the zero

“… and what happens when we take a number out from itself”, asked the primeval Ghot.
“Nothing remains … at all”, the primeval master answered.
“So how do we show that there is nothing left in that?” the primeval Ghot continued.

The primeval Master closed his eyes and contemplated for a while. After he was done pondering over this question … an answer to which would change the course of human history, he opened his eyes again, picked up a piece of charcoal and  scribbled something on the parchment, that lay on the ground. Having done this, he stared at his handiwork in amazement and wonder.

The primeval Ghot peered into the parchment expecting to see something out-of-the-ordinary scribbled in that, and was quite disappointed when he saw that it was nothing more than a circle.

“That’s it?” he asked incredulously, “a tiny circle?”

The primeval Master smiled back.

— passage of time —

Little did the primeval Ghot and his Master know that by this feat, they had actually changed the way societies would evolve thousands of years down the line. Little did they know that they had by this act, shaped the way cultures would function, the sciences would develop and the world would become what it is today.

The little circle which came to being as a result of a simple question posed by the primeval Ghot, is today better known as the zero. Or, if you are BITSian, a zuc.

So why the sudden fascination for this seemingly well-known everyday little object, a fascination that has even compelled me to dedicate an entire blog post to it?

Why indeed? I wonder.

What does the zero denote?

Several things. For one, it is the answer most unsuspecting IITJEE aspirants tick in an OMR sheet, hoping that to be the correct option and then wonder what went wrong. For another, it’s the thing that comes back on your answer sheet, in red ink when you submit a blank one. For yet another, it is the thing which when added at the end of your paycheck, increases your worries ten-fold.

To the chemist, the concept of Absolute Zero, the theoretical temperature at which all thermodynamic activity ceases, is of profound interest. To the physicist it is the hearing threshold in decibels, amongst other things which projects zero into its numero-uno status. To the computer science student it is the quintessential role zero plays in binary mathematics and Boolean algebra that makes it so very essential. And to the historian, the year zero is the fulcrum about which the Gregorian calender is pivoted.

To the mathematician … lets not get into that.

So as you can see the zero is not only ubiquitous, but varied in it’s application in the real world.

What else does it denote?

Simply put, another of its applications lies in its usage as a symbol for nothingness, as a symbol for voids,  and emptiness. This application is possibly the biggest feather this beautiful number has in its cap, and the reason why it came to exist in the first place.

Which brings me to the thing I had in mind when I began writing this post.

Nothingness.

A queer thing it is. We know what it is, yet we don’t understand what it means.

We seem made out of it, yet we fail to embrace it. 

We come spinning out of nothingness, scattering stars like dust

We know that that’s what is in store for us, yet we don’t want it.

If it is nothingness that awaits us, let us make an injustice of it; let us fight against destiny, even though without hope of victory. 

It is that which is present everywhere, yet we fail to perceive it.

God made everything out of nothing, but the nothingness shows through.

One only needs to look at it the right way.

— pondering —

 Why the hell did I write all this? Forgive me if I’ve wasted your time all this while. I guess it’s the post-Oasis hangover. Need to get some sleep.

PS : my backy shouts and tells me that SENSEX has gone down by 65 points. That’s bad.

On a parting note, here’s some food-for-thought.

cheers 🙂

The Mathematics of Divinty and Evil

Mathematics is a beautiful subject.

Not the stuff we learn in college, though. Those are more of abominations; more of atrocious instances of human rights violation, hell bent on antagonizing innocent, unsuspecting students against this otherwise beautiful natural phenomenon. But, that apart, there still IS a mathematics which isn’t all about memorising formulae, which isn’t all about attending classes for getting to know which approach works best for which problem. Very little is known of this mathematics. And this mathematics, is the beautiful mathematics. The beauty of which comes to light, when one goes out of the text book, out of the constrained and contrived “syllabus” and delves into the sheer simplicity of stuff that goes on around us.

One such fascinating concept is that of the Golden Ratio, or the Golden Section. Considerably less known than the mainstream, stereotyped mathematics … but surprisingly ubiquitous in its application in the real world, this concept draws upon two things, and stands out from the rest: simplicity and beauty.

What is it?

Pretty simple. Take a line segment. Find a point on this line segment, and divide it into two portions such that the whole : bigger portion = bigger portion : smaller portion. The following figure will illustrate.

When you form an equation, and then solve it you get the following value for this “golden ratio” commonly represented by phi (φ).

Solving it yields the value

But all this is standard mathematics and juggling with numbers. Where’s the beauty in all this, the skeptic interjects.

Patience, I reply.

The ubiquitousness of this apparently simple and “dry” number is mind-numbing. From seemingly random assortment of florets in a sunflower or the petals of a rose, to the architecture involved in the making of the Pyramids of Giza and the Greek Parthenon, this little number holds the secrets of beauty, design and simplicity in the natural world like no other. Not surprisingly, it is considered to be the Divine Number or God’s favorite number, which he extensively used during Creation.

You can learn more about this Golden Ratio at http://www.goldennumber.net/ and also at … wait-for-it … http://en.wikipedia.org/wiki/Golden_ratio … so I needn’t mention its widespread applications in my meek little post. What I focus on however, is a little known aspect of the Golden Ratio.

And that is its Divinity.

As I mentioned a few sentences back, the Golden Ratio is considered to be the Divine Number. Now here’s a question. Ever heard of  something “opposite” to this? A number which symbolizes the “opposite” of divinity? An Iron Maiden fan would jump up to his feet and shout “The Number of the Beast! Six-six-six”

And that’s what it is. 666. Six hundred and sixty six. The Number of The Beast. The Number of the Devil. Or generally, the number of Evil.

Now if Divinity and Evil are supposed to be “opposite” to each other, could we come to the same conclusion mathematically?


And presto! We can!

sin(666) = –φ/2

The sine of the Devil’s Number is negative of one half of the Divine Number! In other words, they are opposite in sign! Coincidence? Sheer coincidence? Or God’s way of stating a fundamental truth? Perhaps we shall never know.


Oh and by the way, this was the 100th post on my blog 🙂 Took it’s time, but its finally arrived 🙂

the four color problem

Another post fueled by interest in all things geeky. Hell. It’s math this time. And it’s about something called the four color theorem. A seemingly simple theorem, with certain … er … beauties, that caught my eye, and thus led to me writing this post.

/*sheepish grin
the angle brackets are better off for expressing feelings but Blogger’s smart arse word processor very inconveniently considers any starting angle bracket to be the beginning of an html tag and all oddities arise. Hence the C/C++ style comments. Lol. */

The Four Color Theorem in its bare bones states that, (erm … quoting Wikipedia) given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color. Point to note : two regions meeting at points can have the same color


Well, I am myself not the absolute authority in the four color theorem, and any such assumptions gathered, or unintentionally implied should be … discarded immediately. Ahem.

The beauty I referred to in the opening paragraph is the method used to deal with these map coloring problems.

/*I know how suicidal the American spellings look, but unfortunately none of the browsers I use have spell check for any form English on this side of the Atlantic, so …*/

Yes, so coming back to the method. Here’s how it goes.

Consider the following map, showing a few countries of West Europe.

/* Pics taken from http://www.ctl.ua.edu/math103/mapcolor/mapcolor.htm, but as you can check, I’ve tried to explain in my own words */

The goal is too color the map such that no two countries sharing a common border have the same color. (Also, as a side information the minimum number of colors needed to colour a map is called the chromatic number of the map.) The completed map should look something like this.

So how to go about the predicament? Here’s how.

1. We replace each country with circles, maintaining a roughly correct relative orientation. 
2. Whenever two countries share a common border, we join the two corresponding circles with a straight line.
3. We ensure that multiple common borders are taken care of … France’s with Belgium, Luxembourg, Switzerland and Italy.
4. Now color the circles such that a) two circles at the end of each line segment have different colours and b) the least number of colors are used.

the steps in pictures :

Done 🙂 Well that’s about it. If it seems a bit too abrupt, my apologies. 🙂