Review: Two New Sciences

Review: Two New Sciences

Two New Sciences/A History of Free FallTwo New Sciences/A History of Free Fall by Galileo Galilei

My rating: 4 of 5 stars

But in what seas are we inadvertently engulfing ourselves, bit by bit? Among voids, infinities, indivisibles, and instantaneous movements, shall we ever be able to reach harbor even after a thousand discussions?

When most people think about the Copernican revolution, the name that comes most readily to mind—more even than that of Copernicus himself—is that of Galileo Galilei. It was he, after all, who fought most valiantly for the acceptance of the theory, and it was he who suffered the most for it—narrowly escaping the tortures of the Inquisition. It was also Galileo who wrote the most famous book to come out of the revolution: Dialogue Concerning the Two Chief World Systems, whose publication most directly resulted in Galileo’s punishment.

Some years ago I read and admired that eloquent work. But lately, after slogging my way through Ptolemy, Copernicus, and Kepler, I have come to look upon Galileo’s famous dialogue with more suspicion. For it was only through the work of Kepler that the Copernican system became unquestionably more efficient than the Ptolemaic as a method of calculating celestial movements; and though Kepler was a contemporary and a correspondent of Galileo, the Italian scientist was not aware of the German’s groundbreaking innovations. Thus the version of heliocentrism that Galileo defends is Copernicus’s original system, preserving much of the cumbrous aspects of Ptolemy—epicycles, perfect circles, and separate tables for longitude and latitude, etc.

Added to this, the most decisive advantages in favor of Copernicus’s system over Ptolemy’s—explaining why the planets’ orbits seem related to the sun’s—are given little prominence, if they are even mentioned. Clearly, a rigorous defense of Copernicanism would require a demonstration that it made calculating heavenly positions easier and more accurate; but there is nothing of the kind in Galileo’s dialogue. As a result, Galileo comes across as a propagandist rather than a scientist. But of course, even if his famous dialogue was pure publicity, Galileo would have a secure place in the annals of astronomy from his observations through his improved telescope: of the lunar surface, of the moons of Jupiter, of the rings of Saturn, of sunspots, and of the phases of Venus. But I doubt this would be enough to earn him his reputation as a cornerstone of the scientific revolution.

This book provides the answer. Here is Galileo’s real scientific masterpiece—one of the most important treatises on mechanics in history. Rather inconveniently, its title is easy to confuse with Galileo’s more famous dialogue; but in content Two New Sciences is an infinitely more serious work than Two Chief World Systems. It is also a far less impassioned work, since Galileo wrote it when he was an old man under house arrest, not a younger man in battle with the Catholic authorities. This inevitably makes the book rather more boring to read; yet even here, Galileo’s lucid style is orders of magnitude more pleasant than, say, Kepler’s or Ptolemy’s.

As in Two Chief World Systems, the format is a dialogue between Simplicio, Sagredo, and Salviati (though Galileo cheats by having Salviati read from his manuscript). Unlike the earlier dialogue, however, Simplicio is not engaged in providing counter-arguments or in defending Aristotle; he mostly just asks clarifying questions. Thus the dialogue format only serves to enliven a straightforward exposition of Galileo’s views, not to simulate a debate.

The book begins by asking why structures cannot be scaled up or down without changing their properties. Why, for example, will a small boat hold together if slid down a ramp, but a larger boat fall to pieces? Why does a horse break its leg it falls down, but a cat can fall from the same distance entirely uninjured? Why are the bones of an elephant proportionately so much squatter and fatter than the bones of a mouse? In biology this is known as the science of allometry, and personally I find it fascinating. The key is that, when increasing size, the ratio of volume to area also increases; thus an elephant’s bones must support far more weight, proportionally, than a mouse’s. As a result, inventors and engineers cannot just scale up contraptions without providing additional support—quite a counter-intuitive idea at the time.

Galileo next delves into infinities. This leads him into what is called “Galileo’s paradox,” but is actually one of the defining properties of infinite sets. This states that the parts of an infinite set can be equal to the whole set; or in other words, they can both be infinite. For example, though the number of integers with a perfect square root (4, 9, 16…) will be fewer than the total number of integers in any finite set (say, from 1-100), in the set of all integers there is an infinite number of integers with a perfect square roots; thus the part is equal to the whole. Galileo also takes a crack at Aristotle’s wheel paradox. This is rather dull to explain; but suffice to say it involves the simultaneous rotation of rigid, concentric circles. Galileo attempts to solve it by postulating an infinite number if infinitesimal voids in the smaller circle, and in fact uses this as evidence for his theory of infinitesimals.

As a solution to the paradox, this metaphysical assertion fails to do justice to its mathematical nature. However, the concept of infinitely small instants does help to escape from of the Zeno-like paradoxes of motion, to which Greek mathematics was prone. For example, if you imagine an decelerating object spending any finite amount of time at any definite speed, you will see that it never comes to a full stop: the first second it will travel one meter, the next second only half a meter, the next second a quarter of a meter, and so on ad infinitum. The notion of deceleration taking places continuously over an infinite number of infinitely small instants helped to escape this dilemma (though it is still unexplained how a thing can be said to “move” during an instant).

Galileo had need of such concepts, since he was writing long before Newton’s calculus and too early to be influenced by Descartes’s analytical geometry. Thus the mathematical apparatus of this book is Greek in form. Galileo’s calculations consist exclusively of ratios between lines rather than equations; and he establishes these ratios using Euclid’s familiar proofs. Consequently, his mechanics is relational or relativistic—able to give proportions but not exact quantities.

This did not stop Galileo from anticipating much of Newton’s system. He establishes the pendulum as an exemplar of continually accelerated motion, and shows that pendulums of the same length of rope swing at the same rate, regardless of the height from which they fall. He asserts that an object, once started in motion, would continue in motion indefinitely were it not for friction and air resistance. He recounts experiments of dropping objects of different masses from the same distance, and seeing them land at the same moment, thus disproving the Aristotelian assertion that objects fall with a speed proportional to their mass. (Unfortunately, there is scant evidence for the story that Galileo performed this experiment from the Leaning Tower of Pisa.) Galileo also makes the daring asserting that, in a vacuum, all objects would fall at the same rate.

There are still more riches to be excavated. Galileo asserts that pitches are caused by vibrating air, that faster vibrations causes higher pitch, and that consonant harmonies are caused by vibrations in regular ratios. He exhaustively calculates how the time and speed of a descending object would differ based on its angle of descent—straight down or on an inclined plane. He also shows that objects shot into the air, as in a catapult, descend back to earth in a parabolic arc; and he shows that objects travel the furthest when shot at 45 degrees. In an appendix, Galileo uses an iterative approach to find the center of gravity of curved solids; and in an added dialogue he discusses the force of percussion.

As you can see, this book is too rich and, in parts, too technical for me to appraise it in detail. I will say, however, that of all the scientific classics I have read this year, the modern spirit of science shines through most clearly in these pages. For like any contemporary scientist, Galileo assumes that the behavior of nature is law-like, and is fundamentally mathematical; and with Galileo we also see a thinker completely willing to submit his speculations to experiment, but completely unwilling to submit them to authority. Far more than in the metaphysical Kepler—who speculated with wild abandon, though he was a scientist of comparable importance—in Galileo we find a true skeptic: who believed only what he could observe, calculate, and prove. The reader instantly feels, in Galileo, the force of an exceptionally clear mind and of an uncompromising dedication to the search for truth.

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Review: Early Socratic Dialogues

Review: Early Socratic Dialogues

ApologyApology by Plato

My rating: 5 of 5 stars

This is perhaps the most iconic of Plato’s works, the closest thing that philosophy has to a Sermon on the Mount. And just as with our Biblical narratives, the dialogue presents a historical difficulty. To what extent is this speech fact, and to what extent invention? The only other record we have of the trial is from Xenophon, who wasn’t even there. Plato was there—or at least he asserts that he was—and yet it beggars belief that the young, would-be amanuensis could retain the entire speech in his mind after one hearing, or that he could write it down with tolerable accuracy as the events unfolded. It seems far more likely (to me at least) that this speech is more or less a fabrication made well after the fact, attempting to preserve the flavor and impression of Socrates’ final speech but not the exact words themselves.

All speculation notwithstanding, the essential facts are preserved: Socrates was accused of denying the gods and of corrupting the youth, made a bold and waggish defense of himself, was convicted, refused to mitigate the consequences, and triumphantly accepted the death penalty. Yet what really emerges from this speech is not a record of events but the portrait of a man.

Here Plato reveals himself to be a writer of the highest order. Fact or fiction, Plato’s Socrates is one of the great characters of literature. Though Socrates’ life is at stake, he does not falter for a moment. He treats the accusations with amusement, dismissing them with playful arguments that reveal his absolute indifference to the outcome. Far from bowing and scraping to preserve his life, Socrates flaunts his superiority to his accusers, couching his boasts in an ironical humility. He is a man in perfect control of himself and in perfect peace with the world.

Even if the real Socrates was truly this remarkable, it would have taken a writer of exquisite talent to effectively render him in prose. And if this is largely Plato’s invention, we must rank him along with Shakespeare, for Socrates utters now-famous phrases nearly as quickly as Hamlet. Western philosophy could not have asked for a more rousing beginning.

CritoCrito by Plato

My rating: 4 of 5 stars

The saga of Socrates’ trial and death continues. This time his friend, Crito, visits him in his cell to try to persuade him to escape into exile. Socrates is true to form, insisting that nothing—not the reputation of himself or his friend, nor concern for his own life—ought to be considered except reason. Crito must attempt to persuade Socrates to escape. The dialogue ends with the famous personification of the Laws of Athens, in the course of which Plato hits upon one of the earliest formulations of the social contract: by living in Athens, Socrates implicitly agrees to be bound by her laws. Since Socrates’ enjoyed the benefits of the laws, he must accept their penalties.

More so than in the Apology, one feels here that this is Plato’s invention and not something that actually occurred. The dialogue seems especially crafted to rehabilitate Socrates’ reputation, portraying the old philosopher as a dutiful citizen with a patriotic love of Athens. As a piece of drama the dialogue is one of Plato’s finest. It has considerable philosophic importance, too, for its aforementioned prefiguring of the social contract. Nevertheless I confess that I find Socrates’ reasoning extremely thin. Surely laws may be unjust; and a law may be just in itself and yet unjust or mistaken in its execution. If that is so, should the citizen passively accept it simply because it is the law? One senses the fine Socratic irony here, too, arguing playfully rather than sincerely. Socrates surely had compelling reasons to accept his death—but one doubts that pure patriotic regard of law was the whole of it.

CharmidesCharmides by Plato

My rating: 3 of 5 stars

This is one of the early inconclusive Socratic dialogues. Socrates, just come back from fighting in the Peloponnesian War, meets two of Plato’s relatives, Critias and Charmides. The latter of these is portrayed as a handsome youth, graceful of form and pure of mind. (Ironically enough, after the disastrous defeat of Athens in the war, both Critias and Charmides went on to become members of the Thirty Tyrants.) Socrates takes the opportunity to question Charmides about a Greek term that is rather unsatisfactorily translated into English as “temperance.”

The conversation takes many twists and turns, following the normal Socratic procedure: a definition is proposed (in this case, living quietly), an exception to the definition is found, a new one is proposed, and the process continues. As often happens in these early dialogues, the conversants seem to only get further from the point the longer they speak, getting hopelessly lost in the weeds of dialectic. Here we also see a quality that commonly irks readers of Plato, the tendency of Socrates’ interlocutors to give their unwavering assent to whatever rhetorical question, thought experiment, or logical distinction that Socrates poses, even when obviously fallacious. We also see Plato’s early tendency to get wrapped up in merely verbal confusions that hardly make sense when translated.

In any case, the dialogue takes an interesting turn when Critias proposes that temperance is a kind of meta-knowledge, the knowledge of knowledge. But how could we know for sure whether we knew something or not? And besides, how would that knowledge be useful? Merely knowing that we knew the art of medicine, for example, would be inconsequential compared to the knowledge of medicine itself. But how could temperance be inconsequential knowledge, if it is an important and noble attribute? The dialogue proceeds thus, seeming to intentionally confuse the issue through its series of involutions. But Plato will return to these questions with a vengeance.

LachesLaches by Plato

My rating: 3 of 5 stars

Here is another of the inconclusive dialogues. Socrates is asked by a couple of older men, Lysimachus and Melesias, whether to educate their sons in the art of fighting in armor. Socrates characteristically shifts the theme to a more abstract inquiry: What is courage? Commonsense definitions—such as “to stand and fight” or “to endure”—are quickly eliminated as admitting of exceptions. Nicias, a well-educated general, then proposes that courage is a certain kind of knowledge: that of future good and evil. After further dialectical maneuvering, the conversants find that they have gotten too general and have defined all of virtue and goodness, while leaving the specific nature of courage undefined. Socrates shrugs his shoulders and they break for lunch.

Though the question of courage is of somewhat limited philosophical interest, I do think that Plato hits upon the oft-overlooked role of knowledge (or lack of knowledge) in this seemingly physical or emotional virtue. This is characteristic of Plato, of course, for whom knowledge and goodness are tightly linked. Argument aside, the well-drawn characters of this dialogue are yet another example of Plato’s talent as a dramatist.

LysisLysis by Plato

My rating: 3 of 5 stars

This dialogue is normally grouped along with Laches and Charmides as an early, inconclusive dialogue. They are also alike in providing amusing portraits of life in Athens. This dialogue, for example, has a humorous beginning. Ctesippus complains to Socrates that Hippothales is always going on about his great love for the beautiful youth, Lysis, and composing horrid love poems in honor of his beloved. Socrates chides Hippothales and professes to demonstrate the correct way to speak to a beloved. What commences from this, however, is a rather ordinary Socratic interrogation—this time about the relationship of privilege to knowledge—which I doubt was very useful to the would-be wooer.

The topic of the dialogue then abruptly shifts to the nature of friendship. My general impression from reading Ancient Greek writings it that friendship was a far more important institution for the Greeks than it is for us. In any case Socrates and his interlocutors make little headway with this seemingly obvious problem. Is friendship the attraction of like to like? of like to unlike? of good to good? of neutral to good?—and so on, until they call it quits. I do think that the nature of friendship, which we are wont to take for granted, is an interesting topic to explore. But this dialogue contains, at best, only suggestions for future investigation.

MenexenusMenexenus by Plato

My rating: 2 of 5 stars

This work hardly merits the term “dialogue,” being mainly taken up by a lengthy speech. Socrates professes to have learned a funeral oration from a woman named Apia, who was Pericles’ consort. Plato seems to have been simultaneously parodying the practice of giving these speeches, but also proving his superiority to other writers of the genre, particularly Thucydides. If it was Plato’s goal to best the historian, he fell far short; and nowadays the speech reads like a silly rhetorical exercise, albeit of some historic importance.

IonIon by Plato

My rating: 4 of 5 stars

This lovely little dialogue, one of Plato’s shortest works, involves Socrates and the rhapsode, Ion. Ion is a rhapsode, which means that he recites, embellishes, and interprets poetry. In Ion’s case he is specialized in Homer, and admits that he knows nothing about any other poet. Socrates pounces upon this. How is it possible to master the best and most difficult of something, and leave the rest untouched? Also, how can Ion give sensible interpretations of the events of Homer’s poetry, when he does not have any of the skills—fishing, sailing, leading armies, and so on—mentioned in the poems?
Ion is not the brightest fellow, and is not able to give any sensible answer to these questions.

Socrates presses his point that Ion has no real knowledge and instead practices his art through inspiration. This, of course, is a famous Platonic assertion, which reappears many times throughout his works. However, I find his reasoning supremely unconvincing here. There is no absurdity in only understanding Homer and no other poet; poetry is not mathematics, with the more complex manifestations derived from the simpler. Further, there is no absurdity in being able to interpret a poetic passage about fishing while knowing fairly little about fishing itself. These ideas apparently did not occur to Ion (or Plato). But the simplicity of Ion, who is oblivious to Socrates’ irony, is winsome enough to make this a delightful read.

EuthyphroEuthyphro by Plato

My rating: 5 of 5 stars

Euthyphro begins the story of the trial and death of Socrates. It is one of Plato’s best known and, I think, best executed pieces. Here we see the Socratic dialogue form stripped to its bare essentials, with only two speakers, one problem, and minimal framing. Socrates is on his way to his trial; he has been accused, among other things, of impiety. He meets Euthyphro, a soothsayer, who is on his way to his own trial; he is prosecuting his father for murder, after his father’s negligence led to the death of a worker who had, himself, killed a slave. Socrates asks Euthyphro how he can be sure that this prosecution is the right thing to do, which leads to a discussion of piety.

The argument takes many turns, of course, but boils down to the famous Euthyphro dilemma: Is an action pious because it is beloved by the gods, or beloved by the gods because it is pious? While this may seem like mere sophistry, the implications of this question are immensely destructive to theistic ethical codes. For if morality exists independently of God (or, in other words, if we can know what is right or wrong without consulting the divine will) why consider God the fountain of good? And if morality is defined by the will of a God, how can we know what that will is? Perhaps via revelation: but then how distinguish legitimate and fake revelation? For if morality had no existence except the will of God, then no revelation, however apparently abominable, could be discounted. And since eyewitness testimony is nefariously unreliable, virtually no test would be able to unequivocally determine which “revelation” was to be followed. The only way out of the dilemma is to accept that good and bad can be distinguished without any supernatural considerations.

Euthyphro is, thus, of immense philosophical interest. It is also a dramatic masterpiece. Socrates’ ironic demeanor in dealing with the dense Euthyphro is delicious. Perhaps in no other work has Plato so convincingly shown the contrast between the reflective and the non-reflective mind. I continually found myself chuckling as I read. Yet again I am amazed that Plato, who started the Western philosophic tradition, remains its most able writer.

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