I feel that she was a child-genius like Ramanujan, but was unfortunate to be not "discovered" by a mentor like G.H.Hardy. She had great memorization skills and logical thinking, so obviously excelled at writing puzzles' books. It's a pity that her contributions to modern mathematics is zilch. I still wonder why didn't she take up number theory. She went into astrology (yea, not astronomy), which is still debated as a pseudo-science. She could've done so much, but alas it's too late now. But well, each person to his own, each -ology to itself. RIP.
Indian Astrology is quite a lucrative field. Almost every other person in India believes in it, including wealthy businessmen who are interested in everything from calculating the right time to start a new venture to the most numerologically lucky name for themselves.
On the other hand, most mathematicians end up as school teacher in India, especially if you are only good at arithmetic (which I believe was the case, based on her feats and books). Being a school dropout, she would have faced huge barriers in any Indian academic institution to conduct research in Mathematics.
So, you are right, in the absence of a mentor there were not many options left for Shakuntala Devi. Mathematical calculations are heavily applied in Indian astrology and now computers are used for this purpose. Hence, Astrology would have been an interesting diversion for her.
You should look up the tragic case of the Indian mathematician V.N. Singh to get some perspective :( http://articles.timesofindia.indiatimes.com/2013-04-19/patna... Shakuntala Devi had amazing calculation prowess, but to me it was always seemed more in the savant zone.
Despite no direct contributions to modern mathematics, the people she inspired with her skill could have a huge effect. That can be considered a contribution, especially since she actively showed off her talents repeatedly to different audiences.
>Rated as one in 58 million for her stupendous mathematical feats by one of the fastest super-computers ever invented —the Univac — 1108 —, Ms. Devi believed in using grey cells to silicon chips.
This is somewhat unclear. Wikipedia clears up what's probably meant here:
>In 1977 in Dallas she competed with a computer to see who give the cube root of 188138517 faster. She won. At an American university she was asked to give the 23rd root of 91674867692003915809866092758538016248310668014430862240712651642793465704086709659 3279205767480806790022783016354924852380335745316935111903596577547340075681688305 620821016129132845564805780158806771. She answered in 50 seconds. Her answer of 546372891 took a UNIVAC 1108 computer a full minute (10 seconds more) to confirm that she was right after it was fed with 13000 instructions.
Anyway, the point isn't that she's faster than a computer (I mean, my laptop can conjure up that answer with PARI/GP in under a millisecond). The point is a) she pushed the limits of human achievement and showed that such feats were, in fact, possible, particularly for an adult beyond their twenties, and b) her passion for math inspired so many others. I mean, who wouldn't be impressed by someone who could calculate that? I doubt I could even keep track of all those digits given all the time in the world, much less give any answer better than an order of magnitude estimation in 50 seconds. Her intention was to show people (generally kids) that math is not this impossible, unconquerable monster of a subject, even though it may seem that way when you first encounter it, and even afterwards, as long as you treat it that way.
Did she ever document her mental process for these sorts of feats? I mean, I doubt I could come up with the correct answer given an unlimited time, a ream of paper, and a pocket calculator, so I'm fascinated how she did. Was she very good at complex math, or did she leverage a huge working memory to split the problem up into a larger number of simpler calculations, or some other combination of factors?
This is somewhat related. I remember watching an episode of "Stan Lee's Super humans" on the Discovery channel. They were with a man who was also able to do lightning fast calculations, not of the complexity as described in the article, but he could easily recall dates, multiply 5 digit numbers faster than someone with a calculator etc.
They put this man under an MRI scanner while giving him problems to solve. What they noticed was an unusually high activity in a part of the brain that is responsible for eye movement. So – perhaps not very scientifically responsible – the neurologist offered the explanation that he was using a part of his brain that is normally used to solve complex mathematics subconsciously in order to position our eyes properly throughout the day. Apparently this motor movement is very complex and he was leveraging the ability of this area to solve these arithmetic problems and engage in pattern matching in order to recollect past dates.
Reminds me of Joe Haldeman's scifi short None So Blind. I won't spoil it but I'll give the first 2 sentences as a teaser:
It all started when Cletus Jefferson asked himself
"Why aren't all blind people geniuses?" Cletus was only
13 at the time, but it was a good question, and he would
work on it for 14 more years, and then change the world forever.
I don't know how much Devi has revealed about the superhuman feats mentioned in the article, but she did write a book on how to do basic math very quickly. It's a good read.
It has 201 digits (it's on the order of 10^200), so it would be about 9.167 googol googol. Yeah, that's incomprehensible. Not the biggest integer I can think of (see Graham's Number) but I'd say it's big enough.
There was a post on HN a few days ago that illustrated U.S. government spending; namely, what does 1 trillion dollars look like.
Apparently 1 trillion dollars is a veritable warehouse of pallets of stacked bills.
Take the 201 digit number; what does that look like as dollar bills laid side-by-side? i.e. how much surface area of the earth could be covered? (if not the whole thing and parts of this galaxy and beyond ;-)).
Just trying to visualize the number to scale.
p.s. reminds me a bit of the Buddha's enlightenment analogies vis-a-vis: take all the grains of sand in the river Ganges; if each grain of sand was a world, and you were to take each grain of sand in each world, even then you would not approach [the scale] of enlightenment -- a 201 digit number is finite, but still, well and truly incomprehensible ;-)
Shakuntala Devi had also inspired an entire generation to read and understand her books about recreational mathematics. Her books like 'Puzzles to Puzzle You' were used to prepare for interviews in IT companies which used to have several rounds of puzzle solving.
She would probably be the last human (that I am aware of) who could beat a computer in arithmetic.
That's still a better uptime than any computer I've ever seen! (Come to think of it, with my health and with my luck, that's a better uptime than my mortal solenoid is probably ever going to have... :/)
Calculating 23rd roots is a different story, but finding the day of the week for any date isn't actually that hard. John Conway came up with a manageable method, which was improved a few years back. I think I've simplified it a bit further: http://gcanyon.wordpress.com/2013/04/09/a-better-way-to-calc...
