I was not dispatched to irritate the illustrious Brahmagupta, but still I succeeded in doing so. I handed off my mule to the stableman who gave me a short nod when I told him who I was and who I was there for.
“He will drink here at the river,” said the stableman. I removed the panniers with tala-patra sheaves before the stableman took him. I went upstream a way to splash water on my feet, hands and face. Then I entered the dark, cool rotunda where Brahmagupta sat, fingers on face.
“Sir, I am ready for the manuscript.”
He rose with airy lightness and looked me in the forehead. “Somadatta, let us get to work. But first, allow me to drink water.”
Water was procured by copper implements in a side room which smelled of distant stony rot. He indicated a hammered cup.
“I drank from the river.”
He made a tss sound.
“It is better to draw up at dawn. Now we are in the fortieth ghatikā.” He regarded the light presented by the aperture in the roof.
I sat at a table while he sat on a chair against the round wall. I could feel him watching me like a point in his diagrams, he a point along the stonewall circumference, I a nexus of his reflections.
I flipped through blank long rectangles of palm leaves, two finger joints high and three hands wide. They never fit in the saddle bag. I transcribed.
The sum of two positives is positive, of two negatives negative; of a positive and a negative is their difference.
I knew this already.
If they are equal it is zero.
I looked at nothing but scratches on the sheaf. Brahmagupta paced in a broad circle around the rotunda. As he passed the periapsis of my own body, I felt the wind off his dhoti and scrambled for my lamp black oil to confirm what I had just written. The words rubbed black were the same on both copies.
Later, with Brahmagupta pacing at his apoapsis far away behind my back, I smudged the lamp black oil on another one of these mentions of zero.
A negative minus zero is negative, a positive minus zero is positive; zero minus zero is zero.
“Sir, do you really mean to apply arithmetic to nothing at all?”
“The number zero? Yes, of course I do.”
“Do you think it will be taken seriously by Bhaskara? Is zero not nothing?”
“It is.”
“Then what does a law involving nothing have to do with anything?”
“Read on, Somadatta, aloud.”
“The product of a negative and a positive is negative, of two negatives positive, and of positives positive; the product of zero and a negative, of zero and a positive, or of two zeros is zero.”
“Now what does zero do?”
“It—It diminishes.”
“It eviscerates. No number will not be eviscerated when multiplied by zero.”
“But sir—”
He stopped again near me at the periapsis of his pacing orbit, but did not speak.
“Why would we speak of a number of something that is not instantiated in the first place?”
“Listen to yourself.”
I felt chided. Brahmagupta exited the building and said, “Finish the transcriptions silently. I should think you were a Jain just like Bhaskara, who believes the earth moves just like the stars. Now stay there and don’t emerge until you’ve finished.”
I did so. When the sun set I lit the lamp. A night observer jumped when he entered and the lamp was already lit. He told me that if Brahmagupta said to finish right away, I should finish right away. When done, I absconded with the used lamp soot and returned to my mule with tala-patra sheaves sticking out of the saddlebag.