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18 October 2005

beautiful strange powerful fast mysterious seductive

It's just very beautiful.

Please inspect and admire it for a few moments, just as you would a famous painting in a gallery.

A mystical genius discovered it, but it's really pretty simple to understand, just whole-number arithmetic, high-school algebra, addition, multiplication, division, a square root.

Beautiful, and very strange. It's an equation for pi, so it must have something to do with a perfect circle, with roundness, circularity.

But what? What do these strange numbers have to do with circles? Where do they come from?

Particularly striking is how precise a value of pi it computes before it even begins to go to work, when n = 0.

But the equation will not be "true" -- the left side will not equal the right side -- until n = infinity, until the stuff to the right side of the Sigma sign (a fairly simple kind of sum) has been computed and summed and computed and summed an infinite number of times.

It's a map, a set of instructions to travel to Infinity. But of course Infinity is a Realm no human being has ever reached or can ever experience. Our world, our human experience is Finite. We know Many, we know A Lot, we know Thousands, Millions, Billions -- but we can never reach or experience or know Infinity. We can only imagine or guess what Infinity is like, what goes on there.

Srinivasa Ramanujan
(1887 - 1920) was a self-taught Indian mathematician who spent most of his mental life in the Realm of the Infinite, and in the Realm of Pure Numbers. He had very little use for our familiar and finite world, and no interest whatsoever in any practical applications of mathematics.

Ramanujan told his Cambridge colleague Hardy that the Hindu Goddess Namagiri gave him many of his mathematical discoveries in dreams. He wrote them down when he woke.

Ramanujan discovered this equation around 1915 -- about 35 years before electronic digital computers existed. It belongs to a group of his discoveries which are still the most efficient, fastest ways known to compute the decimal expansion of pi.

pi is defined as the ratio of a circle's circumference to its diameter; but expressed in digits, pi is a decimal fraction which never ends, which can never be perfectly expressed. Around 1990, the Chudnovsky Brothers, refugee mathematicians from the Soviet Ukraine, used one of Ramanujan's equations to break the world's record of computing pi beyond a billion digits on a homebrew supercomputer they built from mail-order parts in their New York City slum apartment.

Arguably, computing more than a few dozen digits of pi is a useless task with no possible practical or real-world application. And yet, since even before Archimedes (an early pi precision record-breaker), the world's most brilliant mathematicians have routinely been mesmerized and seduced by the problem, not just to compute more digits of precision, but to squeeze mathematical meaning out of pi and to find new, more elegant, more powerful ways to compute it.

Googling 26390 will return dozens of websites about Ramanujan's pi equations, Ramanujan, and related mathematical lore about related problems; these are among the most esoteric, profound and strangest of all mathematical discoveries. While in England he fell ill with tuberculosis, but was awarded a doctorate from Cambridge University, and elected a Fellow of the Royal Society before he sailed home to die in India. India's premier center of advanced mathematical research is the Ramanujan Institute; Ramanujan himself has been honored on an Indian postage stamp.


Anonymous DespicableTeacher said...

"An equation for me has no meaning, unless it represents a thought of God."

(Srinivasa Ramujan)

Anonymous despicableTeacher said...

An equation for me has no meaning, unless it represents a thought of God."

(Srinivasa Ramanujan)

Blogger Bob Merkin said...

You know you've really hit the Big Time when the world just throws away your first name and only refers to you as "Ramanujan."

I don't remember being crazy for math as a boy, but my childhood rabbi must have noticed because he gave me a treasure -- his 3-volume edition of James Newman's "The World of Mathematics" (it's been out of print for a long time.) I jumped into it and drowned. I still have it 40 years later. It's within arm's length of me right now. It's not math itself, but just a treasury of biographies, essays, literature, history, even a few poems -- it's Meta-Math, the literature and culture and history of math and mathematicians.

And that's where I first met Ramanujan. At that time, about the only chronicle of his life and achievements was Hardy's memoirs of him, of how they met -- a strange letter from India with about 20 equations in it that just knocked Hardy for a loop.

The equations must be true, he realized immediately, because no one would have had the imagination to invent them if they weren't true. And the letter-writer must be honest, because mathematical geniuses are more common than "humbugs" or confidence men of such amazing skill.

Hardy almost demanded that Ramanujan come to England. As an entirely self-taught mathematician, he didn't know anything about the progress math had made in the last 40 years (after the only advanced math textbook he'd ever read). His mother wouldn't give Ramanujan her permission, and he couldn't go. But then the Goddess Namagiri came to the rescue again and told his mother in a dream that he must go to Europe. She showed her a vision in which the greatest men of Europe were all gathered to honor Ramanujan.

Hardy was shocked when he asked Ramanujan about his religious beliefs. Ramanujan was a devout practicing Hindu -- but he told Hardy that as far as he could figure out, all the world's religions were probably "equally true."

The really wonderful thing is that they've recently found two of his lost mathematical notebooks, and his reputation has become even greater. Now there are several bios -- I think one is called "The Man Who Saw Infinity."

Ramanujan never liked proof much, or understood why it was so important to professional mathematicians. He just discovered these amazingly arcane mathematical truths. Hardy and others had to take all the aspirin to try to prove R's icredibly complicated, strange formulas. (Some of which weren't True ... Namagiri wasn't perfect.)

Math or Not, I nominate Ramanujan as the Strangest Human Being who ever lived. If Earth has really ever been visited by Aliens from Outer Space, I nominate Ramanujan (or his daddy). There really isn't another theory which can explain anyone like him.


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