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.

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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.

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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 History & Literature

Keys To Music

On a piano, the simplest key is the C major key. The C major scale starts from the middle C key, then the seven white keys to the right are pressed in order. The notes are named as follows: C-D-E-F-G-A-B-C. This is known as the diatonic order of the piano. There are various other keys, but every one involves the black keys as sharp and flat notes are used.

Why does the diatonic order – the simplest scale – start at C instead of A?

When the modern system of written music came to be, the lowest available note was named “A” for simplicity, then each note above it was named alphabetically. However, at the time the notes were not matched to any specific scales. Furthermore, they started by only using seven letters, but later agreed on a 12-note octave. To make room for the extra five notes, they invented accidentals – the flats (b) and sharps (#). When the piano keyboard was invented, they made the white keys play natural notes and black keys play accidentals (flats and sharps).

As Western music developed, people became fonder and fonder of major keys (the “happier” sounding keys, to simplify things). This created a problem, as the simplest major key to only use natural notes was the C major key, which starts at C. The notes return to alphabetical order in the natural minor key, as the A minor scale plays as A-B-C-D-E-F-G-A.

Posted in History & Literature

Shibboleth

We are often corrected by others (as much as we correct others) on the proper pronunciation of words. Luckily, improper pronunciation is rarely consequential (other than sparking debates such as how to pronounce the word “gif”). However, on numerous occasions throughout history, this was not the case.

During World War 2, American soldiers in the Pacific Theatre came up with a questionable way of detecting enemy soldiers pretending to be allies to sneak in to bases. If a suspicious person was to approach a checkpoint claiming that they were an American or Filipino soldier, the sentry would ask them to say a certain word. The word was “lollapalooza” – an American colloquialism for something that is exceptional and extraordinary. The basis for this test was that Japanese people tend to pronounce the English letter “l” as “r” due to the difference in the two languages. Therefore, if the person was to repeat back “rorra-” they would be immediately shot.

This seems like a highly inaccurate method. What if they were an American soldier who had a bad head cold, or a lisp? But this type of racial profiling by the way someone pronounces a certain word has been commonly used throughout history to filter out people of certain races. Lollapalooza is an example of a shibboleth – a word that can distinguish people of a certain race by their inability to properly pronounce it.

The word comes from the Biblical story of the Ephraimites. When the Gileadites were invaded by the Ephraimites, they fought back and repelled the Ephraimites, who tried to retreat by crossing the River Jordan. The Gileadites planned ahead by securing the river so that they could capture the Ephraimites. They ordered each person crossing the river to say the word “shibboleth”. Because the Ephraimite’s dialect did not include a way to pronounce the “sh” sound, they would repeat back “sibboleth” and were killed on the spot.

Unfortunately, shibboleths have typically been used to identify members of a certain race so that they could be massacred. Nowadays, shibboleths are used in a more light-hearted manner. For example, New Zealanders and Australians mock each other on how each pronounce the words fish and chips. Because New Zealanders pronounce the “i” with a shorter sound, Australians tease that they say “fush and chups”. On the other hand, New Zealanders mock Australians on their long “i” sounds that make it sound as if they are saying “feesh and cheeps”.

Posted in History & Literature

Fortune Telling

Humanity has always been interested in trying to predict the future. Even if the future cannot be changed, we seem to have a primal craving to know something that should not be known. The history of fortune telling can be traced back to ancient times in almost every culture.

The ancient Greeks were particular fans of divination – the art of foreseeing with the inspiration of a god – and the most famous example is of course the Oracle of Delphi. The priestesses of the Temple of Apollo at Delphi were known to give very accurate, yet cryptic, prophecies inspired by Apollo. For example, when Croesus, king of Lydia, consulted the Oracle regarding his invasion of Persia, he was advised: 

“If you cross the river, a great empire will be destroyed”. 

Croesus believed this to mean that he would conquer Persia, but ultimately, the invasion failed and his own empire was destroyed by the Persians instead.

However, as the Oracle of Delphi would only give prophecies on the 7th day of every month, most commoners could not afford to have their fortunes told by them and would instead turn to seers. Seers told fortune through variable method, all with the purpose of interpreting “signs from the gods”. An example would be a haruspicy – divination through the inspection of an animal’s organs, commonly a sacrificed sheep’s liver.

Divination was an important part of Native American cultures. Diviners would use potent hallucinogens to reach an altered state of mind to derive visions. Scrying was also common – the practice of “seeing” the future by using reflections in mirrors or water surfaces.
In ancient China, oracles would read the future by reading the patterns of cracks on a burnt turtle shell (plastromancy). Nostradamus, the famous French seer, would scry the future in a bowl of water. The most classic, stereotypical image of a fortune teller is a gypsy woman gazing into a crystal ball or reading the palm of a person to foresee an individual’s future.

Fortune telling still plays an important role in the modern world, with a significant proportion of people in multiple cultures believing that the future can be predicted by fortune tellers. In the Western world, horoscopes are a common feature of newspapers and astrologists and tarot card readers are frequented by people seeking advice. In countries such as Korea, China and Japan, a significant number of people will seek fortune tellers to see how “well-matched” a couple are before marriage is decided.

There has been zero scientific evidence to suggest that clairvoyance is real. However, perhaps that is not the point of fortune telling. Another name for fortune tellers is soothsayers – perhaps having our fortune told gives us a sense of comfort as it eases our morbid curiosity for what the future holds. The future is an endless sea of possibilities and the realisation that anything could happen can be crippling. So maybe the aim of fortune telling is not to predict the future, but to temporarily treat your fear of the future so that you may live in the present.

Posted in History & Literature

Evolution Of Colour

We often take the beauty of colour for granted. How would you explain the colour red to a blind person? With that in mind, how do we know that the colour we see with our own eyes is the same hue that others see? A scholar by the name of William Gladstone came across a similar question in 1858 while studying ancient Greek literature. He noticed that in most literature of ancient times, the description of colour was wildly inconsistent, such as the sea being described as “wine-dark”, the sky being “copper-coloured” and other oddities such as violet sheep and green honey. After further analysis, Gladstone found that white and black were referenced frequently, while other colours were much rarer, with red, yellow and green being the most common colours respectively.

Another scholar named Lazarus Geiger expanded on Gladstone’s research and found that throughout ancient literature – including the Bible, Hindu poems, ancient Chinese stories and Norse tales – described beautiful scenes while omitting a certain detail: a blue sky. It appeared that the colour “blue” did not appear in most languages until a certain point in time, despite the people having lived under the same blue sky that we do now.

Geiger tracked the appearance of different colours in different languages and found a pattern of development. Each language would typically describe white (light) and black (dark) first. The next colour to develop was red, then yellow and green, with blue being one of the last colours to appear. This is likely related to the abundance of each colour (e.g. blood, dirt, vegetation) and the ease of making coloured dye (blue dye is notoriously difficult to make).

This raises an interesting question: if the ancient Greeks did not have a word for the colour blue, could they still perceive the colour blue? Biologically speaking, our eyes are not so different to that of the ancient Greeks. But of course vision is a two-part processyour eye captures the image and then your brain processes the image. Does language have a significant enough impact on how we perceive our world?

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There is a tribe in Namibia whose language does not distinguish blue and green. A study was held where people from this tribe were shown a circle of 12 squares – 11 green and 1 blue. To the researcher’s intrigue, the men and women of the Himba tribe could not tell which square was the odd one out – suggesting that their brain was processing the two colours as identical. However, the Himba language has more words distinguishing shades of green than English. In another study involving a circle of green squares with one square being a slightly different shade of green, the Himba tribe could pick out the different square much more easily than English-speakers.

The so-called “colour debate” is a hotly debated topic, with some arguing that language plays a crucial role in determining our perception of the world, while others state that language is separate to our senses. What did the ancient Greeks see when they gazed up into the sky? If we cannot describe something with words, then does it truly exist? But one thing is clear – things are not always as they seem.

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Posted in History & Literature

Morse Code

In 1825, an artist by the name of Samuel Morse was travelling to a city far from his home to paint a commission. While working on his painting, he received a letter from his father, which informed Samuel that his wife was ill with an infection. The next day, another letter came, but this time detailing his wife’s sudden death. Upon receiving the letter, Morse immediately returned to his home as fast as possible, but he arrived after they had already buried his wife. This was the age before fast long-distance communication, where messages could only be sent as fast as the horses that carried them.

Frustrated by the inefficient communication methods of his time, Morse became dedicated to devising a better way to send messages over long distance at a much faster speed. After intensive studying of electromagnetism, Morse eventually developed the first concept of a single-wire telegraph. The telegraph could send electrical signals of variable length at fast speeds down wires with a simple button.

Together with the telegraph, Morse devised a code alphabet so that messages could be sent encoded into short and long signals on the telegraph. A dot (“dit”) represents a short press, a dash (“dah”) represents a long press (three times longer than a short press). Each letter is separated by a space the length of 3 dots. Words would be spaced out by a slightly longer pause – the length of 7 dots. Morse designed the code to be efficient and so he made the most common letters (E, I, S, T and so forth) the shortest in length.

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Posted in History & Literature

Maps

Think of the world map. Most of you will think of the typical map where Europe and Africa are in the middle, with Russia dominating the Eurasian landmass and Greenland easily outsizing South America.

Mercator projection

The most common world map we use nowadays is based on the Mercator projection. Because the Earth is spherical and maps are two-dimensional rectangles, complex mathematics are involved to project the former on the latter by distorting the picture. The Mercator projection was created by Flemish cartographer Gerardus Mercator in 1569. The map was extremely useful for sailors because it depicted the curvature of the Earth in straight lines, making navigation much easier.

However, the Mercator projection severely distorts the size of each continents, meaning the image of the world we have in our heads is completely misleading. According to the Mercator projection, Greenland is as large as Africa, Alaska is as large as continental USA and Antarctica dwarfs every continent.

Gall-Peters projection

To solve this problem, the Gall-Peters projection was suggested in 1974 as an alternative as it correctly displayed the continents’ respective sizes. As you can see, in reality Greenland is significantly smaller than even Australia, Europe and Russia are much smaller than expected and Africa is an extremely large continent.

Dr. Arno Peters argued that the Mercator projection was a biased, euro-centric projection that harmed the world’s perception of developing countries. This of course, led to extreme controversy over the politics of cartography.

Africa vs Greenland

There are many other distortions commonly found in maps. Maps tend to enlarge the landmass of the own country subtly and some American maps go as far as placing the USA in the middle even if it means splitting Eurasia in half. Even though landmass does not correlate in any way with how well the lives of its inhabitants are, such distortions can be seen even nowadays. This shows that not everything you see is as it seems.

Posted in History & Literature

Beast Of Gevaudan

In 1764, a young woman herding cattle in Gevaudan, France, told the story of how she was attacked by a giant, fearsome beast. She reported that the beast charged towards her, but was only stopped by the bulls that defended her. The beast was described as being as big as a calf, with a large dog-like head with exposed very large fangs and dark reddish fur with black streaks. Not long after this story, a young boy living nearby was violently killed, with his throat torn out. The number of people attacked and killed by this mysterious beast grew and grew. The population of Gevaudan was terrified. No wolf or dog had been known to be as large as the beast reported by survivors, nor as vicious as this.

The story of the so-called “Beast of Gevaudan” was heard by Louis XV, who responded by dispatching professional wolf-hunters to Gevaudan to slay the beast. One of these men was called Francois Antoine – a veteran wolfhunter. Over the coming months, he hunted several large wolves, but the attacks continued.

On September 21, 1765, Antoine finally encountered the beast. It was a ferocious wolf-like animal, about 1.8m long and 70cm tall. Antoine shot it several times, in the eye, shoulder and side. The beast withstood the first couple of shots and finally fell to the ground after the third. But as Antoine and his colleagues cheered, the beast stood back up and charged Antoine. It took two more shots to finally slay the beast. Survivors of attacks were able to identify the beast as the true Beast of Gevaudan. The beast was embalmed and stuffed for display and the populace of Gevaudan celebrated the end of the terror, with Antoine being celebrated as a hero and expert wolfslayer.

However, the story did not end there. Attacks continued for years even after the Wolf of Chazes was slain. The ultimate end to the story is credited to a hunter named Jean Chastel, who shot and killed a large wolf-like beast in 1767, after which the attacks stopped. Some say that he used a blessed silver bullet – possibly originating the myth that werewolves can only be killed by silver bullets.

It is still unclear what exactly the Beast of Gevaudan was. Some believe it to be a large wolf, but most historians agree that it was likely a wolf-dog hybrid given its large size, unusual ferocity and distinct coloured fur. Other theories include the beast being a large red mastiff, an Asian hyena or a pack of wolves, which is likely given the sheer number of attacks in such a short space of time. All in all, the final kill count of the Beast of Gevaudan is estimated between 80 to 120 people, with a further 49 injuries.

Posted in History & Literature, Special Long Essays

Hell

The concept of hell is one of the oldest and most widespread concepts in the history of humanity. The idea that you are punished in the afterlife for your misdeeds during your earthly life is found in both the Western and Eastern hemisphere, from ancient civilisations to tribal communities to modern societies. Hell is typically described as the place the wicked are sent to for eternal damnation. It is often populated by all kinds of demons and monsters, located underground in a hot, fiery location. Depending on the religion, there may be a “death god” ruling over the realm, such as Satan, Yama, Hades or Hel. In hell, sinners are usually punished with various forms of torture, often fitting their crimes or having an ironic twist.

For example, in the Buddhist hell, seven “death gods” judge you for 49 days. One judgement tests whether you committed crimes of the tongue, such as lying or conning. If you are judged guilty, your tongue will be pulled out and it will be ploughed and sowed with seeds for eternity. In another court, you are judged for “how cold you were to others”, turning away from them when they needed your warmth and generosity. If you are guilty, you are locked away in a frozen hell for eternity. After being found not guilty in all seven courts, you are granted a chance to be reborn into your next life.

Why is hell such a common concept around the world? Every child knows the answer to that: if you do bad things, you will burn in hell. Ergo, you should not do bad things. This is the classic appeal to fear fallacy that has been used time and time again by politicians to control the masses. Death is an excellent deterrent to misdemeanour. In ancient times (and in certain modern nations), the death penalty was used to keep order in society, as the threat of death is usually good enough to persuade people out of doing something bad.

However, if a person does not care about death because they believe that all the woes of earthly life end with death, then what do you do? Early religious leaders most likely found the answer in hell – a place where you will suffer for eternity, without relief. Hell is an extremely simple way of persuading the masses that living by the law and a moral code will lead to a peaceful rest in the afterlife. Heaven is the perfect positive reinforcement and hell is the perfect positive punishment.

In Christianity, breaking one of the Ten Commandments is a clear sin. If you do not repent for this sin or ask for forgiveness, then you will be barred entry from heaven and be sent to a fiery hell, where Satan and his minions will put you in a chamber full of torture for the rest of eternity. However, the greatest punishment in Christian hell is not the torture itself, but knowing that you will forever be separated from the love and blessing of God.

(from The Garden of Earthly Delights by Hieronymus Bosch)

As with many aspects of religion, hell was an important part of keeping order in ancient civilisations. To enforce this system, the picture of hell had to be fleshed out with as many grotesque, horrific details as possible. Luckily, hell was a rich source of inspiration for artists and writers throughout history. Dante wrote extensively on how he imagined hell to be structured in The Divine Comedy. Hieronymus Bosch painted large works where he used his twisted imagination to create all kinds of strange monsters. Auguste Rodin made a large sculpture called The Gates of Hell to depict imagery from Dante’s The Divine Comedy (this is where the famous figures of The Thinker and The Kiss come from). Some of the most famous Greek mythology stories involve hell and the underworld in some way, such as Orpheus’ rescue of his wife and the banishment of the Titans to Tartarus by the New Gods.

Hell appears to be the perfect form of divine judgement of your sins, but it also poses a question. Many religions preach that their gods are benevolent, just and moral. How could a god that sends their beloved children into a place of eternal suffering be called just? One would expect this to be too harsh a punishment and unnecessarily immoral. This is especially the case for those who are called “wicked” for being a non-believer. The Rapture described in the Bible explains that on Judgement Day, Jesus Christ will collect those who are good and worthy of God’s love and ascend to heaven, while the rest of the world will be left in hell. This is very different to the doctrine of Buddhism and Judaism where it is believed that hell is a “process” through which you are cleansed of sin after paying for your sins, after which you may receive peace and rebirth.

One proposed answer to the so-called “problem of hell” is that human beings are given free will and what we decide to do with it is our responsibility. Therefore, going to hell is seen as a “choice” you make in life.

(The Last Judgement by Michelangelo, from the Sistine Chapel)

But is going to hell really a choice? I cannot speak for the process of going to the afterlife as I have never been there. However, one interpretation you could consider is that hell is not some fiery realm in another dimension – but Earth itself.
It appears that Earth itself is not the best world to live in. Children die of starvation, men are murdered, women are raped, the elderly suffer from incurable diseases… If that does not sound bad enough, most people live in a hell of their own in one way or another.

Our insecurities prevent us from truly loving. We fail to achieve our dreams because we are too afraid of taking the risk. When things do not go the way we planned, we blame and beat ourselves up about it until we are miserable. The neurotic are trapped in constant anxiety, the depressed cannot see light amongst the darkness they wallow in, the pessimists are too cynical to see joy in this world and the optimists have their hopes and dreams crushed by the cruel face of reality.

We do not know whether there is hell or heaven in the afterlife, but there certainly is a hell on Earth and that is the one you create in your own mind. Instead of worrying about what kind of eternal suffering we may experience after our death, perhaps we should focus on saving ourselves from the hell that we live in. Until you find a way to escape this hell, whether it be through love, happiness or success, you will forever be trapped in misery and regret. Hell is not a fiery underworld of suffering nor a frozen wasteland of damnation – it is a state of mind.

(Image source: http://akirakirai.deviantart.com/art/Fear-194527543)

Posted in History & Literature

Your Other Half

According to Greek mythology, humans were originally created with four arms, four legs and a head with two faces. The humans at this time were complete. They felt as if nothing could harm them and that they could conquer the gods. Zeus feared the humans’ power and split them into two separate parts to create humans as they are now. Two arms, two legs, one face, half a soul.

Thanks to Zeus, all human beings are condemned to spend the rest of their lives in search of their other halves. When one of them meets the other half – that is, the other half of his or her original self – the pair are lost in an amazement of love and friendship and intimacy. There is an unspoken understanding of one another – an unexplainable longing and attraction for each other. One will not be out of the other’s sight, even for a moment. The two continuously yearn for each other and strive to be together until they are finally united.

Love is simply the name for our pursuit of wholeness, for our desire to be complete. It tries to make one out of two and heal the wound of human nature.

1 + 1 = 3

(inspiration from The Symposium by Plato)

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(and here’s a sweet illustration of the myth http://imgur.com/gallery/H0f1u)