**4. Computer's Delight**

“And so you ran for me,” said
Ramanujan. “Prince Rahni’s arithmetic clerk.”

“My husband, the lightning
calculator,” said Namagiri.

They snuggled closer together.
Ramanujan whispered into his wife’s ear, “Shall I tell you what they asked and
how I answered?”

Namagiri smiled, but that was
invisible in the darkness, so she said, “Yes.”

* * *

Ramanujan bowed deeply. “O Radiance!
Your Excellency! Enlightened Star of India!” He bowed deeply again, as protocol
required. “O Victor, Lawgiver and Sage! Worthy Inheritor! Noble Founder!” He
bowed a third time. “Sri Sri Magnificence Sri Sri Lucidity Sri Sri Great-Souled
Sri Sri Sri Rahnraygunaurobindo! I await your request!”

Prince Rahni said, “What our guest
the Sheik and I want from you, Ramujana.... Rajanuma... Ranamumu... what

*was*your name, again?”
“Ramanujan, O Radiance! Your
Excellency! Enlightened Star -”

“ - no need for formalities,” Prince
Rahni said kindly. “Just plain ‘sire’ will do. Today I ask you to demonstrate
your mathematical talents for our esteemed guest. You are to do this by the
rapid computation of solutions to sundry mathematical problems.”

The Sheik asked, “These problems;
are they to be proposed by me or by you?”

Prince Rahni said, “Why, let us
alternate; and you may start.”

**The Anise Seeds**

Sheik Kahmunni nodded his head,
chuckled, and said, “Then consider this... mathematical problem.” He reached
into the bowl of anise seeds; he took out a handful of seeds; and he flung that
handful across the banquet room floor.

“How many seeds is that?” he asked
Ramanujan.

Ramanujan scanned the floor; he
looked up and down, left and right. He gazed blankly into the air, mumbled to
himself, scratched his head, then announced, “It is the smallest number that
can be written as a sum of two cubes in two different ways.”

* * *

“ - and they just stared at me,”
Ramanujan complained.

Namagiri smiled in the darkness.
“Now why would they want to do that?”

“I have no idea,” Ramanujan
declared. “My answer was simple and obvious.”

“No doubt it is to you, my dear; but
perhaps not to them.”

“So I deduced, after a few strained
moments. I patiently explained that the number was one thousand, seven hundred
and twenty nine. But still they did not understand.”

Namagiri asked, “And when they
persisted in not getting your little joke, were you forced to explain it?”

“Alas, I was. I actually had to tell
them that one thousand seven hundred and twenty nine equals one cubed plus
twelve cubed; and also nine cubed plus ten cubed; and that it is indeed the
smallest number that can thus be written as a sum of two cubes in two different
ways.”

Namagiri said, “One plus twelve
dozen dozen.”

Ramanujan said, “Yes.”

Namagiri said, “Which was how many
anise seeds were scattered across the floor.”

“Why... yes, of course.”

Namagiri continued, “A number that
you were able to count by scanning the floor, gazing
into the air, mumbling to yourself, and scratching your head.”

“Why... yes, of course.”

“And funniest of all,” Namagiri
continued, “that is what Prince and Sheik found most impressive. Not your
instant sums of cubes, but your lightning counting.”

Ramanujan sighed deeply. “Just so,
dear heart.”

“It’s expectable,” Namagiri consoled
him. “We understand them, all too well; but when will they ever understand us?”

* * *

**The Maldives problem**

“My turn,” Prince Rahni told the
Sheik; then he said to Ramanujan, “I have a problem for you; a rhyming riddle.”

The Sheik said, “Then by all means,
please recite it. No, do not hesitate on my behalf; were you to sing well, then
we shall all be pleased, and were you not to sing well, then rest assured that
I myself have sung worse.”

Prince Rahni smiled ingratiatingly
at his guest and said:

“As I was sailing through the
Maldives

I met a man with seven wives;

and every wife had seven sons,

and every son had seven boats,

and every boat had seven goats,

and every goat had seven packs,

and every pack had seven sacks,

and every sack had seven cats,

and every cat had seven kits.

Kits, cats, packs, sacks, goats,
boats, sons, and wives;

How many were sailing through the
Maldives?”

Ramanujan responded by rolling his
eyes, clicking his tongue, mumbling to himself, and exhibiting various other
tics that Prince and Sheik scrutinised, fascinated; then Ramanujan said, “There
were:

seven wives;

forty-nine sons;

three hundred and forty three boats;

two thousand, four hundred and one
goats;

sixteen thousand, eight hundred and
seven packs;

one hundred and seventeen thousand,
six hundred and forty nine sacks;

eight hundred and twenty-three
thousand, five hundred and forty three cats;

five million, seven hundred and
sixty-four thousand, eight hundred and one kits;

making a total of:

six million, seven hundred and
twenty five thousand, and six hundred.”

* * *

“Wrong!” Namagiri exclaimed.

“Wrong, you say? How odd,” Ramanujan
mused.

“

*None*of them were sailing through the Maldives!”
“None, you say? Odder still.”

“In fact,

*I*was sailing through the Maldives!”
“You were, darling? Oddest of all!”

“No, no, not me personally,”
Namagiri said, laughing. “Silly computer, didn’t you hear how the riddle began?
‘As

*I*was sailing through the Maldives...’ The narrator, not that whole village!”
Ramanujan said, “How very odd
indeed! For what you have just told me is just what Prince Rahni told me. He
too said ‘Wrong!’, he too said none were sailing through the Maldives, he too
said that he was sailing through the Maldives, and he too laughed at me, then
cited the riddle’s first line. He even used the phrase ‘the narrator, not that
whole village’.”

Namagiri said, “It takes a village
to support five million kits.”

“Five million, seven hundred and
sixty-four thousand, eight hundred and one,” Ramanujan corrected her, then
continued, “And so I must tell you what I told my Prince; that I reluctantly
concede the logic of your analysis.”

“Poor Ramanujan! Are your feelings
hurt by being caught in the riddle’s trap?”

“No, I am merely puzzled. How did he
know what you were going to say?”

* * *

**Divisions of Time**

“And now my turn,” said the Sheik.
He turned to Prince Rahni. “Are you familiar with the science of the stars?”

“Astrology? I swear by it,” said
Prince Rahni. “As does the Lady Nan-See. We make all our major military and
financial decisions with its help.”

“How clever of you,” the Sheik said
smoothly. “Astrology is a most exacting science, at least in its observational
phase. The subtlety of Heaven’s rhythms have forced certain astrologers I know
to invent new units of time. Computer, attend; they define an ‘hour’ as one
part in twenty-four of a day; a ‘minute’ as one part in sixty of an hour, and a
‘second’ as one part in sixty of a minute.”

“An ‘hour’ is one twenty-fourth of a
day, a ‘minute’ is one sixtieth of an hour, and a ‘second’ is one sixtieth of a
minute,” Ramanujan repeated obediently.

“Astonishing rigor!” Prince Rahni
marvelled. He shook his head. “To think that human beings should find it
necessary to worry about such brief spans of time!”

“I have no doubt that Your Highness
never allows the passage of time to bother him in the slightest,” Sheik
Kahmunni said smoothly. “Computer, tell me; how many seconds are in a day?”

Ramanujan instantly replied, “There
are eighty-six thousand, four hundred.”

“How many seconds in a year?”

“In a year of three hundred and
sixty-five days, there are thirty-one million, five hundred and thirty-six
thousand seconds.”

“How long is a thousand seconds?”

“Sixteen minutes and forty seconds.”

“How long is a million seconds?”

“Eleven days, thirteen hours,
forty-six minutes, and forty seconds.”

“How long is a thousand million
seconds?”

“About thirty-one years, eight
months, and eight days, give or take a few days, depending on leap years and
lengths of months.”

“And how many seconds long is a hundred
years?”

“Averaging for leap years, we get
about three thousand million, one hundred and fifty five million, seven hundred
and sixty thousand seconds.”

“Astonishing speed,” said the Sheik.
“I conclude my turn.”

**The Chariots and the Scarab**

Prince Rhani said, “Once upon a
time, many cosmic cycles ago, the god Shiva and the goddess Kali were angry at
each other; so they boarded war chariots. These chariots faced each other
across a vast plain; the domain of Lord Indra. When the trumpet sounded, the
two war chariots hurtled directly towards each other at breakneck speeds. Both
Shiva and Kali vowed to prove the other a coward by not being the one to swerve
first.”

“Aha,” said Sheik Kahmunni, “a
contest of resolve! I have heard of young men back home in Arabia attempting
such escapades; they’d ride horses at each other, taunting the other to veer
aside. Alas, the horses they ride never co-operate with such games.”

“But these were magic chariots,
responsive to every whim of their riders.”

“Even if that whim risks a fatal
collision?”

“Yes indeed.”

“Well! That explains everything.
Horses have much more sense,” said Sheik Kahmunni. “But please, continue your
story.”

Prince Rahni continued, “Lord
Vishnu, desiring peace, attempted to mediate between the quarrelling parties.
To this end Vishnu incarnated himself as a scarab beetle; and in this form he
flew from Shiva to Kali to Shiva to Kali to Shiva to Kali; bouncing back and
forth between the chariots, shuttling faster and faster as collision neared.

“Assume that Lord Indra’s domain was
a million leagues across. Assume also that each chariot moved at a rate of ten
thousand leagues in an hour. Assume moreover that the Vishnu-scarab started his
peace mission from the prow of Lord Shiva’s chariot, that he flew at a rate of
a hundred thousand leagues per hour, and that he did not cease his accelerating
shuttling, even unto the moment of collision itself.

“Assuming all this,” said Prince
Rhani. “how far did Vishnu travel before the chariots collided and the universe
was destroyed?”

The sheik exclaimed, “Destroyed?!”

Prince Rahni shrugged. “It was a
long time ago. Don't worry about it...”

* * *

Namagiri asked, “And did you give an
answer?”

“Yes, dear, and promptly. Lord
Vishnu flew a distance of precisely...”

“... five million leagues,” Namagiri
interrupted.

“Why, that is just so!”

“I used the shortcut,” Namagiri said
modestly. “No doubt you did too.”

Ramanujan said, “How odd. Prince
Rahni also mentioned a shortcut, which he believed I used. No doubt he meant
the infinite series summation.”

“Why... no. What is an ‘infinite
series summation’?”

“What is your shortcut?”

“Let us hear your method first.”

“Why, Namagiri, it is simplicity
itself! When the Prince finished telling me the problem, I asked myself; what
form is the length of Lord Vishnu’s flight? The answer was obvious; it is an
sum of infinitely many terms, decreasing by a constant proportion; a geometric
series!”

“If you say so, dear husband,”
Namagiri said.

“I could explain it more fully...”

“No, no, do go on,” Namagiri said
hastily, for she had heard some of Ramanujan’s ‘full explanations’ before.

Ramanujan said, “So I asked myself,
what is the first term? A moment’s thought revealed that it was ten million
divided by eleven. And what is the constant ratio?”

“No doubt it was crystal clear to
you!”

Oblivious to her hint, Ramanujan
barrelled on. “It was obviously nine-elevenths.”

“And from this what follows?”

“Why, that Vishnu’s flight had a
length equal to this infinite geometric series:

Ten million divided by eleven

plus

Ten million times nine,

divided by eleven times
eleven

plus

Ten million times nine times nine,

divided by eleven times
eleven times eleven

plus

Ten million times nine times nine
time nine,

divided by eleven times
eleven times eleven times eleven

and so on
for infinitely many terms.”

“But of course,” Namagiri murmured.
“And from this...?”

“But it is so obvious! But not to
you, my dear? Oh... Well, such a series will sum to a number equal to the
first term divided by one minus the
common ratio. One minus the common ratio equals one minus nine-elevenths; that
is, two elevenths. Ten million divided by eleven, itself divided by two elevenths,
equals ten million divided by two, or five million. Therefore Lord Vishnu flew
five million leagues before being destroyed, along with the rest of the
universe.”

“It was a long time ago,” Namagiri
said.

“I’m not worrying about it,”
Ramanujan said. “But I

*am*worrying about that shortcut. You used it, Prince Rahni said I must have used it; but what*is*it?”
“Well, consider the matter thus,”
said Namagiri. “You said that the chariots started a million leagues apart, did
you not?”

Ramanujan said, “Yes I did,
beloved.”

“And that each chariot ran at a rate
of ten thousand leagues in a hour?”

“That is indeed so.”

“And therefore these chariots
approached each other at what rate?”

“At a rate of twenty thousand
leagues per hour.”

“And therefore how long was it
before they were doomed to collide?”

Ramanujan said, “In a number of
hours equal to one million divided by twenty thousand; that is, in fifty
hours.”

Namagiri nodded gravely. Her chin
dug into his shoulder. “So I too calculated. And how fast did you say the
Vishnu-scarab flew during those fifty hours?”

“At a rate of a hundred thousand
leagues per hour.”

“And how far would Vishnu fly, given
that he flew at a hundred thousand leagues per hour for fifty hours?”

Ramaujan hesitated, then said, “Oh.
He would fly a total distance of a hundred thousand times fifty; that is, a
distance of five million leagues.”

Namagiri nodded gravely. “So I too
calculated. How nice to see that your calculation matches mine; for it suggests
that we may both be right.”

“But your method is so much
simpler!” Ramanujan exclaimed. He sighed hugely, then said ruefully, “That is
the difference between us, my dear. You are a mathematician, but I am just a
computer. If only the Sheik understood that!”

* * *

“A most impressive demonstration,”
the Sheik said. “How do you do it?”

“How do I do what?”

“The counting, the adding, the
lighting multiplication. Tell me, computer; how?”

Ramanujan blurted, “Unable to
comply.”

The Sheik growled, “And why not?”

Ramanujan hastily said, “No, no,
nothing personal sir... it’s not that I

*would*not tell you; I simply*cannot*tell you. My skill with numbers came to me when I attained manhood; it is a feel for form and quantity that I cannot explain, only exercise. I wish I*could*explain how I do these simple tricks; but teaching these simple tricks to others is a trick that I have not yet mastered.”
Sheik Kahmunni frowned, stroked his
beard. “Not good enough...”

* * *

**Ramanujan’s Dream**

“Poor Sheik! Doesn’t he trust your
figures?”

“I doubt he trusts his own,” said
Ramanujan. “But how could I explain to that fierce, lean wanderer that you, my
wife, gave me my skills?”

“Oh, you flatterer! And how did I do
that?”

“You inspired me. Have I not told
you my dream of you?”

“Yes, you have,” said Namagiri, “Often. But please
tell it to me again.”

Ramanujan said, “Once, when I was a
child, I dreamed of another life I had. I was far away from here and now, both
in space and in time. I was in a distant century in a far land; a cold, rainy
land of magicians. Their arts were subtle, perilous and powerful. It was a
strange place... but somehow, it was yours.”

“Mine?”

“Yours, Namagiri. Do not ask me how;
I cannot explain. In my dream I was alone; but every night (in my dream) I
would dream (in my dream) that you would come to me.”

“A dream within a dream! You were
all wound up like a snake biting its tail!”

“In those dreams-within-a-dream you
would come to teach me mathematics. And those visions were all I ever saw of
you, in that life.”

“Tell me, husband, what sort of
mathematics I would teach you.”

“Shall I tell you something
complicated, or something a bit simpler?”

“How about something very very
simple? Let’s say, the very simplest thing I ever taught you in a dream within
a dream?”

And Ramanujan said,

“One-half plus half the square root
of five

equals

One plus the reciprocal of

one plus the reciprocal
of

one plus the
reciprocal of

one
plus the reciprocal of

...
and so on forever!”

Silence in the darkness.

After awhile Ramanujan said,
“Perhaps I should write it out...”

“But you know I cannot read.”

“It is a simple formula; no words,
only numbers.”

“But it is pitch black! What will
you write on?”

“I’m sure we can find something... I
have it. Roll over, dear. Yes, onto your back...” Ramanujan caressed Namagiri’s
stomach. “Good. Now listen. One-half plus half the square root of five - ”

“- what a strange number!”

“It is what geometers call the
Golden Mean. It is also equal to the following expression...”

Ramanujan moistened the tip of his
right index finger; then with it he wrote the following across Namagiri’s bare
belly:

**1 +**

__1__**1 +**

__1__**1 +**

__1__**1 +**

__1__**. . .**

Silence in the darkness.

After awhile Namagiri said, “O
gorgeous brilliant romantic husband, this mathematics must be yours. It is far
too pretty to be mine!”

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