by Jan Potocki
I have learnt that you have a son. Perhaps I may be able to preserve for him the advantages of which the errors of my ways have deprived you. Meanwhile I have watched over his and your interests. The allodial estates of our house have always belonged to the younger branch. Since you did not claim them they have been combined with those intended for my establishment. But by right they belong to you. Alvar will hand over to you the income of the last fifteen years, and with him you must make whatever arrangements you think suitable for the future.
Reasons connected with the character of the duke have prevented me from making this restitution earlier.
Farewell, Señor Don Enrique. No day passes when I fail to raise my voice in penance and call down heavenly benediction on you and your fortunate wife. Pray also for me and do not reply to this letter.
I have already described to you the power which memory exercised over Don Enrique’s heart. You will not find it difficult to believe that this letter stirred them up again. It was more than a year before he could again take up his favourite pursuits, but the attentions of his wife, the affection he felt for me, and still more the general solution of equations with which mathematicians were then beginning to be preoccupied, together had the effect of bringing strength and peace to his soul. The rise in his income also allowed him to expand his library and his laboratory. He even managed to set up an observatory, which was very well equipped with instruments. I do not need to tell you that he indulged the philanthropic side of his nature. I can assure you that when I left Ceuta there was not a single individual in real distress because my father used all the resources of his genius to procure a decent subsistence for everyone. I could give you an account of all this which would, I am sure, interest you, but I have not forgotten that I undertook to tell you my story and I must not depart from the terms of my proposition.
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 pochettes1 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 conve
rsation.’
‘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.
As Velásquez reached this point in his story, he was interrupted by the cabbalist, who said that he still had important business to discuss with his sister, so we dispersed and everyone went his own way.
The Twenty-fourth Day
We continued our meanderings across the Alpujarras mountains and at last we reached our resting-place. After a meal had reinvigorated us, we asked Velásquez to carry on telling us the adventures of his life, which he did as follows:
VELÁSQUEZ’S STORY CONTINUED
My father wanted to be present at Folencour’s first lesson and wanted my mother to be there too. Encouraged by such signs of respect, Folencour quite forgot that he had passed himself off as a gentleman and discoursed at some length on the nobility of dancing, which he called his art. Then he observed that my toes were pointing inwards. He wished to point out to me that this habit was shameful and quite incompatible with the rank of gentleman. So I pointed my toes outwards and tried to walk in this way, even though it was against the laws of equilibrium. Folencour was not pleased with my attempt. He insisted, moreover, that my feet should point downwards. In the end, in a fit of spiteful impatience, he pushed me from behind. I fell on my nose and hurt myself badly. It seemed to me that Folencour owed me an apology. But far from giving me one he lost his temper with me and said the most disagreeable things, using turns of phrase of whose impropriety he would have been aware had he understood Spanish better. I was accustomed to being kindly treated by all the residents of Ceuta. Folencour’s words seemed to me outrageous and not to be tolerated. Proudly, I went up to him, took his pochette, smashed it on the ground and swore never to be taught to dance by anyone so vulgar.
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 Huygens1 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.
