CHAPTER VIII

[Contents]CHAPTER VIIITHE SCHOOLMASTER: CARPENTRAS (CONTINUED)If he had hearkened only to his tastes, the young schoolmaster of Carpentras would have devoted to the world of animals all the time that was not taken up by his pupils. But his profession itself and the requirements of his future prevented him from following the dominant attraction unchecked. He had formed a resolve “to raise himself above the level of the primary school, which at that time barely fed its teachers,” and to make a place for himself in the ranks of secondary instruction. He had, therefore, to renounce his natural history, since that as yet had no place in the curriculum, and he had to take up mathematics.So we see him submerged in conic sections and the differential and integral calculus, without a guide, without advice, confronted for days on end by some obscure difficulty which tenacious meditation eventually robbed of its mystery. Mathematics, however,[100]formed only the first part of his programme, which comprised also physics and chemistry. These, no doubt, were less abstruse sciences, but the necessary equipment was also less simple. He needed a laboratory; he could not run to the expense of one; so he made one, an “impossible” one, by force of industry.In this desperate struggle what became of the favourite branch of science of this great nature-lover? It was necessarily sacrificed.“I reprimanded myself,” he says, “at the slightest longing for emancipation, fearing to let myself be seduced by some new grass, some unknown beetle. I did violence to myself. My books on natural history were condemned to oblivion, relegated to the bottom of a trunk.”A fine lesson in perseverance in work and sacrifice, which all those who are inspired by some noble desire or merely by some legitimate ambition will find useful and comforting to contemplate:“Qui studet optatam cursu contingere metamMulta tulit fecitque puer, sudavit et alsit;Abstinuit venere et vino.”1But this matter must be expounded in greater detail, were it only to confirm the[101]courage of other students disinherited by fortune, reduced as was Fabre to shaping themselves in the “harsh school of isolation.” They will witness miracles of perseverance; and they will realise that opportunities of exercising the mind and strengthening the will are seldom lacking to those who understand how to seize them.When I left the Normal School, my stock of mathematics was of the scantiest (writes Fabre). How to extract a square root, how to calculate and prove the surface of a sphere: these represented to me the culminating points of the subject. Those terrible logarithms, when I happened to open a table of them, made my head swim, with their columns of figures; actual fright, not unmixed with respect, overwhelmed me on the very threshold of that arithmetical cave. Of algebra I had no knowledge whatever. I had heard the name; and the syllables represented to my poor brain the whole whirling legion of the abstruse.Besides, I felt no inclination to decipher the alarming hieroglyphics. They made one of those indigestible dishes which we confidently extol without touching them. I greatly prefer a fine line of Virgil, whom I was now beginning to understand; and I should have been surprised indeed had any one told me that, for long years to come, I should be an enthusiastic student of the formidable science. Good fortune procured me my first lesson[102]in algebra, a lesson given and not received, of course.A young man of about my own age came to me and asked me to teach him algebra. He was preparing for his examination as a civil engineer; and he came to me because, ingenuous youth that he was, he took me for a well of learning. The guileless applicant was very far out in his reckoning.His request gave me a shock of surprise, which was forthwith repressed on reflection:“I give algebra lessons?” said I to myself. “It would be madness: I don’t know anything about it!”And I left it at that for a moment or two, thinking hard, drawn now this way, now that by my indecision:“Shall I accept? Shall I refuse?” continued the inner voice.Pooh, let’s accept! An heroic method of learning to swim is to leap boldly into the sea. Let us hurl ourselves head first into the algebraical gulf; and perhaps the imminent danger of drowning will call forth efforts capable of bringing me to land. I know nothing of what he wants. It makes no difference: let’s go ahead and plunge into the mystery. I shall learn by teaching.It was a fine courage that drove me full tilt into a province which I had not yet thought of entering. My twenty-year-old confidence was an incomparable lever.“Very well,” I replied. “Come the day after to-morrow at five, and we’ll begin.”[103]This twenty-four hours’ delay concealed a plan. It secured me the respite of a day, the blessed Thursday, which would give me time to collect my forces.Thursday comes. The sky is grey and cold. In this horrid weather a grate well-filled with coke has its charms. Let’s warm ourselves and think.Well, my boy, you’ve landed yourself in a nice predicament! How will you manage to-morrow? With a book, plodding all through the night, if necessary, you might scrape up something resembling a lesson, just enough to fill the dread hour more or less. Then you could see about the next: sufficient for the day is the evil thereof. But you haven’t the book. And it’s no use running out to the bookshop. Algebraical treatises are not current wares. You’ll have to send for one, which will take a fortnight at least. And I’ve promised for to-morrow, for to-morrow certain! Another argument and one that admits of no reply: funds are low; my last pecuniary resources lie in the corner of a drawer. I count the money: it amounts to twelve sous, which is not enough.Must I cry off? Rather not! One resource suggests itself: a highly improper one, I admit, not far removed, indeed, from larceny. O quiet paths of algebra, you are my excuse for this venial sin! Let me confess the temporary embezzlement.Life at my College is more or less cloistered. In return for a modest payment, most of us masters are lodged in the building; and we take our meals at the principal’s table. The science-master, who is the big gun of the staff and lives in the town,[104]has nevertheless, like ourselves, his own two cells, in addition to a balcony, or leads, where the chemical preparations give forth their suffocating gases in the open air. For this reason, he finds it more convenient to hold his class here during the greater part of the year. The boys come to these rooms in winter, in front of a grate stuffed full of coke, like mine, and there find a blackboard, a pneumatic trough, a mantelpiece covered with glass receivers, panoplies of bent tubes on the walls and, lastly, a certain cupboard in which I remember seeing a row of books, the oracles consulted by the master in the course of his lessons.“Among those books,” said I to myself, “there is sure to be one on algebra. To ask the owner for the loan of it does not appeal to me. My amiable colleague would receive me superciliously and laugh at my ambitious aims. I am sure he would refuse my request.”I decide to help myself to the book which I should never get by asking. This is the half-holiday. The science-master will not put in an appearance to-day; and the key of my room is practically the same as his. I go, with eyes and ears on the alert. My key does not quite fit; it sticks a little, then goes in; and an extra effort makes it turn in the lock. The door opens. I inspect the cupboard and find that it does contain an algebra book, one of the big, fat books which men used to write in those days, a book nearly half a foot thick. My legs give way beneath me. You poor specimen of a housebreaker, suppose you were caught at it![105]However, all goes well. Quick, let’s lock the door again, and hurry back to our own quarters with the pilfered volume.A chapter catches my attention in the middle of the volume; it is headed,Newton’s Binomial Theorem. The title allures me. What can a binomial theorem be, especially one whose author is Newton, the great English mathematician who weighed the worlds? What has the mechanism of the sky to do with this? Let us read and seek for enlightenment. With my elbows on the table and my thumbs behind my ears, I concentrate all my attention.I am seized with astonishment, for I understand! There are a certain number of letters, general symbols which are grouped in all manner of ways, taking their places here, there, and elsewhere by turns; there are, as the text tells me, arrangements, permutations, and combinations. Pen in hand, I arrange, permute, and combine. It is a very diverting exercise, upon my word, a game in which the test of the written result confirms the anticipations of logic and supplements the shortcomings of one’s thinking-apparatus.“It will be plain sailing,” said I to myself, “if algebra is no more difficult than this.”I was to recover from the illusion later, when the binomial theorem, that light, crisp biscuit, was followed by heavier and less digestible fare. But, for the moment, I had no foretaste of the future difficulties, of the pitfalls in which one becomes more and more entangled the longer one persists[106]in struggling. What a delightful afternoon that was, before my fire, amid my permutations and combinations! By the evening, I had nearly mastered my subject. When the bell rang, at seven, to summon us to the common meal at the principal’s table, I went downstairs puffed up with the joys of the newly-initiated neophyte. I was escorted on my way bya,b, andc, intertwined in cunning garlands.Next day, my pupil is there. Blackboard and chalk, everything is ready. Not quite so ready is the master. I bravely broach my binomial theorem. My hearer becomes interested in the combinations of letters. Not for a moment does he suspect that I am putting the cart before the horse and beginning where we ought to have finished. I relieve the dryness of my explanations with a few little problems, so many halts at which the mind takes breath awhile and gathers strength for fresh flights.We try together. Discreetly, so as to leave him the merit of the discovery, I shed a little light upon the path. The solution is found. My pupil triumphs; so do I, but silently, in my inner consciousness, which says:“You understand, because you succeed in making another understand.”The hour passed quickly and very pleasantly for both of us. My young man was contented when he left me; and I no less so, for I perceived a new and original way of learning things.The ingenious and easy arrangement of the binomial[107]gave me time to tackle my algebra book from the proper commencement. In three or four days I had rubbed up my weapons. There was nothing to be said about addition and subtraction: they were so simple as to force themselves upon one at first sight. Multiplication spoilt things. There was a certain rule of signs which declared that minus multiplied by minus made plus. How I toiled over that wretched paradox! It would seem that the book did not explain this subject clearly, or rather employed too abstract a method. I read, reread, and meditated in vain: the obscure text retained all its obscurity. That is the drawback of books in general: they tell you what is printed in them and nothing more. If you fail to understand, they never advise you, never suggest an attempt along another road which might lead you to the light. The merest word would sometimes be enough to put you on the right track; and that word the books, hide-bound in a regulation phraseology, never give you.My pupil was bound to suffer the effects. After an attempt at an explanation in which I made the most of the few gleams that reached me, I asked him:“Do you understand?”It was a futile question, but useful for gaining time. Myself not understanding, I was convinced beforehand that he did not understand either.“No,” he replied, accusing himself, perhaps, in his simple mind, of possessing a brain incapable of taking in those transcendental verities.[108]“Let us try another method.”And I start again this way and that way and yet another way. My pupil’s eyes serve as my thermometer and tell me of the progress of my efforts. A blink of satisfaction announces my success. I have struck home, I have found the joint in the armour. The product of minus multiplied by minus surrenders its mysteries to us.2The study of algebra was pursued in this fashion without any undue impediments as far as the pupil was concerned, but at the cost of a prodigious exertion of patience and penetration on the part of the primary schoolmaster who was so venturesome as to act as a professor of the higher mathematics.Audaces fortuna juvat.The young schoolmaster had not too greatly presumed on his powers. His pupil was accepted upon examination, and he himself was able to return the book to its place, having completely assimilated its contents.But he had made too good a start to stop midway. He was burning with eagerness to attack geometry, which was not so unfamiliar to him, but of which he had yet a great deal to learn: “At my normal school,” writes[109]Fabre, “I had learnt a little elementary geometry under a master. From the first few lessons onwards, I rather enjoyed the subject. I divined in it a guide for one’s reasoning faculties through the thickets of the imagination; I caught a glimpse of a search after truth that did not involve too much stumbling on the way, because each step forward is well braced by the step already taken. We start from a brilliantly-lighted spot and gradually travel farther and farther into the darkness, which kindles into radiance as it sheds fresh beams of light for a higher ascent.It is an excellent thing to regard geometry as what it really is, before all things: a superb intellectual gymnastic. By forcing the mind to proceed from the known to the unknown, always explaining what follows in the light of what has gone before, it exercises it and familiarises it with the logical laws of thought. To be sure, “it does not give us ideas, those delicate flowers which unfold one knows not how, and are not able to flourish in every soil,” but it teaches us to present them in a lucid and orderly manner. Fabre tells us:At that time, the College in which, two years before, I had made my first appearance as a teacher[110]had just halved the size of its classes and largely increased its staff. The newcomers all lived in the building, like myself, and we had our meals in common at the principal’s table. I had as a neighbour, in the next cell to mine, a retired quartermaster who, weary of barrack-life, had taken refuge in education. When in charge of the books of his company, he had become more or less familiar with figures; and it was now his ambition to take a mathematical degree. His cerebrum appears to have hardened while he was with his regiment. According to my dear colleagues, those amiable retailers of the misfortunes of others, he had already twice been plucked. Stubbornly, he returned to his books and exercises, refusing to be daunted by two reverses.It was not that he was allured by the beauties of mathematics: far from it; but the step to which he aspired favoured his plans. He hoped to have his own boarders and dispense butter and vegetables to lucrative purpose.I had often surprised our friend sitting, in the evening, by the light of a candle, with his elbows on the table and his head between his hands, meditating at great length in front of a big exercise-book crammed with cabalistic signs. From time to time, when an idea came to him, he would take his pen and hastily put down a line of writing wherein letters, large and small, were grouped without any grammatical sense. The lettersxandyoften recurred, intermingled with figures. Every row ended with the sign of equality and a naught.[111]Next came more reflection, with closed eyes, and a fresh row of letters arranged in a different order and likewise followed by a naught. Page after page was filled in this queer fashion, each line winding up with 0.“What are you doing with all those rows of figures amounting to zero?” I asked him one day.The mathematician gave me a leery look, picked up in barracks. A sarcastic droop in the corner of his eye showed how he pitied my ignorance. My colleague of the many naughts did not, however, take an unfair advantage of his superiority. He told me that he was working at analytical geometry.The phrase had a strange effect upon me. I ruminated silently to this purpose: there was a higher geometry, which you learnt more particularly with combinations of letters in whichxandyplayed a prominent part. How would the alphabetical signs, arranged first in one and then in another manner, give an image of actual things, an image visible to the eyes of the mind alone? It beat me.“I shall have to learn analytical geometry some day,” I said. “Will you help me?”“I’m quite willing,” he replied, with a smile in which I read his lack of confidence in my determination.No matter: we struck a bargain that same evening. We would together break up the stubble of algebra and analytical geometry, the foundation of the mathematical degree; we would make common[112]stock: he would bring long hours of calculation, I my youthful ardour. We would begin as soon as I had finished with my arts degree, which was my main preoccupation for the moment.We begin in my room, in front of a blackboard. After a few evenings, prolonged into the peaceful watches of the night, I become aware, to my great surprise, that my teacher, the past master in these hieroglyphics, is really, more often than not, my pupil. He does not see the combinations of the abscissæ and ordinates very clearly. I make bold to take the chalk in hand myself, to seize the rudder of our algebraical boat. I comment on the book, interpret it in my own fashion, expound the text, sound the reefs, until daylight comes and leads us to the haven of the solution. Besides, the logic is so irresistible, it is all such easy going and so lucid that often one seems to be remembering rather than learning.And so we proceed, with our positions reversed. My comrade—I can now allow myself to speak of him on equal terms—my comrade listens, suggests objections, raises difficulties which we try to solve in unison.After fifteen months of this exercise, we went up together for our examination at Montpellier; and both of us received our degrees as bachelors of mathematical science. My companion was a wreck; I, on the other hand, had refreshed my mind with analytical geometry.3[113]The quartermaster declared himself satisfied with this achievement. Analytic geometry did not precisely strike him as a recreation. He knew enough of it for what he had to do; he did not want to know any more.In vain I hold out the glittering prospect of a new degree, that of licentiate of mathematical science, which would lead us to the splendours of the higher mathematics and initiate us into the mechanics of the heavens: I cannot prevail upon him, cannot make him share my audacity. He calls it a mad scheme, which will exhaust us and come to nothing. I am free to go and break my neck in distant countries; he is more prudent and will not follow me.My partner, therefore, leaves me. Henceforth, I am alone, alone and wretched. There is no one left with whom I can sit up and thresh out the subject in exhilarating discussion.4And now let us note the words and the emotions with which he approaches for the last time, in his declining years, this town of Carpentras, where, from his earliest[114]youth, he suffered so greatly and laboured so valiantly:Once more, here am I, somewhat late in life, at Carpentras, whose rude Gallic name sets the fool smiling and the scholar thinking. Dear little town where I spent my twentieth year and left the first bits of my fleece upon life’s bushes, my visit of to-day is a pilgrimage; I have come to lay my eyes once more upon the place which saw the birth of the liveliest impressions of my early days. I bow, in passing, to the old College where I tried my prentice hand as a teacher. Its appearance is unchanged; it still looks like a penitentiary. Those were the views of our mediæval educational system. To the gaiety and activity of boyhood, which were considered unwholesome, it applied the remedy of narrowness, melancholy, and gloom. Its houses of instruction were, above all, houses of correction. The freshness of Virgil was interpreted in the stifling atmosphere of a prison. I catch a glimpse of a yard between four high walls, a sort of bear-pit, where the scholars fought for room for their games under the spreading branches of a plane-tree. All around were cells that looked like horse-boxes, without light or air; those were the class-rooms. I speak in the past tense, for doubtless the present day has seen the last of this academic destitution.Here is the tobacco-shop where, on Wednesday evening, coming out of the college, I would buy on credit the wherewithal to fill my pipe and thus[115]to celebrate on the eve the joys of the morrow, that blessed Thursday5which I considered so well employed in solving difficult equations, experimenting with new chemical reagents, collecting and identifying my plants. I made my timid request, pretending to have come out without my money, for it is hard for a self-respecting man to admit that he is penniless. My candour appears to have inspired some little confidence; and I obtained credit, an unprecedented thing, with the representative of the revenue.How I should love to see that room again where I pored over differentials and integrals, where I calmed my poor burning head by gazing at Mont Ventoux, whose summit held in store for my coming expedition6those denizens of Arctic climes, the saxifrage and the poppy! And to see my familiar friend, the blackboard, which I hired at five francs a year from a crusty joiner, that board whose value I paid many times over, though I could never buy it outright, for want of the necessary cash! The conic sections which I described on that blackboard, the learned hieroglyphics!7Fabre has somewhere written, lamenting the dearth of family reminiscences which[116]does not enable him to go back beyond the second generation of his ancestry, this touching passage, full of modesty and filial feeling: “The populace has no history. Strangled by the present, it cannot give its mind to cherishing the memories of the past.” Yet how instructive would those records be.Let us bow our heads before this child of the peasantry who labours so unremittingly and drives so deep a furrow; let us bow our heads before this humble primary schoolmaster who seeks to uplift himself, not as so many have done, by futile political agitation or the criminal fatuities of irreligion, but solely by virtue of knowledge and personal worth.We shall see later on with what vindictive energy Fabre scourges the pseudo-scientists, “hateful malefactors,”maufatan de malur, who, in the name of a false science, rob men’s souls of the true and ancient Christian faith, thereby leading society toward the most terrible catastrophes. For the moment our only desire is to do homage to our worthy schoolmasters in the person of one of their old comrades who has become one of our greatest national glories. There are others, too, among us who have exalted by their virtues or their talents the humble nature[117]of their origin or their calling. Of such, as every Frenchman knows, to mention only one of the best known and best beloved, is the author of thePoésie des Bêtes, ofVoix rustiques, ofLa Bonne Terre, ofLe Clocher, etc.—François Fabié, that poet who, by his original style, his career, and his genius, which has been too much obscured by his modesty, may in so many respects be compared with Jean-Henri Fabre.8Of such, too, and among the most eminent writers of thelanguage d’oc, is Antonin Perbosc,9who does honour to our primary schools, in one of which he is still teaching, by the remarkable works of literature which place him beside his friend, the Abbé Besson,10in the first rank of theOccitanian Félibrige.[118]1Horace,Ars Poetica, 412.↑2Souvenirs,IX., pp. 164–170.The Life of the Fly, chap. xii., “Mathematical Memories: The Binomial Theorem.”↑3Souvenirs,IX., pp. 172–183passim.The Life of the[113]Fly, chap. xii., “Mathematical Memories: The Binomial Theorem.”↑4Souvenirs,IX., p. 184passim.The Life of the Fly, chap. xii., “Mathematical Memories: The Binomial Theorem.”↑5The weekly half-holiday in the French schools.—A. T. de M.↑6The Hunting Wasps, chap. xi., “An Ascent of Mont Ventoux.”↑7Souvenirs,III., pp. 191–193.The Life of the Fly, chap. iv., “Larval Dimorphism.”↑8M. Fabié was never officially a schoolmaster, but he was trained as one, and was a pupil at the Normal College at Rodez.↑9M. Perbosc is a schoolmaster at Lavilledien (Tarnet-Garonne). He has published through Privat of Toulouse:Lo Got occitan,Cansous del Got occitan,Contes populars Gascons,Guilhem de Tolosa,Remembransa,l’Arada, etc., and has repeatedly been crowned by theAcadémie des Jeux Florauxof Toulouse.↑10M. Besson is also a laureate of theAcadémie des Jeux Floraux, and is at present Canon of Rodez. He has published through Carrère of Rodez:Dal Brès à la Tounbo,Bagateletos,Besucarietos,Countes de la Tata Mannou,Countes de l’Ouncle Janet, etc. This last volume is dedicated:A mon Amic Antouni Perbosc.↑

CHAPTER VIIITHE SCHOOLMASTER: CARPENTRAS (CONTINUED)

If he had hearkened only to his tastes, the young schoolmaster of Carpentras would have devoted to the world of animals all the time that was not taken up by his pupils. But his profession itself and the requirements of his future prevented him from following the dominant attraction unchecked. He had formed a resolve “to raise himself above the level of the primary school, which at that time barely fed its teachers,” and to make a place for himself in the ranks of secondary instruction. He had, therefore, to renounce his natural history, since that as yet had no place in the curriculum, and he had to take up mathematics.So we see him submerged in conic sections and the differential and integral calculus, without a guide, without advice, confronted for days on end by some obscure difficulty which tenacious meditation eventually robbed of its mystery. Mathematics, however,[100]formed only the first part of his programme, which comprised also physics and chemistry. These, no doubt, were less abstruse sciences, but the necessary equipment was also less simple. He needed a laboratory; he could not run to the expense of one; so he made one, an “impossible” one, by force of industry.In this desperate struggle what became of the favourite branch of science of this great nature-lover? It was necessarily sacrificed.“I reprimanded myself,” he says, “at the slightest longing for emancipation, fearing to let myself be seduced by some new grass, some unknown beetle. I did violence to myself. My books on natural history were condemned to oblivion, relegated to the bottom of a trunk.”A fine lesson in perseverance in work and sacrifice, which all those who are inspired by some noble desire or merely by some legitimate ambition will find useful and comforting to contemplate:“Qui studet optatam cursu contingere metamMulta tulit fecitque puer, sudavit et alsit;Abstinuit venere et vino.”1But this matter must be expounded in greater detail, were it only to confirm the[101]courage of other students disinherited by fortune, reduced as was Fabre to shaping themselves in the “harsh school of isolation.” They will witness miracles of perseverance; and they will realise that opportunities of exercising the mind and strengthening the will are seldom lacking to those who understand how to seize them.When I left the Normal School, my stock of mathematics was of the scantiest (writes Fabre). How to extract a square root, how to calculate and prove the surface of a sphere: these represented to me the culminating points of the subject. Those terrible logarithms, when I happened to open a table of them, made my head swim, with their columns of figures; actual fright, not unmixed with respect, overwhelmed me on the very threshold of that arithmetical cave. Of algebra I had no knowledge whatever. I had heard the name; and the syllables represented to my poor brain the whole whirling legion of the abstruse.Besides, I felt no inclination to decipher the alarming hieroglyphics. They made one of those indigestible dishes which we confidently extol without touching them. I greatly prefer a fine line of Virgil, whom I was now beginning to understand; and I should have been surprised indeed had any one told me that, for long years to come, I should be an enthusiastic student of the formidable science. Good fortune procured me my first lesson[102]in algebra, a lesson given and not received, of course.A young man of about my own age came to me and asked me to teach him algebra. He was preparing for his examination as a civil engineer; and he came to me because, ingenuous youth that he was, he took me for a well of learning. The guileless applicant was very far out in his reckoning.His request gave me a shock of surprise, which was forthwith repressed on reflection:“I give algebra lessons?” said I to myself. “It would be madness: I don’t know anything about it!”And I left it at that for a moment or two, thinking hard, drawn now this way, now that by my indecision:“Shall I accept? Shall I refuse?” continued the inner voice.Pooh, let’s accept! An heroic method of learning to swim is to leap boldly into the sea. Let us hurl ourselves head first into the algebraical gulf; and perhaps the imminent danger of drowning will call forth efforts capable of bringing me to land. I know nothing of what he wants. It makes no difference: let’s go ahead and plunge into the mystery. I shall learn by teaching.It was a fine courage that drove me full tilt into a province which I had not yet thought of entering. My twenty-year-old confidence was an incomparable lever.“Very well,” I replied. “Come the day after to-morrow at five, and we’ll begin.”[103]This twenty-four hours’ delay concealed a plan. It secured me the respite of a day, the blessed Thursday, which would give me time to collect my forces.Thursday comes. The sky is grey and cold. In this horrid weather a grate well-filled with coke has its charms. Let’s warm ourselves and think.Well, my boy, you’ve landed yourself in a nice predicament! How will you manage to-morrow? With a book, plodding all through the night, if necessary, you might scrape up something resembling a lesson, just enough to fill the dread hour more or less. Then you could see about the next: sufficient for the day is the evil thereof. But you haven’t the book. And it’s no use running out to the bookshop. Algebraical treatises are not current wares. You’ll have to send for one, which will take a fortnight at least. And I’ve promised for to-morrow, for to-morrow certain! Another argument and one that admits of no reply: funds are low; my last pecuniary resources lie in the corner of a drawer. I count the money: it amounts to twelve sous, which is not enough.Must I cry off? Rather not! One resource suggests itself: a highly improper one, I admit, not far removed, indeed, from larceny. O quiet paths of algebra, you are my excuse for this venial sin! Let me confess the temporary embezzlement.Life at my College is more or less cloistered. In return for a modest payment, most of us masters are lodged in the building; and we take our meals at the principal’s table. The science-master, who is the big gun of the staff and lives in the town,[104]has nevertheless, like ourselves, his own two cells, in addition to a balcony, or leads, where the chemical preparations give forth their suffocating gases in the open air. For this reason, he finds it more convenient to hold his class here during the greater part of the year. The boys come to these rooms in winter, in front of a grate stuffed full of coke, like mine, and there find a blackboard, a pneumatic trough, a mantelpiece covered with glass receivers, panoplies of bent tubes on the walls and, lastly, a certain cupboard in which I remember seeing a row of books, the oracles consulted by the master in the course of his lessons.“Among those books,” said I to myself, “there is sure to be one on algebra. To ask the owner for the loan of it does not appeal to me. My amiable colleague would receive me superciliously and laugh at my ambitious aims. I am sure he would refuse my request.”I decide to help myself to the book which I should never get by asking. This is the half-holiday. The science-master will not put in an appearance to-day; and the key of my room is practically the same as his. I go, with eyes and ears on the alert. My key does not quite fit; it sticks a little, then goes in; and an extra effort makes it turn in the lock. The door opens. I inspect the cupboard and find that it does contain an algebra book, one of the big, fat books which men used to write in those days, a book nearly half a foot thick. My legs give way beneath me. You poor specimen of a housebreaker, suppose you were caught at it![105]However, all goes well. Quick, let’s lock the door again, and hurry back to our own quarters with the pilfered volume.A chapter catches my attention in the middle of the volume; it is headed,Newton’s Binomial Theorem. The title allures me. What can a binomial theorem be, especially one whose author is Newton, the great English mathematician who weighed the worlds? What has the mechanism of the sky to do with this? Let us read and seek for enlightenment. With my elbows on the table and my thumbs behind my ears, I concentrate all my attention.I am seized with astonishment, for I understand! There are a certain number of letters, general symbols which are grouped in all manner of ways, taking their places here, there, and elsewhere by turns; there are, as the text tells me, arrangements, permutations, and combinations. Pen in hand, I arrange, permute, and combine. It is a very diverting exercise, upon my word, a game in which the test of the written result confirms the anticipations of logic and supplements the shortcomings of one’s thinking-apparatus.“It will be plain sailing,” said I to myself, “if algebra is no more difficult than this.”I was to recover from the illusion later, when the binomial theorem, that light, crisp biscuit, was followed by heavier and less digestible fare. But, for the moment, I had no foretaste of the future difficulties, of the pitfalls in which one becomes more and more entangled the longer one persists[106]in struggling. What a delightful afternoon that was, before my fire, amid my permutations and combinations! By the evening, I had nearly mastered my subject. When the bell rang, at seven, to summon us to the common meal at the principal’s table, I went downstairs puffed up with the joys of the newly-initiated neophyte. I was escorted on my way bya,b, andc, intertwined in cunning garlands.Next day, my pupil is there. Blackboard and chalk, everything is ready. Not quite so ready is the master. I bravely broach my binomial theorem. My hearer becomes interested in the combinations of letters. Not for a moment does he suspect that I am putting the cart before the horse and beginning where we ought to have finished. I relieve the dryness of my explanations with a few little problems, so many halts at which the mind takes breath awhile and gathers strength for fresh flights.We try together. Discreetly, so as to leave him the merit of the discovery, I shed a little light upon the path. The solution is found. My pupil triumphs; so do I, but silently, in my inner consciousness, which says:“You understand, because you succeed in making another understand.”The hour passed quickly and very pleasantly for both of us. My young man was contented when he left me; and I no less so, for I perceived a new and original way of learning things.The ingenious and easy arrangement of the binomial[107]gave me time to tackle my algebra book from the proper commencement. In three or four days I had rubbed up my weapons. There was nothing to be said about addition and subtraction: they were so simple as to force themselves upon one at first sight. Multiplication spoilt things. There was a certain rule of signs which declared that minus multiplied by minus made plus. How I toiled over that wretched paradox! It would seem that the book did not explain this subject clearly, or rather employed too abstract a method. I read, reread, and meditated in vain: the obscure text retained all its obscurity. That is the drawback of books in general: they tell you what is printed in them and nothing more. If you fail to understand, they never advise you, never suggest an attempt along another road which might lead you to the light. The merest word would sometimes be enough to put you on the right track; and that word the books, hide-bound in a regulation phraseology, never give you.My pupil was bound to suffer the effects. After an attempt at an explanation in which I made the most of the few gleams that reached me, I asked him:“Do you understand?”It was a futile question, but useful for gaining time. Myself not understanding, I was convinced beforehand that he did not understand either.“No,” he replied, accusing himself, perhaps, in his simple mind, of possessing a brain incapable of taking in those transcendental verities.[108]“Let us try another method.”And I start again this way and that way and yet another way. My pupil’s eyes serve as my thermometer and tell me of the progress of my efforts. A blink of satisfaction announces my success. I have struck home, I have found the joint in the armour. The product of minus multiplied by minus surrenders its mysteries to us.2The study of algebra was pursued in this fashion without any undue impediments as far as the pupil was concerned, but at the cost of a prodigious exertion of patience and penetration on the part of the primary schoolmaster who was so venturesome as to act as a professor of the higher mathematics.Audaces fortuna juvat.The young schoolmaster had not too greatly presumed on his powers. His pupil was accepted upon examination, and he himself was able to return the book to its place, having completely assimilated its contents.But he had made too good a start to stop midway. He was burning with eagerness to attack geometry, which was not so unfamiliar to him, but of which he had yet a great deal to learn: “At my normal school,” writes[109]Fabre, “I had learnt a little elementary geometry under a master. From the first few lessons onwards, I rather enjoyed the subject. I divined in it a guide for one’s reasoning faculties through the thickets of the imagination; I caught a glimpse of a search after truth that did not involve too much stumbling on the way, because each step forward is well braced by the step already taken. We start from a brilliantly-lighted spot and gradually travel farther and farther into the darkness, which kindles into radiance as it sheds fresh beams of light for a higher ascent.It is an excellent thing to regard geometry as what it really is, before all things: a superb intellectual gymnastic. By forcing the mind to proceed from the known to the unknown, always explaining what follows in the light of what has gone before, it exercises it and familiarises it with the logical laws of thought. To be sure, “it does not give us ideas, those delicate flowers which unfold one knows not how, and are not able to flourish in every soil,” but it teaches us to present them in a lucid and orderly manner. Fabre tells us:At that time, the College in which, two years before, I had made my first appearance as a teacher[110]had just halved the size of its classes and largely increased its staff. The newcomers all lived in the building, like myself, and we had our meals in common at the principal’s table. I had as a neighbour, in the next cell to mine, a retired quartermaster who, weary of barrack-life, had taken refuge in education. When in charge of the books of his company, he had become more or less familiar with figures; and it was now his ambition to take a mathematical degree. His cerebrum appears to have hardened while he was with his regiment. According to my dear colleagues, those amiable retailers of the misfortunes of others, he had already twice been plucked. Stubbornly, he returned to his books and exercises, refusing to be daunted by two reverses.It was not that he was allured by the beauties of mathematics: far from it; but the step to which he aspired favoured his plans. He hoped to have his own boarders and dispense butter and vegetables to lucrative purpose.I had often surprised our friend sitting, in the evening, by the light of a candle, with his elbows on the table and his head between his hands, meditating at great length in front of a big exercise-book crammed with cabalistic signs. From time to time, when an idea came to him, he would take his pen and hastily put down a line of writing wherein letters, large and small, were grouped without any grammatical sense. The lettersxandyoften recurred, intermingled with figures. Every row ended with the sign of equality and a naught.[111]Next came more reflection, with closed eyes, and a fresh row of letters arranged in a different order and likewise followed by a naught. Page after page was filled in this queer fashion, each line winding up with 0.“What are you doing with all those rows of figures amounting to zero?” I asked him one day.The mathematician gave me a leery look, picked up in barracks. A sarcastic droop in the corner of his eye showed how he pitied my ignorance. My colleague of the many naughts did not, however, take an unfair advantage of his superiority. He told me that he was working at analytical geometry.The phrase had a strange effect upon me. I ruminated silently to this purpose: there was a higher geometry, which you learnt more particularly with combinations of letters in whichxandyplayed a prominent part. How would the alphabetical signs, arranged first in one and then in another manner, give an image of actual things, an image visible to the eyes of the mind alone? It beat me.“I shall have to learn analytical geometry some day,” I said. “Will you help me?”“I’m quite willing,” he replied, with a smile in which I read his lack of confidence in my determination.No matter: we struck a bargain that same evening. We would together break up the stubble of algebra and analytical geometry, the foundation of the mathematical degree; we would make common[112]stock: he would bring long hours of calculation, I my youthful ardour. We would begin as soon as I had finished with my arts degree, which was my main preoccupation for the moment.We begin in my room, in front of a blackboard. After a few evenings, prolonged into the peaceful watches of the night, I become aware, to my great surprise, that my teacher, the past master in these hieroglyphics, is really, more often than not, my pupil. He does not see the combinations of the abscissæ and ordinates very clearly. I make bold to take the chalk in hand myself, to seize the rudder of our algebraical boat. I comment on the book, interpret it in my own fashion, expound the text, sound the reefs, until daylight comes and leads us to the haven of the solution. Besides, the logic is so irresistible, it is all such easy going and so lucid that often one seems to be remembering rather than learning.And so we proceed, with our positions reversed. My comrade—I can now allow myself to speak of him on equal terms—my comrade listens, suggests objections, raises difficulties which we try to solve in unison.After fifteen months of this exercise, we went up together for our examination at Montpellier; and both of us received our degrees as bachelors of mathematical science. My companion was a wreck; I, on the other hand, had refreshed my mind with analytical geometry.3[113]The quartermaster declared himself satisfied with this achievement. Analytic geometry did not precisely strike him as a recreation. He knew enough of it for what he had to do; he did not want to know any more.In vain I hold out the glittering prospect of a new degree, that of licentiate of mathematical science, which would lead us to the splendours of the higher mathematics and initiate us into the mechanics of the heavens: I cannot prevail upon him, cannot make him share my audacity. He calls it a mad scheme, which will exhaust us and come to nothing. I am free to go and break my neck in distant countries; he is more prudent and will not follow me.My partner, therefore, leaves me. Henceforth, I am alone, alone and wretched. There is no one left with whom I can sit up and thresh out the subject in exhilarating discussion.4And now let us note the words and the emotions with which he approaches for the last time, in his declining years, this town of Carpentras, where, from his earliest[114]youth, he suffered so greatly and laboured so valiantly:Once more, here am I, somewhat late in life, at Carpentras, whose rude Gallic name sets the fool smiling and the scholar thinking. Dear little town where I spent my twentieth year and left the first bits of my fleece upon life’s bushes, my visit of to-day is a pilgrimage; I have come to lay my eyes once more upon the place which saw the birth of the liveliest impressions of my early days. I bow, in passing, to the old College where I tried my prentice hand as a teacher. Its appearance is unchanged; it still looks like a penitentiary. Those were the views of our mediæval educational system. To the gaiety and activity of boyhood, which were considered unwholesome, it applied the remedy of narrowness, melancholy, and gloom. Its houses of instruction were, above all, houses of correction. The freshness of Virgil was interpreted in the stifling atmosphere of a prison. I catch a glimpse of a yard between four high walls, a sort of bear-pit, where the scholars fought for room for their games under the spreading branches of a plane-tree. All around were cells that looked like horse-boxes, without light or air; those were the class-rooms. I speak in the past tense, for doubtless the present day has seen the last of this academic destitution.Here is the tobacco-shop where, on Wednesday evening, coming out of the college, I would buy on credit the wherewithal to fill my pipe and thus[115]to celebrate on the eve the joys of the morrow, that blessed Thursday5which I considered so well employed in solving difficult equations, experimenting with new chemical reagents, collecting and identifying my plants. I made my timid request, pretending to have come out without my money, for it is hard for a self-respecting man to admit that he is penniless. My candour appears to have inspired some little confidence; and I obtained credit, an unprecedented thing, with the representative of the revenue.How I should love to see that room again where I pored over differentials and integrals, where I calmed my poor burning head by gazing at Mont Ventoux, whose summit held in store for my coming expedition6those denizens of Arctic climes, the saxifrage and the poppy! And to see my familiar friend, the blackboard, which I hired at five francs a year from a crusty joiner, that board whose value I paid many times over, though I could never buy it outright, for want of the necessary cash! The conic sections which I described on that blackboard, the learned hieroglyphics!7Fabre has somewhere written, lamenting the dearth of family reminiscences which[116]does not enable him to go back beyond the second generation of his ancestry, this touching passage, full of modesty and filial feeling: “The populace has no history. Strangled by the present, it cannot give its mind to cherishing the memories of the past.” Yet how instructive would those records be.Let us bow our heads before this child of the peasantry who labours so unremittingly and drives so deep a furrow; let us bow our heads before this humble primary schoolmaster who seeks to uplift himself, not as so many have done, by futile political agitation or the criminal fatuities of irreligion, but solely by virtue of knowledge and personal worth.We shall see later on with what vindictive energy Fabre scourges the pseudo-scientists, “hateful malefactors,”maufatan de malur, who, in the name of a false science, rob men’s souls of the true and ancient Christian faith, thereby leading society toward the most terrible catastrophes. For the moment our only desire is to do homage to our worthy schoolmasters in the person of one of their old comrades who has become one of our greatest national glories. There are others, too, among us who have exalted by their virtues or their talents the humble nature[117]of their origin or their calling. Of such, as every Frenchman knows, to mention only one of the best known and best beloved, is the author of thePoésie des Bêtes, ofVoix rustiques, ofLa Bonne Terre, ofLe Clocher, etc.—François Fabié, that poet who, by his original style, his career, and his genius, which has been too much obscured by his modesty, may in so many respects be compared with Jean-Henri Fabre.8Of such, too, and among the most eminent writers of thelanguage d’oc, is Antonin Perbosc,9who does honour to our primary schools, in one of which he is still teaching, by the remarkable works of literature which place him beside his friend, the Abbé Besson,10in the first rank of theOccitanian Félibrige.[118]

So we see him submerged in conic sections and the differential and integral calculus, without a guide, without advice, confronted for days on end by some obscure difficulty which tenacious meditation eventually robbed of its mystery. Mathematics, however,[100]formed only the first part of his programme, which comprised also physics and chemistry. These, no doubt, were less abstruse sciences, but the necessary equipment was also less simple. He needed a laboratory; he could not run to the expense of one; so he made one, an “impossible” one, by force of industry.

In this desperate struggle what became of the favourite branch of science of this great nature-lover? It was necessarily sacrificed.

“I reprimanded myself,” he says, “at the slightest longing for emancipation, fearing to let myself be seduced by some new grass, some unknown beetle. I did violence to myself. My books on natural history were condemned to oblivion, relegated to the bottom of a trunk.”

A fine lesson in perseverance in work and sacrifice, which all those who are inspired by some noble desire or merely by some legitimate ambition will find useful and comforting to contemplate:

“Qui studet optatam cursu contingere metamMulta tulit fecitque puer, sudavit et alsit;Abstinuit venere et vino.”1

“Qui studet optatam cursu contingere metam

Multa tulit fecitque puer, sudavit et alsit;

Abstinuit venere et vino.”1

But this matter must be expounded in greater detail, were it only to confirm the[101]courage of other students disinherited by fortune, reduced as was Fabre to shaping themselves in the “harsh school of isolation.” They will witness miracles of perseverance; and they will realise that opportunities of exercising the mind and strengthening the will are seldom lacking to those who understand how to seize them.

When I left the Normal School, my stock of mathematics was of the scantiest (writes Fabre). How to extract a square root, how to calculate and prove the surface of a sphere: these represented to me the culminating points of the subject. Those terrible logarithms, when I happened to open a table of them, made my head swim, with their columns of figures; actual fright, not unmixed with respect, overwhelmed me on the very threshold of that arithmetical cave. Of algebra I had no knowledge whatever. I had heard the name; and the syllables represented to my poor brain the whole whirling legion of the abstruse.Besides, I felt no inclination to decipher the alarming hieroglyphics. They made one of those indigestible dishes which we confidently extol without touching them. I greatly prefer a fine line of Virgil, whom I was now beginning to understand; and I should have been surprised indeed had any one told me that, for long years to come, I should be an enthusiastic student of the formidable science. Good fortune procured me my first lesson[102]in algebra, a lesson given and not received, of course.A young man of about my own age came to me and asked me to teach him algebra. He was preparing for his examination as a civil engineer; and he came to me because, ingenuous youth that he was, he took me for a well of learning. The guileless applicant was very far out in his reckoning.His request gave me a shock of surprise, which was forthwith repressed on reflection:“I give algebra lessons?” said I to myself. “It would be madness: I don’t know anything about it!”And I left it at that for a moment or two, thinking hard, drawn now this way, now that by my indecision:“Shall I accept? Shall I refuse?” continued the inner voice.Pooh, let’s accept! An heroic method of learning to swim is to leap boldly into the sea. Let us hurl ourselves head first into the algebraical gulf; and perhaps the imminent danger of drowning will call forth efforts capable of bringing me to land. I know nothing of what he wants. It makes no difference: let’s go ahead and plunge into the mystery. I shall learn by teaching.It was a fine courage that drove me full tilt into a province which I had not yet thought of entering. My twenty-year-old confidence was an incomparable lever.“Very well,” I replied. “Come the day after to-morrow at five, and we’ll begin.”[103]This twenty-four hours’ delay concealed a plan. It secured me the respite of a day, the blessed Thursday, which would give me time to collect my forces.Thursday comes. The sky is grey and cold. In this horrid weather a grate well-filled with coke has its charms. Let’s warm ourselves and think.Well, my boy, you’ve landed yourself in a nice predicament! How will you manage to-morrow? With a book, plodding all through the night, if necessary, you might scrape up something resembling a lesson, just enough to fill the dread hour more or less. Then you could see about the next: sufficient for the day is the evil thereof. But you haven’t the book. And it’s no use running out to the bookshop. Algebraical treatises are not current wares. You’ll have to send for one, which will take a fortnight at least. And I’ve promised for to-morrow, for to-morrow certain! Another argument and one that admits of no reply: funds are low; my last pecuniary resources lie in the corner of a drawer. I count the money: it amounts to twelve sous, which is not enough.Must I cry off? Rather not! One resource suggests itself: a highly improper one, I admit, not far removed, indeed, from larceny. O quiet paths of algebra, you are my excuse for this venial sin! Let me confess the temporary embezzlement.Life at my College is more or less cloistered. In return for a modest payment, most of us masters are lodged in the building; and we take our meals at the principal’s table. The science-master, who is the big gun of the staff and lives in the town,[104]has nevertheless, like ourselves, his own two cells, in addition to a balcony, or leads, where the chemical preparations give forth their suffocating gases in the open air. For this reason, he finds it more convenient to hold his class here during the greater part of the year. The boys come to these rooms in winter, in front of a grate stuffed full of coke, like mine, and there find a blackboard, a pneumatic trough, a mantelpiece covered with glass receivers, panoplies of bent tubes on the walls and, lastly, a certain cupboard in which I remember seeing a row of books, the oracles consulted by the master in the course of his lessons.“Among those books,” said I to myself, “there is sure to be one on algebra. To ask the owner for the loan of it does not appeal to me. My amiable colleague would receive me superciliously and laugh at my ambitious aims. I am sure he would refuse my request.”I decide to help myself to the book which I should never get by asking. This is the half-holiday. The science-master will not put in an appearance to-day; and the key of my room is practically the same as his. I go, with eyes and ears on the alert. My key does not quite fit; it sticks a little, then goes in; and an extra effort makes it turn in the lock. The door opens. I inspect the cupboard and find that it does contain an algebra book, one of the big, fat books which men used to write in those days, a book nearly half a foot thick. My legs give way beneath me. You poor specimen of a housebreaker, suppose you were caught at it![105]However, all goes well. Quick, let’s lock the door again, and hurry back to our own quarters with the pilfered volume.A chapter catches my attention in the middle of the volume; it is headed,Newton’s Binomial Theorem. The title allures me. What can a binomial theorem be, especially one whose author is Newton, the great English mathematician who weighed the worlds? What has the mechanism of the sky to do with this? Let us read and seek for enlightenment. With my elbows on the table and my thumbs behind my ears, I concentrate all my attention.I am seized with astonishment, for I understand! There are a certain number of letters, general symbols which are grouped in all manner of ways, taking their places here, there, and elsewhere by turns; there are, as the text tells me, arrangements, permutations, and combinations. Pen in hand, I arrange, permute, and combine. It is a very diverting exercise, upon my word, a game in which the test of the written result confirms the anticipations of logic and supplements the shortcomings of one’s thinking-apparatus.“It will be plain sailing,” said I to myself, “if algebra is no more difficult than this.”I was to recover from the illusion later, when the binomial theorem, that light, crisp biscuit, was followed by heavier and less digestible fare. But, for the moment, I had no foretaste of the future difficulties, of the pitfalls in which one becomes more and more entangled the longer one persists[106]in struggling. What a delightful afternoon that was, before my fire, amid my permutations and combinations! By the evening, I had nearly mastered my subject. When the bell rang, at seven, to summon us to the common meal at the principal’s table, I went downstairs puffed up with the joys of the newly-initiated neophyte. I was escorted on my way bya,b, andc, intertwined in cunning garlands.Next day, my pupil is there. Blackboard and chalk, everything is ready. Not quite so ready is the master. I bravely broach my binomial theorem. My hearer becomes interested in the combinations of letters. Not for a moment does he suspect that I am putting the cart before the horse and beginning where we ought to have finished. I relieve the dryness of my explanations with a few little problems, so many halts at which the mind takes breath awhile and gathers strength for fresh flights.We try together. Discreetly, so as to leave him the merit of the discovery, I shed a little light upon the path. The solution is found. My pupil triumphs; so do I, but silently, in my inner consciousness, which says:“You understand, because you succeed in making another understand.”The hour passed quickly and very pleasantly for both of us. My young man was contented when he left me; and I no less so, for I perceived a new and original way of learning things.The ingenious and easy arrangement of the binomial[107]gave me time to tackle my algebra book from the proper commencement. In three or four days I had rubbed up my weapons. There was nothing to be said about addition and subtraction: they were so simple as to force themselves upon one at first sight. Multiplication spoilt things. There was a certain rule of signs which declared that minus multiplied by minus made plus. How I toiled over that wretched paradox! It would seem that the book did not explain this subject clearly, or rather employed too abstract a method. I read, reread, and meditated in vain: the obscure text retained all its obscurity. That is the drawback of books in general: they tell you what is printed in them and nothing more. If you fail to understand, they never advise you, never suggest an attempt along another road which might lead you to the light. The merest word would sometimes be enough to put you on the right track; and that word the books, hide-bound in a regulation phraseology, never give you.My pupil was bound to suffer the effects. After an attempt at an explanation in which I made the most of the few gleams that reached me, I asked him:“Do you understand?”It was a futile question, but useful for gaining time. Myself not understanding, I was convinced beforehand that he did not understand either.“No,” he replied, accusing himself, perhaps, in his simple mind, of possessing a brain incapable of taking in those transcendental verities.[108]“Let us try another method.”And I start again this way and that way and yet another way. My pupil’s eyes serve as my thermometer and tell me of the progress of my efforts. A blink of satisfaction announces my success. I have struck home, I have found the joint in the armour. The product of minus multiplied by minus surrenders its mysteries to us.2

Besides, I felt no inclination to decipher the alarming hieroglyphics. They made one of those indigestible dishes which we confidently extol without touching them. I greatly prefer a fine line of Virgil, whom I was now beginning to understand; and I should have been surprised indeed had any one told me that, for long years to come, I should be an enthusiastic student of the formidable science. Good fortune procured me my first lesson[102]in algebra, a lesson given and not received, of course.

A young man of about my own age came to me and asked me to teach him algebra. He was preparing for his examination as a civil engineer; and he came to me because, ingenuous youth that he was, he took me for a well of learning. The guileless applicant was very far out in his reckoning.

His request gave me a shock of surprise, which was forthwith repressed on reflection:

“I give algebra lessons?” said I to myself. “It would be madness: I don’t know anything about it!”

And I left it at that for a moment or two, thinking hard, drawn now this way, now that by my indecision:

“Shall I accept? Shall I refuse?” continued the inner voice.

Pooh, let’s accept! An heroic method of learning to swim is to leap boldly into the sea. Let us hurl ourselves head first into the algebraical gulf; and perhaps the imminent danger of drowning will call forth efforts capable of bringing me to land. I know nothing of what he wants. It makes no difference: let’s go ahead and plunge into the mystery. I shall learn by teaching.

It was a fine courage that drove me full tilt into a province which I had not yet thought of entering. My twenty-year-old confidence was an incomparable lever.

“Very well,” I replied. “Come the day after to-morrow at five, and we’ll begin.”[103]

This twenty-four hours’ delay concealed a plan. It secured me the respite of a day, the blessed Thursday, which would give me time to collect my forces.

Thursday comes. The sky is grey and cold. In this horrid weather a grate well-filled with coke has its charms. Let’s warm ourselves and think.

Well, my boy, you’ve landed yourself in a nice predicament! How will you manage to-morrow? With a book, plodding all through the night, if necessary, you might scrape up something resembling a lesson, just enough to fill the dread hour more or less. Then you could see about the next: sufficient for the day is the evil thereof. But you haven’t the book. And it’s no use running out to the bookshop. Algebraical treatises are not current wares. You’ll have to send for one, which will take a fortnight at least. And I’ve promised for to-morrow, for to-morrow certain! Another argument and one that admits of no reply: funds are low; my last pecuniary resources lie in the corner of a drawer. I count the money: it amounts to twelve sous, which is not enough.

Must I cry off? Rather not! One resource suggests itself: a highly improper one, I admit, not far removed, indeed, from larceny. O quiet paths of algebra, you are my excuse for this venial sin! Let me confess the temporary embezzlement.

Life at my College is more or less cloistered. In return for a modest payment, most of us masters are lodged in the building; and we take our meals at the principal’s table. The science-master, who is the big gun of the staff and lives in the town,[104]has nevertheless, like ourselves, his own two cells, in addition to a balcony, or leads, where the chemical preparations give forth their suffocating gases in the open air. For this reason, he finds it more convenient to hold his class here during the greater part of the year. The boys come to these rooms in winter, in front of a grate stuffed full of coke, like mine, and there find a blackboard, a pneumatic trough, a mantelpiece covered with glass receivers, panoplies of bent tubes on the walls and, lastly, a certain cupboard in which I remember seeing a row of books, the oracles consulted by the master in the course of his lessons.

“Among those books,” said I to myself, “there is sure to be one on algebra. To ask the owner for the loan of it does not appeal to me. My amiable colleague would receive me superciliously and laugh at my ambitious aims. I am sure he would refuse my request.”

I decide to help myself to the book which I should never get by asking. This is the half-holiday. The science-master will not put in an appearance to-day; and the key of my room is practically the same as his. I go, with eyes and ears on the alert. My key does not quite fit; it sticks a little, then goes in; and an extra effort makes it turn in the lock. The door opens. I inspect the cupboard and find that it does contain an algebra book, one of the big, fat books which men used to write in those days, a book nearly half a foot thick. My legs give way beneath me. You poor specimen of a housebreaker, suppose you were caught at it![105]However, all goes well. Quick, let’s lock the door again, and hurry back to our own quarters with the pilfered volume.

A chapter catches my attention in the middle of the volume; it is headed,Newton’s Binomial Theorem. The title allures me. What can a binomial theorem be, especially one whose author is Newton, the great English mathematician who weighed the worlds? What has the mechanism of the sky to do with this? Let us read and seek for enlightenment. With my elbows on the table and my thumbs behind my ears, I concentrate all my attention.

I am seized with astonishment, for I understand! There are a certain number of letters, general symbols which are grouped in all manner of ways, taking their places here, there, and elsewhere by turns; there are, as the text tells me, arrangements, permutations, and combinations. Pen in hand, I arrange, permute, and combine. It is a very diverting exercise, upon my word, a game in which the test of the written result confirms the anticipations of logic and supplements the shortcomings of one’s thinking-apparatus.

“It will be plain sailing,” said I to myself, “if algebra is no more difficult than this.”

I was to recover from the illusion later, when the binomial theorem, that light, crisp biscuit, was followed by heavier and less digestible fare. But, for the moment, I had no foretaste of the future difficulties, of the pitfalls in which one becomes more and more entangled the longer one persists[106]in struggling. What a delightful afternoon that was, before my fire, amid my permutations and combinations! By the evening, I had nearly mastered my subject. When the bell rang, at seven, to summon us to the common meal at the principal’s table, I went downstairs puffed up with the joys of the newly-initiated neophyte. I was escorted on my way bya,b, andc, intertwined in cunning garlands.

Next day, my pupil is there. Blackboard and chalk, everything is ready. Not quite so ready is the master. I bravely broach my binomial theorem. My hearer becomes interested in the combinations of letters. Not for a moment does he suspect that I am putting the cart before the horse and beginning where we ought to have finished. I relieve the dryness of my explanations with a few little problems, so many halts at which the mind takes breath awhile and gathers strength for fresh flights.

We try together. Discreetly, so as to leave him the merit of the discovery, I shed a little light upon the path. The solution is found. My pupil triumphs; so do I, but silently, in my inner consciousness, which says:

“You understand, because you succeed in making another understand.”

The hour passed quickly and very pleasantly for both of us. My young man was contented when he left me; and I no less so, for I perceived a new and original way of learning things.

The ingenious and easy arrangement of the binomial[107]gave me time to tackle my algebra book from the proper commencement. In three or four days I had rubbed up my weapons. There was nothing to be said about addition and subtraction: they were so simple as to force themselves upon one at first sight. Multiplication spoilt things. There was a certain rule of signs which declared that minus multiplied by minus made plus. How I toiled over that wretched paradox! It would seem that the book did not explain this subject clearly, or rather employed too abstract a method. I read, reread, and meditated in vain: the obscure text retained all its obscurity. That is the drawback of books in general: they tell you what is printed in them and nothing more. If you fail to understand, they never advise you, never suggest an attempt along another road which might lead you to the light. The merest word would sometimes be enough to put you on the right track; and that word the books, hide-bound in a regulation phraseology, never give you.

My pupil was bound to suffer the effects. After an attempt at an explanation in which I made the most of the few gleams that reached me, I asked him:

“Do you understand?”

It was a futile question, but useful for gaining time. Myself not understanding, I was convinced beforehand that he did not understand either.

“No,” he replied, accusing himself, perhaps, in his simple mind, of possessing a brain incapable of taking in those transcendental verities.[108]

“Let us try another method.”

And I start again this way and that way and yet another way. My pupil’s eyes serve as my thermometer and tell me of the progress of my efforts. A blink of satisfaction announces my success. I have struck home, I have found the joint in the armour. The product of minus multiplied by minus surrenders its mysteries to us.2

The study of algebra was pursued in this fashion without any undue impediments as far as the pupil was concerned, but at the cost of a prodigious exertion of patience and penetration on the part of the primary schoolmaster who was so venturesome as to act as a professor of the higher mathematics.Audaces fortuna juvat.The young schoolmaster had not too greatly presumed on his powers. His pupil was accepted upon examination, and he himself was able to return the book to its place, having completely assimilated its contents.

But he had made too good a start to stop midway. He was burning with eagerness to attack geometry, which was not so unfamiliar to him, but of which he had yet a great deal to learn: “At my normal school,” writes[109]Fabre, “I had learnt a little elementary geometry under a master. From the first few lessons onwards, I rather enjoyed the subject. I divined in it a guide for one’s reasoning faculties through the thickets of the imagination; I caught a glimpse of a search after truth that did not involve too much stumbling on the way, because each step forward is well braced by the step already taken. We start from a brilliantly-lighted spot and gradually travel farther and farther into the darkness, which kindles into radiance as it sheds fresh beams of light for a higher ascent.

It is an excellent thing to regard geometry as what it really is, before all things: a superb intellectual gymnastic. By forcing the mind to proceed from the known to the unknown, always explaining what follows in the light of what has gone before, it exercises it and familiarises it with the logical laws of thought. To be sure, “it does not give us ideas, those delicate flowers which unfold one knows not how, and are not able to flourish in every soil,” but it teaches us to present them in a lucid and orderly manner. Fabre tells us:

At that time, the College in which, two years before, I had made my first appearance as a teacher[110]had just halved the size of its classes and largely increased its staff. The newcomers all lived in the building, like myself, and we had our meals in common at the principal’s table. I had as a neighbour, in the next cell to mine, a retired quartermaster who, weary of barrack-life, had taken refuge in education. When in charge of the books of his company, he had become more or less familiar with figures; and it was now his ambition to take a mathematical degree. His cerebrum appears to have hardened while he was with his regiment. According to my dear colleagues, those amiable retailers of the misfortunes of others, he had already twice been plucked. Stubbornly, he returned to his books and exercises, refusing to be daunted by two reverses.It was not that he was allured by the beauties of mathematics: far from it; but the step to which he aspired favoured his plans. He hoped to have his own boarders and dispense butter and vegetables to lucrative purpose.I had often surprised our friend sitting, in the evening, by the light of a candle, with his elbows on the table and his head between his hands, meditating at great length in front of a big exercise-book crammed with cabalistic signs. From time to time, when an idea came to him, he would take his pen and hastily put down a line of writing wherein letters, large and small, were grouped without any grammatical sense. The lettersxandyoften recurred, intermingled with figures. Every row ended with the sign of equality and a naught.[111]Next came more reflection, with closed eyes, and a fresh row of letters arranged in a different order and likewise followed by a naught. Page after page was filled in this queer fashion, each line winding up with 0.“What are you doing with all those rows of figures amounting to zero?” I asked him one day.The mathematician gave me a leery look, picked up in barracks. A sarcastic droop in the corner of his eye showed how he pitied my ignorance. My colleague of the many naughts did not, however, take an unfair advantage of his superiority. He told me that he was working at analytical geometry.The phrase had a strange effect upon me. I ruminated silently to this purpose: there was a higher geometry, which you learnt more particularly with combinations of letters in whichxandyplayed a prominent part. How would the alphabetical signs, arranged first in one and then in another manner, give an image of actual things, an image visible to the eyes of the mind alone? It beat me.“I shall have to learn analytical geometry some day,” I said. “Will you help me?”“I’m quite willing,” he replied, with a smile in which I read his lack of confidence in my determination.No matter: we struck a bargain that same evening. We would together break up the stubble of algebra and analytical geometry, the foundation of the mathematical degree; we would make common[112]stock: he would bring long hours of calculation, I my youthful ardour. We would begin as soon as I had finished with my arts degree, which was my main preoccupation for the moment.We begin in my room, in front of a blackboard. After a few evenings, prolonged into the peaceful watches of the night, I become aware, to my great surprise, that my teacher, the past master in these hieroglyphics, is really, more often than not, my pupil. He does not see the combinations of the abscissæ and ordinates very clearly. I make bold to take the chalk in hand myself, to seize the rudder of our algebraical boat. I comment on the book, interpret it in my own fashion, expound the text, sound the reefs, until daylight comes and leads us to the haven of the solution. Besides, the logic is so irresistible, it is all such easy going and so lucid that often one seems to be remembering rather than learning.And so we proceed, with our positions reversed. My comrade—I can now allow myself to speak of him on equal terms—my comrade listens, suggests objections, raises difficulties which we try to solve in unison.After fifteen months of this exercise, we went up together for our examination at Montpellier; and both of us received our degrees as bachelors of mathematical science. My companion was a wreck; I, on the other hand, had refreshed my mind with analytical geometry.3

It was not that he was allured by the beauties of mathematics: far from it; but the step to which he aspired favoured his plans. He hoped to have his own boarders and dispense butter and vegetables to lucrative purpose.

I had often surprised our friend sitting, in the evening, by the light of a candle, with his elbows on the table and his head between his hands, meditating at great length in front of a big exercise-book crammed with cabalistic signs. From time to time, when an idea came to him, he would take his pen and hastily put down a line of writing wherein letters, large and small, were grouped without any grammatical sense. The lettersxandyoften recurred, intermingled with figures. Every row ended with the sign of equality and a naught.[111]Next came more reflection, with closed eyes, and a fresh row of letters arranged in a different order and likewise followed by a naught. Page after page was filled in this queer fashion, each line winding up with 0.

“What are you doing with all those rows of figures amounting to zero?” I asked him one day.

The mathematician gave me a leery look, picked up in barracks. A sarcastic droop in the corner of his eye showed how he pitied my ignorance. My colleague of the many naughts did not, however, take an unfair advantage of his superiority. He told me that he was working at analytical geometry.

The phrase had a strange effect upon me. I ruminated silently to this purpose: there was a higher geometry, which you learnt more particularly with combinations of letters in whichxandyplayed a prominent part. How would the alphabetical signs, arranged first in one and then in another manner, give an image of actual things, an image visible to the eyes of the mind alone? It beat me.

“I shall have to learn analytical geometry some day,” I said. “Will you help me?”

“I’m quite willing,” he replied, with a smile in which I read his lack of confidence in my determination.

No matter: we struck a bargain that same evening. We would together break up the stubble of algebra and analytical geometry, the foundation of the mathematical degree; we would make common[112]stock: he would bring long hours of calculation, I my youthful ardour. We would begin as soon as I had finished with my arts degree, which was my main preoccupation for the moment.

We begin in my room, in front of a blackboard. After a few evenings, prolonged into the peaceful watches of the night, I become aware, to my great surprise, that my teacher, the past master in these hieroglyphics, is really, more often than not, my pupil. He does not see the combinations of the abscissæ and ordinates very clearly. I make bold to take the chalk in hand myself, to seize the rudder of our algebraical boat. I comment on the book, interpret it in my own fashion, expound the text, sound the reefs, until daylight comes and leads us to the haven of the solution. Besides, the logic is so irresistible, it is all such easy going and so lucid that often one seems to be remembering rather than learning.

And so we proceed, with our positions reversed. My comrade—I can now allow myself to speak of him on equal terms—my comrade listens, suggests objections, raises difficulties which we try to solve in unison.

After fifteen months of this exercise, we went up together for our examination at Montpellier; and both of us received our degrees as bachelors of mathematical science. My companion was a wreck; I, on the other hand, had refreshed my mind with analytical geometry.3

[113]

The quartermaster declared himself satisfied with this achievement. Analytic geometry did not precisely strike him as a recreation. He knew enough of it for what he had to do; he did not want to know any more.

In vain I hold out the glittering prospect of a new degree, that of licentiate of mathematical science, which would lead us to the splendours of the higher mathematics and initiate us into the mechanics of the heavens: I cannot prevail upon him, cannot make him share my audacity. He calls it a mad scheme, which will exhaust us and come to nothing. I am free to go and break my neck in distant countries; he is more prudent and will not follow me.My partner, therefore, leaves me. Henceforth, I am alone, alone and wretched. There is no one left with whom I can sit up and thresh out the subject in exhilarating discussion.4

My partner, therefore, leaves me. Henceforth, I am alone, alone and wretched. There is no one left with whom I can sit up and thresh out the subject in exhilarating discussion.4

And now let us note the words and the emotions with which he approaches for the last time, in his declining years, this town of Carpentras, where, from his earliest[114]youth, he suffered so greatly and laboured so valiantly:

Once more, here am I, somewhat late in life, at Carpentras, whose rude Gallic name sets the fool smiling and the scholar thinking. Dear little town where I spent my twentieth year and left the first bits of my fleece upon life’s bushes, my visit of to-day is a pilgrimage; I have come to lay my eyes once more upon the place which saw the birth of the liveliest impressions of my early days. I bow, in passing, to the old College where I tried my prentice hand as a teacher. Its appearance is unchanged; it still looks like a penitentiary. Those were the views of our mediæval educational system. To the gaiety and activity of boyhood, which were considered unwholesome, it applied the remedy of narrowness, melancholy, and gloom. Its houses of instruction were, above all, houses of correction. The freshness of Virgil was interpreted in the stifling atmosphere of a prison. I catch a glimpse of a yard between four high walls, a sort of bear-pit, where the scholars fought for room for their games under the spreading branches of a plane-tree. All around were cells that looked like horse-boxes, without light or air; those were the class-rooms. I speak in the past tense, for doubtless the present day has seen the last of this academic destitution.Here is the tobacco-shop where, on Wednesday evening, coming out of the college, I would buy on credit the wherewithal to fill my pipe and thus[115]to celebrate on the eve the joys of the morrow, that blessed Thursday5which I considered so well employed in solving difficult equations, experimenting with new chemical reagents, collecting and identifying my plants. I made my timid request, pretending to have come out without my money, for it is hard for a self-respecting man to admit that he is penniless. My candour appears to have inspired some little confidence; and I obtained credit, an unprecedented thing, with the representative of the revenue.How I should love to see that room again where I pored over differentials and integrals, where I calmed my poor burning head by gazing at Mont Ventoux, whose summit held in store for my coming expedition6those denizens of Arctic climes, the saxifrage and the poppy! And to see my familiar friend, the blackboard, which I hired at five francs a year from a crusty joiner, that board whose value I paid many times over, though I could never buy it outright, for want of the necessary cash! The conic sections which I described on that blackboard, the learned hieroglyphics!7

Here is the tobacco-shop where, on Wednesday evening, coming out of the college, I would buy on credit the wherewithal to fill my pipe and thus[115]to celebrate on the eve the joys of the morrow, that blessed Thursday5which I considered so well employed in solving difficult equations, experimenting with new chemical reagents, collecting and identifying my plants. I made my timid request, pretending to have come out without my money, for it is hard for a self-respecting man to admit that he is penniless. My candour appears to have inspired some little confidence; and I obtained credit, an unprecedented thing, with the representative of the revenue.

How I should love to see that room again where I pored over differentials and integrals, where I calmed my poor burning head by gazing at Mont Ventoux, whose summit held in store for my coming expedition6those denizens of Arctic climes, the saxifrage and the poppy! And to see my familiar friend, the blackboard, which I hired at five francs a year from a crusty joiner, that board whose value I paid many times over, though I could never buy it outright, for want of the necessary cash! The conic sections which I described on that blackboard, the learned hieroglyphics!7

Fabre has somewhere written, lamenting the dearth of family reminiscences which[116]does not enable him to go back beyond the second generation of his ancestry, this touching passage, full of modesty and filial feeling: “The populace has no history. Strangled by the present, it cannot give its mind to cherishing the memories of the past.” Yet how instructive would those records be.

Let us bow our heads before this child of the peasantry who labours so unremittingly and drives so deep a furrow; let us bow our heads before this humble primary schoolmaster who seeks to uplift himself, not as so many have done, by futile political agitation or the criminal fatuities of irreligion, but solely by virtue of knowledge and personal worth.

We shall see later on with what vindictive energy Fabre scourges the pseudo-scientists, “hateful malefactors,”maufatan de malur, who, in the name of a false science, rob men’s souls of the true and ancient Christian faith, thereby leading society toward the most terrible catastrophes. For the moment our only desire is to do homage to our worthy schoolmasters in the person of one of their old comrades who has become one of our greatest national glories. There are others, too, among us who have exalted by their virtues or their talents the humble nature[117]of their origin or their calling. Of such, as every Frenchman knows, to mention only one of the best known and best beloved, is the author of thePoésie des Bêtes, ofVoix rustiques, ofLa Bonne Terre, ofLe Clocher, etc.—François Fabié, that poet who, by his original style, his career, and his genius, which has been too much obscured by his modesty, may in so many respects be compared with Jean-Henri Fabre.8Of such, too, and among the most eminent writers of thelanguage d’oc, is Antonin Perbosc,9who does honour to our primary schools, in one of which he is still teaching, by the remarkable works of literature which place him beside his friend, the Abbé Besson,10in the first rank of theOccitanian Félibrige.[118]

1Horace,Ars Poetica, 412.↑2Souvenirs,IX., pp. 164–170.The Life of the Fly, chap. xii., “Mathematical Memories: The Binomial Theorem.”↑3Souvenirs,IX., pp. 172–183passim.The Life of the[113]Fly, chap. xii., “Mathematical Memories: The Binomial Theorem.”↑4Souvenirs,IX., p. 184passim.The Life of the Fly, chap. xii., “Mathematical Memories: The Binomial Theorem.”↑5The weekly half-holiday in the French schools.—A. T. de M.↑6The Hunting Wasps, chap. xi., “An Ascent of Mont Ventoux.”↑7Souvenirs,III., pp. 191–193.The Life of the Fly, chap. iv., “Larval Dimorphism.”↑8M. Fabié was never officially a schoolmaster, but he was trained as one, and was a pupil at the Normal College at Rodez.↑9M. Perbosc is a schoolmaster at Lavilledien (Tarnet-Garonne). He has published through Privat of Toulouse:Lo Got occitan,Cansous del Got occitan,Contes populars Gascons,Guilhem de Tolosa,Remembransa,l’Arada, etc., and has repeatedly been crowned by theAcadémie des Jeux Florauxof Toulouse.↑10M. Besson is also a laureate of theAcadémie des Jeux Floraux, and is at present Canon of Rodez. He has published through Carrère of Rodez:Dal Brès à la Tounbo,Bagateletos,Besucarietos,Countes de la Tata Mannou,Countes de l’Ouncle Janet, etc. This last volume is dedicated:A mon Amic Antouni Perbosc.↑

1Horace,Ars Poetica, 412.↑

2Souvenirs,IX., pp. 164–170.The Life of the Fly, chap. xii., “Mathematical Memories: The Binomial Theorem.”↑

3Souvenirs,IX., pp. 172–183passim.The Life of the[113]Fly, chap. xii., “Mathematical Memories: The Binomial Theorem.”↑

4Souvenirs,IX., p. 184passim.The Life of the Fly, chap. xii., “Mathematical Memories: The Binomial Theorem.”↑

5The weekly half-holiday in the French schools.—A. T. de M.↑

6The Hunting Wasps, chap. xi., “An Ascent of Mont Ventoux.”↑

7Souvenirs,III., pp. 191–193.The Life of the Fly, chap. iv., “Larval Dimorphism.”↑

8M. Fabié was never officially a schoolmaster, but he was trained as one, and was a pupil at the Normal College at Rodez.↑

9M. Perbosc is a schoolmaster at Lavilledien (Tarnet-Garonne). He has published through Privat of Toulouse:Lo Got occitan,Cansous del Got occitan,Contes populars Gascons,Guilhem de Tolosa,Remembransa,l’Arada, etc., and has repeatedly been crowned by theAcadémie des Jeux Florauxof Toulouse.↑

10M. Besson is also a laureate of theAcadémie des Jeux Floraux, and is at present Canon of Rodez. He has published through Carrère of Rodez:Dal Brès à la Tounbo,Bagateletos,Besucarietos,Countes de la Tata Mannou,Countes de l’Ouncle Janet, etc. This last volume is dedicated:A mon Amic Antouni Perbosc.↑

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