Posted in History & Literature

## Tic Tac Toe

Tic Tac Toe is a simple game where you and an opponent make a mark (X or O) on a 3×3 grid once per turn, until one person has made a line of three marks in a row (horizontal, vertical or diagonal).

However, it is so simple that there are only a certain number of permutations, meaning that if you know the algorithm, you can win most of your games (assuming your opponent does not also know the algorithm). This is called a solved game – unlike chess, where there is a near infinite number of ways the game can play out.

First, let’s take the case of you starting first. Put a X in a corner. If your opponent does not put an O in the centre, you automatically win. Your next move is to put an X in any corner away from the O. Your opponent will have to put an O between the two X’s to prevent a loss. Once they do this, you can either put an X in the centre or another corner to create two possible winning moves and your opponent can only block one. You win.

If your opponent puts their O in the centre, things get more complicated. Now you can only win if your opponent makes a mistake – otherwise the game is guaranteed to end in a draw. You can take one of two options:

– Place an X in the corner diagonally opposite to your first X. If your opponent puts an O in a corner, you win by putting an X on the last corner to block their attack and create your own double-attack.
– Place an X on an edge square that is not next to your X. You can win if your opponent puts an O in a corner not next to an X by blocking their attack and creating a double-attack.

If your opponent plays first, then you can never lose. If an opponent starts in the corner, put your X in the centre. All you have to do now is block your opponent’s attacks and you will force a draw.
The same strategy applies if your opponent starts in the centre – put an X in any corner then block every attack. The game will end in a draw unless your opponent slips up.

As you can see, there are only so many ways a game can play out, meaning it is very easy to force a draw.
A more interesting game is omok (오목 in Korean, gomoku in Japanese) – where you put white or black stones on a 15×15 board to try and connect five stones in a row.

Posted in Philosophy

## Zugzwang

Chess is a game of choice. Each move sets in motion a myriad of possible games and a single misplay can drastically turn the tables. A skilled chess player will deliberate on each move as they try to predict how the game will flow on from the decision they make, but in an infinite sea of possibilities, choosing the best outcome is extremely difficult.

However, there is one situation that is the direct opposite. Zugzwang is a state in which the most viable, ideal move is an impossible one – to not move. In zugzwang, whatever decision you make will reduce your odds of winning compared to skipping your turn. In some cases, you are even forced to make a choice that will spell your inevitable doom.

Life is similar to chess in that we are always faced with choices. What outfit will you wear today? Will you sit in the front seat or the back? Who will you ask to be your date for the ball? Should I take this job offer to change my career path, or stay in my current, stable job? Some choices are simple and appear inconsequential, yet others make us feel stressed even considering the implications. We often regret choices we made, looking back and wondering “What if?”. How would my life be different had I chosen differently?

But in the grand scheme of things, how important is it that we make “the best choice” each time? A majority of the time, it is highly unlikely that a single poor decision will completely ruin your life. Sure, your life may turn out different for better or for worse in a certain way, but we neglect to account for all of the other ways our life may change. Chaos theory teaches us that even a small change like a butterfly flapping its wings can wildly and unpredictably affect the future. For example, it could be that changing jobs results in your career progress being delayed by five years. However, by changing jobs you may meet the woman or man of your dreams, when you would have not met them had you not changed jobs.

We often trap ourselves in a state of zugzwang – pondering all the horrible ways our decisions may cause regrets in the future. Our fear of the unknown causes us to be paralysed by these choices. But as discussed above, our choices do not cause purely good or bad outcomes, but instead result in a simply different future due to the sheer number of variables that can change.

Ergo, there is no point stressing about each and every choice you make – you might as well pick one, see how it plays out and learn from the experience.

Posted in Philosophy

## The First Move

In the game of chess, every move counts. Each action you take can drastically change the way the game will play out from there on. By the second move, there are 72,084 possible games. By the third move, 9 million possible games exist. By the fourth, there are 318 trillion possible games. Essentially, after the first move, the game becomes nearly impossible to predict. There are more possible games on a chessboard than there are atoms in the universe. What spawns all of these possibilities is the first move.

This makes the first move all that terrifying. One mistake and you have destroyed countless possibilities where you are victorious. On the last few moves of the game, the results are much more predictable as the possibilities have been weeded out. Therefore, you can have more confidence in your moves. But the first move is as far as you can get from the end move, with an infinite sea of possibilities between you and the other side.

The corollary to this is that if you do make a mistake on your first move, then you have infinite ways to fix that mistake. So don’t be afraid of taking the first move – simply relax and play the game.

(inspiration/paraphrased from Harold Finch, Person of Interest)

Posted in Psychology & Medicine

## Child Prodigy

At the age of 6, Wolfgang Amadeus Mozart toured Europe to astound audiences with his mastery of the violin, organ and keyboard. At the age of 11, Judit Polgár defeated a Grandmaster in chess, later becoming a Grandmaster herself at the age of 15. By the time he finished elementary school, Saul Kripke had taught himself ancient Hebrew, finished the works of Shakespeare and mastered the works of Descartes and complex mathematical problems.

Each of these people is considered a child prodigy – person who develops and shows extreme talent in a skill at a level far beyond the norm for their age. The term wunderkind (German for “wonder child”) is also used. For some unexplained reason, these people are far beyond the average level of children at their age in terms of intelligence or a certain talent.

Prodigies are actually a subset of a condition known as precocity, where a young child shows unusually early development or maturity, especially in mental aptitude. For example, a German child called Christian Friedrich Heinecken is known to have talked within a few hours after his birth, learnt the key events of the first five books of the Torah within a year, mastered the Bible at age 2 and had a working knowledge of universal history and geography, Latin and French at age 3. Unfortunately, he was struck ill at the age of 4, and shortly after predicting his death, passed away. Heinecken’s case is an extreme example of precocity, but nonetheless most precocious children show at least an outstandingly advanced level of mental maturity compared to other children. Along with prodigies, savants and children with extraordinarily high IQ (over 160) are also considered precocious.

Although precocious children enjoy their extreme talent (for which they usually have deep passion for) and may even become famous for it like Mozart, they are almost always at risk of certain problems. One common issue is that they tend to be placed on pedestals as people constantly praise their ability. This can quickly evolve into narcissism, setting a major expectation that the child battles with throughout his or her life. Children with advanced intellect are often unable to fit in to society as they are far more intelligent than their peers. Not only do other children shy away from them, but they feel too bored and unstimulated by other children and choose to alienate themselves. Furthermore, although they may have the intelligence and maturity to comprehend philosophical concepts, they still have the emotions of a child, meaning they are tormented by the dissonance between the rational mind and their emotions. All of these factors combined lead to a great increase in risk of depression in precocious children.

Essentially, the main conundrum for child prodigies is trying to balance their amazing talent with a happy life in a “normal” society. This could be achieved by parents keeping things real and not placing excessive expectations on the child, and giving the child a way to vent their genius in some way. For example, chess has been a classic way of keeping children with high intellect engaged. Having this kind of vent allows the child to still engage with other members of his or her society (other children), while honing their great skills for an even brighter future. The child must stay engaged and passionately practise and advance their skill so that they do not stay in a perpetual rut all their life.

With great power, comes great responsibility.

Posted in History & Literature

## En Passant

In chess, there are three special moves: castling, pawn promotion and en passant. The first two are quite well known, but the third is less recognised by amateurs and is more of a “secret move” for more experienced players. Thus, many beginners complain their opponent is cheating, when they are using a perfectly legal move.

En passant is French for in passing – the etymology becomes clear once one understands how the move works.
Although a pawn can usually only move one space forwards, it can move up to two spaces on its first move. En passant only applies to a pawn that has moved two spaces. For example, if a white pawn moves two spaces forward and a black pawn is positioned to its left or right, the black pawn can move diagonally behind the white pawn to take it. This is because if the white pawn had moved one space, it would have been in the normal attacking range of the black pawn. Ergo, en passant is a technique that can stop a pawn from penetrating the defensive line and charging forwards.

This move must be used the turn after the pawn moves two spaces. Otherwise, the right to en passant disappears (i.e. cannot wait a turn to use it). In chess, this is the only move where the attacking piece lands on a space other than the taken piece.

Why was the en passant created? The reason being, the two-space first move rule came into place around then, so the en passant was devised to balance it, while complementing the pawn’s short attack range and inability to move backwards.