Namagiri and Ramanujan
[ by Charles Cameron — in which we glimpse the (female) divinity hidden behind infinity ]
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It is one of the curiosities of mathematics that the great Indian mathematician Srinivasa Ramanujan claimed to have received many, if not all, of his equations from the goddess Namagiri in dreams — and that this idea is all too often quietly omitted from discussions of his uncanny brilliance.
Now that The Man Who Knew Infinity is out in theaters, it might be wise to explore the connection between Namagiri and Ramanujan a little more closely.
Dream and waking, darshan and mathematics, inspiration and intuition, intuition and proof, quality and quantity — these polarities are all involved..
To its credit, the film contains the line:
You want to know how I get my ideas? God speaks to me.
However, the idea that “God” might be a goddess seems a reach too far for the screenwriters and director.
Viewing:
Here’s one version of the trailer:
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Stephen Wolfram posted a fine article on his blog last week, Who Was Ramanujan?. He was willing to mention that Ramanujan’s friend and collaborator, GH Hardy, “could be very nerdy — whether about cricket scores, proving the non-existence of God, or writing down rules for his collaboration with Littlewood” — but fails in 31 pages to mention Ramanujan’s own belief that he received his equations from a goddess.
All of which caused me to pose a question to Wolfram’s own algorithmic genie, Wolfram Alpha:
Did Namagiri reveal equations to Ramanujan?
WolframAlpha skipped the words “Did Namagiri reveal” and “to” and concentrated on responding to “equations” and “Ramanujan” — not quite up to par with AlphaGo, I’m afraid, let alone Ramanujan himself, or better, Namagiri.
Below’s the DoubleQuote I made to by way of comment — note that I’ve only had space for the first line of WolframApha’s extended response:
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Readings:
Scott:
May 1st, 2016 at 11:21 pm
Can anyone recommend a good book on Ramanujan that also talks about his actual mathematics?
Charles Cameron:
May 2nd, 2016 at 3:15 am
It looks as though Krishnaswami Alladi, Ramanujan’s Place in the World of Mathematics: Essays Providing a Comparative Study would be a decent place to0 start — but I’ no mathematician, so I hope others more knowledgeable will chime in.
Grurray:
May 2nd, 2016 at 3:21 pm
The movie is based on a book by the same name. I’ve not read it, but that’s probably a good place to start. The first chapter contains much about Namagiri
http://bit.ly/1rqYlFO
Grurray:
May 2nd, 2016 at 3:38 pm
Regarding Wolfram’s article, Numberphile has a video that explains the sum of all pos integers = -1/12:
http://www.numberphile.com/videos/analytical_continuation2.html
Their videos are usually just entertaining and quirky, but that one caused quite an uproar. Well, as much of an uproar as a bunch of math geeks can muster. It’s still a weird idea that defies common sense. In fact, in his letter to Hardy, Ramanujan mentioned they would probably put him in a lunatic asylum for it.
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The legend of Ramanujan is this savant that magically derived near-impossibly complex calculations in his short mysterious life, seen in things like Hardy’s famous story about the no. 1729 taxi cab.
The more I read about him though, the more I tend toward that it was more like near-impossibly hard self-studying combined with some creativity that got him to Cambridge. Who knows.
The math is mostly beyond me, but his notebooks with abridged commentary are available online. Particularly with the -1/12 series, he was able to figure out the same things the great Euler did 200 years before without knowing some key concepts. They mention that his approaches were non-rigorous, and the explnation on wikipeida even calls it dangerous.
However, he still got there. A leap, a wing and a prayer. Personally, I think it was just good old fashioned diagonal thinking, but I can’t rule out divine intervention either.
Charles Cameron:
May 2nd, 2016 at 10:35 pm
Double thanks, Grurray.
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From my POV, “divine intervention” and “good old fashioned diagonal thinking” may not be two separate categories, but two framings of the same thing. But then, I’m with the Isa Upanishad:
larrydunbar:
May 7th, 2016 at 7:29 pm
A wheelchair ramp has a slope of 1/12. Considering the “-” sign in -1/12 only denotes direction, I have to wonder, after watching Grurray’s linked video, if the slope of the wheelchair ramp was created out of the number for infinity.
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It is these kinds of numbers that designers look for, so it wouldn’t surprise me that it was. Then again, it might just be that the slope to infinity and the path for those humans who are restricted in motion would, in nature,be the same. In other words, it just had to come out as 1/12 slope.
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I am not designing a wheelchair ramp, but an infinity ramp.
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I better use the name before someone else does. 🙂
Charles Cameron:
May 8th, 2016 at 5:13 pm
Ha! That question — whether infinity is something you can ramp uo to, or whether it’s a sudden and total leap — has its Zen analogue in the question of sudden vs gradual enlightenment:
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The Northern Ch’an School And Sudden Versus Gradual Enlightenment Debates In China And Tibet
larrydunbar:
May 8th, 2016 at 11:48 pm
Ha, ha, of course it does, because the ramp is cause by the difference in time from “being” there and “doing” the math.