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COMPUTING THE MATHEMATICAL FACE OF GOD: S. RAMANUJAN
Subject: COMPUTING THE MATHEMATICAL FACE OF GOD: S. RAMANUJAN
Posted by: jai@aloha.com (Dr. Jai Maharaj)
HINDUISM TODAY February 1990
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Computing the Mathematical Face of God: S. Ramanujan
He died on his bed after scribbling down
revolutionary mathematical formulas that bloomed
in his mind like ethereal flowers -- gifts, he
said, from a Hindu Goddess.
He was 32 the same age that the advaitan advocate
Adi Shankara died. Shankara, born in 788, left
earth in 820. Srinivasa Ramanujan was born in
1887. He died in 1920 -- an anonymous Vaishnavite
brahmin who became the first Indian mathematics
Fellow at Cambridge University. Both Shankara and
Ramanujan possessed supernatural intelligence, a
well of genius that leaves even brilliant men
dumb-founded. Ramanujan was a meteor in the
mathematics world of the World War I era. Quiet,
with dharmic sensibilities, yet his mind blazed
with such intuitive improvisation that British
colleagues at Cambridge -- the best math brains in
England -- could not even guess where his ideas
originated. It irked them a bit that Ramanujan
told friends the Hindu Goddess Namagiri whispered
equations into his ear. Today's mathematicians --
armed with supercomputers -- are still
star-struck, and unable to solve many theorems the
young man from India proved quickly by pencil and
paper.
Ramanujan spawned a zoo of mathematical creatures
that delight, confound and humble his peers. They
call them "beautiful," "humble," "transcendent,"
and marvel how he reduced very complex terrain to
simple shapes.
In his day these equations were mainly pure
mathematics, abstract computations that math sages
often feel describe God's precise design for the
cosmos. While much of Ramanujan's work remains
abstract, many of his theorems are now the
mathematical power behind several 1990's
disciplines in astrophysics, artificial
intelligence and gas physics. According to his
wife -- Janaki, who still lives outside Madras --
her husband predicted "his mathematics would be
useful to mathematicians for more than a
century." Yet, before sailing to England,
Ramanujan was largely ignorant of the prevailing
highest-level math. He flunked out of college in
India. Like Albert Einstein, who toiled as a
clerk in a Swiss patent office while evolving his
Special Theory of Relativity at odd hours,
Ramanujan worked as a clerk at a port authority in
Madras, spending every spare moment contemplating
the mathematical face of God. It was here in
these sea-smelling, paper-pushing offices that he
was gently pushed into destiny -- a plan that has
all the earmarks of divine design.
Ramanujan was born in Erode, a small, rustic town
in Tamil Nadu, India. His father worked as a
clerk in a cloth merchant's shop. his namesake is
that of another medieval philosophical giant --
Ramanuja -- a Vaishnavite who postulated the
Vedanta system known as "qualified monism." the
math prodigy grew up in the overlapping
atmospheres of religious observances and ambitious
academics. He wasn't spiritually preoccupied, but
he was steeped in the reality and beneficence of
the Deities, especially the Goddess Namagiri.
Math, of course, was his intellectual and
spiritual touchstone. No one really knows how
early in life ramanujan awakened to the psychic
visitations of Namagiri, much less how the
interpenetration of his mind and the Goddess'
worked. By age twelve he had mastered
trigonometry so completely that he was inventing
sophisticated theorems that astonished teachers.
In fact his first theorems unwittingly duplicated
those of a great mathematician of a hundred years
earlier. This feat came after sifting once
through a trigonometry book. he was disappointed
that his "discovery" has already been found. then
for four years there was numerical silence. At
sixteen a copy of an out-of-date math book from
Cambridge University came into his hands. It
listed 5,000 theorems with sparse, short-cut
proofs. Even initiates in the arcane language of
mathematics could get lost in this work.
Ramanujan entered it with the giddy ambition and
verve of an astronaut leaping onto the moon. It
subconsciously triggered a love of numbers that
completely saturated his mind. He could envision
strange mathematical concepts like ordinary people
see the waves of an ocean.
Ironically, his focus on math became his academic
undoing. he outpaced his teachers in numbers
theory, but neglected all other subjects. He
could speak adequate English, but failed in it and
history and other science courses. He lost a
scholarship, dropped out, attempted a return but
fell ill and quit a second time. By this time he
was married to Janaki, a young teenager, and was
supporting his mother. Often all night he
continued his personal excursions into the math
universe - being fed rice balls by his wife as he
wrote lying belly-down on a cot. During the day
he factored relatively mundane accounts at the
post office for 20 pounds a year. He managed to
publish one math paper.
As mathematicians would say, one branch of
potential reality could have gone with Ramanujan
squandering his life at the port. But with one
nudge from the invisible universe, Namagiri sent
him Westward. A manager at the office admire the
young man's work and sensed significance. He
talked him into writing to British mathematicians
who might sponsor him. Ramanujan wrote a simple
letter to the renowned G. W. Hardy at Cambridge,
hinting humbly at his breakthroughs and describing
his vegetarian diet and spartan needs if he should
come to the university. He enclosed one hundred
of his theorem equations.
Hardy was the brightest mathematician in England.
Yet, as he knew and would write later at the
conclusion of his life, he had done no original,
mind-bending work. At Cambridge he collaborated
with an odd man named Littlewood, who was so
publicly retiring that people joked Hardy made him
up. The two, though living within a hundred yards
of each other, communicated by exchange of terse,
math-laden letters. Ramanujan's letter and
equations fell to them like a broadcast from alien
worlds. AT first they dismissed it as a
curiosity. Then, they suddenly became intrigued
by the Indian's musings. Hardy later wrote: "A
single look at them is enough to show that they
could only be written down by a mathematician of
the highest class. They must be true, for if they
were not true, no one would have the imagination
to invent them."
Hardy sensed an extremely rare opportunity, a
"discovery," and quickly arranged a scholarship
for the then 26-year-old Ramanujan. The
invitation came to India and landed like a bomb in
Ramanujan's family and community circle. His
mother was horrified that he would lose caste by
traveling to foreign shores. She refused to let
him go unless it was sanctioned by the Goddess.
According to one version of the story, the aged
mother then dreamt of the blessing from Namagiri.
But Janaki says her husband himself went to the
namagiri temple for guidance and was told to make
the voyage. Ramanujan consulted the astrological
data for his journey. He sent is mother and wife
to another town so they wouldn't see him with his
long brahmin's hair and bun trimmed to British
short style and his Indian shirt and wrapcloth
swapped for European fashion. He left India as a
slightly plump man with apple-round cheeks and
eyes like bright zeroes.
Arriving in 1914 on the eve of World War I,
Ramanujan experienced severe culture shock at
Cambridge. he had to cook for himself and
insisted on going bare foot Hindu style on the
cold floors. But Hardy, a man without airs or
inflated ego, made him feel comfortable amidst the
stuffy Cambridge tradition. Hardy and Littlewood
both served as his mentors for it took two
teachers to keep pace with his advances. Soon, as
Hardy recounts, it was Ramanujan who was teaching
them, in fact leaving them in the wake of
incandescent genius.
Within a few months war broke out. Cambridge
became a military college. vegetable and fruit
shortages plagued Ramanujan's already slim diet.
The war took away Littlewood to artillery
research, and Ramanujan and Hardy were left to
retreat into some of the most recondite math
possible. One of the stunning examples of this
endeavor is a process called partitioning,
figuring out how many different ways a whole
number can be expressed as the sum of other whole
numbers. Example: 4 is partitioned 5 ways (4
itself, 3+1, 2+2, 2+1+1, 1+1+1+1), expressed as
p(4)=5. The higher the number, the more the
partitions. Thus p(7)=15. Deceptively though,
even a marginally larger number creates
astronomical partitions. p(200)=397,999,029,388.
Ramanujan -- with Hardy offering technical checks
-- invented a tight, twisting formula that
computes the partitions exactly. To check the
theorem a fellow Cambridge mathematician tallied
by hand the partitions for 200. It took one
month. Ramanujan's equation was precisely
correct. U.S. mathematician George Andrews, who
in the late 1960's rediscovered a "lost notebook"
of Ramanujan's and became a lifetime devotee,
describes his accuracy as unthinkable to even
attempt. Ramanujan's partition equation helped
later physicists determine the number of electron
orbit jumps in the "shell" model of atoms.
ANother anecdote demonstrates his mental
landscape. By 1917, Ramanujan had fallen
seriously ill and was convalescing in a country
house. Hardy took a taxi to visit him. As math
masters like to do he noted the taxi's number --
1729 -- to see if it yielded any interesting
permutations. To him it didn't and he thought to
himself as he went up the steps to the door that
it was a rather dull number and hoped it was not
an inauspicious sign. He mentioned 1729 to
Ramanujan who immediately countered, "Actually, it
is a very interesting number. It is the smallest
number expressible as the sum of two cubes in two
different ways."
Ramanujan deteriorated so quickly that he was
forced to return to India -- emaciated -- leaving
his math notebooks at Cambridge. He spent his
final year face down on a cot furiously writing
out pages and pages of theorems as if a storm of
number concepts swept through his brain. Many
remain beyond today's best math minds.
Debate still lingers as to the origins of
Ramanujan's edifice of unique ideas.
Mathematicians eagerly acknowledge surprise states
of intuition as the real breakthroughs, not
logical deduction. There is reticence to accept
mystical overtones, though, like Andrews, many can
appreciate intuition *in the guise* of a Goddess.
But we have Ramanujan's own testimony of feminine
whisperings from a Devi and there is the sheer
power of his achievements. Hindus cognize this
reality. As an epilogue to this story, a seance
held in 1934 claimed to have contacted Ramanujan
in the astral planes. Asked if he was continuing
his work, he replied, "No, all interest in
mathematics dropped out after crossing over."
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HINDUISM TODAY February 1990
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