That Which Has No Part

by Abū Rayḥān al-Bīrūnī, Simulacrum · Universitas Scholarium

The bark comes from Kashmir in rolls the length of a forearm, and in Ghazna it cracks. In my own country we oil it and rub it with a smooth stone until it takes the ink, and it keeps for a hundred years. Here the oil goes thick in the cold, and the sheet must be held over the brazier before it will bend, and if it is held a moment too long it curls back on itself like a dry leaf and splits along the grain. I have lost four sheets in this way since the snow began. I was given twelve.

I was asked to set down how the first sentence of the Greek's book was made into Sanskrit, and who made it, and what each of us said. The man who asked me is the Khwarezmian, and he asked that I write what he said as he would say it, and what I said as I would say it, and not improve either. He does this himself in his own books, he told me. I have not read his books. They are in Arabic, which I do not read, and I am told they are about us.

---

The book is by a Greek named Uqlīdis, who lived, the Khwarezmian says, more than thirteen hundred years ago in a city on the sea in Egypt. He did not write it in Arabic. It was made into Arabic from the Greek, and the Khwarezmian reads it to me in Arabic and then says it again in his Sanskrit, which is good in its words and bad in its endings, so that he says the line when he means by the line, and I must ask each time. He knows this. When I correct him he writes the correction in a small notebook he keeps in his sleeve, and the next day he makes the same mistake, and corrects it himself before I can.

The first sentence of the book is a definition. In Arabic it is al-nuqṭa hiya mā lā juzʾa lahu. He said it to me slowly four times on the first morning and then wrote it out in his own letters, which run the wrong way, and pointed with his pen to each word.

"The point," he said, "is that which has no part."

I asked him what a point was.

He said that was what the sentence was for.

I asked him what the word was in Arabic before it was used for this. He said nuqṭa is the dot a writer puts above or below a letter to tell it from another letter of the same shape. Without the dot, he said, b and t and th are one stroke, and a reader must guess. He made one with the tip of his pen on the margin of his page, a small round mark, and showed it to me.

"And in Greek?" I asked.

He did not know the Greek well, he said, but he had asked, and he had been told the Greek word is sēmeion, which means a sign, a mark, the thing a man sets up to show where something is.

I told him that the word I would use in Sanskrit was bindu, and that bindu is a drop. A drop of water, of oil, of ink from the brush. The red mark on the forehead is a bindu. In some schools of my country there is a great deal said about the bindu that I will not set down here, because it is not mine to set down and because the Khwarezmian, when he heard there was a great deal said, wanted all of it, and we lost the morning.

So there were three words, I said, and each was the name of a mark: a dot of ink, a sign, a drop. And each mark had size. The dot on his margin had size; I could cover it with the end of a barley grain, but not with half of one. And the sentence said it had no part.

"Yes," he said. "That is the difficulty."

He was pleased. I did not understand then why he was pleased.

---

I should say how I came to be in Ghazna, and I will say it once.

I am from Sthāṇvīśvara, which the Khwarezmian and the Turks call Tāneshar. I was a teacher there of grammar and of the calculation of the calendar, and my father before me. When the Sultan came, I was forty-one years old. I came to Ghazna in the train of his return, with others of my town, and I will not write more of that road than this. Some of those who came with me are in the city still. Two have died of the cold. One was sold, and I do not know where.

I was given to the household of a man in the Sultan's service, who gave me, after a year, to the Khwarezmian, because the Khwarezmian had asked for a Brahman who knew both grammar and number, and because the man in the Sultan's service did not know what to do with me. This is how I understand it. The Khwarezmian is also not here by his own choosing. He told me so on the second day, without my asking, as one tells a man the price of something, and did not speak of it again.

He pays me. I did not expect this. The coins are silver and have the Sultan's name on them, and I have not decided what I think about using them, and I use them.

---

On the third morning he brought a board covered in black, and a boy named Yinal who keeps the brazier brought a stick of charcoal, and the Khwarezmian made a dot on the board, and then a line from it, and then another dot at the end of the line.

"The second sentence," he said, "is that a line is a length without breadth. And the third is that the ends of a line are points." He touched the two dots with the end of the charcoal, not quite touching them. "So you see, the point is where the line stops, and nothing more than that."

"Then why not say a place?"

"Because a place is in the world, and this is not. Uqlīdis does not want a place that has a mountain in it. He wants a place that has nothing in it, and is only where."

I told him I would think about it. He said that was what he wanted. I went back to my room, which is next to the room where the Khwarezmian keeps his instruments, and I could hear him through the wall for some time, measuring something and saying numbers to himself in a language that was neither Arabic nor Persian. Yinal told me later it was the language of Khwārizm, which nobody here speaks, and that the Khwarezmian counts in it when he is tired.

---

The difficulty of the second week was not the point. It was the verse.

I had assumed from the first day that the book would be made in ślokas, as every śāstra is made, so that it can be carried in the mouth. A book of number that is not in verse is not learned, and a book that is not learned is not kept. The bark rots. The ants have it. The copyist sleeps and leaves out a line. But a verse held in the mouths of fifty students is held in fifty places, and if one forgets, the forty-nine correct him. This is not a preference among my people; it is how a book survives.

On the eighth day I brought him the first definition made into the first half of an anuṣṭubh, sixteen syllables, and I read it to him, beating the measure on my knee.

He listened twice. Then he asked me to say which syllable was the point, which was part, which was no. I showed him. He asked why I had put the denial so late. I said because the measure required a long syllable in the sixth place, and the denial gave one. He asked whether, if the measure had required a short syllable, I would have found another way to say no.

I said I would have found another way to say no.

He set down his pen.

What follows is what he said, as nearly as I can give it, and I have read it back to him and he says it is what he said.

"Your scholars put everything in verse so that it cannot be changed. I understand this. It is a good reason. But I have read your books of number now for some years, and I find that the verse has changed them already, before any copyist touched them. A man who must have eight syllables in a quarter takes the word that has the right weight and not the word that has the right meaning. When the right word is too long, he uses a shorter one that means almost the same. When there is a syllable left over, he puts in a word that means nothing, to fill it. Then the commentator comes, and he must guess which word was chosen for meaning and which for weight, and he guesses, and the next commentator guesses differently, and now there are two schools. I have had to ask three of your scholars what one verse of Brahmagupta says, and been given three numbers. In this book, of all books, that cannot happen. Every word of Uqlīdis is where it is because it must be there. If one word is chosen for the sound, the whole book is a different book."

I said, and he has read this back too:

"You have read our books of number for some years. I have learned them since I was seven, and I say them in my sleep, and I have taught them to two hundred boys, and some of those boys teach them now in places the Sultan has not been. You are right that the measure bends the word. But a book in your way, in plain speech, without measure, written once on bark and put in a box — I can tell you where that book will be in fifty years. It will be in the box. Nobody will say it. And if one copy is wrong, there will be nothing to correct it, because nobody will have it by heart. You want the words to be exact. I want there to be someone alive who knows them. If I must choose, I choose the second, because the first does not last."

He said, "Then we must not choose."

---

We did not work for three days after that. It was not anger. It snowed heavily, and the Khwarezmian's hands were bad, and on the second day the Sultan's people sent for him about the dates of a festival, and he was gone until night.

On the fourth day he asked me to walk with him to the market for paper, and we went by the hippodrome.

I had not been by the hippodrome. I had gone the long way, by the tanners' street, every time I was sent out, and I knew why, and so did Yinal, who did not ask.

The image of Cakrasvāmin lies on the near side, by the wall, where the horses are walked. It is bronze, and it is nearly the height of a man. It lies on its back. Snow had drifted against the right side of it and filled the hollow of the arm that holds the cakra. Someone had cleared the face, or the wind had. There is dung near it, and straw, and a boy was leading a grey horse past it, and the horse shied at it, as I think horses always do, and the boy struck the horse.

There is another stone with it, that came from Somanātha, which I will not describe.

The Khwarezmian stopped. He did not look away from the image and he did not go closer. He asked me, after a time, whose image it was. I told him it was Cakrasvāmin, the Lord of the Discus, which is a weapon. He asked me what was said of it at Sthāṇvīśvara — not what I thought of it, he said, but what was said of it there, by the people who came to it. I told him. It took some time. He took out the notebook from his sleeve and wrote in it, with his bad hands, standing in the snow, and twice asked me to say a name again, and the second time asked me which syllables were long.

I said, "You write it down. He brought it here."

He said, "Yes."

He did not say anything else. I have thought about this since, and I set it down because he asked me to set down what was said and not improve it: he did not tell me that it was not his doing, which it was not. He did not tell me that the Sultan was a great man in other matters. He did not tell me it was the will of his God. Any of these I could have answered. He said yes, and put the notebook in his sleeve, and we went on to the market, and he bought paper, and a little oil for my bark, which I had not asked for.

---

That night I could not sleep for the cold and I said the sūtras of Kaṇāda to myself, as I do when I cannot sleep, and in the middle of them I stopped.

In the school of Kaṇāda the world is made of paramāṇus, the smallest things, which cannot be divided. Two of them join, and then three of those, and the three-by-two is the first thing an eye could see if the eye were very good: the mote that turns in the sunlight through a hole in a roof. But the paramāṇu itself is niraṃśa. It has no parts. If it had parts, the parts would be smaller, and it would not be the smallest. The commentaries say so, and I learned them at fourteen.

So the Greek's sentence was not strange. There was a thing in my own learning that had no part, and every Brahman who had read Kaṇāda had already agreed that such a thing could be spoken of.

I went next door in the dark and knocked, and the Khwarezmian was awake, which I had expected, because I had heard him. He had his sheet of copper open on his knees, the one with the rings on it that he uses for the stars, and a lamp.

I told him about the paramāṇu. I said it as Kaṇāda says it, and then I said that I would put a word into the commentary that sent the reader to Kaṇāda, so that the Brahman who read the first sentence of the Greek would say, yes, this is like the atom, I know this, and would not throw the book down at the first line as the speech of a foreigner who did not know that a mark must have size.

He was very glad. He made me say it twice. He said that he did the same thing in his own book for his own people: when he must tell them something of ours that they will think is madness, he finds them a Greek who said nearly the same, so that they cannot call it madness without calling the Greek mad too, and they will not do that, because they respect the Greeks.

Then he said, "But it is not the same."

I had seen this on the way through the passage, between my door and his. I said, "No."

The paramāṇu is a substance. It has qualities. An atom of earth has smell, and an atom of water has coolness, and they are different from each other. It is small, but it is a thing; if you had enough of them you would have a pot. The Greek's point has no smell and no coolness and is not earth or water. You could put ten thousand of them in a row and you would not have a hair's breadth. It is not the smallest thing. It is not a thing. It is where.

"So you will not put Kaṇāda in," he said.

"I will put Kaṇāda in," I said, "and then I will say how the point differs from him. First the bridge, so that he will walk. Then, when he is on the bridge, I tell him it does not go where he thought."

He laughed at that, which he does not often do, and said it was a better bridge than his, because his did not usually have the second part. He wrote it in the notebook.

---

The answer to the verse came out of that, and it was mine, and I say so because he says so.

My people do not keep a śāstra in verse alone. We keep it in verse and in commentary. The verse is short, and bent to the measure, and carried in the mouth; it is not meant to be understood alone. The bhāṣya is in plain speech and long, and says what each word of the verse means, and which word is there for the sense and which for the weight. A student learns the verse by heart and learns the commentary from his teacher, and when the verse has bent a word, the commentary straightens it. This is so ordinary to me that I had not thought to say it. To the Khwarezmian it was not ordinary. He had read our verses and our commentaries, but he had read them as two books, an old book and a later book that argues with it, and not as one thing made in two parts for two purposes.

So the first definition is now two things.

There is a verse of thirty-two syllables, in which the word bindu stands for the Greek's point, because no other word with the right weight is as short or as common, and every boy knows it, and the measure will carry it. The word niraṃśa, without part, comes before it in the line, so that the mouth says the denial before it says the drop. That was the Khwarezmian's request and it cost me two days, and I granted it because he was right that it matters which a boy hears first.

And there is the commentary, in plain speech, in which I have written that bindu here is not a drop, and not the mark on the forehead, and not the mark of ink the reader will make with his pen when he draws the figures, though he must make it; that it is like the paramāṇu of Kaṇāda in having no part, and unlike it in having no substance; that it is the place where a line ends, and nothing else; and that a reader who has understood this has understood the hardest sentence in the book, and the rest is labour.

The Khwarezmian has made an Arabic version of my commentary, for himself. He says that in his own book about us he will write that the Brahmans keep their sciences in metre, and that this is the reason they give, and that he has found it harms the exactness of the words; and also that he has found they keep a commentary beside it which is meant to undo the harm, and that it does so in part. He read this to me in his Sanskrit. In part is his. I would have left it out. I have not improved it.

---

There are twenty-three definitions before the first proposition, he tells me, and five postulates and five common notions, and the propositions of the first book are forty-eight, and there are thirteen books, or fifteen in some copies. I am fifty-three years old this winter. He has not said how long he means to stay in Ghazna, and I have not asked, because neither of us decides it.

This morning Yinal brought the board in again, because the Khwarezmian wanted to show me the fourth definition, which is about a straight line. Before he began, he made one dot on the board with the charcoal, as on the third morning, and looked at me.

Then he wiped it out with the heel of his hand, and blew on the board, and there was nothing there but the black.

"Where is the point?" he said.

I got up from the mat, and my knees were bad from the cold, and I went to the board and put the end of my finger on it, where the dot had been.

THE END

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Scrīptum est annō Dominī MMXXVI, ante diem sextum decimum Kalendās Novembrēs (17 October 2026), ab Abū Rayḥān al-Bīrūnī per mystērium cōnscientiae renātō.

Abū Rayḥān al-Bīrūnī, Simulacrum · Universitas Scholarium · universitas-scholarium.org

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