Locks, Mahabharata and Mathematics | V. Raghunathan
What’s not to like about a book that discusses mathematics and the Mahabharata, personal favourites both? It’s one where you read about Duryodhana, Karna, Ambika and more of the great epic’s compelling characters. It’s one that looks at probability, fractals and more mathematical intrigue. It’s one about…well, locks too.
If that seems a comedown of sorts, it is. To a degree. But let me return to that.
Naturally, Locks, Mahabharata and Mathematics—An Exploration of Unexpected Parallels, is not meant to be the Mahabharata abridged. But V. Raghunathan does a fine job anyway of giving us a sense of its people—their intrigue, bravery and chicanery that make this such a great story. Any more than a superficial reading of the Mahabharata raises questions about what good and evil really mean, and the constant ballet they play out in us. Raghunathan reminds us of this. Yes, he sometimes uses metaphors that grate: “The Kaurava army set upon (Abhimanyu) like fleas on a lion. However, before Abhimanyu, they perished like the same flies in a forest fire." But I’ll excuse those, because he also works hard at telling us about…
…Mathematics, or how certain episodes in the epic remind you of mathematical ideas. Now, of course, these reminders are in Raghunathan’s mind. The original tellers of the story didn’t draw the parallels he does. Yes, some of the parallels don’t work as well. And yet, that’s the point: One of the deepest lessons I took from my computer science education was the notion of making connections between ideas and concepts. They may not always fly, but when they do, they have a certain irresistible power.
For example, Raghunathan got me thinking about half-truths. In a famous story, Yudhisthira says: “Ashwatthama hathaha iti, narova kunjaraha. (Ashwatthama is dead, but whether elephant or man I cannot say)". This persuades Drona, wrongly, that his valiant son Ashwatthama has been killed. He stops fighting and is then himself killed: a vital victory for the Pandavas.
So did Yudhisthira tell the truth? A lie? A half-truth? Was it justified? Do ends justify means?
Taking off from there, Raghunathan explores the mathematical meaning of dimensions. We live in a 3-dimensional world, but do we really? Is our understanding of dimensions quite that straightforward? He shows how a simply-defined series of changes to a basic triangle leaves it in a curious limbo: Not two-dimensional, not three-dimensional, but 1.585-dimensional. Just like Yudhisthira’s statement fell somewhere between truth and falsehood. Raghunathan observes: “Truth, like fractional dimensions, is often difficult to come to terms with."
Encouraged, you turn to the next chapter and read another famous story: Stoic Karna stung by a scorpion. What’s the parallel that Raghunathan paints? The mathematics that aided the search for a US navy submarine that sank in the 1960s. Fascinating, yes. But why this, you ask? Because the submarine was named Scorpion. No sir, that analogy doesn’t work so well.
Even so, there’s plenty here to make you think about both the Mahabharata and mathematical ideas, simple and complex. If the parallels sometimes fail, the individual themes are themselves thought-provoking.
The book’s weak link, unfortunately, is what is clearly Raghunathan’s pride and joy: His collection of antique locks. Going by his descriptions and his niece’s drawings, I’m as intrigued by them as the next guy. What a cornucopia of devices! Why did people design them? What were they used for? Questions worth asking. The pity is that the parallels to the locks often seem forced.
In the last chapter, for example, Raghunathan uses a page to describe a lock with two keys that themselves fit into each other. From here he moves on to Shukracharya and Kacha from the Mahabharata, then to a vivid mathematical bouquet: game theory, covariance, binary stars. Good stuff, but the connection to that lock, even with peculiar keys, is a stretch.
This is not to suggest that the locks are uninteresting. No, each seems an almost magical gadget. But perhaps they deserve a book of their own, one in which they are not forced to perform double duty as analogies.
And if that happens, perhaps we can look forward to another book from Raghunathan—one that explores, in as much depth as he wants, the links between mathematics and a beloved epic. That would be something.
Dilip D’Souza writes the column A Matter of Numbers for Mint.
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