I got the cue from Google’s home page.
For those of us children growing up in India in the 80’s, she was a legend. The prodigal mathematician. So, researching around a little bit on the web, I found this fascinating article about Shakuntala Devi by University of California, Berkeley Professor of psychology, Arthur Jensen. Its long and academic. Am posting the first few paragraphs. Jump to the full article here.
Speed of Information Processing in a Calculating Prodigy
Arthur R. Jensen
University of California, Berkeley.
Shakuntala Devi, one of the world’s most prodigious mental calculators on record, past or present, is especially remarkable for the incredible speed with which she performs mental calculations on very large numbers. This rare phenomenon prompted the question of whether such exceptional performance depends on the speed of elementary information processes. Devi’s rather unexceptional reaction times on a battery of elementary cognitive tasks, which were compared with the mean RTs of college students and older adults on the same tasks, contrasts so markedly with her amazing speed of performing huge arithmetic calculations as to indicate that her skill with numbers must depend largely on the automatic encoding and retrieval of a wealth of declarative and procedural information in long-term memory rather than on any unusual basic capacities. 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 than does psychometric g or the speed of elementary information processes.
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.”
An article in the New York Times (November 10, 1976, cited in Smith, 1983, p. 306) reported that Shakuntala Devi added the following four numbers and multiplied the result by 9,878 to get the (correct) answer 5,559,369,456,432:
She was reported to have done this calculation in “20 seconds or less.”
At Southern Methodist University, in 1977, Devi extracted the 23rd root of a 201-digit number in 50 s. Her answer—546,372,891—was confirmed by calculations done at the U.S. Bureau of Standards by the Univac 1101 computer, for which a special program had to be written to perform such a large calculation (Smith, 1983).I first learned of Shakuntala Devi many years ago in Time magazine (personal communication, July 4, 1952). I was amazed, but also rather skeptical, that anyone could extract cube roots of large numbers entirely in one’s head in a matter of seconds. Many years later I read biographical sketches of Devi in books on famous calculating prodigies, by Barlow (1952) and Smith (1983).Then, in 1988, Devi visited the San Francisco Bay Area, when I had the opportunity to observe a demonstration she gave at Stanford University before an audience filled with mathematicians, engineers, and computer experts, who had come with their electronic calculators or printouts of large problems that had been submitted to the University’s main-frame computer.I was curious, first of all, to see if Devi had the kind of autistic personality so commonly associated with such unusual mental feats. Also, I wanted to measure her performance times myself, to see if they substantiated the astounding claims I had read of her calculating prowess. But mainly, if the claims proved authentic, I hoped I could persuade her to come to Berkeley to be tested in my chronometric laboratory, so we could measure her basic speed of information processing on a battery of elementary cognitive tasks (ECTs) for which the results could be compared with the reaction time (RT) data we had obtained on the same ECTs in large samples of students and older adults. Indeed, Devi kindly consented to come to my laboratory and spent about 3 h taking various tests. In addition, she spent some 2 h with me, discussing her life and work.
Speed of Performing Arithmetic Calculations
At her Stanford appearance, Shakuntala Devi, in a colorful silk sari, sat at a table in front of the blackboard in a lecture hall. The demonstration lasted almost 90 min. (Engaging in such intense mental activity beyond that length of time, Devi said, she begins to feel tired.) Problems involving large numbers were written on the blackboard by volunteers from the audience, many of whom knew of Devi’s reputation and had brought along computer printouts with the problems and answers. Devi would turn around to look at a problem on the blackboard, and always in less than 1 min (but usually in just a few seconds) she would state the answer, or in the case of solutions involving quite large numbers she would write the answer on the blackboard.
Seated in the first row nearest to Devi, I was equipped with a HP computer and a notebook. Beside me, my wife held a stopwatch to measure Devi’s solution times, while I copied problems from the blackboard. (Devi solved most of the problems faster than I was able to copy them in my notebook.) Solution times were measured as accurately as possible with an ordinary stopwatch. When occasionally it was not exactly clear just when Devi began to work on a problem, this was noted, and in those instances the time is not reported here. The solution times in those cases, however, were not atypical of the times that could be accurately measured. It should be noted that Devi’s actual solution times might have been either under- or overestimated in many instances, because we had no control of the specific form of her responses, which varied from problem to problem. In every case, timing began as soon as the whole problem had been presented, and ended the moment Devi had given the complete answer. But she often preceded her answer with a phrase such as “The answer is . . .”, or “That could be . . .”, or “That was a (Friday).” Thus the problem may have been solved either entirely before these initial utterances or in parallel with the brief statement preceding the answer. Also, when large problem resulted in solutions that were quite large numbers, Devi would write out the answer on the blackboard, always quickly, and there was no way of telling whether the answer was complete in her mind before she began to write or the problem was being solved sequentially while she wrote out the answer. Since timing stopped only on the completion of the answer, the reported solution times, if anything, are probably slightly overestimated. Yet these were only a matter of seconds, and never as long as 1 min in the entire performance.When I handed Devi two problems, each on a separate card, thinking she would solve first one, then the other, my wife was taken by surprise, as there was hardly time to start the stopwatch, so quick was Devi’s response. Holding the two cards side-by-side, Devi looked at them briefly and said, “The answer to the first is 395 and to the second is 15. Right?” Right, of course! (Her answers were never wrong.) Handing the cards back to me, she requested that I read the problems aloud to the audience. They were: (a) the cube root of 61,629,875 (= 395), and (b) the 7th root of 170,859,375 (= 15). I was rather disappointed that these problems seemed obviously too easy for Devi, as I had hoped they would elicit some sign of mental strain on her part. After all, it had taken me much longer to work them with a calculator.But cube roots could almost be called Devi’s specialty. To “warm up” she requested a large number of cube root problems, that is, extracting the cube roots of large numbers, mostly in the millions, hundreds of millions, and trillions. The average time Devi took for extracting all of these cube roots was just 6 s, with a range of 2 to 10 s. Some examples:
|Time: 2 s
Time: 5 s
Time: 10 s
Then Devi took on more obviously difficult problems. For example:
|8√20,047,612,231,936 Ans. 46 Time: 10 s
Ans. 46,295 Time: 40 s
In all of the above examples the numbers have here been marked off with commas, as is customary, for ease of reading. But Devi refused to accept large numbers marked off with commas, claiming that the commas break up a number artificially. For Devi, grouping the numbers in triplets by commas hinders the solution process. Hence the large numbers written on the blackboard for Devi were always strings of equally spaced digits, ungrouped in any fashion. A given large number, as she takes it in, rather automatically “falls apart” in its own way. and the correct answer simply “falls out.” Apparently she does not apply a standard algorithm uniformly to every problem of a certain type, such as square roots, or cube roots, or powers. Each number uniquely dictates its own solution. so to speak. Hence the presence of commas only interferes with the “natural” (and virtually automatic) dissolution of the number in Devi’s mind. I have since learned from an Indian professor that commas are not used in India’s number system, and it seems likely that their interfering effect for Devi could stem in part from her intensive childhood experience in working with large numbers lacking commas or any other form of triplet grouping. Indians, my professor friend tells me, learn to group numbers mentally in terms of logarithms to the base 10, that is, 10°, 10¹, 10², and so forth.It will be noticed that all of the roots in the above problems are whole integers. But Devi also does noninteger roots almost as fast as integer roots— averaging about 3 to 4 s longer—provided the root is not an irrational number. For example, she could state the cube root of 12,812.904 as 23.4 almost without hesitation. Irrational roots, however are apparently more of a problem. She has reportedly done them, rounding off to two decimal places. But when the following number was presented at her Stanford demonstration, she took one look at it and dismissed it as a “wrong number.” It was 9√743,895,212. The answer (figured by computer) is an irrational number: 9.676616492+. I suspect that Devi could have solved it to at least two decimals, but the time required would have been too far out of line with her brief time on all the other problems to have made a good show. I got the impression that Devi’s professional showmanship doesn’t allow her to fumble over a problem or to spend much time on it if she sees that she can’t solve it rather quickly. It is nevertheless interesting that she so quickly recognized that the 9th root of this nine-digit figure is an irrational number.Devi also possesses the calendar skill that is frequently demonstrated by other calculating prodigies and by some so-called “idiot savants” or “autistic savants” (e.g., Hermelin & O’Connor, 1986). But I have not found any accounts in the literature of persons who can perform this feat so fast over such a wide range of dates, past and future. Given any specific date, Devi immediately states the day of the week it falls on. If the date was stated in the usual way (i.e., month, day, year) her average response time was about 1 s. But when the dates were stated to her in the order year, month, day, an ordinary stopwatch proved useless for measuring Devi’s response times, because her answers came about as fast as one could start the stopwatch. To determine if anything besides sheer calculation enters Devi’s thought process while she is doing calendrical calculations, I called out “January 30, 1948,” to which she instantly answered, “That was a Friday—and the day that our great leader Mahatma Gandhi was assassinated.” Obviously her calendrical calculating does not entirely usurp her other memory or thought processes. Devi can also name, about as fast as anyone could articulate, all the dates on which a given day, say Thursday, falls throughout a given year; or name all the days falling on a given date each month throughout the year; and she did this in both the forward and the reverse temporal directions with about equal speed. The total times for these tasks ranged between 15 and 30 s.
Personal Characteristics. The first thing most observers would notice about Devi is that her general appearance and demeanor are quite the opposite of the typical image of the withdrawn, obsessive, autistic savant, so well portrayed by Dustin Hoffman in the recent motion picture, Rain Man. Devi comes across as alert, extraverted, affable, and articulate. Her English is excellent, and she also speaks several other languages. She has the stage presence of a seasoned performer, and maintains close rapport with her audience. At an informal reception after her Stanford performance, I noticed that among strangers she was entirely at ease, outgoing, socially adept, self-assured, and an engaging conversationalist. To all appearances, the prodigious numerical talent resides in a perfectly normal and charming lady. She is divorced and has a daughter attending college in England, who, Devi remarks with mock dismay, uses a computer in her science and math courses. In fact, Devi claims none of her relatives has ever shown any mathematical talent.Shakuntala Devi was born in Bangalore, India, in 1940, to a 15-year-old mother and 61-year-old father, who was a circus acrobat and magician. Devi traveled with him since she was 3, performing card tricks, from which she cultivated her facility with numbers. Her talent in this sphere was manifested early; at age 5 she could already extract cube roots quickly in her head, and she soon began supporting herself and the rest of her family as a stage performer, traveling throughout India billed as a calculating prodigy. Even before she was in her teens, she began traveling around the world, performing numerical feats, usually before audiences in colleges and universities. She has written five books, three published in the U.S. (Devi, 1977, 1978a, 1978b). More biographical information can be found elsewhere (Barlow, 1952; Smith, 1983).