Tag: greek

Posted in History & Literature

Halcyon Days

Posted on by Jinavie

There is a story in Greek mythology about a woman named Alcyone. Alcyone was married to Ceyx and the two were madly in love with each other. They would go as far as playfully calling each other Zeus and Hera (the king and queen of the gods). When Zeus heard of this, he became infuriated and plotted a way to punish the couple for their sacrilege.

One day, while Ceyx was sailing, Zeus threw a thunderbolt to raise a furious storm. The storm made quick work of Ceyx’s ship and Ceyx sank to the bottom of the sea. With his dying breath, he prayed to the gods to bring his body to the shore so that Alcyone may see him one last time and give him a funeral. The gods took pity and arranged for this to happen.

Meanwhile, Morpheus, god of dreams, appeared before Alcyone in the image of Ceyx, to gently inform her of her husband’s death. Alcyone ran to the shore in grief. There, she found the cold, lifeless body of her beloved husband. The loss of her true love was too much for her to bear. After Ceyx’s funeral, she threw herself in to the sea and drowned, so that she may meet her husband again in the underworld.

The gods, who were admirers of Alcyone and Ceyx’s beautiful love, were deeply saddened by this tragic fate. Zeus decided to atone for his rash actions by transforming the couple into a pair of kingfishers. The two birds lived happily ever after, but found that whenever they tried to lay eggs on the beach during the winter, strong waves would wash them away. Alcyone’s father Aeolus, god of the winds, saw this and calmed the winds for two weeks every winter, so that the couple may lay their eggs and make a nest in peace. Kingfishers have been referred to as halcyons since then.

Nowadays, the term halcyon days refers to a period of peace and calm, particularly during times of hardship.
Perhaps it is an allusion to the fact that we can navigate through any adversity when we are with our loved ones.

Posted in History & Literature

Evolution Of Colour

Posted on by Jinavie

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 process – your 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

Marathon

Posted on by Jinavie

In 490BC, The Greek city states were hard at war with the almighty Persian Empire. One well-known battle (out of many) is the Battle of Marathon, fought between about 10,000 Athenian soldiers (with some Plataean reinforcements) versus 26,000 Persian soldiers. Despite the Persians having superior numbers and cavalry, the battle concluded with a decisive victory to Athens thanks to a well-implemented flanking strategy and the temporary absence of the Persian cavalry at the base camp. The battle was a turning point in the First Greco-Persian War and the crushing defeat drove the Persian invasion force off Greek lands for ten years.

The popular story goes that a runner named Pheidippides was sent from Marathon to Athens after the battle to bring the good news, as the people of Athens were still gripped in fear that the Persians would directly strike the city soon. It is said that Pheidippides ran a distance of about 40 kilometres back to Athens and on arrival cried out “We have won!”, then collapsed and died from exhaustion.
When the modern Olympics was being designed at the late 19th century, the organisers decided to use this story to inspire what we now call the marathon – a 42.195km endurance run. The story was to recall the glory of ancient Greece and the heroic act of Pheidippides (also referred as Philippides in some texts).

Unfortunately, the story is a romantic amalgamation of two separate stories. But then again, the actual story is just as incredible.
Despite the decisive Athenian victory at the Battle of Marathon, the war still raged on and the Persians changed directions and headed for Athens instead. The Athenian army marched swiftly back home to pre-empt the Persian landing force. They marched 40km within a day – an amazing feat considering the fact that they just fought a massive battle and were armoured from head to toe.
The runner, Pheidippides, actually ran a distance of 225 kilometres from Athens to Sparta seeking reinforcements before the Persian army landed in Marathon (i.e. before the Battle of Marathon). He then ran back to Athens, meaning he ran roughly 450~500km within a few days. There is not much historical evidence of whether he actually ran this far in such short time but there are some anecdotal recordings.

The world record for the fastest marathon is 2 hours 3 minutes 23 seconds (as of 2014) by Wilson Kipsang of Kenya. The world record for the longest marathon ever run is set by Shiso Kanakuri, who started the marathon on July 14, 1912, during which collapsed from heat exhaustion around the 27km mark. He had to withdraw from the race, but could not bear with his “failure” all throughout his life. In 1967, he challenged himself again at the age of 75 to finish the remaining 15km, eventually setting the record time for the longest marathon ever run – 54 years, 8 months, 6 days, 5 hours, 32 minutes and 20.3 seconds.

Posted in History & Literature

To End All Wars

Posted on by Jinavie

In his play Lysistrata, Greek playwright Aristophanes gives a comic account of one woman’s extraordinary mission to end the Peloponnesian War – a 30 year old war between Athens and Sparta. How did one woman bring an end to such a deadly war?

In the play, Lysistrata (the female protagonist) becomes sick and tired of men treating women like simplistic hedonists incapable of functioning on their own. She believes that the war is a result of irrational men making stupid decisions and the long war is a waste as young, nubile women are aging away. She holds a convening of the women of various city states and proposes that the women must rise up to stop the war. Lysistrata’s plan is simple: withhold sex from the men until they cave (i.e. a sex strike). The women are reluctant at first, but agree to join her. They then take over the acropolis of the city, setting up a safe haven for women, barring any man from entering.

The men initially scoff at this revolution and try repeatedly to lay siege on the acropolis. However, they fail and the women continue to not provide any sexual pleasures to any male. The men constantly make snide comments about how women are hysterical and only seek pleasure, but sooner or later, they become desperate for sex. One by one, desperate men (sporting “burdens”, i.e. erections) come to the acropolis, pleading for relief (funnily, some women desert the acropolis in desperation for sex as well). The women take the men in, but only to tease them and leave them disappointed.

Eventually, the men (of both Athens and Sparta) cave and surrender, agreeing to end the war. There is a hilarious scene during the peace talks where Lysistrata brings out a stunning young girl named Reconciliation in front of the men, quashing any complaints or objections. Even the men who protest against the women’s demands are overcome by their lust and want(/need) for sex. Once peace is declared, the men and women all come together in the acropolis for singing and dancing, celebrating the women’s success in ending the war.

Although the play is only a comic exploration of the battle of the sexes, it clearly shows the power women have over men, and how they can use that power to easily control men.

Posted in Philosophy

Achilles And The Tortoise

Posted on by Jinavie

In 450 BC, a Greek philosopher named Zeno thought of the following paradox. Let us imagine that Achilles and a tortoise were to have a footrace. Achilles, obvious being faster than the tortoise, allows the tortoise to have a head start of 100 metres. Once the race starts, Achilles will quickly catch up to the tortoise. However, within the time he took to cover the distance, the tortoise would have travelled some distance as well (say 10 metres). When Achilles runs the 10m to catch up again, the tortoise has once again toddled on another metre. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Because there are an infinite number of points Achilles must reach where the tortoise has already been, theoretically the tortoise will be ahead of Achilles for eternity.

According to this thought experiment, motion is paradoxical and theoretically impossible. However, we know for a fact that motion happens. So how can we break Zeno’s paradox?

The main flaw of Zeno’s paradox is that he uses the concept of “eternity”. If we record the story mathematically, the time taken for Achilles to run the footrace is (if it took him 10 seconds to run 100m): 10 + 1 + 0.1 + 0.01 + 0.001… = 11.111… Ergo, the tortoise is only ahead of Achilles for less than 11.2 seconds (rounded). After 11.2 seconds pass, the time passed exceeds the sum of the infinite series and the paradox no longer applies.

Although it is a flawed paradox, the story of Achilles and the tortoise teaches the concept of geometric series – that something finite can be divided an infinite amount of times. For example, 1 = ½ + ¼ + 1/8 + 1/16… ad infinitum. This principle is a crucial part of mathematics and has significant implications in the field of economics. For example, it can be used to calculate the value of money in the future, which is necessary for working out mortgage payments and investment returns. Perhaps it is because of this mathematical principle that it seemingly takes an infinite amount of time to pay off a mortgage.

Zeno’s paradox teaches us that one should not take the concept of infinity for granted.

Posted in History & Literature

Helepolis

Posted on by Jinavie

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

Posted on by Jinavie

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 History & Literature

Charon’s Obol

Posted on by Jinavie

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 Science & Nature

A Simple Task

Posted on by Jinavie

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 History & Literature

Judgement Of Paris

Posted on by Jinavie

This is the story of how one man’s choice lead to a great war.

One day, Zeus held a banquet to celebrate a marriage, but did not invite Eris, the goddess of discord, for obvious reasons. Infuriated, she came up with a cunning plan, in which she arrived at the banquet, tossed a golden apple at the crowd, and disappeared.
On the apple, it was inscribed: For the fairest one.

Three goddesses approached the apple, claiming that it belonged to them: Hera, Athena and Aphrodite. They demanded that Zeus be the judge of who was the fairest, but Zeus knowing it was a catch-22 delegated the task to a mortal: Paris of Troy. This shepherd-prince was approached by each goddess, who offered a bribe using their godly powers.
Hera, the queen of gods, offered to make him the king of Eurasia, symbolising power and wealth.
Athena, the goddess of wisdom and war, offered great strength and wisdom.
Aphrodite, the goddess of love and beauty, offered the most beautiful woman in the world: Helen of Sparta.

After some thought, Paris presented the apple to Aphrodite, giving her the title of the “fairest one”. This earned him not only the beautiful Helen – who became infatuated with him under Aphrodite’s powers and brought to Troy – but also the scorn of the other two goddesses. Using their influences, and the fact that Helen was the wife of Menelaus – king of Sparta – the Trojan War sparked as Sparta formed a Greek alliance force to attack Troy, to reclaim their queen and seek vengeance and blood.

This goes to show how a man’s life, or his nation in the case of Paris, can be destroyed by the basic instinct of lust.