Monday, 12 August 2013

The Mirror of Reality

I looked into the mirror and saw
A jolly face grinning back-
A face that radiated vigour and youth,
As if it had not a single care in the world!

I was beginning to turn away,
But then, something caught my eye;
I looked more closely, and with a critical eye,
And the face didn't look so jolly after all-
Even the grin now seemed somewhat strained,
Almost as if it hid a grimace of pain.

I looked even more closely, and was taken aback.
The youthful exuberance slid away
To reveal a haggard and careworn face;
'Twas a face scarred by many battles,
A face with lines etched deep into it-
The unmasked face of a Survivor!

Sunday, 11 August 2013

The Spectre of Carnage

In the rotting decadence I stealthily prowl,
Ignoring reason, and its warning growl!
A piercing hunger gnaws steadily at my gut
As I stumble along with my eyes clenched shut.
In the deepest of shadows I silently lurk,
While centuries of evolution leave their mark-
Seeking a place which I could call home,
Like a restless soul I ceaselessly roam.
All around me the world lies ravaged-
The brutal savagery of man, uncaged!

Saturday, 10 August 2013

The Immortal Game

The Immortal Game was a chess game played by Adolf Anderssen and Lionel Kieseritzky on 21 June 1851 at the Simpson's-in-the-Strand Divan in London. It was an informal game played between the two great players during a break in the London 1851 chess tournament, which was also the first international chess tournament. Incidentally, Adolf Anderssen went on to win the sixteen-player tournament, earning him the status of the best player in Europe.

The French chess magazine La Régence published the game in July 1851. It was nicknamed "The Immortal Game" in 1855 by the Austrian chess master Ernst Falkbeer. In this game, Anderssen, playing white, sacrificed a bishop (on move 11), both rooks (on moves 18 and 19), and the queen (on move 22) to produce checkmate against Kieseritzky who had only lost three pawns. In doing so, he successfully managed to illustrate that two active pieces can be worth a dozen inactive pieces.

This game is acclaimed as an excellent demonstration of the style of chess play in the 19th century, where rapid development and attack were considered the most effective way to win, and where many gambits and counter-gambits were offered. In fact, in that era, not accepting gambits was considered slightly ungentlemanly. These games, with their rapid attacks and counter-attacks, are often entertaining to review, even though some of the moves would no longer be considered the best by today's standards.

 Animation of The Immortal Game

The game in algebraic chess notation -

1.   e4         e5
2.   f4         exf4
3.   Bc4      Qh4+
4.   Kf1       b5
5.   Bxb5     Nf6
6.   Nf3       Qh6
7.   d3         Nh5
8.   Nh4      Qg5
9.   Nf5       c6
10. g4         Nf6
11. Rg1       cxb5
12. h4         Qg6
13. h5         Qg5
14. Qf3       Ng8
15. Bxf4     Qf6
16. Nc3      Bc5
17. Nd5      Qxb2
18. Bd6       Bxg1
19. e5         Qxa1+
20. Ke2       Na6
21. Nxg7+   Kd8
22. Qf6+     Nxf6
23. Be7#

At the end, black is ahead in material by a considerable margin: a queen, two rooks, and a bishop. But the material does not help black. Through sheer strategic brilliance, white has been able to use his remaining pieces - two knights and a bishop - to force mate.

I have intentionally not annotated the game and left it as an exercise for the reader to figure out the motives behind some of the rather surprising moves and their possible alternatives. If you have too much trouble deciphering a particular move (or sequence of moves), please feel free to leave a comment and I'll be happy to explain. So, my fellow chess enthusiasts, go ahead and rack your brains, and have fun while doing it. Enjoy!

Confessions of an Eternal Optimist

I have been to hell and come back again;
I have lived through droughts and excess rain;
I have had my share of mirth and pain;
Sometimes I lose, sometimes I gain;
Yet, all the while, before your eyes,
I have dared to live life king-size!

Friday, 9 August 2013

Bangla Kobita - 2

আমি এক ছন্নছাড়া,
জীবনের বাঁধনহারা;
অনিয়মই নিয়ম আমার-
কথা নেই কোথাও থামার!

দুর্বল হয়েছে শরীর কদাচিত-
আক্রমণ করেছে মোরে জরা;
শুকিয়েছে ভাবনার জলাশয়,
মনেতে দেখা দিয়েছে খরা।

তবু প্রতিবারই সুপ্ত শক্তির জাগরণে
পলাতক হয়েছে সে জরা;
আর সৃজনশীলতার বাঁধভাঙ্গা উচ্ছাস
নিশ্চিহ্ন করেছে সে খরা।

হয়েছে যখনই চিত্ত ম্রিয়মাণ,
নতুন সুরে গেয়ে উঠেছে প্রাণ!

Thursday, 8 August 2013

Chess Puzzle - 1

Today, I am going to share a brilliant chess puzzle I came across on the internet.

The position below is taken from a game in 1737 involving the English chess master Philipp Stamma (c.1705–55). He authored the book 'Essai sur le jeu des echecs' (English translation: 'The Noble Game of Chess') in 1737, which introduced algebraic chess notation in an almost fully developed form before the now obsolete descriptive chess notation evolved. His name is also attached to Stamma's mate, which is a rather rare checkmate.

Take a look at the position above (white to move) and note that black is just one move away from enforcing a checkmate. Now, here's the challenge: can you come up with a forced sequence of 8 moves that leads to a checkmate for white?

You can post your answer (preferably in algebraic chess notation) as a comment below.

Lets see how many of you can solve this correctly. All the best!

Wednesday, 7 August 2013

Dominating Set in a Graph

Here is a nice little problem in graph theory that was posed to me recently (by Swagato) -

A dominating set of an undirected graph is a set of vertices $U$ such that every vertex in $V - U$ has at least one neighbour in $U$. Now, in an undirected graph $G = (V,E)$ having minimum degree $d$, if $(V_1, V_2)$ be a cut of size less than $d$, then prove that every dominating set of $G$ has a non-null intersection with both $V_1$ and $V_2$. [Note: size of a cut = number of cross edges]

My proof follows -

Let $|V| = v$, $|V_1| = v_1$ and $|V_2| = v_2$.
Without loss of generality, we can assume that $v_1 \leq v_2$.

Also, its easy to see that we must have $v_1 > 1$, because otherwise, if we have $v_1 = 1$, then all the edges incident to the single vertex belonging to $V_1$ cross the cut $(V_1, V_2)$. The minimum degree of the graph $G$ being $d$, there has to be at least $d$ edges incident to this solitary vertex belonging to $V_1$, which in turn implies that there has to be at least $d$ edges crossing the cut. However, this directly contradicts the fact that the cut $(V_1, V_2)$ has size less than $d$.

Now, since the graph $G$ has minimum degree $d$, each vertex $u \in V_1$ must have at least $d$ edges incident to it, out of which a maximum of $v_1-1$ edges can have a vertex also belonging to $V_1$ as its other endpoint. Thus, each vertex $u \in V_1$ must contribute at least $d-(v_1-1)$ cross edges to the cut $(V_1, V_2)$, which means that the size of the cut has to be at least $v_1.(d-(v_1-1))$. However, we already know that the size of the cut is strictly less than $d$. Combining the above two facts, we get:
\begin{align} v_1.(d-(v_1-1)) < d &\implies d.(v_1-1) < v_1.(v_1-1) \\\\ &\implies d < v_1 \hspace{44mm} \hbox{[ sincev_1 > 1]} \end{align}
This implies that the size of the cut has to be strictly less than $v_1$.

Let $U$ be any dominating set in the graph $G$.

If possible, let us assume that $U \cap V_1 = \emptyset$, which implies that $U \subseteq V_2$. Going by the definition of dominating set, each vertex $u \in V_1$ must be adjacent to at least one vertex belonging to $U$. Since $U \subseteq V_2$, this implies that each vertex $u \in V_1$ must be contributing at least one cross edge to the cut $(V_1, V_2)$. Thus, the size of the cut must be at least $v_1$, which leads to a contradiction.

Again, if possible, let us assume that $U \cap V_2 = \emptyset$, which implies that $U \subseteq V_1$. Going by the definition of dominating set, each vertex $u \in V_2$ must be adjacent to at least one vertex belonging to $U$. Since $U \subseteq V_1$, this implies that each vertex $u \in V_2$ must be contributing at least one cross edge to the cut $(V_1, V_2)$. Thus, the size of the cut must be at least $v_2$, and hence at least $v_1$, which leads to a contradiction.

Since both our assumptions $U \cap V_1 = \emptyset$ and $U \cap V_2 = \emptyset$ lead to contradictions, any dominating set in the graph $G$ must have a non-null intersection with both both $V_1$ and $V_2$. Hence proved.

Bangla Kobita - 1

গগনপটে রক্তাক্ত মেঘের আনাগোনা;
কালসিটে পড়া চোখে সূর্যটাও আনমনা।
জীবনের আতিশয্যে ধুঁকছে আজ প্রাণ;
সভ্যতার গরিমা আজ হয়ে আসে ম্লান।

আজ মানুষের ধমনীতে মিশে গেছে প্রবল এক বিষ;
স্বার্থের চীত্কারে ডুবে যায় বিবেকের ফিসফিস!
দেহের কারাগারে রুদ্ধ যত অশান্ত মানবাত্মা;
আত্মমগ্নতার এ যুগে সাহচর্য্যও বেপাত্তা!

Tuesday, 6 August 2013

Mind Warp

Harken back to those sleepless nights-
When reality fades and conscience bites;
When surreal thoughts begin to take hold
And distort our vision of the world manifold;
When we begin to realize the bitter truth,
In the grip of desires both foul and uncouth;
When the wind brings back the eternal pain;
When the universe threatens to lie still again!
In those moments, before we come around,
Germinate the seeds of ideas profound!

Monday, 5 August 2013

Standing still at a crossroad in my life,
I find myself unable to choose a way;
Balancing somehow on the edge of a knife,
I pray to survive just one more day;
Recklessly entering the dragon’s lair,
I try to think of a reason to stay.
Stumbling along, sans any verve or flair,
I still keep enjoying life while I may!

Yet another blogger strolls into cyberspace

Hello! So, here I am - yet another blogger starting off his journey on cyberspace. Finally decided it was time for me to jump on to the blogging bandwagon. This decision was probably inevitable given the number of friends I have who maintain such excellent blogs. It was just a matter of overcoming my characteristic laziness (ল্যাদ) and getting down to creating a blog of my own. Anyway, now that I've finally entered the fray as well, I guess they'll soon be facing some stiff competition.

Before starting off, it is my moral responsibility to convey a small word of caution to you all. As the name of the blog suggests, I will be pretty much writing about any random thing that catches my fancy. So, I guess you should be prepared for quite an eclectic mishmash - starting from amateurish attempts at poetry to geeky discussions regarding interesting problems in theoretical computer science; from passionate eulogies to tips on fitness and bodybuilding; from an occasional article or two analyzing a brilliant strategy employed by some grandmaster in chess to philosophical meanderings pondering over the meaning of life and the universe - you can never be sure of what you might come across here!

Anyway, now I have blabbered long enough for this to qualify as my first blog post. I sincerely hope that, in the days to come, you have as much fun reading this blog as I will surely be having while writing it. Ciao!