Friday, June 14, 2013

Source of the Cipher 5: Nothing To It

            5. Nothing To It

            Namagiri briefly stopped pounding the laundry in the washbasin, sat up, and looked across the room. Ramanujan was still sitting there!
            “Dear?” she said. “You’re still working?”
            Ramanujan said, “So many sums... so much merchandise to count... each computation is fast, but reading and writing them all, one after another, that takes time. I am only one computer; that is what the Prince and the Sheik need to understand.” He scanned a tally, picked up some counters, and placed them on the board in front of him.
            Namagiri returned to her laundry. Shall I tell him yet, she wondered. Is there anything to tell? Almost eight weeks! But still, perhaps a false alarm. Perhaps she had merely skipped one. Wait a bit to be sure...
            She finished the load and set it aside. She was about to start the next bundle, but paused to look at Ramanujan. “Why... you’re still on the first stack!” Curious, she walked over to look down at Ramanujan, seated cross-legged at a board full of bins full of counters. Ramanujan scanned a tally, placed some counters in some bins, and moved counters from bin to bin. “What a funny game you are playing!”
            “It’s work, not play,” he said. “This is a counting board. Sit, Namagiri, sit beside me, I’ll explain it... thank you,” he said, as they leaned against each other. Ramanujan scanned a list and added counters to the counting board. “See that? This tally - ” - and he held up a piece of papyrus covered with tally marks -  “ - has two hundred and fify-four marks, so watch; I put two counters here, five here, and four here. See?”
            “I see! So these are ones, these are tens, these are hundreds?”
            “Just so. Ten counters in a place are worth one counter one place to the left.”
            “I see; so worth on the counting-board is mostly a matter of position?”
            “Just so.”
            “Like here in the palace?”
            “Just so.” And Ramanujan returned to his sums. He discarded one tally and picked up the next one in the stack. Namagiri inspected the discarded tally.
            “What is this strange stuff?” she asked.
            “It is called papyrus,” Ramanujan said. “From far Egypt. Very useful in holding records and tallys. Our guests have consented to trade one plus twelve dozen dozen sheets for equally many drams of curry.”
            “One plus twelve dozen dozen! Why does the Prince want so much papyrus?”
            “He wishes to record all our laws and treaties and accounts; so he got that much just to make sure it was enough.”
            “One plus twelve dozen dozen sheets should suffice for any sensible task.”
            “Just so,” Ramanujan said. “And dear? perhaps you can help me. Sit here... yes. I’ll call out the numbers, you place the counters...”
            Ramanujan and Namamgiri changed places; she placed counters as Ramanujan called out, “One hundred and fifty-six... yes... three thousand four hundred and twenty-five... fifty-six... now, take out ten from there and put one over there... yes... six hundred and forty-one... eleven... five hundred and fifty... yes, no ones... four hundred and two...”
            “No tens?”
            “Just so. One hundred and sixty-nine...” And so it went; soon they finished the first count. Ramanujan read the counting board, then wrote on a blank sheet of papyrus:
                        Seventeen thousand, four hundred and sixty-six.
            “What are those strange marks, dear?” Namamgiri asked.
            “Words, of course. I know you can’t read them...”
            “No, not those squiggles! These squiggles!”
            “Oh! They are digits.” Ramanujan blushed. “Really I should spell them out in full, but it’s shorter this way... I’ll write these figures out properly once I’m done.”
            Namagiri glanced from record to counting-board and back again. “So that is a one,   that is a seven,  that is a four,  those are sixes.”
            “Just so,” Ramanujan said. He turned aside from the counting-board, picked up a small bright object, and started manipulating it.
            Namagiri stared at it. “What are you doing with that baby rattle?”
            “So that’s what it is.” Ramanujan held the toy up. Glass beads slid on wires strung on a wooden frame. “I thought it was a glass-bead game. The caravan trader didn’t say.”
            “And what are you using a glass-bead game for?”
            “As a counting board. See? One of these beads equals ten of these... we can do the exact same kind of arithmetic.”
            Namagiri looked at the baby rattle, then at the counting board, and back. She laughed. “Leave it to you to see these as one and the same!”
            “I was thinking of getting a few more glass-bead games. No more than twelve...”
            “Twelve!” Namagiri exclaimed. She stood up and said, “Sure, let us have a dozen dozen dozen sheets of papyrus and a dozen baby rattles to count them with.” Then she walked across the room, squatted at the washbasin, and started the second laundry load.
                        *                      *                      *
            The next day was the eighth week. Namagiri was almost certain, but wanted to wait just a bit longer before telling him anything.
            As before, she was doing laundry (quickly) and he was doing sums (slowly). “I am only one computer,” he complained. “Even with all these ‘abaci’-” and he indicated the dozen baby rattles surrounding him on the floor.
            “What an odd name!” Namagiri said.
            “That’s what the Lady Nan-See calls them. Even with more than one abacus, I can only do one arithmetical operation at a time!”
            “Poor dear. I would help you if I could-”
            “Thank you! Come over here... good! I’ll call out numbers, you compute! Do you want the counting board?”
            “No, I’ll take an ‘abacus’,” Namagiri said while picking up a baby rattle. Ramanujan called out numbers and Namagiri manipulated beads. It was a relaxing break from laundry-pounding; and she had been feeling out of sorts lately.
            Soon Ramanujan was recording their calculations. “If only you could help with this part! It all has to go through me,” he complained. “You see, dear, counting-board and abacus solve only half the problem. We have to record our results, so that others can do more sums on them!”
            “Perhaps we could just keep the numbers on the abacuses?”
            For answer Ramanujan tilted an abacus. Beads rattled down. “Too unstable for records. It'll never do to have envoys carry baby rattles about! And so I am forced to write it all out in longhand!” He wrote:
                        6 myriads, 8 thousands, 3 hundreds, 4 tens, 7 ones.
            “What is that word? I sort of recognize the others...”
            “‘Myriad’, dear. Meaning ten thousand.” Ramanujan sighed. “Each power of ten needs its own number-name. There’s no end to it.”
            “But why do you use words?” Namagiri said. “You know I can’t read them! And neither can our Arab partners.”
            “And we are as illiterate in Arabic as they are in Sanskrit,” Ramanujan said. “And so it all comes back to me! I have overheard the Sheik complaining...”
            Namagiri smiled. She knew all about overhearing complaints.
            Ramanujan continued, “He was scolding the Prince. Scolding him, mind you! He said, ‘One single genius will not suffice for our needs!’ He said, ‘My clerk, the rabbi Shmuel ben-Tennon; is he a genius? No! But he is hard-working, and he is systematic, and systematic work will serve when inspiration flags!’ He said, ‘We need an army of fools, and a way to organize these fools into something effective!’ And so I have been wondering...” Ramanujan stopped calculating, and said to Namagiri, “Could we record these calculations... by drawing  pictures of the counting board?”
            “Pictures? Too cumbersome,” Namagiri judged.
            “But you see, that is how I do it. With pictures in my head.”
            “What if you just used digits? No number-names?”
            Ramanujan stared at the counting-board in front of him. “So this number in front of me... I write it as six eight three four seven?”
            “That’s what’s on the counting-board, after all!”
            “Interesting idea. Perhaps you can help me out. I’ll call the digits, you write them.”
            “I would be glad to; but first show me how to draw the digits.”
            “There are nine in all. They look like this.” And Ramanujan wrote down nine symbols. “This is the One,” Ramanujan said earnestly, drawing the digit. “Here is the Two. Here, the Three.” And so on; he went doggedly, step by careful step, from one to nine. “And those are all the digits,” he concluded. “Let’s get to work. Write the numbers in columns, like I did over here. Ready? Good.” He scanned a tally. “Six hundred and twenty-one.” Namagiri wrote a tremulous 621. “Good! Four seven nine. Good. Three one four two. Eight nine nine three. One one one...”
            After a few minutes the tallys were recorded. Namagiri looked over the list and said, “You know... I could sum these up for you.”
            “On the counting board, of course. You showed me how yesterday, remember? And I’ll record them for you, the same way.”
            “Why, thank you, darling! For all that writing was making my arm sore.”
            “But in turn you must do some work for me.” And Namagiri pointed to the laundry basin.
            “You mean... let’s swap counting-board and washbasin? Sure! Washing is easy!”
            “And summing is work? For you, perhaps,” said Namagiri. “For me it is the other way around.” And she started playing with the counters. Namagiri shuffled counters, Ramanujan pounded laundry; a change of pace for both.
            Soon both were done. Namagiri jotted down the final sum, then handed the sheet to Ramanujan. She said, “You know, if you just used digits and never number-names, then I could help you all the time, and we’d get your work done faster.”
            “What an interesting idea,” Ramanujan said. “Numbers using only nine digits!”
            “Tell Prince and Sheik this idea,” she urged. “Make a point of how important position is for these numbers. One counter is worth ten counters of the rank below! I’m sure that both Prince and Sheik will understand that part right away.”
            “I will try it,” Ramanujan promised, gathering up papyruses and abacuses. “Oh... and dear? Later this week, could you help me do...”
            “Some more tallies?” Namagiri sighed. “Yes.”
                        *                      *                      *

            The next day, it was eight weeks and a day; two cycles missed. There was no question about it anymore; so Namagiri resolved to tell.
            But Ramanujan was too upset to hear anything just yet. “Disaster, dear!” he cried. “I tried to show Prince and Sheik the nine-digits positional system, but it failed!”
            “What went wrong?”
            “The Prince was agreeable to all my suggestions, as ever.”
            “He is Prince Rahni to his friends, which means practically everybody.”
            Ramanujan nodded. “But the Sheik was critical. He asked me these sums; fifty-four plus one hundred forty-nine; one hundred thirteen plus one hundred seventeen; and twelve plus eleven!”
            “And what of it?”
            “Why, try these sums yourself!” So Namagiri sat at the counting-board and proceeded to add 54 to 149. “See?” Ramanujan said when she was done. “A blank column in the middle, between a two and a three! Now try one-one-three plus one-one-seven!” Namagiri did so. “See that? Now the blank column is on the end! Two-three-blank! And eleven plus twelve makes two-three, no blanks at all!”
            “I see all this; and what is the trouble?” Namagiri asked, then said, “Oh. How do we write these down?”
            “How do you write them down!” Ramanujan exclaimed. “For look!” He wrote:
                                    2    3
                                    2 3 
                                       2 3
            “Which is the two-blank-three, which is the two-three-blank, and which is the blank-two-three? That is what the Sheik asked me.” Ramanujan shook his head. “The blanks are invisible! I was unable to answer, so he dismissed me.  He told me to come back when I've got something.”
            Namagiri stared at the counting board.
            “This is so frustrating!” Ramanujan exclaimed. “So close yet so far! A tiny little problem like this, and we are back to me writing longhand!”
            Namagiri stared at the empty column. “This is not a tiny problem. It is no problem at all.”
            “Yes, and this no-problem stops everything!” Ramanujan cried. He paced back and forth. “If only there were some elegant, simple way to count and calculate; but what is it?”
            Namagiri continued to stare at the empty column.
            Ramanujan said, “It is as if there were something too clear, something too obvious, that we're all missing, right in front of our noses, but we don't notice it. But what is it?”
            Namagiri looked up. “You mean... you really don’t see it? How odd!”
            “If you can see something that I do not, please tell me!”
            “No, it is not something...” she said. “More like nothing.”
            “So you see nothing too.”
            “Yes. No. Yes. No. I see something, but it’s really a kind of nothing.”
            Ramanujan stopped pacing. “What?”
            Namagiri indicated the empty column. “There is nothing in here, right? No counters? Yes. And you need to number how many counters are in each column, yes? So you need to number how many counters are in this empty column.”
            “But what number is that? There are no counters.”
            “The counters are missing; very well! But a number is missing, too; the one to fill these blanks.” Namagiri tapped the paper with the 2's and 3's. “You need a new digit; one indicating an empty column.”
            Ramanujan looked puzzled. “A digit for counters that aren’t there?”
            “Call it a placeholder; a way to keep the places straight. But yes, you can call it a number for nothing,” she said. “It counts the void.”
            “A new number...” Ramanujan sat down. He contemplated the idea awhile. Then he said, “But what are we to call this void number?”
            “ ‘Void’ is as good a name as any,” she replied; and since they spoke in Sanskrit, they used the Sanskrit word for void, which is ‘Sunyata’.
            “And how are we to write this Sunyata-digit?”
            Namagiri picked up a pen and drew a tiny circle. “There. Small. Round. Unnoticed. Invisible. Like me.” She smiled. “Tell the Sheik that we have something better than Something; namely, Nothing.”
            Ramanujan said, “And why should he listen to nothing?”
            “And why not?” Namagiri replied. “Doesn’t he have most of his trouble with nothing? The money that he doesn’t get, the goods that aren’t there? And doesn’t he live with nobodies doing nothing, all the time?”
            “Nobodies such as you and I?”
            “Just so!” Namagiri replied. “Prince and Sheik would multiply themselves by ten, by a thousand, by a million! Therefore they should seek sunyatas. Quiet, transparent, ignored; this placeholder is emptiness, but it means multiplication times ten.”
            Ramanujan said, “This Sunyata is nothing, but it is no ordinary nothing.”
            Namagiri said, “It is a fertile void.” She paused. She might as well tell now. “Like me.”
            Ramanujan’s eyes widened. “Why, why, darling, what do you mean?”
            She mused, “How convenient that you bought all those baby-rattles. We shall be needing them soon.” Namagiri patted her belly and said, “It has been eight weeks and a day since my last period. Two cycles missed. Do you understand?”
            Ramanujan understood. He leaned over and kissed her belly.

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