|The Modulus function X|
Yesterday, I had an interesting lecture on the concept of Inequalities and the modulus function. The absolute function (modulus function) of a real number basically looks like the one in the image above. The mathematical definition states that,
For any real number ‘a’, the absolute value or modulus of ‘a’ is denoted by |a| (a vertical bar on each side of the quantity) and is defined as
|a| = a (if a is greater than or equal to zero)
|a| = -a (if a is less than zero)
In simple language, the modulus function ensures that a quantity has only positive or zero values but not negative. It means that anything inside the modulus |a| |b| |c| |1| |2| |-3| |-1000| will have a positive value once the modulus sign ( || ) is removed.
The gravity and importance of this function and concept holds good not only in the mathematical world but also in the real world. It can be applied to even our lives. So, we can place ourselves in the place of the variable ‘a’ in the definition whereas the modulus sign ( || ) can be thought of as the obstacles we face in our lives. Obstacles, barriers, rigid mindsets, defeat, disease, accidents: it could be anything which hinders our progress or our lives for that matter.
Consider the following images.
|The varying heights of the Modulus sign in the function|
We have seen that in any modulus function, once the modulus sign is removed the variable takes a positive value, which means that all negative values get left behind. Similarly, in a modulus like situation in our lives, we must look inside ourselves and see if there is any negativity present or not. To get out of the situation, all such negative thoughts have to be left behind. In fact, such thoughts should not occur even once in our minds.
Consider yourself in place of the variable ‘x’ in the diagram. The only way you are going to be able to scale that sign of modulus is by using all of your positive energy, your positiveness. With increasing heights, the amount of positive energy needed will be even higher. Our positive thinking, ability to overcome Inertia and keep moving forward is what helps us overcome situations of great adversity. Although the path may be painful, although the process may take some time, although everything seems to be lost, there is always our positive thoughts to guide us.
Man is the most unique and sophisticated creature to have inhabited the Earth till now. The process of evolution has been most accentuated in the case of humans. The factor which has worked in the favor of evolution is- Hope, man’s most potent source of positiveness. Without hope, we would have just collapsed and might not have it this far into history. Hope is what differentiates us from other creatures and hope is what has kept us alive.
|The pit from The Dark Knight Rises|
In the recently released film, The Dark Knight Rises, Director Christopher Nolan has depicted a similar type of situation. In the first encounter, Bane proves to be too strong for Batman and breaks his back. Instead of killing Bruce Wayne (Batman), Bane sends him to a prison that features a winding pit which no one has ever escaped, except for a child. Bruce first regains his strength and power and then attempts to climb the treacherous pit but fails in two attempts. His anger starts rising but then he is made to realize that it is not his anger but his fear of death which will make him more powerful. He learns that in order to get out, he must climb with fear of death in his mind, which means climb without the rope. At the entrance of the pit, there is a final jump needed to be made between two landings.
This situation is exactly like the modulus function I spoke of earlier. Without using the rope, the only thing which can guarantee you escape from the modulus sign and in Batman’s case, the pit is the Positive energy.
A negative thought would have said “It’s impossible” “I can’t do this” but a positive thought would have thought otherwise “I will make the climb” “I am going out of this prison”.
In the film, we see that Batman is able to make the jump, the final ‘leap of faith’ and escape from the prison because he had a hope, that he would survive, escape and save the city.
Coming back to the first image of the post. I wish that all of us are able to make that climb out of our personal hurdles, our personal pits, our own Modulus function-like situation. Just like how Batman did it, just like the variable ‘a’ in the definition of modulus function and the variable ‘x’ in the first image. Make the following conversion a possibility in your lives:
[ This post is a dedication and tribute to my Aunt in Mumbai who was recently diagnosed with throat cancer. She had to undergo a surgery to get it removed, however, the number of surgeries increased as a result of complications. She has just regained consciousness yesterday and now embarks on the journey of recovery.
With great positiveness comes hope and with hope comes everything, including recovery. Godspeed. ]