Education: How Old The New

by James J. Walsh

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.