MILLION DOLLAR QUESTION

Yes, that’s true. If you solve this puzzle you get cool $1,000,000!! That is only the prize money, without considering the perks and fame that will come with it. You will be as famous as some Mr. Einstein or Mr. Newton. History will remember you as the person who solved a 150 year problem!!!


Yep, that’s right too!! It’s a 150 year old problem. For 150 years the best minds of the world tried to solve this problem and came up short. The great minds were convinced that a solution to this problem exists but were unable to find it. Even taking the aid of high performance computers couldn’t help the matter. Now, you must be thinking-“what the big deal about a damn puzzle!!”. Well, to answer that you have to understand the puzzle.

Let get introduced to the hardest unsolved problem in mathematics since 1859---“REIMANN HYPOTHESIS”.

And yes, I didn’t forget about the $1 million. Boston Clay Mathematics Institute declared in 2000 a list of 7 unsolved problem of mathematics. For each problem $1 million was announced as prize money. Since then 6 problems have been solved and the 7th and the most important one is still waiting.
In 1859, Bernard Reimann published his eight page article where he discussed this idea. It’s about prime numbers. So, let’s dig into the problem.
Prime numbers are type of numbers which can be divided only by 1 and itself. The series of prime numbers look like this.
1,2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73…and so on.
You can clearly see it. It is NOT a series. There is no sequence in the numbers. We can’t say what will be the number next to 59 without calculating individually each number. To make my point clear consider the following series, which is actually a series.
1,4,9,16,25,36,49,64,81,100,121,144,169,__.
We can see the sequence and we can also deduce the last number, it is 196. For the mathematically challenged people the series is simply the square values of natural numbers i.e. 1, 2, 3, 4, 5…and so on. We can even say what will the 500th number of the series without checking the in between numbers. By this definition the prime numbers do not constitute a series. It’s too haphazard.
But it is also mathematics. Mathematics can’t be haphazard. There must be a method in madness. People (not normal people, mathematicians I mean) tried and failed to find a formula of prime numbers. In a desperate attempt to find any resemblance of order they tried to find the occurrences of prime numbers. See for yourself.
In 1 to 10 there are 4 prime numbers, which means 40%, so there should be 40 prime numbers in between 1 to 100, but there are 25 actually i.e. 25%. In case of less than 1000 it is 168 or 16.8%.
And between 9999901 to 10000000 it is just 9. The next 100 contains just 2. This was a total chaos.
But, there are some who do not conform to the norms. They think in their own way using their own logic. We call them genius.
One such genius was Leonardo Eular. This guy found an order where seemingly everyone had failed. What he showed was not only remarkable was incredibly easy too.

1+ 1/2^2 +1/3^2 +1/4^2 +1/5^2 +⋯=2^2/(2^2-1)*3^2/(3^2-1)*5^2/(5^2-1)*7^2/(7^2-1)*…

It was really wonderful. On the left hand side was natural numbers like 1, 2, 3, 4…..and on the right side was the prime numbers 2, 3, 5, 7…..
There was an order here. It was a start, but wasn’t an end. This equation was developed further and it was proved that the power of the numbers is not only limited to 2. It can be raised further i.e. the following equation will also hold true
1+ 1/2^3 +1/3^3 +1/4^3 +1/5^3 +⋯=2^3/(2^3-1)*3^3/(3^3-1)*5^3/(5^3-1)*7^3/(7^3-1)*…

and also if the power is 4, 5, 6 anything.

Now, the stage was set for Mr. Reimann to appear and did so in style. He developed the equation one more step and proved that the power of the numbers is not only limited to natural numbers, it can be complex numbers too i.e. the equation will hold true even if the power is a complex number.

Complex numbers are numbers which are created using rational and √-1. √-1 is square root of -1 which is an imaginary number.
Now, the question that naturally arises is that WHY THE HELL DID HE USED COMPLEX NUMBER????
Well, the answer to this question is the topic we started on. Reimann kept on developing the equation and discovered this


1+ 1/2^(0.5+7√-1) +1/3^(0.5+7√-1) +1/4^(0.5+7√-1) +1/5^(0.5+7√-1) +⋯=0


The most important aspect of this equation is that the co-efficient of √-1, which is 7 here, is of NO IMPORTANCE.
Yes, you read it right. It is of no importance as long as the first rational part is 0.5. You can change the co-efficient to anything you like, positive, negative, fraction, real anything, it doesn’t matter.
So, this is also same as the above.
1+ 1/2^(0.5+3√-1) +1/3^(0.5+3√-1) +1/4^(0.5+3√-1) +1/5^(0.5+3√-1) +⋯=0


This is Reimann Hypothesis. But it is never going to be possible to physically check every number imaginable to see if the equation works. Reimann said that the equation will be equal to zero if the rational part of the power is 0.5 and the co-efficient of the irrational part is any number. That was 1859.

150 years passed. So many other problems were solved using Reimann Hypothesis. They are proved as “if Reimann Hypothesis is true, then……”. So, if those answers are right then Reimann Hypothesis must also be true. But that doesn’t solve the problem. It has to be proved using mathematical logic and the quest still eludes the man. Solve it and the glory is yours. 1 Million dollars doesn’t hurt either!!

Copyright=My Right To Copy?

I687, London:
The tall guy was sitting under a tree in a park; sipping tea and thinking about the inflation and the grocery bill. Suddenly something dropped on his head.
-Ouch!!
He looked upwards and discovered an apple tree and looked downwards and discovered gravity (figuratively speaking of course!).He published his findings in “Philosophiae Naturalis Principia Mathematica”


2008, Kolkata:
I was sitting in my friend’s house, sipping tea and talking about joining date of TCS and music of “Rock On!!” and listing to Debankar’s guiter .Suddenly something dropped on my head. I looked up and discovered a disk of “Munnabhai MBBS ”. I looked down on the disk and discovered copyright.

Actually I didn’t discovered copyright; I discovered the disk was original. Now that’s a bit complicated, what the hell original disk means? Most of us go through life without seeing a single original disk of anything i.e. movie, software etc. And here in my hand was an original piece, written behind “buy original CD or DVD, kill piracy”.

I heard so many times on TV, radio that musicians are requesting people to buy music and save their livelihood. I also saw people saying copyright means my right to copy. I looked at my computer, it was starting up. The OS was pirated Windows XP. The anti-virus was pirated; most of the softwares I use are pirated. Almost all the songs that sit on my machines are copyrighted and haven’t paid anything for them. The movies I have watched till now were all pirated. Where that does leaves me? In fact everywhere I look I see rampant copyright violation. I tried to calculate the damage done to entertainment industry by me. It came to around 500 movies and so around 20000 bucks. I alone cost that much!!! That too without considering the songs or eBooks collections that I pride myself. I didn’t dare to calculate further.

Then something struck me. I never heard any musician or author (of course of modern times) dying of starvation. That obviously doesn’t mean anything. I decided to probe further. An audio CD costs around Rs.100. Which is not very cheap considering it contains around 8-10 songs all of which are not good, whereas one can download it for free. And there is not much difference between qualities. So the choice is between high priced over hyped products and free illegal materials. No prize for guessing the winner.

I remember about a particular incident. It was 19th July 2007, Harry Potter and deathly hallows was to come out 2 days later and I was already reading it in eBook format. When it finally came out I have finished it by then. Now, if I was author it would be terribly distressing to know that my creation wasn’t fetching me anything or will it be? It would also probably mean that people like my writing so much that they are willing to suffer damage to eyesight by staring to computer monitor to read a book!!!

Actually it is very difficult to find a solution. One possible solution could be to lower the prices of original pieces or maybe to make the quality of original pieces better so that copying them damages their quality.

Its no point crying over piracy, otherwise it wasn’t possible to listening songs or watching movie so much. So, keep on doing whatever you do, just be careful to avoid using traceable downloads. CHEERS!!!

Browsing browsers-part II

Continuing from where I left earlier.

http://atanucybermidasblog.blogspot.com/2008/04/browsing-browsers.html

The times couldn't have been more exciting for net-addicted people like me;two new browsers are soon going to be launched and their beta versions are already available.

First,the old and much abused Internet Explorer is coming out with IE8.Its simply amazing to think how a once great corporation can come out with a worse version and declare it a new version.This happened with IE7;it was worse than IE6.Maybe it was more secure or things like that but its speed was awful.Hope that IE8 fares better.


Second and most important is Google Chrome.The product from the stable of the undisputed rulers of web world.I tried its beta version and its excellent.Its lightweight(takes very little resource) and slick.The only problem I can see is the customization options are very limited.Maybe it will be taken care of in the stable version.


Anyway thst was just to keep this blog alive.When the two browsers come out with their stable version I will write about them.