The Story of Western Science
Page 3
And here is Peter Kalkavage’s translation of the same passage:
Now let us say through what cause the constructor constructed becoming and this all. Good was he, and in one who is good there never arises about anything whatsoever any grudge, and so, being free of this, he willed that all things should come to resemble himself as much as possible. That this above all is the lordliest principle of becoming and cosmos one must receive, and correctly so, from prudent men. For since he wanted all things to be good and, to the best of his power, nothing to be shoddy, the god thus took over all that was visible, and, since it did not keep its peace but moved unmusically and without order, he brought it into order from disorder, since he regarded the former to be in all ways better than the latter.10
Kalkavage’s translation is carefully literal, unpacking each Greek construction and largely refraining from interpretation; Jowett’s combines translation with an explanation of Plato’s meaning, and so is easier for the nonspecialist to grasp.
If you’re anxious to understand the full dimensions of the philosophical problems, choose Kalkavage. If you simply want to get a general sense of Platonic idealism as it affected the practice of science over the next thousand years, stick with Jowett.
* * *
* Dissection was not practiced widely, most likely because of the ancient Greek belief that proper burial was the door into a satisfactory afterlife. James Longrigg provides a useful overview of the Greek attitudes toward dead bodies in Greek Rational Medicine: Philosophy and Medicine from Alcmaeon to the Alexandrians (Routledge, 1993), 184ff.
† They are often jointly known as the “pre-Socratic philosophers,” a misleading term because it covers both the philosophers who came before Socrates (ca. 469–399 BC) and those who came after him but who disagreed with the Platonic point of view.
THREE
Change
The first theory of evolution
Everything which is altered is altered by things which are
perceptible to the senses.
—Aristotle, Physics, Book VII, ca. 330 BC
Nature passes so gradually from inanimate to animate things
that the boundary between them is indistinct.
—Aristotle, History of Animals, Book VIII
Like his teacher Plato, Aristotle saw beauty and order around him. But while Plato saw this beauty as proof of a Craftsman at the beginning, Aristotle saw it as a signpost pointing toward fulfillment at the end.
This altered everything—most especially, change.
For Plato, change does not mean progress. Only decay. His natural world is an inferior copy of the Craftsman’s original concept, which means that it is an inherently flawed work of art—like a perfectly written play that inevitably accumulates myriad minor defects as soon as it is staged by real actors, in real costumes, wandering through real scenery. The physical world is always less than it was meant to be, and any change inevitably pulls it further and further away from the ideal.
But Aristotle, watching a sprout grow into a tree, a cub into a lion, an infant into a man, saw something else.
First, he wanted an explanation of the process: How do these changes happen? In what stages does one entity, one being, assume more than one form? What impels the change, and what determines its ending point?
Then, he wanted a reason. Why does a kitten become a cat, a seed a flower? What impels it to begin the long journey of transformation? Why is the state of kittenness, the existence of a seed in itself, not enough?
Today, when the cellular changes of growth are common knowledge, when every kindergarten class sprouts a bean on damp cotton, these questions seem superfluous. But part of the genius of Aristotle (wrongheaded though his conclusions often were) was to ask them. He did not assume that growth and change, as natural processes, were simply to be accepted. It was because they were natural processes that he questioned them; it was because they occurred as part of the natural cycle that he hoped to understand them.
This was science.
And so Aristotle’s most seminal scientific work, the Physics, is all about change. Change in every sense: the natural change that happens when a young creature ages; the change that happens when an object moves from one place to another; whether the object is the same in the latter place as it was in the former; the explanation for why movement takes place at all.
The answer to this last is not, as it was for Plato, decay. It is, rather, that each object and being in the natural world must move from its present state into a future, more perfect one. Built into the very fabric of the seed, the kitten, the infant, is the potential for change: the “principle of motion,” tracking steadily toward a glorious fulfillment. Aristotle’s natural world, the phusis around him, is not a play that has declined from its ideal imagining. It is a documentary drama, moving toward a satisfying conclusion.
The results on the practice of science were dramatic.
For one thing, only Aristotle’s point of view makes empirical inquiry—the observation and understanding of the physical world—a true path to real knowledge, valuable knowledge. Platonic thought, always casting the physical world as inferior to the Ideal, inevitably devalued scientific study, making it a lower-order, second-rate enterprise. (George Sarton, the chemist-historian who founded the discipline of the history of science, went so far as to call the influence of the Timaeus on later scientific thinking “enormous and essentially evil.”) But in Aristotle’s philosophy, science leads to truth.1
Furthermore, only Aristotle’s thought makes evolution possible.
In Plato’s world, change is corruption, and movement is always away from the ideal, toward a less effective, less developed state. But in Aristotelian science, nature is developing inexorably toward a more fully realized end.
This is not exactly what we mean by evolution today. Biological evolution has no predetermined goal, no overall design. Aristotle’s science is teleological, firmly convinced that nature is moving purposefully, in the direction of perfection.
Teleology can be an expression of faith in a Creator, a God who has set the world on a certain course that cannot be avoided. But Aristotle did not see nature as the creation of a divine Designer. He did not break from his master so far as to do away with a First Cause; at the beginning of all movement, Aristotle surmised, must be the original Force, that which cannot be worked on by any other cause, the Unmoved Mover. But this Unmoved Mover does not shape nature from the outside. It is no potter, and the world is not clay. A sprout becomes a tree because its treeness is already inherent inside it. For Aristotle, teleology is not an external guiding force, but an internal potentiality. The key to nature’s final form is already inside it.
The philosophical basis for what Darwin would later articulate had been laid.
Aristotle’s vision of a world where movement is always forward, always purposeful (never purely random, as Democritus and the atomists had proposed) served as the framework for what he called the scala naturae, the Scale of Nature: a graded, continuous ranking of natural organisms from the simplest to the most complex. Plants were at the bottom, human beings nearer the top. In the hands of medieval philosophers, Aristotle’s Scale of Nature would become the Great Chain of Being, a connected ranking of all natural elements and beings. Rock sat on the bottom rung, God at the top.2
To locate living organisms on the Scale of Nature, the natural scientist had to understand them. Aristotle’s other great scientific works, his natural-history compendiums (History of Animals, Generation of Animals, Parts of Animals), describe, organize, and classify living things, discovering within unwieldy nature itself the principles of purposeful change laid out, in the abstract, in the Physics.
This task was complicated by the total lack of Greek terms for such an enterprise. Doing science before the language of science had been created, Aristotle had to make up his own vocabulary, his own terms and titles and divisions, as he went along. In doing so, he invented taxonomy: the science of grouping living th
ings together by their shared characteristics. His most essential division—between bloody and bloodless animals, the red-blooded and the nonsanguinous—still exists today, restated as the separation between vertebrates and invertebrates.3
He also lent to later science plenty of whopping errors: spontaneous generation, a spherical universe made up of rotating crystalline shells, and the inheritance of acquired traits (even wounds and blows). But even wrong—sometimes perversely wrong—his theories were always based on his own observations of natural change. He had rescued change from Plato’s dust heap and elevated it into the central principle of nature: an engine that would drive scientific study inexorably forward.
To read relevant excerpts from the History of Animals and the Physics, visit http://susanwisebauer.com/story-of-science.
ARISTOTLE
(384–322 BC)
History of Animals
Richard Cresswell’s still-readable nineteenth-century translation is available as a free e-book.
Johann Gottlob Schneider, ed., Aristotle’s History of Animals in Ten Books, trans. Richard Cresswell, Henry G. Bohn (e-book, 1862).
The best print version is the much more expensive Loeb Classical Library version in three volumes.
Aristotle and A. L. Peck, Aristotle: History of Animals, Books I–III (Loeb Classical Library no. 437), Harvard University Press (hardcover, 1965, ISBN 978-0674994812).
Aristotle and A. L. Peck, Aristotle: History of Animals, Books IV–VI (Loeb Classical Library no. 438), Harvard University Press (hardcover, 1970, ISBN 978-0674994829).
Aristotle, Allan Gotthelf, and D. M. Balme, Aristotle: History of Animals, Books VII–X (Loeb Classical Library no. 439), Harvard University Press (hardcover, 1991, ISBN 978-0674994836).
ARISTOTLE
(384–322 BC)
Physics
The R. P. Hardie and R. K. Gaye translation, done as part of a forty-year effort to translate Aristotle into a standard English version (the “Oxford Translation”), is available as a free e-book or as a paperback reprint.
Aristotle, Physics, trans. R. P. Hardie and R. K. Gaye, Clarendon Press (1930, e-book at “The Internet Classics Archive” online, paperback reprint by Digireads, ISBN 978-1420927467).
A more recent and very readable translation by Robin Waterfield is worth investigating if you intend to read all eight books of the Physics.
Aristotle, Physics, trans. Robin Waterfield, Oxford World’s Classics, Oxford University Press (paperback, 1999, ISBN 978-0192835864).
FOUR
Grains of Sand
The first use of mathematics to measure the universe
These things will appear incredible to the great majority of
people who have not studied mathematics, but . . . to those
who are conversant therewith . . . the proof will carry
conviction.
—Archimedes, “The Sand-Reckoner,” ca. 250 BC
Up until this point, the brand-new field of science had made almost no use of mathematics. Greek mathematics had been following its own separate, somewhat winding road; and there had, as yet, been no major crossroads with the study of nature.
The god-believing mathematician Thales was credited with first coming up with the formulation of abstract, universal mathematical laws. The Greeks were not the only ancient people who knew their geometry—mathematicians in the Indus valley were already there—but before Thales, we have no record of any thinker going beyond specific geometric observations (“A circle is bisected by any of its diameters”) to proofs showing that those observations are always true, for all circles, everywhere in the universe.1
Since Thales, geometry—the study of angles and lengths, the areas they create and the patterns they follow—had developed into the root and trunk of Greek mathematics. Arithmetic (the branch of mathematics dealing with numerals) was derived from it. Numerals were, first and foremost, ways of measuring geometric properties such as area and length. And those measurements were usually expressed not simply as numbers, but as ratios.
In other words, asked the measurements of this rectangle:
we would most naturally label the long sides as 3 inches in length, the short sides as 1½ inches each. But the Greek mathematician would express this measurement as the relationship between the two sides:
2:1
because the relationship of the sides to each other is the same as the relationship of the numeral 2 to the numeral 1.
The Greeks could use ratios to add, multiply, and perform all of the other operations you learned to carry out in arithmetic class. It is for this reason that mathematics still speaks of rational numbers: any number that expresses the ratio between two integers is rational.*
After Thales and before Plato, the most active mathematical work was done by the Pythagoreans: followers of Pythagoras, a Greek mystic who lived sometime in the sixth century BC, and about whom practically nothing is known. What details of his life survive come entirely through his later disciples, such as Iamblichus, who lived some eight hundred years after the master and took as his life’s work a ten-volume encyclopedia of Pythagoras’s teachings. Pythagoras, says Iamblichus, was descended on both his mother’s and father’s sides of the family from Zeus, and it was rumored that the boy himself was the son of Apollo, who visited his mother while his father was away. (This, Iamblichus admits, is “by no means” certain, but “no one will deny that the soul of Pythagoras was sent to mankind from Apollo’s domain.”)2
Pythagoras was venerated as a divine mouthpiece, and his mathematics was primarily not a tool to understand the natural world. It was a method of understanding truth itself. Mathematics, Pythagoras taught, was the only path to knowledge: without numbers, nothing could be truly apprehended. Numerals had oracular power—particularly 1, 2, 3, and 4, which could be joined to create all existing dimensions. The sum of these four numbers, 10, was a holy number, the tetractys.3
Pythagoreans were vegetarians and teetotalers. They believed in the transmigration of souls, practiced shrouded black rites, and taught that the intervals of musical notes revealed deep truths about the universe (a theory that developed, long after, into the medieval Harmony of the Spheres). But interwoven with the cabalism was some authentically meticulous mathematics. The Pythagorean theorem, the first geometric idea encountered by most seventh-graders, had long been known to ancient mathematicians (the Egyptians certainly understood it), but the Pythagoreans first phrased it as a universal law, a truth that applied to all right-angled triangles everywhere.4
This theorem seems to have led the Pythagoreans to realize, apparently for the first time in recorded history, that there were such things as irrational numbers.
4.1 THE PYTHAGOREAN THEOREM: a2 + b2 = c2
Later writers chalked the discovery up to the Pythagorean philosopher Hippasus, who lived just before 400 BC. Hippasus, working on triangles, realized that no single unit could be used to measure both c and a. The two lines are “incommensurable,” having no common measure. In other words, there is no way to express the relationship between them using the numerals that the Pythagoreans had available to them; it is impossible, for example, to say that a is ⅓ or ¼ of c. The discovery of incommensurables in geometry led shortly after to their arithmetical parallel, irrational numbers—numbers that cannot be expressed in terms of the ratio of one whole number to another.
Apparently this was a staggering blow to Pythagorean mysticism, since the entire system was built around the conviction that all natural relationships could be expressed using ratios. Hippasus’s discovery was so disturbing that it brought down the ire of the universe on his unfortunate head: “It is well known,” remarks a later commentary, “that the man who first made public the theory of irrationals perished in a shipwreck in order that the inexpressible and unimaginable should ever remain veiled.”5
A mathematical tradition that shies so strongly away from its own implications in the real world is a mathematical tradition that probably won’t be useful in scie
nce; and for the first centuries of its existence, Pythagorean mathematics remained both shielded from the uninitiated and separate from the slowly developing new field of science. It was a religion, not a science, designed almost entirely for the contemplation of the divine, rather than the study of the earth.
•
Neither the Aristotelian nor the Platonic tradition made much use of mathematics in scientific writings, for completely different reasons.
Aristotle wanted to know what things were in themselves, not what their measurements were. Weight, height, circumference, diameter: all of these things change, and none of them, for Aristotle, point to what a natural object is. Mathematics gave him no insight into the plantness of a plant, the waterness of water. His natural classifications, like his physics, made use of qualities, not quantities; the presence of blood rather than the size of the heart, the habits of the burrower rather than the measurements of the burrow. Mathematics, for Aristotle, was irrelevant.
For Plato, mathematics was essential—as long as it wasn’t corrupted by contact with the physical world.
He explains this most clearly in Book VII of the Republic, which famously contains the “Allegory of the Cave.” There is a difference, Plato insists, between the uncorrupted and perfect universe, the Ideal as it exists in the mind of the Demiurge, and the visible and inferior Copy in which we live. The unphilosophical man sees only the Copy. He is like a prisoner chained in a cave, able to see only the shadows of the reality outside reflected on the cave wall, while the reality itself remains blocked from his eyes. Should the prisoner be suddenly unchained and brought into the full sunlight of the world outside the cave, the glare would be so painful and dazzling that he would be unable to see clearly. He would willingly return to captivity in the cave, preferring to gaze at the shadows rather than reality.