Monday, 17 June 2013


"The world owes most to India in the realm of mathematics, which was developed in the Gupta period to a stage more advanced than that reached by any other nation of antiquity. The success of Indian mathematics was mainly due to the fact that Indians had a clear conception of the abstract number as distinct from the numerical quantity of objects or spatial extension."
A.L. Basham, noted Australian historian

In the year 1911, noted Vedic scholar Bharati Krishna Tirthaji, a scholar of history, mathematics, Sanskrit and philosophy. and had made a comprehensive study of the four Vedas, Rigveda, Atharvaveda, Yajurveda, and Samaveda. Studying these texts for years, he was able to reconstruct a series of mathematical formulae, called Sutras. He continued the study for 7 years and compiled them together in a major single volume, which got published five years after his death, Vedic Mathematics, in the year 1965.

Repeated attempts of a few British mathematicians finally bore results duting the years 1981 to 1987, when Vedic mathematics started being taken seriously. A number of London and Indian schools took it up as subjects, and intellectuals started delving more time and energy into the same.

The Content:
The entire Vedic mathematics is divided into 16 Sutras or formulae, which when translated to english and analyzed, makes up 19 major aphorisms and 14 sub-aphorisms. It would be a bit too ambitious to include each one of them here, I would like to pick up a few simpler ones  which would strengthen my point..

Mental Multiplication:
So, what do you do when you are to multiply, say, 78X92?
You jot down the numbers hurrily on a notepad, do a quick 8X2, write down 6, carry over 1...blah blah blah...something like this
Because thats what was taught in schools. Now, what Vedic Maths asks you to do is, think beyond the obvious(am I sounding like some management Guru?)
The nearest 10s base to 78 (and 92) is 100
Step 1) We subtract 100 from both numbers
78 - 100 = -22
92 - 100 = -8
Step2) Add 78 and 92 and subtract 100 from it 78+92-100=70
Step3) Multiply -22 and -8  -22 X -8 = 176
Step4) Carry the 1 from 176 and add it to the result obtained in Step 2 70+1 = 71
Step5)Concatenate the two 71 and 76=7176
And this can be done mentally, which is almost impossible in the first approach. A similar approach could be taken up for two digits or three digit numbers

Mental Squaring:
What would you do if someone asks you to calculate the area of a 42m X 42 m land? Again take out your notepad and scribble?
Or maybe take the above approach and solve it out much quicker?
Or maybe take another better and much interesting approach?
Step 1)Round of 42 to the nearest 10s, ie 40.
Step 2)Now add the remaining amount, ie 2 to 42 ie 44
Step 3) Multiply 40 and 44(much easier), ie 1760
Step4)Now take the number from step 2, ie 2 and square it, ie 4. Add the number to result of Step 3, ie 1764

Cubing a two digit number:
What would you do if someone asks you to find the volume of a 25X25X25 box?
Consider ab=25(where a=2, b=5)
Step 1)Cube a, is 8
Step 2)Divide b by a, ie 5/2=2.5
Step 3) Now write four subsequent products of a with the result of Step 2 and prepare a matrix
8    20     50     125
Step 4) Double the number at 2nd and 3rd place and add them at their subsequent places. Carry over the leftmost digit if the sum is of two digits
8    20     50     125
      40     100
8    60     150   125
8    60     162    5
8    76     2        5
15     6    2         5
The answer is 15625

Multiply and two 2-digit numbers:
If the base 100 method(the first in this blog), still looks tougher to compute mentally, or if you want to explore some more of it, here is another
Consider you have to multiply 12X34. Prepare a matrix of the two numbers.
1     2
3     4
Step1) Multiply ac, ie 1X3=3
Step 2)Multiply bd, ie 2X4=8
Step 3)Add ad and bc, ie 4 and 6=10
Step 4)Prepare another matrix mentally with the results of Step1, 3 and 2 respetively
3     10     8
Step 5) Carry over any extra digit to the left
4   0   8
The Answer is 408

More practical usage of Vedic Maths: Convert kilo to pounds:
Often people switch to Google in the blank of an eye when asked to fill up a form with weight as pounds(when they are more familiar with kilo). Or they would switch to their cellphones.
Well, its much easier to do it mentally, and a better way to keep the mind healthy.
If we have to convert 85 kilo to pounds,
Step 1) Double the kilos, 85X2=170
Step 2) Divide the answer by 10, ie 170/10=17
Step 3) Add the two numbers, 170+17=187, and thats the answer.(to the nearest integer)

Adding to time:
Whats the fastest way to calculate if the current time is 4:15, and someone asks you to calculate the time 2 hours 55 minutes later?
You first add the minutes and then the hours, which is quite simple as such, but then what would you say about this
Step1) Add 415 and 255, ie 670
Step 2) Add 40 to the answer, ie 670+40=710,and 7:10 is the answer

Concept of infinity and zero:
Two concepts highly useful in almost every practical application of maths in daily lives and even for astronomical calculations.
Infinity finds its first usage in the Yajurveda. Vedic men had several terms to describe what is infinity, ananta, purnam, asamkhya being few of them. Consider the following shloka out of the Yajur Veda,

पूर्णमदः पूर्णमिदम पूर्णत पूर्णमुदच्यते
पूर्णस्य पूर्णमादाय पुर्नामेवावासिश्यते 

From infinity is born infinity. When infinity is taken out of infinity, only infinity is left.
Till then, the Greeks used to distinguish between numbers with positional systems, like 27,207,270 would be represented as 27, 2 7, 27 . this system did not provide much flexibility to them to write large numbers with regular instances of 0.
Similarly, Romans didnt have the concept of 0, and had to write numbers like 101,000 as 101MMM.
AtharvaVeda described how the vale of a single digit number increases by 10 by writing 0 in front of it.

A fact iterated in the movie Namaste London, Trigonometry even got its name from Vedic mathematics, the word being Tri(three)-kon(angle)-mati(perimeter). Though, now the concepts have already been discovered and have been in use since years, The circular nature of Sin, Cos and Tan finds its mention in the Vedas.
The fact that Sinx/Cosx = Tanx finds its mention in the Vedas.

Currently, as you are reading all of this, researches are being carried on, and undertaken, including the effects of Vedic mathematics on children. Major research is being done on how to develop more powerful and simpler application of Vedic mathematics in geometry, calculus, etc.
What makes Vedic mathematics different from other schools and branches of theoretical and practical mathematics, is the flexibility of Vedic mathematics in providing them freedom with creating their own methods and breaking the "correct answer" jinx.
Vedic Mathematics provides us with quick and fast one-line formulae which speeds up mental calculation. It is a mental tool which not only helps a person solve complex problems quickly, but with repeated practice, also helps a person concentrate better.

Its absolute pity, that in spite of it being such a great marvel as "Vedic Mathematics", some elitist, from within the Indian sub-continent itself, claim it to be a farce. They say that they dont find any such reference in Vedas, and that it was a result of imagination of Tirthaji himself.
The Vedas, primarily, have been known to reveal the true knowledge and meaning of the verses, the hidden secrets to those who are worthy. While this may appear to be a line straight out of a Dan Brown book, it is a mighty known fact that Vedas are written in a cryptic language and a mere translation would mean nothing or may produce some relevant results. The Vedas are believed not to reveal the true meaning to the reader, but rather help the reader find certain answers, which others wont be able to see or even validate.
The irony is, that while the western world is embracing and opening up itself to the charms and secrets of Vedic Mathematics, there are Indians themselves, who claim the Vedic Mathematics to be a lie.
Nothing is greater a tragedy than to not believe in your achievements while the world celebrates them

Realists, as always, would claim that Vedas do not actually teach mathematics on the face of it, but the fact is Vedic mathematics is gradually making a stronghold in the education system of the entire world and is soon becoming a force to reckon.

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Monday, 3 June 2013

The Krishna Advantage

In older times, old enough to be termed mythological, the kings used to have a council of ministers, The Board of directors, who used to suggest various methods and tools to improve and expand their kingdom, generate more profits, while keeping the people happy.
Now, not all the kings were exactly concerned with keeping their people happy, they were more concerned with their exploits and trying hard for their names to be etched into the memory of all future generations to come. So, you have books and songs written about them, huge palaces built by them, and cities being named after them. Out of these kings, seldom came the ones, who had perfected the art and skills of management so well, that not only they grew to the divine status they deserved and commanded back in those times, they are synonymous to God even thousands of years later in this modern world. Lord Rama was one, Lord Krishna, another.

They didnt have any educational degrees back then, and neither the colleges which would specialize in such courses, so the practice of "branding" people with their educational qualification didnt exist. Whatever knowledge they possessed was majorly on account of them being earned through their initial years in Gurukuls and then while gaining experience when interacting with the world. It therefore, would be no smaller a feat, if a legend rises high, so as to attain a divine status. Sri Krishna had all what it takes to be one of the greatest managers of all times, and we are not talking of Bhagvad Gita yet.

Ethics first: So, Arjuna was the husband of Krishna's half sister. And that would make him an ideal choice for Krishna to take sides with. Why the dilemma then, when both Duryodhana and Arjuna visited him to ask for his help?
Being an upholder of Dharma, Krishna would never take sides based on relations. An attribute similar to the concept of Internal Equity in management terms.
So, Krishna not only gives both of them an equal opportunity to take him into their sides(and Duryodhana pretty much knows it, the reason why he approaches Krishna), he also decides to be fair again and asks Arjuna to make a choice between himself and his entire army. Arjuna chooses Krishna himself, and the entire army is given to Duryodhana. So, Krishna always put ethics ahead of priorities. But now the question, why did Krishna give Arjuna the chance to make a choice?

Why Arjuna? As per legends, Krishna was sleeping when both Duryodhana and Arjuna arrived near his bed side to ask for his help. Duryodhana arrived first, and considering himself to be the superior one, sat besides Krishna's head. Arjuna, who respected Krishna as a father-figure sits near his feet. When Krishna wakes up, he sees Arjuna first, and thus, decides to give him the choice of choosing first.
Krishna makes this decision, not because he knows that Arjuna respects him a lot and considers him a father-figure(that would have been a bad management skill!)
Krishna is always considered a father-figure, a Guru in the entire Mahabharata. If legends are to be believed, he has already shown God-like attributes and miracles before this setting. Still, Duryodhana, bitten by his ego, chooses not to respect Krishna, costing him the opportunity to make the first choice. Arjuna, a warrior himself greater than all his contemporaries, displays the qualities of a humble person. Arjuna places his aim and vision ahead of his ego and thus, Krishna chooses him to make his choice first.

On a side note, Duryodhana was quite happy on being given the army, this was what he would have chosen anyways.
(Image taken from internet)

Raas-Leela: I have never seen a divine and sacred term being misused and quoted in such derogatory terms as Raas-Leela, special thanks to Bollywood. 
As per legends, in Raas Lila, Krishna plays flute and girls danced around him. The Raas Leela happens in dark forests, where the girls are away from security of home and family, yet feel secure enough. They dance around Krishna, not for any duty or custom, they do so for the love of him, at their own free will. Krishna is believed to be giving complete attention to each and every girl, and the moment they try to gather more part of his attention or feel Krishna loves her more, Krishna disappears for her.

The above setting is the perfect model of how an organizational setup is ought to be. Everyone feels equally appreciated and safe within the realms of the organizational culture. No one is supposed to be jealous and there should be gradual warmth among people. There should be perfect harmony, and its all in the hands of the manager, the leader, the Krishna.

(Image taken from internet)

On another side-note, Krishna was only 8-10 years old when he performed the Raas Leelas, so to use the term in derogatory terms by Bollywood is not only incorrect, it is highly stupid.

Commitments First: Radha was the first and the biggest love of Krishna's life. They loved each other like the body and soul(jeev-Atma and Param-atma). What then, made him leave her and travel to Mathura?

(Image taken from internet)

Krishna and Radha were together since their early childhood days. It is even believed that radha was born blind, and she gained her sight only after seeing Krishna. The childhood pranks, the games they played together and their celebration of Holi is legendary. But, as a child, Krishna never knew that he was destined to be a king, nor did Radha.
Once Krishna knew he was to kill Kansa and then be crowned as the King, Radha choses to stay back and keep alive the memroies of their love together. A staunch believer of Karma, Krishna knew his destiny was now different from Radha and their love would never be the same once they are together in the palace. Her staying back would etch their eternal love forever in the Vrindavan.

Krishna chose to follow his commitments over his personal prefernces. He could have chosen to stay back, but then the world would never have seen such a just and enigmatic King. The Mahabharat would not have been won by Pandavas, the Bhagvad Geeta never told. The power of letting your personal desires go in the pursuit of betterment of organization is what he teaches us.

(Image taken from internet)

The Strategist: Krishna knew, had guessed it from the start itself, that with a smaller force, the Pandavas dont have much of a chance against the mighty Kauravas who had the likes of Duryodhana, Karna, Bhish-Pitamah, to name a few. He also knew that though Kauravas would stoop low to unethical methods, if situation demands it, but the Pandavas would never do it under Yudhishtira.
As a smart strategist, he never broke any rule, but bent the semantics of the rules much to the benefit of the Pandavas.
He knew Bhishm-Pitamah would never attack a eunuch, so he asks Shikhandi to stand in front of Arjuna while Arjuna shoots his arrows at him. Arjuna vowed that he would kill Jayadratha before sunset and Jayadratha goes into hiding. Krishna stages a solar eclipse to make Jayadratha believe the sun has set and come out of hiding.
A good and ethical manager never breaks the rules of the organization and the society, but should be smart enough to bend these rules, being in the realms of ethical processes, to the benefit of his company.

(Image taken from internet)

The Motivator: And finally the Bhagvad Geeta. For the sake of upliftment of Dharma, and the destruction of Adharma, Krishna would never shy away from taking any step. Even if it would mean destruction, it would be creative. Arjuna was worried that the people he is fighting are his own family, and there will be blood shed. Krishna not only motivates him to gear up for the battle to follow, he emphasizes on creative destruction. He controls the entire army of Pandavas under his single command and guides them to victory, in spite of facing the mammoth Kauravas.

And to think of it, in the end, Krishna had vowed not to play any combative role in the entire war. He was there as a strategist, motivator, a guiding force, never really taking part in the war physically, the qualities a good manager ought to have. In-spite of a smaller workforce, he guides them to success, purely based on his management skills. Skills, which no one taught him,which cannot be imparted, he learnt it himself. Each chapter of his life, be it his friendship with Sudama, his friendship with Arjuna, his fight with Kansa, has a lot to teach us. No wonder, he commands one of the biggest headcount of devotees in Hinduism.

Jai Shri Krishna

Coming up with a book based on Indian history/mythology.
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I would like to end the post as of now, and would like to know what you thought about it. If you are on Facebook and are interested in such topics, please click on the link below and like the page which comes up.Khoj-In Search of Lost Signs