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PM Essence
The Square Root of Minus One
- Shekar Hariharan

Let me start with a story of 17 camels. It sure is not what I wrote or created but then I am just “borrowing” it to come to a point.


Once there was a Sheikh who had three sons. Through his life he had seen many ups and downs. Now as he lay on his deathbed - he thought of writing his “Will” so he can distribute his so called wealth. It read – One-Half of my total asset should go to my first son, One-Third to my second and One-Ninth to my third one. Shortly after writing the will, he died.


After the funeral, the sons wanted to proceed ahead with the distribution as per their fathers will. But they struck a dead-end. There were two issues. One – the only asset that the old man had were camels. And Two – they were seventeen in number!



No matter what they did, they could not think of how one can divide seventeen by two, or three or nine! This was an insolvable problem using all the wisdom they had.


Then came a traveler who was crossing the village and happen to cross these fellas. He heard the “dilemma” and offered one solution. He said – “Why don't you take my camel and then see if it helps”.


So now they had eighteen (18) camels, One half (=9) went to First son, One- Third (=6) went to the second and One- Ninth (=2) went to the third.


So 9 (First Son) + 6(Second Son) + 2 (third Son) = 17.


After this transaction – to their surprise – The camel that they had loaned from the traveler was still left.


So the traveler took his camel back and proceeded back to his journey while the three sons sat perplexed – “How did this happen”


Okay – So why am I telling this story?


Well sometimes in our corporate life, we come across problems – technical, business, people, strategic or anything else where no “real” solution seems possible! It's almost like all those hours of brainstorming, stand-up meetings and/or review meetings just don't give us the solution we want.


We almost reach a point of “deadlock”, “brain freeze” or whatever else we may call it.


Does that mean “solution” doesn't exist? Or does it simply mean that “new problems” can't be solved using “old thoughts or methods”?


That's when “square root of minus one” comes handy!


Mathematically – Square root of minus one is called an “imaginary” number denoted by “i” and is used by Mathematicians and Scientists to solve “complex” problems. (Curious readers can google and find out loads of more information on it)


Like the name suggests – it doesn't exist (or rather need not exist) but merely by assuming its presence, complex problems can be solved.


Not many are aware, but “imaginary” or “complex” numbers are used widely for complex modeling such as determining how electrical circuits flows when alternating in those sinusoidal waves. Or modeling the forced spring/damper systems and movement of the shock absorber of a car as it goes over a bump. Or even in modeling the flow of a fluid around various obstacles, like around a pipe!


Using the concept of “imaginary” number is indeed very valuable for transforming the problem into a much simpler one.

Okay so what then?


In reality - the 18th camel could as well have been a figment of imagination (the “imaginary number”). It could have been conveniently added to the original problem and once the solution found, could have been simply discarded. We need not have had a traveler in the story.


Likewise in our own day-to-day corporate life (or even personal), the problems that look so complex just needs a different thought, a different assumption and a different “imagination” to simplify and arrive at a solution.


So the question I want to leave all of you with is –


Is it possible that the current “problem” or the “issue” that you are drowned in right now just needs that “imaginary” 18th camel to help get closer to the solution?


What is that 18th camel? Find that out and possibly you would be nearer to your solution.