Scientific method in Ptolemy's Harmonics / Andrew Barker. p. cm. Includes bibliographical references and indexes. ISBN 0 5. 1. Ptolemy, 2nd cent. Claudius Ptolemy was a mathematician, astronomer, geographer and astrologer. He lived in .. Ptolemy also wrote an influential work, Harmonics, on music theory and the mathematics of music. .. country of the Seres (China) (English translation); Almagest books 1–13 The complete text of Heiberg's edition (PDF) Greek. xi PORPHYRY'S DISTORTION OF PTOLEMY HARMONICS II.1 Cristian Tolsa P orphyry's COMMENTARY on Ptolemy's Harmonics is best known as an.
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[Access article in PDF]. Andrew Barker. Scientific Method in Ptolemy's Harmonics. New York: Cambridge University Press, Pp. viii + Cloth, $ The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader). This groundbreaking book is the first to reconstruct Ptolemy's general philosophical system—including his explore its relationship to astronomy, harmonics, element theory, astrology, cosmology, psychology, and theology. Chapter 1 [PDF].
He believes in witchcraft and the evil eye, in demons and ghosts, — but prefers, if you please, to talk of these in the morning. His vivacity and abundance never leave him to loiter or pound on an incident. I admire his rapid and crowded style, as if he had such store of anecdotes of his heroes that he is forced to suppress more than he recounts, in order to keep up with the hasting history.
His surprising merit is the genial facility with which he deals with his manifold topics. There is no trace of labor or pain. He gossips of heroes, philosophers, and poets; of virtues and genius; of love and fate and empires. It is for his pleasure that he recites all that is best in his reading: he prattles history. But he is no courtier, and no Boswell: he is ever manly, far from fawning, and would be welcome to the sages and warriors he reports, as one having a native right to admire and recount these stirring deeds and speeches.
I find him a better teacher of rhetoric than any modern. His superstitions are poetic, aspiring, affirmative. A poet might rhyme all day with hints drawn from Plutarch, page on page.
No doubt, this superior suggestion for the modern reader owes much to the foreign air, the Greek wine, the religion and history of antique heroes. Thebes, Sparta, Athens, and Rome charm us away from the disgust of the passing hour. But his own cheerfulness and rude health are also magnetic. In his immense quotation and allusion, we quickly cease to discriminate between what he quotes and what he invents.
We sail on his memory into the ports of every nation, enter into every private property, and do not stop to discriminate owners, but give him the praise of all. This facility and abundance make the joy of his narrative, and he is read to the neglect of more careful historians. Yet he inspires a curiosity, sometimes makes a necessity, to read them.
He disowns any attempt to rival Thucydides; but I suppose he has a hundred readers where Thucydides finds one, and Thucydides must often thank Plutarch for that one. He has preserved for us a multitude Edition: current; Page: [xiv] of precious sentences, in prose or verse, of authors whose books are lost; and these embalmed fragments, through his loving selection alone, have come to be proverbs of later mankind.
At all events, it is in reading the fragments he has saved from lost authors that I have hailed another example of the sacred care which has unrolled in our times, and still searches and unrolls papyri from ruined libraries and buried cities, and has drawn attention to what an ancient might call the politeness of Fate, — we will say, more advisedly, the benign Providence which uses the violence of war, of earthquakes, and changed watercourses, to save underground through barbarous ages the relics of ancient art, and thus allows us to witness the upturning of the alphabets of old races, and the deciphering of forgotten languages, so to complete the annals of the forefathers of Asia, Africa, and Europe.
Many examples might be cited of nervous expression and happy allusion, that indicate a poet and an orator, though he is not ambitious of these titles, and cleaves to the security of prose narrative, and only shows his intellectual sympathy with these; yet I cannot forbear to cite one or two sentences which none who reads them will forget. Whereas the Sibyl, with her frantic grimaces, uttering sentences altogether thoughtful and serious, neither fucused nor perfumed, continues her voice a thousand years through the favor of the Divinity that speaks within her.
When Theanor had said this, he looked attentively on Epaminondas, as if he designed a fresh search into his nature and inclinations. There is, of course, a wide difference of time in the writing of these discourses, and so in their merit.
Many of them are mere sketches or notes for chapters in preparation, which were never digested or finished. Many are notes for disputations in the lecture-room. The plain-speaking of Plutarch, as of the ancient writers generally, coming from the habit of writing for one sex only, has a great gain for brevity, and, in our new tendencies of civilization, may tend to correct a false delicacy.
We are always interested in the man who treats the intellect well. We expect it from the philosopher, — from Plato, Aristotle, Spinoza, and Kant; but we know that metaphysical studies in any but minds of large horizon and incessant inspiration have their dangers. One asks sometimes whether a metaphysician can treat the intellect well. The central fact is the superhuman intelligence pouring into us from its unknown fountain, to be received with religious awe, and defended from any mixture of our will.
But Edition: current; Page: [xvi] this high Muse comes and goes; and the danger is that, when the Muse is wanting, the student is prone to supply its place with microscopic subtleties and logomachy.
It is fatal to spiritual health to lose your admiration. Whilst we expect this awe and reverence of the spiritual power from the philosopher in his closet, we praise it in the man of the world, — the man who lives on quiet terms with existing institutions, yet indicates his perception of these high oracles, as do Plutarch, Montaigne, Hume, and Goethe. These men lift themselves at once from the vulgar, and are not the parasites of wealth.
Perhaps they sometimes compromise, go out to dine, make and take compliments; but they keep open the source of wisdom and health. Plutarch is uniformly true to this centre. He had not lost his wonder. He wonders with Plato at that nail of pain and pleasure which fastens the body to the mind. The mathematics give him unspeakable pleasure, but he chiefly liked that proportion which teaches us to account that which is just, equal; and not that which is equal, just.
Of philosophy he is more interested in the results than in the method. That vice of theirs shall not hinder him from citing any good word they chance to drop. He is an eclectic in such sense as Montaigne was, — willing to be an expectant, not a dogmatist. In many of these chapters it is easy to infer the relation between the Greek philosophers and those who came to them for instruction.
This teaching was no play nor routine, but strict, sincere, and affectionate. The part of each of the class is as important as that of the master. They are like the base-ball players, to whom the pitcher, the bat, the catcher, and the scout are equally important. Now and then there are hints of superior science. You may cull from this record of barbarous guesses of shepherds and travellers statements that are predictions of facts established in modern science. Usually, when Thales, Anaximenes, or Anaxi mander are quoted, it is really a good judgment.
His Natural History is that of a lover and poet, and not of a Edition: current; Page: [xviii] physicist. His humanity stooped affectionately to trace the virtues which he loved in the animals also. Hence his love of heroes, his rule of life, and his clear convictions of the high destiny of the soul.
Plutarch is genial, with an endless interest in all human and divine things; Seneca, a professional philosopher, a writer of sentences, and, though he keep a sublime path, is less interesting, because less humane; and when we have shut his book, we forget to open it again. There is a certain violence in his opinions, and want of sweetness. He lacks the sympathy of Plutarch. He is tiresome through perpetual didactics. He is not happily living.
Cannot the simple lover of truth enjoy the virtues of those he meets, and the virtues suggested by them, so to find himself at some time purely contented? He ventured far — apparently too far — for so keen a conscience as he inly had. Yet we owe to that wonderful moralist illustrious maxims; as if the scarlet vices of the times of Nero had the natural effect of driving virtue to its loftiest antagonisms. Plutarch, meantime, with every virtue under heaven, thought it the top of wisdom to philosophize, yet not appear to do it, and to reach in mirth the same ends which the most serious are proposing.
He thinks it impossible either that a man beloved of the gods should not be happy, or that a wise and just man should not be beloved of the gods. To him the Epicureans are hateful, who held that the soul perishes when it is separated from the body. His grand perceptions of duty lead him to his stern delight in heroism; a stoic resistance to low indulgence; to a fight with fortune; a regard for truth; his love of Sparta, and of heroes like Aristides, Phocion, and Cato.
He insists that the highest good is in action. He thinks that the inhabitants of Asia came to be vassals to one only, for not having been able to pronounce one syllable; which is, No. So keen is his sense of allegiance to right reason, that he makes a fight against Fortune whenever she is named.
At Rome he thinks her wings were clipped: she stood no longer on a ball, but on a cube as large as Italy. He thinks it was by superior virtue that Alexander won his battles in Asia and Africa, and the Greeks theirs against Persia.
But this Stoic in his fight with Fortune, with vices, effeminacy, and indolence, is gentle as a woman when other strings are touched. He is the most amiable of men.
The Arcadian prophet, of whom Herodotus speaks, was obliged to make a wooden foot in place of that which had been chopped off. A brother, embroiled with his brother, going to seek in the street a stranger who can take his place, resembles him who will cut off his foot to give himself one of wood.
He thought, with Epicurus, that it is more delightful to do than to receive a kindness. Morgan, the editor and in part writer of this Translation of In his dedication of the work to the Arch bishop of Canterbury, Wm. If he did not compile the piece, many, perhaps most, of the anecdotes were already scattered in his works.
If I do not lament that a work not his should be ascribed to him, I regret that he should have suffered such destruction of his own. What a trilogy is lost to mankind in his Lives of Scipio, Epaminondas, and Pindar!
He persuaded the Sogdians not to kill, but to cherish their aged parents; the Persians to reverence, not marry their mothers; the Scythians to bury, and not eat their dead parents. What a fruit and fitting monument of his best days was his city Alexandria to be the birthplace or home of Plotinus, St. If Plutarch delighted in heroes, and held the balance between the severe Stoic and the indulgent Epicurean, his humanity shines not less in his intercourse with his personal friends.
He was a genial host and guest, and delighted in bringing chosen companions to the supper-table. He knew the laws of conversation and the laws of good-fellowship quite as well as Horace, and has set them down with such candor and grace as to make them good reading to-day. He thought it wonderful that a man having a muse in his own breast, and all the pleasantness that would fit an entertainment, would have pipes and harps play, and by that external noise destroy all the sweetness that was proper and his own.
I cannot close these notes without expressing my sense of the valuable service which the Editor has rendered to his Author and to Edition: current; Page: [xxiii] his readers.
For the most part, he follows the order of Ptolemy's text closely, providing historical background information in excursus form. One needs to read a complete text of Ptolemy's treatise along with Barker's exposition in order to understand some of his arguments.
One is rewarded with a detailed and in-depth analysis of the passages that helps one understand Ptolemy's method in harmonics as it unfolds in his treatise. This is so even if one disagrees with Barker's claims concerning Ptolemy's methodology. The methodological program Barker filters out of the text remains vague in a number of important respects.
One misses, for example, a clear exposition on what will count as a sufficient integration of "empirical and theoretical phases," and on what will count as "empirical.
The drawback is aggravated by the fact that the already vague terms of the postulated methodology have to be watered down considerably in the subsequent chapters to make them fit with Ptolemy's actual procedures. Ptolemy does not seem to deliver even on the vague terms.
One may very well remain unconvinced both by Barker's initial arguments concerning Ptolemy's methodology, and by his attempts to show that Ptolemy's procedure in the Harmonics can count as a satisfactory instantiation. Perhaps Ptolemy's intentions are less ambitious. When he states 5. In my view, he certainly delivers on this less ambitious program. In fact, it seems to me that the understanding of Ptolemy's argumentative path is impeded by Barker's interpretation of Ptolemy's goal of "saving the hupotheseis" as a commitment to the integration of a genuine empiricist trait.
Chapters 7 and 8 give an exposition of Ptolemy's tetrachord divisions.