Posted in History & Literature

Elements: Four Elements Of The West

Human beings have believed that all matter can be divided into basic elements for a very long time. Although we now know that the basic building block of the universe is atoms, what did ancient people believe matter was made of?

In ancient Greece, the seat of Western culture, it was believed that everything was made from the four elements: earth, fire, water and air. According to Aristotle, every element has a primary and secondary characteristic, with the four characteristics being hot, cold, dry and wet. Air is primarily wet and secondarily hot, fire is primarily hot and secondarily dry, earth is primarily dry and secondarily cold and water is primarily cold and secondarily wet. He also spoke of a fifth element (quintessence) beyond the four elements. The name of the fifth element is aether and it is a pure and heavenly element that cannot be corrupted like the earthly four elements. Furthermore, it was thought that aether was the element of the sky and stars were composed of it as they were heavenly, not earthly.

The four classic elements of ancient Greece had an impact not only on physics and chemistry, but also on philosophy and culture (the concept of the four elements is popular in modern games too). The most interesting example of these is a theory by Hippocrates, the father of Western medicine, that states that the human body is composed of four bodily fluids (humours) and an imbalance between the humours caused diseases. The four humours are yellow bile (fire), black bile (earth), blood (air) and phlegm (water). Furthermore, he believed that the four humours affected personalities too. For example, an excess of black bile (“melan chole” in Greek) would cause a person to become introspective and think negatively, leading to depression or “melancholy”. This is quite possibly the first medical records on clinical depression.

The four classic elements of ancient Greece can also be found in ancient Egypt and many other ancient civilisations. It also had a significant influence on alchemy in the Middle Ages.

(Image source

Posted in Science & Nature

Golden Ratio

The golden ratio is a magical number that divides a line into the most beautiful ratio. It bestows a mystical power in an object and allows for the creation of excellent architecture and art.
This magical ratio is (1 + √5)/2, or 1.618033988. If there is a line divided by the golden ratio called a + b, then b:a and a:(a + b) are both the same ratio.

We can find the golden ratio in countless values seen in animals and plants. A snail shell’s golden spiral allows for the snail to grow without changing shape, while the distribution of branches on a tree also follows the ratio. The golden ratio controls everything from the spiral pattern of galaxies to the pattern of our brain waves. The golden ratio is the law of the universe.

Using this magical ratio, we can find the most beautiful composition of a human being. The Venus of Milo, considered as one of the most beautiful figures in history, has a ratio of 1:1.618 between her upper and lower body (divided at the belly button) – the golden ratio. The same can be said for the ratio between the head and neck compared to the rest of the upper body, and the length from the belly button to the knee compared to the length below the knee. The exact same composition was used to construct the statue of Doryphoros, one of the most famous examples of ancient Greek sculptures. The diagram that illustrates these ratios is the Vitruvian Man by Leonardo da Vinci (Vitruvius was a Roman architect who utilised the ancient Greek knowledge of applying the proportions of a human being, i.e. the golden ratio, in constructing temples). 

The Great Pyramids of Giza, Solomon’s Temple and the Parthenon are all partially constructed according to the golden ratio. It is said that buildings constructed outside of the golden ratio will collapse over time. The same is seen in Eastern constructions, such as buildings and inventions from the Goryeo Dynasty of Korea. 

Interestingly, the golden ratio applies to intangible objects as well. For example, Chopin’s Nocturne pieces tend to climax at the point of the golden ratio (roughly two-thirds in). The ratio is still used in modern day design, with the standard credit card size being the best example.

The golden ratio is an eternal beauty that does not go out of fashion with time.

Posted in History & Literature


Apples are strewn throughout history and mythology, acting as a key component of human societies. Its symbolism ranges from the sin of Adam and Eve to the love of Aphrodite. Let us look at some apples that have made a significant impact in the world – real or mythical.

Apple of Temptation: According to the bible, Eve is tempted by the snake to take the forbidden fruit from the Tree of Knowledge. By taking from the tree and eating this fruit (then sharing it with Adam), the two are banished from the Garden of Eden and humanity is cursed to live in the harsh world and for women to suffer the pain of childbirth. Although the bible never defines the forbidden fruit as an apple, artistic depictions during the Renaissance has solidified the idea. The eponymous Adam’s apple (the lump on men’s necks) is said to be a piece of the apple being stuck in Adam’s throat.

Apple of Discord: According to Greek mythology, Eris (goddess of discord) threw a golden apple into a wedding after not being invited to it. The apple was inscribed with the message: “For the fairest one” and Hera, Athena and Aphrodite all claimed the apple was for them. Eventually, the judgement was delegated to Paris, prince of Troy. Each goddess bribed him with power, strength and love respectively but Paris eventually chose Aphrodite and in return, received the most beautiful woman in the world – Helen of Sparta. This sparked the great Trojan War, resulting in the destruction of Troy by the Greek alliance.

Apple of Love: Atalanta (Greek mythology) was a beautiful woman who had sworn virginity to the goddess Artemis. To avoid marriage, she challenged suitors to a footrace and only the winner would take her hand in marriage (the rest were killed). A man named Hippomenes went to Aphrodite’s temple to seek advice and was given three golden apples. He used the apples to distract Atalanta during the race by tossing it near her. This allowed him to win the race and ultimately took Atalanta’s hand in marriage. This story also shows how the ancient Greeks saw apples as a symbol of love, as evidenced by the gesture of one throwing an apple to the person they are in love with. Catching the apple was accepted as a sign of reciprocity.

Apple of Challenge: One of Hercules’ twelve challenges was to take the Golden Apples of Hesperides, protected by Ladon, a dragon with a hundred heads. Hercules bargained with Atlas to hold the Earth while he retrieved it. Atlas tried to walk away free from his damned task, but Hercules tricked him by asking to hold the Earth while he shifted his cloak.

Apple of Death: In the fairy tale, Snow White, the evil queen uses a poisonous apple to murder Snow White. The symbolism of the apple is similar to the biblical story mentioned above. Despite the dwarves warning her about stranger danger, Snow White takes the gift of a stranger without enough caution and suffers the consequences. However, she is resurrected by the kiss of the prince. Perhaps Aphrodite’s apple of love counters the evil apple of death and sin.

Apple of Revolution: A famous Swiss folklore describes how William Tell had to shoot an apple from his son’s head with his crossbow as punishment for not submitting to the occupying Austrians’ leader, Gessler. Being an expert marksman, he successfully hit his target instead of killing his son. When he was questioned why he drew two bolts from his quiver, Tell replied that he was aiming to shoot Gessler if he accidentally killed his son. This infuriated Gessler, who arrested William Tell. However, Tell escaped and went on to lead the revolution against the oppressors, aiding in the liberation of Switzerland (according to the legend).

Apple of Philosophy: There is a record of a young Martin Luther (who founded the protestant church) writing in his diary: “Even if I knew that tomorrow the world would go to pieces, I would still plant my apple tree”. The philosophy behind this saying is not that gardening is important. Here, Luther is saying that we should live every day as if it is the last day. Live without regrets. Besides, would we not look silly if the world did not end and we had wasted a day panicking and doing absolutely nothing productive?

Apple of Knowledge: The story of how Isaac Newton devised the theory of gravity after being hit on the head with an apple is a famous story. Although the “hitting on the head” part is dubious, evidence suggests that he used apples falling from a tree as an example of how gravity works. Although the concept of gravity was already established, Newton focussed on how apples always fell perpendicular to the ground and deduced that objects have a gravitational pull on other objects (as the Earth pulls the apple and vice versa). He extrapolated from the apple to discover how Earth’s gravitational field controls the orbit of the Moon. Thus, it can be said that apples played a “crucial” role in the advancement of modern physics (although Newton probably did not need the apples for his theory).

Apple of Innovation: In 1976, Steve Jobs co-founded Apple Inc. to develop the first personal computer. The company would go on to revolutionise mainstream digital technology by coming up with innovative products such as the iPod. Steve Jobs was the face of this new wave of innovation; with his bold outlook on the future and powerful leadership he made Apple Inc. one of the most successful companies in the 21st century. Jobs successfully popularised many pieces of technology, such as personal computers, portable music players and tablet PCs. Interestingly, he came up with the logo and name of the company after seeing a cartoon of Newton and his apple. Perhaps Jobs was seeking to create a company that would be one of the many “apples” that were turning points in history.

Posted in History & Literature

Laconic Phrase

The Spartans are well-known to us as some of the bravest and toughest soldiers in Western history, with a culture completely focussed on breeding the best of the best warriors. However, during ancient times they were famous for another trait.
Spartans were famous for stating their arguments in concise statements, able to express their ideas with just a few words. This type of speech was known as laconic phrase, named after the region of Laconia where Sparta was located. Laconic phrases are not only short, but extremely efficient and often witty. In fact, another trait that Spartans shared was a sense of dry wit known as laconic humour.

There are plenty of records, such as Socrates’, that describe the Spartan’s ability to effortlessly throw off pithy comments in retaliation. Ergo, the Spartans did not use little words because they were illiterate or did not value education and culture; they used as little words as possible to conceal their wisdom in a concentrated phrase. The Spartans deemed this a valuable skill as a true professional is efficient in whatever he does, including language.

Many examples of laconic phrase can be drawn from the historic Battle of Thermopylae – the battle portrayed by the movie 300 (which, despite a rather dramatic presentation, quite accurately portrays many aspects of the battle).

  • Before the war, a Persian envoy came to Sparta demanding an offering of soil and water – a traditional symbol of surrender. The Spartans threw them in a well and said “Dig it out for yourselves”.
  • This infuriated the Persian Empire and war broke out. As King Leonidas departed for the Battle of Thermopylae, he advised her wife: “Marry a good man and bear good children”.
  • When Xerxes of Persia offered to spare the Spartan army in exchange for their surrender and giving up their weapons, Leonidas simply retorted: “Molon labe”, which translates to “Come and take them”.
  • On the morning of the last day of the battle, Leonidas knew that defeat was inevitable. To boost his troop’s morale, he spoke the famous line: “Eat well, for tonight we dine in Hades”.

The Spartans’ efficiency with words and wit inspired many famous words over history. These range from responding to the enemy’s demand for surrender (at the end of the Battle of Waterloo, British forces demand the French surrender, to which General Cambronne replied: “Merde” or “Go to hell”), a pithy description of a disastrous situation (during the Battle of Imjin River of the Korean War, Lieutenant Colonel Carne – surrounded by the Chinese and his forces utterly destroyed – described the situation as “A bit sticky”), to the modern day epic burn.


Posted in History & Literature


Helen of Troy is infamous for her pivotal role in the Trojan War after she left Sparta for her new lover, Paris of Troy. She was deemed the “most beautiful woman” in the world by Aphrodite, the goddess of love, who made her fall in love with Paris in return for him choosing Aphrodite as the most beautiful goddess.

Helen is said to have been so beautiful that she had “the face that launched a thousand ships” (in reference to the Trojan War and the massive navy of Greece). Using this statement, clever authors such as Isaac Asimov and W.A.H. Rushton invented the “Helen (H)” unit – an international, standardised measurement of beauty. As Helen launched a thousand ships, a milliHelen (mH) of beauty equates to the amount of beauty required to launch a single ship.
For example, according to The Iliad, the total number of ships that joined the expedition to Troy was 1186. This means that Helen had a beauty rating of 1.186 Helens – ergo, capable of launching more than one thousand ships.

The unit also goes both ways as negative Helen units are possible. For example, -1 mH would mean “beauty” (read: ugliness) that drives a single ship away. The units can be subdivided further, such as a picoHelen (10^-12) being the amount of beauty that “tosses an inflatable tube into the pool”.
Another interpretation of the Helen is the number of women that said woman is more beautiful than. For example, during Helen of Troy’s time (1100 BC), about 50 million women existed on Earth. Therefore, 1 Helen is amount of beauty sufficient to be greater than the beauty of 50 million women.

Finally, beauty is considered to be on a logarithmic scale of base 2. Simply put, for beauty to increase by 1H, the woman must be the most beautiful of double the number of women. In practical terms, the most beautiful woman who ever lived (using the cumulative female population of the world) has a beauty rating of 1.34H. The most beautiful of a dozen women would be 0.14H.

Posted in History & Literature

Charon’s Obol

According to ancient Greek mythology, a person’s soul must cross five rivers to enter Hades’ underworld after death. Charon ferries souls across the first river, Acheron, also known as the river of pain. To use Charon’s services, one had to pay a silver coin (obolus). If one could not pay the fee, one could not cross the river and would circle the Earth for eternity. Thus, the ancient Greeks had a custom of putting a coin in the deceased’s mouth for their journey.

Even for something as unavoidable as death, Charon asks for money. This not only shows that the ancient Greeks had a good understanding of market economies, but also teaches us something important about capitalism.
Just as the reaper takes a fee, nothing in the world is free. A market is the most effective economy system that man has devised and no other system (especially communism) has overcome it. But we have a tendency to denounce corporations for only taking advantage of poor, helpless citizens. Although there is corruption in reality, corporations are still subject to the invisible hand and bound by the basic principle of capitalism, supply and demand.

We only see the negative sides of capitalism and decry Charon’s greed. “How could you ask a helpless soul for money? Is that not robbery?”, we cry. But such words can only be said by someone who has devised a better system than the market, or found a way to keep Charon well-fed. Instead of criticising the economy or policies, it is far more efficient to think of a way to improve the market system. Blindly criticising and trying to destroy capitalism like Karl Marx did will only result in splitting the world in two and cause everyone to starve to death.
The reason being, money is an invention as important as fire to mankind.

Posted in History & Literature


Both human beings and ants know how to make mead, also called honey wine. Ants use aphid honeydew, we use bee honey. The ancient Greeks called this drinkhydromeli (hydro(water) + meli(honey)). It is the same drink that the gods of Olympus and the priests of Galia all enjoyed.

Here is an introduction to how to brew mead:

Boil 6 kilograms of honey and clear away the foam. Add 15 litres of water, 25 grams of ginger powder, 15 grams of amomum seeds and 15 grams ofcinnamon to the honey. Simmer until about a quarter has boiled away, then take off the fire to cool.
When the mixture is warm, add three tablespoons of yeast and let the solids settle over about 12 hours.
Then, pour the liquid into a small wooden barrel while filtering out the residue. Seal the barrel tight and leave in a cold place for 2 weeks.
Lastly, pour the mead in a bottle, seal with a cork and wire, then let it mature in the basement cellar.

It is best to open it about two months later, maybe in time for a wild party just like the ancient Greek bacchanalia (a wild, mystic festival in honour of Dionysus/Bacchus, the god of wine, through uncontrolled drinking and orgies).

(from The Encyclopaedia of Relative and Absolute Knowledge by Bernard Werber)

Posted in Life & Happiness

Eleusis Game

The victory condition for this card game, named after an ancient Greek city, is quite simple: discover the pre-determined law via induction.
This game needs at least four people, with one person acting the position of God. God decides on a certain law (in the form of a single statement) and writes it down on a paper, thus creating the way of the universe
Next, the deck of cards is split evenly between the other players, then one person places a card in the centre. After “the world begins to exist”, God looks at the card and says “This card qualifies” or “This card fails”. The next player also places a card in the centre and the God judges whether it fits the way of the universe.

Players carefully study which cards qualify or fail to try discover the way of the universe. If someone thinks they figured the law out, he or she proclaims themself as the prophet, who begins to take over the role of God to announce whether the cards qualify or not. If at any point the prophet is wrong, he is dismissed. If the prophet correctly judges ten cards in a row, he states his hypothesised law and compares it to the piece of paper. The prophet wins if the two laws coincide, but is dismissed if it is not. When all 52 cards are played without a successful prophet, God becomes victorious.

However, as this is a game, the way of the universe cannot be too complex. To make it fun, the God player must devise a law that is simple yet difficult to discover. For example, the law “Alternate a card higher than 9 and a card lower than 9” is tricky as players tend to focus on picture cards or the colours of the cards. Also, laws such as “Only red cards qualify, except the tenth and thirtieth cards are disqualified” and “Accept all cards that are not the 7 of Hearts” are illegal, as they are too detailed. A God who comes up with such ways of the universe that cannot be found using logic and the scientific method loses his right to play the game. Ergo, the God must seek simplicity that is not easily conceived.

So what is the most successful strategy for this game? Even if there is the risk of being dismissed, proclaim yourself as the prophet as soon as possible for the best chance of winning.