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I heard about Shakuntala Devi for the first time today, an Indian Savant who allegedly performed such feats as finding the 23rd root of a 201 digit number in 50 seconds, unaided.

There seems to be some documentation of these feats, but there also exists plenty of documentation for the tricks of psychics and others (i.e. plenty of people, and maybe even experts, will witness the power in action and be unable to detect the trick). Given that her father was a travelling magician, and she was a practising astrologer, I'm more inclined to believe that there's a trick at work than that this woman could factor 200 digit numbers in her head.

My question is:

  • Could Shakuntala Devi actually perform these feats? If so, are there other living people who can do this? If not, what sort of tricks were (or might have been) used to make people think she could?

Some additional information for comparison: A little more poking around turns up the Mental_Calculation_World_Cup, a modern, international event. Multiplication events consist of finding the product of two 8-digit numbers, which takes about 30 seconds per problem for the winners. Shakuntala Devi is claimed to have found the product of two 13-digit numbers in the same time period, which seems to be a super-linearly harder task. Similarly, the competition for root finding is to find the square root of a 6-digit number, a task which takes the world record holder about 42 seconds. Shakuntala Devi is claimed to have found a 23rd root of a random 201-digit number in 50 seconds, again, a task that seems much harder.

  • I think you might need to clarify the time periods involved for this question. From the looks of Wikipedia she started touring in the 1950's when computers weren't exactly very fast when it came to working with large numbers. – rjzii Mar 26 '14 at 19:55
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    @rob This is a good, point, but on reflection, I don't think I actually care about whether she was faster than a computer in her time. A person multiplying 13 digit numbers, or factoring 200 digit ones, in a matter of seconds, seems far-fetched in any era. I've edited the title to reflect this. – John Doucette Mar 26 '14 at 21:12
  • @John Doucette: however one can cheat much faster if he has a fast computer doing the calculations! – nico Mar 27 '14 at 10:30
  • @nico True. But for the problems specified one could just as easily work out the answer in advance by hand. With pen and paper, it would take a couple or hours, or even days perhaps, but could be done. – John Doucette Mar 27 '14 at 19:04
  • @ElliottFrisch I'm not sure what you're getting at here. Doubtless there exist people who are fast at math. But this person is claimed to have an enormously faster capability than the best in the world today, and has other dubious credentials. Also, surely you don't mean to imply that being Indian would confer some advantage in this regard? – John Doucette Mar 27 '14 at 19:06
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During her 1988 visit to the United States, educational psychologist Professor Arthur Jensen, University of California, Berkeley, have tried to unlock the secret of her abilities.

He published his work in Journal of Intelligence.

Speed of Information Processing in a Calculating Prodigy

Note: It's also the source of the answers in this post.


Could Shakuntala Devi actually perform these feats?

Did she do it? Answer is yes.

It seems hard to believe, but the following is reported in the Guinness Book of Records (1982), which has a reputation for the authenticity of its claims: "Mrs. Shakuntala Devi of India demonstrated the multiplication of two 13-digit numbers of 7,686,369,774,870 × 2,465,099,745,779 picked at random by the Computer Department of Imperial College, London on 18 June 1980, in 28 s. Her correct answer was 18,947,668,177,995,426,462,773,730."


If so, are there other living people who can do this?

Answer. Only handful.

Source: Shakuntala Devi and Other Human Calculators


Was Shakuntala Devi was exceptional genius in comparison to normal people?

Answer: Surprisingly No. Prof. Jensen's three experiment :

Experiment 1: Raven Matrices.

The Advanced Progressive Matrices (APM) is a highly g-loaded nonverbal test of abstract reasoning based on 36 multiple-choice items consisting of complex nonrepresentational figures.

Result:

She took 58 minutes to solve, which is within range of other people(students and older people) in the this study.

...this measure of psychometric g, Devi is not exceptional, in marked contrast to her phenomenal calculating ability.

Experiment 2: Digit Span.

The Digit Span subtest of the WAIS was of particular interest because it involves the recall of a series of digits immediately following their auditory presentation at the rate of 1 digit per second.

Result:

Devi correctly recalled 9 digits forward and 4 digits backward.

The score is not exceptional, she was in 63rd Percentile according to her age group. But actually the test was faulty and she broke it in forward scoring of 9, but there is no percentile for forward and reverse, so, the lowest being 4. she is considered normal.

Experiment 3: Chronometric Tests

The same tests were taken by college student of ages 18-25, and older adults from 51-87 years. This group consisted mostly of university graduates and had a mean of ~15 year+ of formal education.

Result

enter image description here

Jensen's quotes on this test:

Her feats of calculation, with their extraordinary speed of processing numerical information, are of course so far beyond the normal distribution of capability in mental arithmetic that she is considered in a class with only a handful of the world's greatest mental calculations, past or present, on whose performance we have authentic records.

Google's tribute to Human Calculator

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    Well, I'm still surprised, but this does seem to be legitimate. Thanks for making such a comprehensive answer. – John Doucette Aug 14 '14 at 16:57
  • @JohnDoucette: She was a great lady. Once she came to our school(long ago). – Devashish Das Aug 14 '14 at 17:17
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    What I'd really like to know is if anyone has a theory about how her brain managed to do this. – Benjol Aug 18 '14 at 5:28
  • @Benjol: Nice question. I think you can find the answer in the paper, I mentioned as source. She can actually see the number in different way than most of us. It is like you see a number 12 and visualize it as 1x2x3x2 or 3^2 + 3, etc. Add that with, she can remember most of the number if she already came across that. – Devashish Das Aug 18 '14 at 6:14

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