Saturday, June 18, 2011

Attacking Chess

I recently played a game of speed chess at chess.com in which I attacked my opponent from the outset. The result was a game which ended in resignation after my 24th move. My opponent was Roxy of Jamaica who played black. Here are the moves of the game along with my commentary:

1. e4 d5
2. exd Qxd5
3. Nc3 Qa5
4. Nf3 Bg4

Black pins my knight but only for one move.

5. Be2 c6

Black makes an unusual move. Nc6 is far more popular.

6. 0-0 Nf6
7. h3 Bf5

Black decides to keep the bishop.

8. d3 h5

Black's move weakens his kingside.

9. Bd2 Qc7
10. Nd4 Bh7

Black moves the bishop again.

11. a4 e6

I play a4 to prevent expansion on the queenside with b5.

12. Bxh5 Nxh5

Black makes the move I want. Now I can win a pawn.

13. Qxh5 Qb6

Black threatens my pawn and knight but he should tend to the safety of his king with a move such as Be7 or Bc5 which permits castling on the following move.

14. Nxe6 g6

My knight cannot be captured because fxe6 puts black in check. Black's move creates a double attack but the black king is still in the centre.

15. Qe2 fxe6

Black has more material but the black king is too exposed.

16. Qxe6+ Be7
17. Bg4 Qc7

I pin the bishop.

18. Rfe1 Bg8

Black desperately tries to chase away my queen.

19. Qxe7+ Qxe7

Black's move is forced.

20. Rxe7+ Kf8

My rook and bishop are beautifully coordinated. Every black piece is on the back rank.

21. Rae1 Na6
22. Rxb7 Nc5

Black attacks my rook but this move is a mistake. I prepare a fork.

23. Be7+ Kg7
24. Bxc5+

Black decides to resign. I am up a knight and four pawns and black has three isolated pawns. With such a dismal position, he realizes the game is over. I win this game because of my superior pawn structure, good coordination of my pieces and well-protected king. At the moment of resignation, the three black pieces are on the back rank and the rooks are not connected. Black fails to develop them and I take advantage.

Sunday, June 12, 2011

Comparative Advantage

An important concept in economics is comparative advantage. It helps to illustrate the importance of trade between countries. Though one country may produce a number of goods more efficiently and at a lower cost than another, it is beneficial to trade if the other country has a comparative advantage.

Imagine that countries A and B both produce tractors and wheat. However, the number of hours needed to produce them is different in both countries. For one tractor, Country A needs 12 hours and Country B needs 4. For one tonne of wheat, Country A needs 4 hours and Country B needs 2. Here is a chart to summarize:

Country A tractor- 12 hours wheat- 4 hours
Country B tractor- 4 hours wheat- 2 hours

By comparing these numbers, it is clear that Country B can produce both tractors and wheat in less time than Country A. In other words, Country B is more efficient in the production of these goods and can produce both at a lower cost. It may thus seem that it is unnecessary for Country B to trade these goods with Country A.

However, trade is beneficial because the ratios spent on the production of the two goods are different in the two countries. If we compare opportunity cost, we notice that it is beneficial for both to specialize in the good which they produce most efficiently.

What does Country A give up if it produces a tractor? For every tractor that Country A produces, it gives up the opportunity to produce 3 tonnes of wheat.

What does Country B give up if it produces a tractor? For every tractor that Country B produces, it gives up the opportunity to produce 2 tonnes of wheat.

Likewise, we can also analyze what each country gives up in tractor production to produce one tonne of wheat. What does Country A give up if it produces one tonne of wheat? It gives up the opportunity to produce 1/3 of a tractor.

What does Country B give up if it produces one tonne of wheat? It gives up the opportunity to produce 1/2 a tractor.

It is clear that when the two countries produce tractors, Country A gives up more in wheat production. However, when the two countries produce wheat, Country B gives up more in tractor production. It is clear that trade can benefit both countries. Country A should specialize in wheat production and Country B should specialize in tractor production.

Though Country A can produce both tractors and wheat at a lower cost than Country B, it is beneficial for the two countries to trade with one another. Country A has a tractor-wheat ratio of 3:1 but Country B has a tractor-wheat ratio of 2:1. Viewed in a different light, Country A has a wheat-tractor ration of 1/3 and Country B has a wheat-tractor ratio of 1/2.

Country A can focus on the good which it produces most efficiently, wheat, and trade it for tractors from Country B. Country B can focus on the good which it produces most efficiently, tractors, and trade them for wheat from Country A. As a result, both countries benefit.

Thursday, June 9, 2011

Irish Numbers

Irish is an Indo-European language of the Celtic language family. Though it is an Indo-European language, it is nevertheless quite different from languages such as English and French. To demonstrate, here are the numbers from one to ten:

1) a haon
2) a dó
3) a trí
4) a ceathair
5) a cúig
6) a sé
7) a seacht
8) a hocht
9) a naoi
10)a deich

All of these numbers are written as two words. The number one has the "o" and "n" of English. The number two looks similar. It has a "d" instead of the "t" of English. The number three also looks similar to English. The number four does not look similar to the number four in English, but looks a little like the French number "quatre." The number five does not look similar to English but shares some similarity with the French number "cinq." The numbers six and seven both start with an "s", the same as English. The number eight also ends with a "t" and actually looks closer to the French word for eight which is "huit." The numbers nine and ten do not look so similar to English but nine also starts with a nasal and ten has a "d" instead of a "t" as in English.

Most of the Irish numbers from one to ten are not so similar to those of English, but a few, two and three, share many similarities. In a number of cases such as four and eight, the Irish numbers are actually more similar to those of French than those of English. From an analysis of the Irish numbers, one can see that Irish is an Indo-European language, but not a language that is very similar to English. For this reason, it is a Celtic language and not a closely-related Germanic language such as German, Dutch and Danish.