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Monday, August 03, 2020

Explained: What was the secret of Shakuntala Devi’s calculating abilities?

Shakuntala Devi, the subject of a new film, was never formally educated, and her performance in cognitive tests was not exceptional. How then could she multiply 13-digit numbers in seconds, and extract cube roots instantly?

Written by Kabir Firaque , Edited by Explained Desk | New Delhi | Updated: August 3, 2020 8:52:56 am
Shakuntala Devi, Shakuntala Devi movie, who is Shakuntala Devi, Shakuntala Devi movie review, Shakuntala Devi math abilities, Shakuntala Devi skills, Indian Express Shakuntala Devi at Himachal Bhavan in April 1987. (Express Archive/R K Sharma)

Shakuntala Devi (1929-2013), the subject of a new film released on Amazon Prime on Friday, has always been associated with an element of mystery. She was not formally educated, and was far from exceptional in cognitive tests, and yet she could perform calculations with large numbers in a few seconds, sometimes instantly. A look at her skills, and what is known about how she cultivated them:

So, what were her skills?

* Cube roots: It began with extracting cube roots of large numbers, which she could do in her head rapidly while still a child in the 1930s. Then in 1988, in a test of her abilities conducted by the psychologist Arthur Jensen at the University of California-Berkeley, Shakuntala Devi mentally calculated the cube roots of 95,443,993 (answer 457) in 2 seconds, of 204,336,469 (answer 589) in 5 seconds, and of 2,373,927,704 (answer 1334) in 10 seconds.

* Higher roots: She calculated the 7th root of 455,762,531,836,562,695,930,666,032,734,375 (answer 46,295) in 40 seconds. This means that 46,295 multiplied by itself seven times yields that number of 27 digits; Shakuntala Devi worked backwards from the 7th power to derive the root. This too was recorded in the test at Berkeley in 1988.

* Long multiplication: This is the skill that got her into the Guinness Book of Records in 1982. At Imperial College on June 18, 1980, Shakuntala Devi was asked to multiply two 13-digit numbers:

7,686,369,774,870 × 2,465,099,745,779.

She got the answer in 28 seconds — 18,947,668,177,995,426,462,773,730.

* Calendar calculations: Given any date in the last century, she could instantly say which day of the week that date fell on. For example, if you gave her the date July 31, 1920, she would immediately tell you that it was a Saturday. If the date was stated in the order month, day, year (for example, July-13-1920), her average response time was about 1 second. But when the dates were stated to her in the order year, month, day (for example 1920-July-31), “her answers came about as fast as one could start the stopwatch”, the 1988 test at Berkeley found.

Shakuntala Devi, Shakuntala Devi movie, who is Shakuntala Devi, Shakuntala Devi movie review, Shakuntala Devi math abilities, Shakuntala Devi skills, Indian Express Shakuntala Devi was popularly known as the ‘human calculating machine’. (Express Archive/R K Sharma)

Where did she learn these skills?

By all accounts, Shakuntala Devi was entirely self-taught. Daughter of a circus performer, she travelled with her parents since she was three years old, and is said to have cultivated her calculating abilities while performing card tricks. Once she began to extract cube roots rapidly in her head, she became a performer exhibiting her skills. By the time she was a teenager, she was already travelling around the world, usually before audiences in colleges and universities.

Beyond her numerical skills, how much mathematics did she study?

Shakuntala Devi authored several books, including at least half a dozen on calculations, mathematical puzzles, and grooming children in mathematical skills. The books show she was familiar with certain mathematical concepts that one usually learns during a formal education. For example, in some of her writings she discusses trigonometry and logarithms. It is most likely that she learnt these concepts from extensive reading, but there is not much literature available on this aspect of her life.

Even the film does not throw any light on this. While it is full of glimpses about her extraordinary calculating abilities, the film dwells very little on the mental processes these abilities were based on.

Shakuntala Devi review: A Vidya Balan show

So, what explains her calculating abilities?

One of the most comprehensive accounts is the report on the tests at University of California-Berkeley in 1988. The psychologist Jensen, who died in 2012, published his findings in the journal Intelligence in 1990.

The short answer: Jensen could not figure out the secret of her skills: “[None] of the objective test results begins to explain why or how Devi is able to perform feats with numbers that are so far beyond what most of us can do in this sphere as to seem incredible. Her peculiar ability is indeed rare, perhaps one in hundreds of millions,” he wrote in his report.

Jensen noted a marked contrast between Shakuntala Devi’s calculating abilities and her “rather unexceptional reaction times” in elementary cognitive tasks. “Some kind of motivational factor that sustains enormous and prolonged interest and practice in a particular skill probably plays a larger part in extremely exceptional performance …,” he wrote.

Did the tests provide even a hint on the processes she followed?

In his report, Jensen speculated that most of the basic operations involved in her performance probably became automatised during her childhood. “Devi ‘perceives’ large numbers differently from the way most of us ordinarily do. When she takes in a large number (and she must do this visually), it undergoes some transformation, almost instantly — usually some kind of simplification of the number,” Jensen wrote.

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Shakuntala Devi, Shakuntala Devi movie, who is Shakuntala Devi, Shakuntala Devi movie review, Shakuntala Devi math abilities, Shakuntala Devi skills, Indian Express Shakuntala Devi authored several books, including at least half a dozen on calculations, mathematical puzzles, and grooming children in mathematical skills.

Are there any other accounts of her mental processes?

Some clues can be found in Shakuntala Devi’s own writings. In ‘Figuring: The Joy of Mathematics’, she described methods for mental multiplication, as well as a method for working out the day of the week for any date in the previous century. Both of these are long processes that fill up pages. And yet she could give her answers in seconds, if not instantly.

It would require a genius as rare as herself to emulate her skills at her speed — if one were to follow the methods she described. Or possibly, as Jensen wrote in his report, “Devi obviously does not go about her calculations in the same way that most of us would do.”

If these skills remain unexplained, what is the film about?

Directed by Anu Menon, with Vidya Balan playing the title role, the film focuses more on Shakuntala Devi’s personal life. Beyond her mathematics books, Shakuntala Devi also wrote a book on homosexuality, indulged in astrology, contested against Indira Gandhi in Medak during the 1980 Lok Sabha elections (she managed 6,514 votes against Gandhi’s 3 lakh-plus), and has a daughter living in London. The film dwells on some aspects more extensively than others.

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