflies.
In that serene pantheon where the souls of great writers dwell, I can imagine Nabokov smiling: a few years ago in the Proceedings of the Royal Society of London, one of the most authoritative scientific journals, an article was published announcing that his most audacious scientific theory had been confirmed. His name will remain forever in the annals of science: he was the first to understand the migration of the Blue Icarus (Polyommatus icarus), the enchanting blue butterfly that can be admired in the museum in Milan. This was the kind of fame he was looking for: to be "the godfather of an insect."
Nabokov's theory was about the mode of migration of these butterflies on the continent of America. In 1945 he published the hypothesis that they had evolved in Asia and had arrived in the United States by crossing the Bering Strait in five successive waves, during the course of ten million years. No one took him seriously. It was difficult to imagine that butterflies living in warm climates could push so far north. And yet Nabokov was right: modern DNA sequencing techniques have made it possible to reconstruct the genealogy of the species and to confirm his hypothesis exactly. In addition, the reconstruction of changes in climate over time has shown that the Bering Strait underwent phases of sufficiently warm climate to make it possible for the passage of such waves of butterflies, precisely in the periods that Nabokov had suggested.
Nabokov was the curator of the Lepidoptera section in the Harvard University Museum of Comparative Zoology. He published detailed descriptions of hundreds of species. He used to collect butterflies in his childhood, the happy descendant of an extremely wealthy family of the Russian aristocracy. When he was eight years old, his father was imprisoned for political reasons: the young Vladimir carried a butterfly to his cell. With his father murdered and the family fortune lost in the Revolution, he escaped to Europe, where he eventually used the earnings from his second novel to pay for a butterfly-hunting expedition in the Pyrenees.
He was forced to flee from Europe too, after the Nazis came to power, and continued to cultivate his passion for entomology in the United States. He was regarded as a skillful amateur, capable of describing the different species of butterfly, being himself one of the last specimens of a type nearing extinction: nineteenth-century aristocrats who collected Lepidoptera as a pastime. But a decade after his death in 1977, various entomologists began to take his scientific work seriously. His classifications turn out to be astute. One of the butterflies he described is named Nabokovia cuzquenha in his honor. A book published in 1999, Nabokov's Blues, tells the story of the rediscovery of Nabokov's classifications. But another ten years elapsed before the spectacular proof arrived of his hypothesis about butterflies crossing the Bering Strait, and with it the recognition of his status as a scientist of real worth.
Is there a connection between Nabokov's science and his literary work? It is hard to resist the temptation of associating Lolita with butterflies, especially the Lolita seen through the lens of Humbert Humbert's desperate love. But this is probably too facile. The issue is discussed in an essay by Stephen Jay Gould with the suggestive title "No Science without Fancy, No Art without Facts: The Lepidoptery of Vladimir Nabokov," in which he argues that Nabokov's acute focus, his almost obsessive concern for observation and detail, is at the root of both his success as a butterfly collector and his technique as a novelist. Which is probably true. Nabokov himself has written: "A writer should have the precision of a poet and the imagination of a scientist."
