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James Grime answers your Shakuntala Devi questions

This is a follow-up to James’s FAQ for the 2014 film The Imitation Game.

Shakuntala Devi is a 2020 Indian Hindi-language film about Shakuntala Devi, a performer of impressive mental calculations, available now on Amazon Prime.

Who was Shakuntala Devi?

Shakuntala Devi was known for her impressive feats of mental calculations. These included multiplying large numbers almost instantly, calculating roots of large numbers and giving the day of the week for any date. Devi appeared in the Guinness book of world records for multiplying two 13-digit numbers in 28 seconds, including the time it took to say the answer. 

Devi’s skills were so impressive that she was dubbed “The Human Computer” and travelled the world entertaining audiences with her mathematics show.

Amazing! I wish I could have seen that.

No problem, here is a short clip of Devi performing some of her skills:

And if you want to see more, here is a longer clip (35 minutes) that gives an even better idea of her act.

I watched those clips. They were really good.

I thought so too! What struck me was how funny she was, and how skilled she was as a performer.

Shakuntala Devi must have been a genius!

Ah. Now we are getting into more difficult areas. I don’t want to diminish Devi’s skills, however there are a number of techniques (or “tricks”) that can make seemingly impossible calculations, possible. It’s fun and entertaining, and you can learn it too.

I can learn it too?

Absolutely.

Like what?

OK. Imagine you ask a volunteer to pick a 2-digit number, then multiply the number by itself 3 times (so cube it). They tell you the result, and it will probably be something quite big, for example the result might be 314,432. Instantly you can tell them what was the original number. In other words, you can tell them the cube-root.

How?

To do this you need to memorise the following table. It is a table of the cubes of the numbers from 1 to 10:

132333435363738393103
1827641252163435127291000


If you are given the number 314,432, then we know the cube-root is between 603 (= 216,000) and 703 (= 343,000), which tells us the first digit is 6. 

And since 8 has the only cube that ends with a 2, (83 = 512), then the second digit must be an 8. 

Therefore, the original number was 68. This technique will work for any 2-digit number.

Whoah. I couldn’t do that instantaneously!

It’s not completely easy. It takes skill and practice and it probably helps if you have a good feel for numbers. But it’s a lot easier than calculating the cube-root of a number without this technique. And very impressive to people who don’t know how it’s done.

Notice that this method would not help you calculate the cube-root of 314,433, where the answer is not a whole number. So, it is a bit of a trick, which is entertaining but not very useful.

So, did Shakuntala Devi just memorise all the answers?

No, it was calculation not memorisation. Another favourite trick of Devi’s was to give the day of the week for any date. This doesn’t involve memorising every calendar of the past century, instead there is a calculation you can learn and perform yourself. You can learn the trick with this page by Jonathan Rawle. I once did the trick in a job interview.

And did you get the job?

I did.

Well, aren’t you cool.

Not really.

Well, Shakuntala Devi sounds cool, and someone should make a film of her life, preferably available on a major streaming service.

Thanks for that segue, for there is such a film, titled “Shakuntala Devi” and available now on Amazon Prime.

Oh really? Well then I’m glad I asked. Is it any good?

Actually, yes, I enjoyed it. I thought it was fun and breezy, particularly the first half of the film which contains most of the biographical details of the Shakuntala Devi story. I think a mathematical audience will get a kick out of that. 

The second half of the film is more soap opera territory, examining Devi’s difficult relationship with her daughter, and in that case your mileage might vary. I didn’t mind it at first, but it could have been shorter.

Is the film accurate? This is very important to me when watching films about famous mathematicians.

It’s hard to tell. There isn’t much biographical information about Shakuntala Devi out there, and the information that is out there might be unreliable – Devi was a performer, who may have embellished the facts. Indeed, in the film, Shakuntala Devi is challenged on this point. 

So, I can’t verify the truth. But I can present the events of the film, with occasional points of order, if you’d like.

Yes, please. Occasional points of order are my favourite. How does the film start?

We start with Devi as a young child and her family discovering her gift for calculation. Which they decide to monetise, taking the young Shakuntala around India to perform shows. This ends in resentment from the young Shakuntala.

Your first point of order is that the film leaves out that Shakuntala’s father was a circus performer and magician himself. I think it’s worth mentioning.

That sounds a little sad so far. Is it a sad film?

Not at all. And here is where we get to the most fun part of the film, where we see Devi as a young woman, moving to 1950s London, and having a great time.

Devi starts performing her shows around London, despite the niche appeal of a mathematics themed show. This all changes when, while on the BBC, Devi makes a calculation that the computer gets wrong. Devi is dubbed the Human Computer and is famous!

And do they ever even bother to explain the maths?

Surprisingly, they do! And not just once, but around six or so occasions throughout the film. And done with enthusiasm.

Really?

Yes. I was surprised and delighted. It made a change from other films about famous mathematicians where the maths is explained reluctantly, or ploddingly. This was a joy.

That’s great. What was Shakuntala Devi like?

Judging from the clips you can see of her online, I think she was pretty cool. She was a smart, funny, independent woman. And that’s what we see in the film which is joyfully feminist in many ways. 

She was certainly a character! And played charmingly in the film by Vidya Balan.

Sounds rosy!

Pretty rosy. Although the film also shows Devi to be far from perfect. She can be defiant to a fault, and her strong personality can be overbearing, especially in relation to her daughter. It’s nice to see some edges, although the film is hardly gritty and never dour.

Is this the soap opera part of the film you mentioned before?

Right. The film tackles the very real-world problem of “having it all”. The career, the success and the family. A very relatable problem, which ends with Devi’s daughter resenting her famous mother.

This thread takes up most of the second half of the film, and could be shorter. If you have come for the maths, then this part of the film might not be for you.

At the same time, this part of the film is also peppered with some of the most famous mathematical and non-mathematical events of Devi’s life.

What kind of non-mathematical events?

Well, I think it’s pretty cool that in 1977 Devi wrote an academic study of homosexuality in India. In which, Devi called for complete acceptance of homosexuality and its decriminalisation. Devi said that the book was inspired by her husband being gay. Yet the film shows this as another example of Devi embellishing her story.

Devi also wrote murder mysteries, dabbled in politics and was an astrologer. All part of her life as an entertainer!

Give me famous mathematical events! What are they?

In 1977, Devi calculated the of the 23rd root of a 201-digit. She did this in 50 seconds, despite the fact it took the computer 60 seconds to calculate the 201-digit number in the first place. An amazing achievement, and the story of beating the computer became part of the Shakuntala Devi legend.

Wow! That’s impressive!

Really impressive. But don’t forget, Devi was a performer, and not everything may be as it seems. Here is a great breakdown of this calculation by Peter S Magnusson.

In short, in not exactly test conditions, with a bit of showmanship and parameters set by Shakuntala, Devi was able to find the 23rd root, similar to the method of finding cube-roots that I explained before.

I’ve heard similar criticism of her Guinness World Record in 1980, when Devi multiplied two 13-digit numbers. Devi would have been able to start her calculations as soon as the number starts to be written on the board, and not just in the 28 seconds it took to say the answer.

Aww. Can I still be impressed?

You can. I still think it’s impressive.

Another famous event depicted in the film was when Devi was tested by Arthur Jensen, a psychology professor at Berkeley. 

Jensen couldn’t explain her mathematical abilities. This is probably unsurprising, given he was not familiar with the techniques of mental calculations.

However, this event became part of the Shakuntala Devi myth, and it was implied that her skills were unexplainable. This is the part of the myth that sits uneasily with me.

How so?

Devi wrote a book explaining some of her methods. It’s called Figuring: The Joy of Numbers. It’s pretty good. It’s full of number-y fun, bits of mathematical trivia, and shows you some of the easier calculations, including a description of the calendar trick. It’s a good maths book for young people.

On the other hand, she would be vague about her methods, particularly in interviews, and gave the impression that it was a special gift and not something anyone can learn. So, it’s mixed messages.

And you could end up believing hard sums to be the height of mathematics.

So, are you a fan?

I am a fan! Shakuntala Devi was a fantastic ambassador for mathematics. 

By performing her shows Devi made mathematics fun, entertaining and inspiring. 

Through her books Devi promoted maths, not just for calculation, but as a way of thinking. 

And I think the film not only captures Shakuntala Devi’s love of mathematics but also her love of life.

How does the film end?

With everyone reconciled and a dance number. Enjoy.

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