Wednesday, April 2, 2014

Blog Post #80 - Zero - our hero and what does Sthanam sthanam dasha gunam have to do with your bank account?

When something great is invented there needs to be a story.

From Eureka Archimedes running naked on streets when he understood buoyancy  to Newton who has a head hit with Apple ( I read somewhere that it is the apple tree which should have fallen on Newton saving us from Calculus and Laws of motion and not the apple from a student of physics!) all the way to accidental inventions.

So some intelligent fellow added this - Aryabhatta woke up from sleep and said "Sthanam sthanam dasha gunam"  - once you sleep you can dream and create wonders!!

Whether you believe in the neighbors and eyewitness who has seen Aryabhatta in India sitting in a bedroom and saying something in sanskrit relating to zero or you use an iphone to check your message you should know that zero is important not just for math but also for shopping!

While reading Predictably Irrational: The Hidden Forces That Shape Our Decisions ( a wonderful book and i am on chapter 2/3)  I stumped about the concept of 'FREE'.

I can paraphrase Dan Ariely but he is funnier and smarter ( a rare trait for intellectuals who explain complex stuff!) and I strongly suggest you read his blog at
http://danariely.com/tag/free/


FREE is not zero
The concept of FREE comes with a price. Have you collected FREE pens and souvenirs or drank a cup of coffee in a Car dealership because it was FREE? I did.

Zero is not a simple idea.

Imagine zero and its friend 1 - they rule the silicon valley and the world!

(if you are in silicon valley you believe that is 'the' world')

In effect every single character and every image that you seen in the screen is being represented by zero and 1.

Zero is nothing. Representing nothing is something!

Zero is  hero when it is next to the number on the right side and the more the zeros and  more happier the receiver is.

Here is the confusion - Brahmagupta  or Aryabhatta do you know who created zero?
While we can read online about these two folks Pingala pops up- invents representation similar to morse code with 1 and 0.

We don't know who was Pingala.But he was before the inventors of zero (or the indians who take credit for it) Pingala did wonders with Binary system and here is what his system was  something like this

23
Does it Divide by 2- no so wrote 1
We get 17.
Does it divide by 2  - no so write 1 to the previous 1 which makes it 11 (another 1 next to the first 1)
Now lets divide 8 by 2
Does it divide by 2 - yes so write 0  so it makes it 110
Now divide 4 by 2 - yes it divides by 2 so makes it 1100
Now divide 2 by 2 - 11000

So he was thinking in binary!!

Solved in binary and worked in binary!

Long Live  Pingala!


Shunya - nothing as known in sanskrit represents words that mean absence of number.

Sthanam sthanam dasha gunam  roughly translates to every zero added adds an extra times 10 (thank god for my rudimentary Sanskrit skill..did i tell you i learnt Sanskrit for 3 years and this is the best translation i have done with that knowledge!)

Thinking in zero is next to impossible. Writing about zero and combining with the words available in a language is a game in itself.

Notice when you say it is not there (your car keys) does not represent zero while there are 0 cars in the parking lot will still be 0 after a bike enters the parking lot.

An un-examined zero is not worth thinking!

Arabs spread the zero from India to the Europeans. While Newton and other folks complicated them with Calculus .


Read this from
 http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut38_zero1.htm

and you lose your interest in Zero once you see what the academics can do with zero.

Rational Zero (or Root) Theorem
If rational zero, where 
rational zeroare integer coefficients and the reduced fraction rational zerois a rational zero, then p is a factor of the constant term rational zeroand q is a factor of the leading coefficient rational zero.

God save zero and our sanity from math
Keep Learning
Sivakumar Manikanteswaran

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