Part 5

It has seemed to me, then, that it would be interesting and opportune to trace the origin, the development and the accomplishments of the first institution of learning that is very similar to our own; and to retrace some of the achievements of its professors, the circumstances in which they were done and the conditions surrounding an ancient school which I think our study will make clear as well deserving of the title of the first modern university. This was not the collection of schools at Athens, though there is no doubt at all that great intellectual and educational work was accomplished there, but not in our modern university sense. The schools were independent, and while the rivalry engendered by this undoubtedly did good so long as genius ruled in the schools, it brought about a degeneration into sophistry, from here comes the word, and argumentativeness, once the great master had been {65} displaced by disciples who were sure that they knew their master's mind, and probably thought, as disciples always do, that they were going beyond their master, but who really occupied themselves with curious and trifling tergiversations of mind within the narrow circle of ideas laid down by the master,--as has nearly always been the case.

The first modern university was that of Alexandria. It was quite as much under Greek influence as the schools of Athens. There have been commentators on the story of Cleopatra, who have suggested that her African cast of countenance did not prove a deterrent to her success as a conqueror of hearts, and who argue from this to the fact that it is not physical charm but personality that counts in woman's power over men, quite forgetting, if they ever knew, that Cleopatra was a Greek of the Greeks, a daughter of the line of the Ptolemys, probably a direct descendant though with the bar sinister of Philip of Macedon, born of a house so watchful over its Greek blood and so resentful of any possible admixture of anything less noble with itself, that for generations it had been the custom for brother to marry sister, in order that the race of the Ptolemys might be perpetuated in absolute purity. Alexandria, while a cosmopolitan city in the inhabitants who dwelt in it and in the wide diffusion of commercial interests that centred there as a mart for East and West, was absolutely ruled by Greeks and represents for many centuries after {66} the decline of Athens had come, the brightest focus of Greek intellectual life, Greek culture and art, Greek letters and education and every phase of that Greek influence in aesthetics which has always meant so much in the world's history.

The interesting fact about Alexandria in the history of education, is that it was the home of a modern university in every sense of that term, having particularly the features that many people are prone to think of as representing modern evolution in education. The buildings of the university were erected practically by a legacy left by the great Conqueror himself, Alexander. The central point of interest in the university was a great library, the nucleus of which was the library of Aristotle, tutor of Alexander, which had been collected with the help of that great Conqueror and was the finest collection of books in the world of that time. The main subject of interest in the university was physical science and its sister subject mathematics, which raises mere nature-study into the realm of science, and this scientific physical education was conducted in connection with the great museum or collection of objects of interest to scientists that had also been made partly by Aristotle himself and partly for his loved tutor by the gratitude of Alexander during his conquering expeditions in the far East. Finally professors were attracted to Alexandria by the offer of a better salary than had ever been paid at educational institutions before this, and {67} by the additional offer of a palace to live in, supplied by the ruler of the country. It is no wonder, then, that in attendance also, as well as in the prestige of its professors, Alexandria resembled a modern university.

It was its devotion to science, however, that especially characterized this first great institution of learning of which we have definite records. This devotion to science went so far that even literature was studied from the scientific standpoint. Such details as we have of the instruction at Alexandria and the books that have come down to us, all show men interested in philology, in comparative literature, in grammar and comparative grammar, rather than in the idealistic modes of knowledge. We have commentaries on the great authors, but no great original works of genius in literature from the professors of Alexandria. The translation of the Septuagint version of the Old Testament is a typical example of the sort of work that was being done at Alexandria. They collected the documents of the nations and translated them for purposes of comparative study. It was an education for information rather than for power. The main idea of the time and place was to know as much as possible about literature, rather than to know what it represented in terms of life, and the real meaning of both literature and life was obscured in the study about and about them. People studied books about books rather than the books {68} themselves. There was much writing of books about books, and it was nearly always comparatively trivial things in the great authors that attracted most attention from the many scholiasts, critics, editors, commentators, lecturers of the time.

Personally I could well understand such an incident happening at Alexandria as is said to have happened at a well-known English (of course not American!) university not long ago. The class was construing Shakespeare and one of the students asked the professor what the meaning of a particular figure used by the great dramatist was. The professor replied that they were there to construe Shakespeare's language and not bother about his meaning--yet it was a class in literature. Literature in recent years as studied at the universities has come to be quite as scientific in its modes and methods as it was at the University of Alexandria. May I also add that it has become quite as sterile of results of any importance. There is very little real study of literature, practically no encouragement of the attempt to draw inspiration from the great authors, but all devotion to the grammar, to the philology, to comparative literature as exemplified in the old writers.

Books were the great essentials at Alexandria. This is not surprising seeing that the university was founded around a great library, and that this library continued to be the greatest in the world in its time. Every student who came to Alexandria bringing a book with him of which there was {69} no copy in the library, was required by a decree of the authorities to leave a copy behind him. In all the university towns of the times--and there were many founded in the rising eastern cities of Alexander's empire, as it gradually crumbled into smaller pieces providing new capitals with less power but with quite as much national feeling as the capital cities of larger states, libraries became the fashion and a city's main claim to prestige in education and the intellectual life was the number of its books. Antioch, Tarsus, Cos, Cnidos and Pergamos are examples of this state of affairs. Pergamos was so jealous of the prestige of the Alexandrian Library that it forbade the exportation of parchment, an invention of Pergamos which received its name from that city. Petty jealousies were quite as much the rule among educational institutions then as they have been at any time since.

To many people it will seem quite absurd to talk of Alexandria as having done serious scientific work because the methods of science and scientific investigation are supposed to have been, as they think, discovered by Lord Bacon in the seventeenth century. It is curious how many educated people, or at least supposedly educated people, have this as their basic notion of the history of science. Men wandered in the mazes of inductive reasoning utterly unable to bring observations together in such a way as to discover laws, utterly incompetent to note phenomena and {70} bring them into relations to one another so as to show their scientific bearing, until Queen Elizabeth's Lord Chancellor came to show the way out of the labyrinth and leave the precious cord through its corridors, by which others may easily thread their way into the free air of scientific truth. I know nothing that is more absurd than this. It is a commonplace among educators, however; it is frequently referred to in educational addresses as if it were a universally accepted proposition, and to dispute it would seem the rankest kind of scientific heresy to these narrow minds. Fortunately there are two writers, Macaulay and Huxley, to whom even these people are likely to listen, who have expressed themselves with regard to this precious historic superstition that Lord Bacon invented the inductive method of reasoning with what my long-worded friend would call appropriate opprobrium.

Macaulay says: "The inductive method has been practised ever since the beginning of the world by every human being. It is constantly practised by the most ignorant clown, by the most thoughtless schoolboy, by the very child at the breast. That method leads the clown to the conclusion that if he sows barley he shall not reap wheat. By that method the schoolboy learns that a cloudy day is the best for catching trout. The very infant, we imagine, is led by induction to expect milk from his mother or nurse, and none from his father. Not only is it not true that {71} Bacon invented the inductive method; but it is not true that he was the first person who correctly analyzed that method and explained its uses. Aristotle had long before pointed out the absurdity of supposing that syllogistic reasoning could ever conduct men to the discovery of any new principle, had shown that such discoveries must be made by induction, and by induction alone, and had given the history of the inductive process, concisely indeed, but with great perspicuity and precision."

And Huxley quite as emphatically points out: "The method of scientific investigation is nothing but the expression of the necessary mode of working of the human mind. It is simply the mode by which all phenomena are reasoned about--rendered precise and exact."

While the whole trend of education, even that of literature, was scientific at Alexandria, the principal feature of the teaching was, as we have said, concerned with the physical sciences and mathematics. It is in mathematics that the greatest triumphs were secured. Euclid's "Geometry," as we use it at the present time in our colleges and universities, was put into form by Euclid teaching at the University of Alexandria in the early days of the institution. Euclid's setting forth of geometry was so perfect that it has remained for over 2,000 years the model on which all text-books of geometry of all the later times have been written. There seems no doubt that {72} writers on the history of mathematics are quite justified in proclaiming Euclid's "Geometry" as one of the greatest intellectual works that ever came from the hand of man. The first Ptolemy was fortunate in having secured this man as the founder of the mathematical department of his university. His example, the wonderful incentive of his work, the absolute perfection of his conclusions, must have proved marvellous emulative factors for the students who flocked to Alexandria.

Commonly mathematicians are said to be impractical geniuses so occupied with mathematical ideas that their influence in other ways counts for little in university life. If we are to believe the stories that come to us with regard to Euclid, however, and there is every reason to believe them, for some of them come from men who are almost contemporaries, or from men who had their information from contemporaries, Euclid's influence in the university must have been for all that is best in education. Proclus tells the story of King Ptolemy once having asked Euclid, if there was any shorter way to obtain a knowledge of geometry than through the rather difficult avenue of Euclid's own text-book, and the great mathematician replied that there was "no royal road to geometry." Stobaeus relates the story of a student who, having learned the first theorem, asked "but what shall I make by learning these things?" The question is so modern that Euclid's {73} answer deserves to be in the memory of all those who are interested in education. Euclid called his slave and said, "Give him twopence, since he must make something out of everything that he does, even the improvement of his mind."

Probably even more significant than the tradition that Euclid did his work at this first modern university, and that besides being a mathematician he was a man of very practical ideas in education, is the fact that he was appreciated by the men of his time and that his work was looked up to with highest reverence by his contemporaries and immediate successors as representing great achievement. It is not ever thus. Far from resenting in any way the magnificent synthesis that he had made of many rather vague notions in mathematics before his time, his contemporaries united in doing him honor. They realized that his teaching created a proper scientific habit of mind. Pappus says of Apollonius that he spent a long time as a pupil of Euclid at Alexandria and it was thus that he acquired a thorough scientific habit of mind. After Euclid's time the value of his discoveries as a means of training the mind was thoroughly appreciated. The Greek philosophers are said to have posted on the doors of their schools "Let no one enter here who does not know his Euclid." In the midst of the crumbling of old-fashioned methods of education in the introduction of the elective system, in the modern time, many of our best educators have insisted {74} that at least this portion of mathematics, Euclid's contribution to the science, should be a required study, and most educators feel, even when there is question of law or medical study, that one of the best preparations is to be found in a thorough knowledge of Euclid.

Almost as wonderful as the work of Euclid was that of the second great mathematician of the Alexandrian school, Archimedes, who not only developed pure mathematics but applied mathematical principles to mechanics and proved besides to have wonderful mechanical ability and inventive genius. It was Archimedes of whom Cicero spoke so feelingly in his "Tusculan Disputations," when about a century and a quarter after Archimedes' death, he succeeded in finding, his tomb in the old cemetery at Syracuse during his quaestorship there. How curious it is to think that after so short a time as 127 years from the date of his death Archimedes was absolutely forgotten by his fellow-Syracusans, who resolutely denied that any trace of Archimedes' tomb existed. This stranger from Rome knew much more of Archimedes than his fellow-citizens a scant four generations after his time. Not how men advance, but how they forget even great advance that has been made, lose sight of it entirely at times and only too often have to rediscover it, is the most interesting phase of history. Cicero says, "Thus one of the noblest cities of Greece and one which at one time had been very {75} celebrated for learning, knew nothing of the monument of its greatest genius until it was rediscovered for them by a native of Arpinum"--Cicero's modest designation for himself.

We have known much more about Archimedes' inventions than about his mathematical works. The Archimedian screw, a spiral tube for pumping water, invented by him, is still used in Egypt. The old story with regard to his having succeeded in making burning mirrors by which he was enabled to set the Roman vessels on fire during the siege of Syracuse, used to be doubted very seriously and, indeed, by many considered a quite incredible feat, clearly an historical exaggeration, until Cuvier and others in the early part of the nineteenth century succeeded in making a mirror by which in an experiment in the Jardin des Plantes in Paris wood was set on fire at a distance of 140 feet. As the Roman vessels were very small, propelled only by oars or at least with very small sail capacity, and as their means of offence was most crude and they had to approach surely within 100 feet of the wall to be effective, the old story therefore is probably entirely true. The other phase of history according to which Archimedes succeeded in constructing instruments by which the Roman vessels were lifted bodily out of the water, is probably also true, and certainly comes with great credibility of the man of whom it is told that, after having studied the lever, he declared that if he only had {76} some place to rest his lever, he could move the world.

The well-known story of his discovery in hydrostatics, by which he was enabled to tell the King whether the royal goldsmiths had made his crown of solid gold or not, is very well authenticated. Archimedes realized the application of the principle of specific gravity in the solution of such problems while he was taking a bath. Quite forgetful of his state of nudity he ran through the streets, crying "Eureka! Eureka! I have found it! I have found it!" There are many other significant developments of hydrostatics and mechanics, besides specific gravity and the lever, the germs of which are at least attributed to Archimedes. He seems to have been one of the world's great eminent practical geniuses. That he should have been a product of Alexandria and should even have been a professor there would be a great surprise if we did not know Alexandria as a great scientific university. As it is, it is quite easy to understand how naturally he finds his place in the history of that university and how proud any modern university would be to have on the rolls of its students and professors a man who not only developed pure science but who made a series of practical applications that are of great value to mankind. Such men our modern universities appropriately claim the right to vaunt proudly as the products of their training.

When we analyze something of the work in {77} pure mathematics that was accomplished by Archimedes our estimation of him is greatly enhanced. His work "On the Quadrature," that is the finding of the area of a segment of the parabola, is probably his most significant contribution to mathematical knowledge. His proof of the principal theorem in this is obtained by the "method of exhaustion," which had been invented by Eudoxus but was greatly developed by Archimedes. This method contains in itself the germ of that most powerful instrument of mathematical analysis in the modern time, the calculus.

Another very important work was "The Sphere and the Cylinder." This was more appreciated in his own time, and as a consequence, after his death the figure of a sphere inscribed in a cylinder was cut on his tomb in commemoration of his favorite theorem, that the volume of the sphere is two-thirds that of the cylinder and its surface is four times that of the base of the cylinder. It was by searching for this symbol, famous in antiquity, that Cicero was enabled to find his tomb according to the story that I have already related.

Within the last few years the reputation of Archimedes in pure mathematics has been greatly enhanced by the discovery by Professor Heiberg of a lost work of the great Alexandrian professor in Constantinople. Archimedes himself stated in a dedication of the work to Eratosthenes the method employed in this. He says: "I have thought it well to analyze and lay down for you {78} in this same book a peculiar method by means of which it will be possible for you to derive instruction as to how certain mathematical questions may be investigated by means of mechanics. And I am convinced that this is equally profitable in demonstrating a proposition itself, for much that was made evident to me through the medium of mechanics was later proved by means of geometry, because the treatment by the former method had not yet been established by way of a demonstration. For of course it is easier to establish a proof, if one has in this way previously obtained a conception of the questions, than for him to seek it without such a preliminary notion. . . . Indeed, I assume that some one among the investigators of to-day or in the future, will discover by the method here set forth still other propositions which have not yet occurred to me." On this Professor Smith comments: "Perhaps in all the history of mathematics no such prophetic truth was ever put into words. It would almost seem as if Archimedes must have seen as in a vision the methods of Galileo, Cavalieri, Pascal, Newton, and many other great makers of the mathematics of the Renaissance and the present time."

Many other distinguished professors of mathematics have, since this declaration of Archimedes came under their notice, declared that he must have had almost a prophetic vision of certain developments of mathematics and especially applied {79} mathematics and mechanics and their relation to one another, that were only to come in much later and indeed comparatively modern times. Undoubtedly Archimedes' works proved the germ of magnificent development not only immediately after his own time but in the long-after time of the Renaissance, when their translation awakened minds to mathematical problems and their solutions that would not otherwise have come.

We know much less of the life of the third of the great trio of teachers and students of Alexandria, Apollonius of Perga. Perhaps it should be enough for us to know that his contemporaries spoke of him as "the great geometer," though they were familiar with Euclid's book and with Archimedes' mighty work. Apollonius was surely a student of Alexandria for many years and he was probably also a professor of mathematics there. He developed especially what we know now as conic sections. His book on the subject contains practically all of the theorems to be found in our text-books of analytical geometry or conic sections of the present time. It was developed with rigorous mathematical logic and Euclidean conclusiveness. These three men show us beyond all doubt how finely the mathematical side of the university developed.