The Manuscript Found in Saragossa (39 page)

As far as I can remember, curiosity was my first passion. There are no horses or carriages on the streets of Ceuta and there are no dangers for children. So I was allowed to go wherever I liked. I would satisfy my curiosity by going down to the harbour and climbing back up to the town a hundred times a day. I went into all the houses, shops, arsenals and workshops, observing the tradesmen, following the porters, questioning the passers-by. Everywhere people were amused by my curiosity and were happy to satisfy it. That wasn't the case in the paternal home, however.

My father had had constructed in the courtyard of his house a separate building in which his library, laboratory and observatory were housed. I was not allowed access to this building. At first I wasn't too concerned about this, but as time went by the fact that I was not allowed access excited my curiosity and was a powerful spur to my first steps in a scientific career. The first science to which I applied myself was that part of natural history known as conchology. My father often went down to the sea-shore, near a particular rock where in calm weather the sea was as transparent as glass. He observed the behaviour of marine animals and when he found a well-preserved shell he took it home with him. Children are mimics so I became a conchologist, but in the process I was bitten by crabs, burnt by sea-nettles and stung by sea-urchins. These unpleasant experiences put me off natural history and I became attached to physics.

My father needed a skilled worker to modify, repair or copy the instruments which arrived for him from England. He taught an armourer whom nature had endowed with some talent how to do this. I spent nearly all my time with this apprentice technician and helped him in his work. I acquired practical skills but still lacked one very essential one, that of reading and writing.

Although I was then eight years old, my father said that provided I knew how to sign my name and dance a saraband I need know no more. There was at Ceuta an old priest who had been exiled there for some monastic intrigue. He was highly thought of by everyone and often came to see us. This good cleric, seeing me thus neglected, pointed out to my father that I had not been instructed in my religion and offered to teach me himself. My father agreed to this. With this as a pretext Father Anselm taught me to read, write and count. I made swift progress, especially in mathematics, in which I soon outstripped my teacher.

So I reached my twelfth year, having a good deal of knowledge for my age, but I was careful not to show it off in front of my father, for if it ever happened that I did, he would unfailingly look at me severely and say, ‘Learn to dance the saraband, my friend, learn to dance and don't meddle with things that will only bring you unhappiness!' At this, my mother would gesture to me to keep quiet and then change the subject.

One day, as we were sitting at table and my father was urging me once again to devote myself to the graces, we saw a man come in. He was about thirty years old and dressed in the French fashion. He bowed to us twelve times in succession. Then, trying to perform some pirouette or other, he bumped into a servant bringing in the soup, and made him drop it. A Spaniard would have apologized profusely. Not so this stranger. He laughed as much as he had bowed on arrival, after which he told us in bad Spanish that his name was the Marquis de Folencour; he had been obliged to leave France for having killed a man in a duel and asked permission to be given asylum until the affair had been settled.

Folencour had no sooner finished his speech than my father, jumping up in great animation, said to him, ‘Monsieur le Marquis, you are the very man I have been waiting for for a long time. Treat my house as your own. Only please be so kind as to give some attention to the education of my son. If one day he could be like you, I should be the happiest of fathers.'

If Folencour had known the meaning my father attached to what he had said, he would perhaps not have been very flattered by it. But he took my father's compliment quite literally and seemed very
pleased by it. Indeed, his impertinence became all the greater. He constantly alluded to the beauty of my mother and the age of my father, who for all this did not stop congratulating him and urging me to admire him.

At the end of the meal my father asked the marquis if he could teach me how to dance the saraband. At this my tutor started laughing even louder than he had done before. When he had recovered from his great outburst of mirth he told us that the saraband had not been danced for two thousand years. Only the passepied and bourrée. And then he drew from his pocket one of those instruments which dancing-masters call
pochettes
¹
and played these two dance tunes.

When he had finished my father said to him in great seriousness, ‘Monsieur le Marquis, you can play an instrument that few noblemen can play, and you lead me to wonder whether you have not been a dancing-master in your time. But it doesn't matter. You will be all the more suitable to fulfil my purposes. I request you to begin tomorrow to educate my son and to make him like a nobleman of the French court.'

Folencour admitted that certain misfortunes had obliged him for a time to take on the profession of dancing-master, but that he was no less of a nobleman for all that and no less suited to educate a young gentleman. So it was decided that the following day I would have my first lesson in dancing and good manners. Before, however, I describe to you that fateful day I must tell you of a conversation which my father had the same evening with his father-in-law, Señor de Cadanza. I have hardly thought about it since, but it has just this instant come back to me and it may be of interest to you.

That day my curiosity kept me at the side of my new mentor and I did not think of roaming about the streets. Passing by my father's study, I heard him say to Cadanza with anger in his voice:

‘My dear father-in-law, I warn you for the last time that if you continue your dispatches into the African interior, I shall denounce you to the minister.'

‘My dear son-in-law,' replied Cadanza, ‘if you want to be privy to
our secrets nothing will be easier. My mother was a Gomelez and my blood flows in the veins of your son.'

‘Señor Cadanza,' continued my father, ‘I am the king's lieutenant here and have nothing to do with the Gomelez and their secrets. You may be sure that tomorrow I shall let the minister know of this conversation.'

‘And you may be sure that the minister will forbid you in future to make reports on things that are not your concern,' said Cadanza.

Their conversation went no further. The secret of the Gomelez preoccupied me all day and part of the night. But the next day the cursed Folencour gave me my first dancing lesson, which turned out altogether differently to what he had hoped and had the effect of directing my mind towards mathematics.

My father did not scold me. He rose gravely, took me by the hand, led me to a low room at one end of the courtyard and, as he locked
me in, he said, ‘Señor, you will not come out of there except to learn to dance.'

Accustomed as I was to complete freedom, prison seemed intolerable to me at first. For a long time I wept a great deal. But as I cried I looked towards a large square window, the only one in that low room, and started counting the panes. There were twenty-six across and as many down. I remembered Father Anselm's lessons, which went no further than multiplication.

I multiplied the panes down by the panes across and realized with surprise that I had the overall number of panes. My sobs grew less frequent, my sorrow less great. I repeated my calculation, taking off one or sometimes two rows of panes, either across or down. I then realized that multiplication is only repeated addition and that surfaces could be measured as well as length. Next, I did the same experiment with the tiles which formed the floor of the room. It worked just as well. I didn't cry any longer. My heart was beating with joy. Even today I cannot talk of this without feeling some emotion.

Towards midday my mother brought me a loaf of black bread and a jug of water. She begged me with tears in her eyes to bow to the wishes of my father and take lessons from Folencour. When she had finished her entreaties I kissed her hand with great affection. Then I asked her to bring me some paper and a pencil and not to concern herself about me any more because I was quite happy in that low room. My mother left me in bewilderment and sent in the things that I had asked for. Then I devoted myself to my calculations with indescribable ardour, convinced that I was making great discoveries from one moment to the next. And indeed the properties of numbers were veritable discoveries for me. I had had no notion of them.

Meanwhile, I noticed I was hungry. I broke the loaf and found that my mother had hidden inside it a roast chicken and a piece of bacon. This token of kindness added to my contentment and I took up my calculations again with renewed pleasure. In the evening a lamp was brought to me and I continued working late into the night.

The following day I halved the side of a pane, and saw that the product of a half and a half was a quarter. I divided the side of a pane into three and came up with a ninth, which made clear to me the
nature of fractions. I confirmed this when I multiplied two and a half by two and a half, and together with the square of two I obtained a square whose value was two and a quarter.

I took my experiments with numbers further. I realized that by multiplying a number by itself and squaring the product I would obtain the same result as if I had multiplied the number four times by itself. All my fine discoveries were not expressed in algebraic language, of which I was ignorant. I had made up my own notation to apply to the window-panes, which lacked neither elegance nor precision.

At last, on the tenth day of my incarceration, my mother said when she brought me my meal, ‘My dear child, I have good news to tell you. Folencour has been unmasked as a deserter. Your father, who abhors desertion, has had him put on a ship. I think you will soon leave your prison.'

I received the news of my release with an indifference which surprised my mother. Shortly afterwards my father came to confirm what she had said, and then added that he had written to his friends Cassini and Huygens
¹
to ask them to send the steps of the most fashionable dances in London and Paris. He, as it happens, had a clear memory of the way his brother Carlos pirouetted on entering a room: it was which above all else that he wanted to teach me. As he spoke, my father saw a notebook sticking out of my pocket, and seized it. He was at first very surprised to see it covered with numbers and certain signs which were unknown to him. I explained them, as well as all my calculations. His surprise grew. It was mingled with a certain look of satisfaction which did not escape me. My father followed the account of my discoveries closely and then said to me:

‘If I added two panes to the width of this window, which is twenty-six panes in both directions, how many panes would have to be added for it to keep the form of a square?'

I replied unhesitatingly, ‘You will have added across and down two blocks each of fifty-two panes, with a little square of four panes at the corner where the two blocks meet, as well.'

This reply gave my father great joy, which he hid as best he could. Then he said to me, ‘But if I added to the base of the window an infinitely small row, what would then be the resulting square?'

I thought for a moment and then said, ‘You would have two blocks as long as the sides of the window but infinitesimally narrow, and as for the square in the corner, it would be so infinitesimally small that I cannot imagine it.'

At this point my father collapsed back in his chair, clasped his hands together, raised his eyes to heaven and said, ‘Merciful Heaven, you are witness to him! He has worked out the law of binomials! If I let him continue, he will work out the differential calculus!'

The state that my father was in frightened me. I undid his cravat and called for help. He came to his senses, embraced me and said, ‘My child, my dear child. Give up your calculations! Learn to dance the saraband, my friend, learn to dance the saraband!' There was no longer any question of prison. That evening I went all round the ramparts of Ceuta and as I walked I repeated to myself, ‘He has discovered the law of binomials!' From then on, I can say, every day that went by was marked by some progress I made in mathematics. My father had sworn never to allow me to learn the subject, but one day I found on the ground in front of me the noble Don Isaac Newton's
Arithmetica Universalis
,
²
and I cannot help thinking that my father had mislaid it there almost by design. Sometimes, too, I found the library open and did not fail to profit from this. On other occasions, however, my father set out to prepare me for entry into polite society. He made me pirouette when I came into a room, hum a tune and pretend to be short-sighted. Then he would dissolve in tears and say, ‘My child, you are not meant for a life of impertinence. Your days will be no happier than mine have been.'

Five years after the period of my incarceration, my mother discovered that she was pregnant. She gave birth to a daughter, who was called Blanca in honour of the beautiful and all-too-fickle Duquesa de Velásquez. Although that lady had not given my father permission to write to her, he believed it to be his duty to inform her of the birth
of the child. He received a reply which revived old sorrows, but my father was growing older and was not so susceptible to such violent emotions.

Thereafter, ten years passed without anything to disturb the regularity of our lives, although for my father and myself they were given variety by the new knowledge which from day to day we were acquiring. My father had even given up his former aloofness with me. He had indeed not taught me mathematics; he had done all in his power to make me learn to dance the saraband. So he had nothing to reproach himself with and indulged himself with a clear conscience in talking to me about everything that related to the exact sciences. These conversations had the effect of stimulating my enthusiasm and increasing my efforts. But at the same time, by commanding all my attention, they developed my tendency towards absent-mindedness, as I have said. I have often had to pay dearly for this distraction, as you will soon learn, for one day I left Ceuta and found myself suddenly, without knowing how, surrounded by Arabs.

As for my sister, she grew in grace and beauty and our joy would have been complete if we still had had a mother with us, but a year earlier a violent illness had carried off the one we loved so much.

My father then took into his household a sister of his deceased wife, called Doña Antonia de Poneras. She was twenty years old and had been a widow for six months. She was not born of the same bed as my mother. When Señor de Cadanza married off his daughter, who was then his only child, he found his house too lonely and decided to remarry. His second wife died six years later giving birth to a daughter, who later married Señor de Poneras, who himself died in the first year of their marriage.

This young and pretty aunt took up residence in my mother's apartment and ran the household, which she did quite well. She was especially attentive to me. She would come into my room twenty times a day to ask whether I wanted chocolate, lemonade or something similar.

These visits were often unwelcome since they interrupted my calculations. Whenever it happened that Doña Antonia did not come, she was replaced by a chambermaid, a girl of the same age and humour as her mistress, whose name was Marita. I soon noticed that
my sister liked neither the maid nor the mistress, and it was not long before I shared her antipathy for them, which was, however, in my case only founded on the annoyance I felt at being interrupted. But I wasn't always caught out by them. I had taken to substituting symbols for values as soon as one of these women entered my room, only to take up my calculations again when she had gone away.

One day, as I was looking up a logarithm, Antonia came into my room and sat down in an armchair next to my table. Then, complaining of the heat, she took off the kerchief she wore on her breast, folded it and put it on the back of my chair. I concluded from this activity that she was going to stay for some time, so I stopped my calculations, shut up my logarithm tables and started musing about the nature of logarithms and the extreme effort that drawing up the tables must have cost the famous Lord Napier.

Then Antonia, who only wanted to annoy me, went behind my chair, put her two hands over my eyes and said to me, ‘Now do your calculations, Señor geometer!'

These words of my aunt seemed to me to contain a real challenge. Having latterly used the tables a great deal, I had retained many logarithms in my memory and knew them by heart, as it were. Suddenly, I had the idea of breaking down into three factors the number whose logarithm I sought. I found three factors whose logarithms I knew, I added them up in my head and, quickly breaking free of Antonia's hands, I wrote out the whole logarithm without missing a single decimal place. Antonia was irritated by this. She left the room, saying somewhat discourteously, ‘What fools geometers are!'

Perhaps she wanted to raise the objection that my method could not be applied to prime numbers, which can only be divided by one. In this she was right, but what I had done proved none the less that I had a considerable facility with calculation and it certainly wasn't the moment to tell me that I was a fool. Soon after, her maid Marita arrived. She also wanted to pinch and tickle me. But her mistress's words still rankled and I sent her away somewhat peremptorily.

The thread of my story now leads me to a period of my life which was noteworthy for the new use to which I began to put my ideas, by directing them all towards a single goal. You will have observed that
in the life of every scientist there comes a moment when, having grasped some principle, he develops its consequences and broadens its applications or, as people say, he builds a system. At such times his courage and strength increase. He goes over what he knows and finishes acquiring the knowledge that he lacked. He considers every notion from all its aspects, which he brings together and classifies. And if he is unable to establish his own system or even to convince himself that it really exists, at least when he abandons it he is more knowledgeable than he was before he conceived of it, and he salvages from it some truths which had not been known before. The moment of system-building had come for me, and this was the occasion which gave me the first inklings of it.

One evening I was working after supper and had just finished a very complex piece of differentiation when my aunt Antonia appeared in my room, dressed in little more than her nightdress. ‘My dear nephew,' she said, ‘I cannot sleep while I can still see a light in your room. Since geometry is such a fine thing I want you to teach me it.'

As I hadn't anything better to do I agreed to do as my aunt requested. I took my slate and demonstrated to her the first two propositions of Euclid. I was about to pass to the third when my aunt tore my slate from me and said, ‘My clot of a nephew, hasn't geometry even shown you how babies are made?'

My aunt's words seemed absurd at first, but after some reflection I thought that she was perhaps asking me for a general expression which would cover all the modes of reproduction found in nature, from cedar trees to lichen and from whales to microscopic animals.

I remembered at the same time thoughts I had had about the smaller and greater mental capacities of every animal whose first cause I had found by investigating their procreation, gestation and manner of birth. In this case, the smaller or greater degree demonstrated to me the existence of increase and decrease, and this brought me back to the sphere of geometry. In the end, I conceived the idea of a particular notation for all the animal kingdom which might represent actions of the same kind but of different values. My imagination suddenly became inflamed. I thought I could glimpse the possibility of determining the geometric locus and the limit of every one of our ideas and the action which resulted from it. In a word, I thought I
glimpsed the possibility of submitting the whole system of nature to the process of calculation. Overwhelmed by the ideas which crowded in upon me, I felt the need to breathe more freely in the open air. I rushed out on to the ramparts and went round them three times without knowing what I was doing.

Eventually my brain slowed down and the day began to dawn, which gave me the idea of writing down some of my principles. I got out my tablets and, as I was writing, walked back along the path to our house, or what I took to be the path to our house. But it turned out that instead of going to the right of the corner tower of the rampart I went to the left and walked down into the moat by a postern gate. There was little light and I could scarcely see what I was writing. I was in a hurry to return home so I walked twice as fast, thinking that I was on the way back to our house, but instead I went along a ramp which had been formed to move out cannon if a sortie was to be made, and soon I found myself on the outer slope. Still thinking that I was on my way home, and still scribbling on my slates, I walked as fast as I could, but hurry as I might I did not get there, as I had taken the direction that led away from the town. So I sat down and began further calculations.