At the recommendation of a friend, I watched the Hindi-language film Shakuntala Devi about a woman who could make complex mathematical calculations in her head very quickly. Born in 1929 in India, Devi grew up to a poor family who couldn’t afford to formally educate her but, by the age of 5 years old, she became the family’s primary breadwinner by performing memorization tricks in the circus. Touring internationally as an adult in the 1970s, Devi stunned audiences with her ability to outperform the computers of the day.
Even though it sometimes seemed stereotypical and cheesy, I found the movie fun to watch – although others found it ‘off-putting’ and full of ‘tired Indian tropes.’ The movie concentrates more on Devi’s relationships, especially with her daughter, than it does on her math skills. As a result, after watching the movie, I wanted to learn more about one of Devi’s most famous achievements – determining the 23rd root of a 201-digit number in under a minute. (Note: The 23rd root is a number which, if you multiplied it by itself 23 times, would be the 201-digit number.)
The achievement happened in 1977 at Southern Methodist University when Devi competed live against a UNIVAC computer. The UNIVAC which was “programmed with 20,000 instructions” took just over a minute to determine the answer while Devi took only 50 seconds. Not surprisingly, this created a sensation in the U.S with newspapers calling Shakuntala Devi ‘the magician of mathematics,’ ‘the world’s most calculating woman,’ and ‘the Houdini of numbers.’
As it turns out, this story has an unexpected twist and one that doesn’t often get reported on. The professor who wrote the 201-digit number on the blackboard made a mistake in two different places, transposing the actual digit to something else. And yet, somehow, Devi managed to calculate the correct 23rd root of the 201-digital number the professor was supposed to write, not the one he actually wrote.
How is this possible?
To start, humans don’t calculate in the same way computers do – Devi didn’t run millions of calculations in her head to arrive at the answer. If she had, she would have arrived at the incorrect answer. Instead, she must have used some sort of heuristic.
For example, there are only 53 different 201-digit numbers that have a whole number as their 23rd root. If you only consider the first 15 digits of the 201-digit number, you can narrow down the possible answers further. Since the mistakes the professor made were further in the sequence, it’s also unlikely they factored into determining the correct answer. Devi’s achievement was more memorization than computation.
If the story had ended here, it would have been an intriguing enough to write about and draw some pithy conclusions.
But, as it turns out, someone dug into the math to determine how Devi must have solved the problem. It’s a long read but worth it, if you like math. For the rest of you, my over-simplified summary is as follows:
- Devi asked for the number to be 201 digits long
Knowing the length of the number ahead of time dramatically simplifies the problem; in fact, she only had to memorize 53 possible answers. - Devi had longer than 50 seconds to solve the problem
Mathematically, the first 6 digits of the 201-digit number are critically important to determining the answer. She could begin as soon as the professor wrote these first six digits and while he was writing the remaining 195 digits. It’s likely she had more than 4 minutes to solve the problem.
Shakuntala Devi pulled off amazing tricks of mathematics. She just wasn’t faster or smarter than a computer.
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