Posted in History & Literature

Eros And Psyche

Once upon a time, there lived a beautiful girl named Psyche. Psyche was so beautiful that she even caught Aphrodite’s eyes. Despite being the goddess of love, Aphrodite was known to be very jealous and felt threatened by Psyche’s beauty. She commanded her son Eros, the god of love, to put a spell on Psyche. Eros uses the Bow of Love and anyone shot by his golden arrows falls immediately and helplessly in love with the first thing they see.

Aphrodite came up with a devious plan to have Eros shoot Psyche and have frogs around her, making her fall in love with frogs and fall into a despairing relationship. But her jealous plan was overthrown by an unexpected event. When Eros first saw Psyche’s face, he became entranced and accidentally pricked himself with his own arrow. Thus, Eros became madly in love with Psyche. Aphrodite, enraged by this, cursed Psyche to never find a mate for the rest of her life. Eros became depressed from not being able to see Psyche and gave up shooting golden arrows. After he gave up his job, no animals or human fell in love and no new life was born. Aphrodite could not bear to see such a scene and begged Eros to start shooting arrows again, offering him one thing that he wanted. Eros said that he desired Psyche without hesitation and Aphrodite reluctantly allowed them to meet.

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While this happened, Aphrodite’s curse made no man come to propose to Psyche. Her parents became worried and asked the advice of the oracle at Apollo’s temple. The oracle stated that as she is destined to marry a monster, she must be placed atop a mountain in bridal attire. Accepting her fate, Psyche stood on the mountain but eventually jumped off a cliff in despair. But Zephyrus the West Wind caught her and brought her safely to Eros’ place, just as Eros planned. Psyche enjoyed a comfortable life in the beautiful castle with many maids at her service. However, her husband only came in the deep dark of the night. Whether it was because he feared Aphrodite’s wrath or the difference between a god and a mortal, he asked her to never try find out who he was and that if she truly loved him, she should trust him. But Psyche eventually fell victim to her jealous sisters’ scheme and her curiosity, leading to her accidentally dropping candle wax on Eros’ face as she took a peek at his face. Eros was awakened and became enraged. He chased her away and forbade her from coming back. Psyche fell in despair and threw herself into the river, but the river carried her to the riverside where the shepherd god Pan rescued and consoled her.

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At first, Psyche tried to find Eros while avoiding Aphrodite, but eventually she decides to plea directly to her. Despite her bravery, Aphrodite threw challenging tasks one after another at her like a mean mother-in-law, ultimately commanding her to retrieve some beauty from Persephone, the queen of the underworld (since travelling to the underworld signifies death, Aphrodite must have truly hated Psyche). 

However, Psyche was determined to see Eros even at the cost of her life. Admiring her commitment, a tall tower before the underworld gave her a hint. It told her to place two coins on her tongue and bread in each hand when going to the underworld. The coins would be to pay Charon the ferryman while the bread would distract Cerberus the three-headed dog guardian. She succeeded in seeing Persephone, who gave her a box of beauty and told her to never open it. But wanting to look beautiful in front of her lover (Eros), Psyche opened the box. The box did not contain beauty, but instead contained a death-like sleep from the underworld, putting Psyche in a deep sleep. Although he chased her away, Eros came back to see Psyche and found her in this sleeping state. He took the corpse-like Psyche and kissed her softly on her lips, awakening her from the deep sleep.

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Eros eventually sought help from the king of gods, Zeus, to persuade Aphrodite. After Zeus’ persuasion and seeing the love the two have for each other, Aphrodite accepted the relationship and Zeus gave Psyche the immortal drink ambrosia to make her into a goddess. The now immortal Psyche and Eros were married and had a daughter named Hedone (like in Hedonism), the goddess of sensual pleasures.

Eros symbolises physical and sensual love while Psyche is a Greek symbol for butterflies, the soul and emotional love. Ergo, Eros and Psyche represent the union of physical and emotional love into perfect love. Love and the soul are inseparable things. The most basic instinct of any organism is to reproduce and human beings have evolved that into the sacred concept that is love. To speak bluntly and without philosophy, from a purely biological perspective there is no greater purpose to life than to find a suitable mate and leave descendants. There is nothing more fundamental than pure love.

Posted in History & Literature

Helepolis

In 305 BC, Demetrius I of Macedon waged war with the island of Rhodes, now known as the siege of Rhodes. During this siege, Demetrius utilised a superweapon that is, to this day, the largest siege tower ever built – the Helepolis. Helepolis loosely translates to “destroyer of cities”, which is interesting as Demetrius’ nickname was Poliorcetes, or “The Besieger” in ancient Greek. In short, Demetrius was set to raze Rhodes or wipe it off the map.

The Helepolis lived up to its name: designed by Polyidus of Thessaly, it was 40m high (about 13 stories), 20m wide, weighed 160 tons and had a crew of 3400 people. It had eight wheels, each 3.7m high, and had compound wheels that allowed it to move side-to-side. The 3400 men both pushed the tower and worked a belt system that moved the wheels forward. The entire structure was clad in iron plates, making it completely arrowproof and fireproof. 

Its armament was just as impressive. One face of the tower was covered in windows, with each concealing a catapult that could hurl heavy objects at the target. The first floor had a pair of catapults that could hurl 80kg projectiles (about the weight of a refrigerator) and one that launched 30kg projectiles. The second floor had three 30kg catapults and the third to eighth floor had ten 15kg catapults in total. Lastly, the roof had four dart throwers which could clear any defenders on the top of castle walls. Essentially, the tower had both the ultimate defensive and offensive capabilities.

Of course, there was no chance the Rhodians could stand a face-off with such a behemoth. So instead, they came up with a cunning plan that exploited the huge size of the Helepolis. The night before the siege began, the Rhodians channelled the water and sewage coming out of the city into the area they expected the attack to come from to create a vast area of mud and bog. When the Helepolis stormed in for the offensive, it immediately started sinking in the mire. Knowing that no amount of horses and men could pull the structure out of the mud, the soldiers abandoned the superweapon without even using it once. 

Ultimately, the siege of Rhodes failed (largely due to the failure of Helepolis) and the Rhodians took apart the Helepolis, melted the iron plates and used it to build the Colossus of Rhodes (one of the Seven Ancient Wonders).

Posted in Science & Nature

Fermat’s Last Theorem

In the 17th century, a lawyer called Pierre de Fermat conjectured many theorems while reading a mathematics textbook called Arithmetica, written by an ancient Greek mathematician called Diophantus. He wrote his theorems on the margins of the books. After his death, a version of the Arithmetica with Fermat’s theorems was published and many mathematicians checked over Fermat’s proofs. However, there was one theorem that could not be solved. Fermat wrote on the theorem: “I found an amazing proof but it is too large to fit in this margin”.

Fermat’s last theorem is as follows:

No three positive integers x, y, and z can satisfy the equation
xⁿ + yⁿ = zⁿ for any integer value of n greater than two.

For example, x² + y² = z² can be solved using Pythaogorean triplets (e.g. 3, 4, 5) but there are no values for x, y and z that solves x³ + y³ = z³. This theorem remained unsolved for 357 years until Andrew Wiles finally found the proof in 1995.

There are many stories surrounding Fermat’s last theorem, but by far the most interesting is related to suicide. In 1908, a German mathematician called Paul Wolfskehl decided to kill himself after being cold-heartedly rejected by the woman he loved so much. He decided to shoot himself at midnight and in the remaining time started reading some mathematics texts until he found a flaw in Kummer’s theory, which disproved Cauchy and Lamé’s solution (the leading solution at the time. After Kummer’s essay, most mathematicians of the time gave up on Fermat’s last theorem). After researching Kummer’s essay, Wolfskehl found that it was far past midnight and he felt great pride in reinforcing Kummer’s solution. His depression was gone and through mathematics he found new meaning in his life. Wolfskehl, who believed that the theorem saved his life, made a resolution to donate his wealth to whoever solved Fermat’s last theorem, putting up 100,000 marks as a prize. This prize was claimed by Wiles in 1996 (then worth $50,000).

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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

Apple

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.

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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

Mead

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 Science & Nature

A Simple Task

A plague struck the ancient Greek island of Delos. As the disease ravaged the island, the people went to the oracle at Apollo’s temple for help. This is what the oracle said:

Double the volume of the cube-shaped altar in Apollo’s temple

People considered this a simple task and made a new altar where each side was double the original length. However, instead of disappearing, the plague worsened and people were confused.

Reason being, given that the length of one side of a cube is a, the volume is a³; if one side is 2a, the volume becomes 8a³, or eight times the original volume. Therefore, to double the volume of a cube, the number ³√2 is required. The problem is, whether ³√2 can be found using only compass and straightedge construction (where only the two tools are used to solve a geometric problem).

This problem, also known as the Doubling the cube problem, is one of three geometric problems known to be unsolvable by compass and straightedge construction. In other words, without the help of other mathematical methods, the answer cannot be found.
However, the solution to the above story is very simple.

Find a new god.

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.

(Sourcehttp://iraka.deviantart.com/art/Playing-his-cards-right-55647521?q=boost%3Apopular%20in%3Aphotography%20playing%20cards&qo=21)