Locks, Mahabharata And Mathematics (An Exploration of Unexpected Parallels)

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Item Code: NAG360
Author: V. Raghnathan
Publisher: Harper Collins Publishers
Language: English
Edition: 2013
ISBN: 9789350296431
Pages: 222
Cover: Paperback
Other Details 8.5 inch X 5.5 inch
Weight 440 gm
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Book Description
About The Book

Jarasandha, a tyrannical ruler in the Mahabharata, was born as two symmetric halves - one from each of a king’s two wives. The half-infants joined to make a whole when a demoness juxtaposed them while preparing to devour the lumps of flesh. Thus, Jarasandha could be split apart, but would come together if the halves were laid side by side in the correct way. Until Bhima, the strongest of the Pandavas, split him asunder, and ensured he stayed dead by throwing the left half to the right and vice versa.

In a similar vein, there is a symmetrical lock, each side of which is only half the whole. To open or close it, you need to work both the halves.


About The Author

An academic for much of his professional life, V. Raghunathan (Raghu to his friends) taught finance at IIM, Ahmadabad, for nearly two decades before turning a banker as the president of ING Vysya Bank in Bengaluru. He is currently the CEO of GMR Varalakshmi Foundation and continues to be an adjunct professor at the University of Bocconi, Milan, Italy, where he has been teaching every year for the last twenty-two years.

Raghu has probably the largest collection of antique locks in the county, has played chess at all-India level, and was briefly a cartoonist for a national daily. He has been writing extensively for leading newspapers and magazines; his books include Ganesha on the Dashboard, Don’t Sprint the Marathon and Games Indian Play.



What could possibly be the common thread running through locks, the Mahabharata and mathematics? Truth be told, a very thin one! One could conjecture that there would be parallels between locks and certain aspects of coding and decoding techniques in mathematics relating to computer science. But anything beyond must surely feel like a bit of a stretch, especially if one states that one intends to tie stories from the Mahabharata into it as welL And yet, that is what I have tried to do in this book. Why would I try to tie these disparate elements (and therefore put in so much effort into writing it) if the book were merely an exercise in self-indulgence? It is simply to explore unexpected parallels, even if rough, across three entirely different worlds: of an Indian chronicle of epic proportions, centuries-old brilliant craftsmanship manifested in clever devices like locks, and the only absolute truth in the universe - mathematics.

Perhaps the only reason why my idle curiosity got me to loop a common thread through locks, the Mahabharata and mathematics was to indulge in an exercise in divergent thinking. To be able to say, so to speak, that it is possible to find anything if you look for it hard enough! But why these three entirely dissimilar ingredients?

In the case of locks, I have been collecting them for nearly three decades and I know something about old Indian padlocks - their beguiling inner mechanics and beauty; the ingenuity of the locksmiths fashioning them in our forefathers' times, with primitive tools but exquisite skills; and the bastardized metallurgy of ancient India that produced such timeless works of ingenuity, M~' collection adds up to some 800 different pieces, all in working condition, from the length and breadth of India. And r could not have been amidst them for nearly three decades without some intrinsic fascination with the variety and mystery they represent. The fact is, I discovered an entirely new world when I stumbled upon the intriguing imagination of the bygone locksmiths captured in the timeless contraptions they made.

As far as mathematics is concerned, I am hardly a mathematician, but my deep respect, awe and fascination for it arises from the fact that it is probably the only absolute truth in the universe. As Roger Penrose observes, while observed science may be limited by' the constructs of the human intellect, there is no such limitation as far as pure mathematics is concerned, This means, while perceived realities of physics or chemistry, for example, may vary across different universes, 2 + 2 must always be 4 and (a + b)2 must always yield a2 + b2 + 2ab in any universe. Now isn't that fascinating?

As for the Mahabharata, who cannot but be enthralled by the epic? At one level, it is a soap opera of epic proportions, capable of holding millions upon millions of us glued to our televisions on weekends even in the twenty-first century, At another level, it is a complicated human construct, encapsulating every conceivable nobility and foible humans are capable of, delineating every shade of grey that goes into making the human animal, presenting every conceivable dilemma - or rather, every difficulty of being good, as Gurcharan Das would put it.

The common thread across the three worlds was revealed to me for no apparent reason in a burst of inspiration over some four months. I decided to pen down the thoughts as they came, and the result is this book.

However, I must add a word here for the benefit of the readers. The book purports to be nothing more than a simple, fun text, and they will find no other takeaway, apart from an inkling of how completely unrelated things may have some fascinating underlying commonalities. It has no profound insights into how out-of-the-box thinking happens, and adds nothing to the existing body of knowledge about any of the three worlds it explores. The treatment of stories from the Mahabharata is fun and tongue- in-cheek, that of mathematics is equally light - scarcely beyond the high-school level, and the insight into locks just sufficient to hopefully leave readers clicking their tongues, saying, 'Oh I didn't know there was more to padlocks than what we see hanging on most doors.' Also, if the readers expect exact, one-to-one identity, correspondence or congruence between the stories, locks and the mathematical principles invoked in the context, they are bound to be disappointed. And if they wish to enjoy the sense of discovery of the unexpected parallels captured in the book, they will have to stretch their imaginations a bit as well. Expectations of a reader looking for an answer as to why there should be a parallel between only selected stories from the Mahabharata, some locks and some mathematics, I am afraid, are bound to remain unmet! Having said that, I hope readers will share the sense of wonderment I have experienced while exploring the parallels that bind the three non-parallel realms.

Some special individuals need mention. Meena, my best friend and wife, is always the first one I thank, for she always spends hours after hours editing drafts after drafts of my manuscripts. This book has been no exception. My niece Roopalika, an outstanding freelance graphic illustrator and graphic designer who, having enlivened the book by redrawing my photographs of the locks into the beautiful hand-drawn illustrations one sees in the book, deserves my heartfelt thanks. But for her, the book would have been drabber. And no less indebted am J to Krishan Chopra, my editor at HarperCollins, whose exacting standards have doubtless improved the quality of the book substantially. I am equally thankful to Prema Govindan for her outstanding copy-editing support, which has enriched the quality of this book significantly. And finally, my excellent friend Nilofer Suleman (a leading artist) and her daughter Shilo Shiv Suleman (an outstanding designer, illustrator and artist) who have done the wonderful cover of the book. And I am also indebted to my friend Ajit Rangnekar whose gracious comments on my manuscript encouraged me as much as they helped me improve the manuscript.

I would also like to thank Google and Wikipedia, the life-saving search engines to which I turn every time I have to search for my misplaced keys! Given the ease of making quick preliminary reference checks online, I for one - I am not sure about other authors - do often wonder how we were writing books in the BG and BW era. So thank you Google and thank you Wikipedia.




  Preface ix
1 Draupadi, the Lock with Five Keys and Polynomials 1
2 Jarasandha, the Split Lock and Symmetries 33
3 The Illusory Palace, Invisible Keyholes and Elusive Codes 51
4 Yudhisthira's Gamble, Chancy Locks and Mathematical Probabilities 75
5 Hanuman's Tail, the Monkey Lock and Long-tailed Distributions 87
6 The Enchanted Pool, a Lock That Thwarts Insertion 103
  of the Key and Problems That Resist Direct Attacks  
7 Abhimanyu, the One-way Lock and the Spaceship from the Moon 119
8 Ashwatthama Kunjaraha', Fractional Locks and Keys, and Fractals 133
9 The Scorpion Bite of Karna, Scorpion Locks and 163
  Bayesian Search for the USS Scorpion  
10 Shukracharya and Kacha, a Pair of Interacting Keys, and Binary Stars 185
  Appendix 201
  Notes 203
  Index 207
Sample Pages

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