5 facts you need to know about music in Ancient Hellas

The Greek Herald has put together a list of five facts you need to know about music in Ancient Hellas, so I thought I'd share! 

1. Music as a gift of the Gods:

In Ancient Hellas, music was seen as a gift of the Gods and they considered that music could have a valuable effect on both body and mind of the listener.

The invention of musical instruments was attributed to specific deities including the lyre to Hermes, the flute to Athena and the panpipes to Pan.

2. Music and Education:

According to historical evidence, Hellenes started studying the theory of music from the 6th century BC. The earliest surviving text on music is the Harmonic Elements of Aristoxenos, which was written in the 4th century BC.

Music developed into an important element in the studies of philosophy by the followers of Pythagoras, the Hellenic philosopher and mathematician, who supposed that music was a mathematical expression.

3. The first school of musical education:

According to Plato, the first school of musical education was founded from the people of Crete followed by the music schools of Athens, where students were taught to sing and play the lyre. In Ancient Hellas, they believed that music taught order and discipline while allowing the educated to appreciate better the musical performance.

4. Music and Religion:

Music was associated with religious occasions in Hellenic cities including the Panathenaia and the Dionysia festivals in Athens.

Music contests in athletic competitions had a religious nature in honour of the Gods and the earliest such competitions were held in Argos, Paros and Sparta.

5. Musicians and Social Class:

The musicians of Hellas, also known as the makers of songs or melopoioi, were often regarded as composers and lyricists of the music they performed.

In Ancient Hellas, musicians had an elevated society status, indicated from robes and their presence on the lists of the royal household.

• Monday, June 21, 2021
  ancient Hellenic culture Apollon archeology Hermes Pan Pythagoras

"Don’t mix a fire with a knife"

 Swamped today, sorry, everyone. Here are some ancient words of wisdom!

“These are the sayings attributed to Pythagoras: don’t mix a fire with a knife; don’t step over a balance beam; don’t sit on a bushel; don’t eat your heart; don’t help with a burden but put it on; always make your bed; don’t put a god’s image on a ring; don’t leave the outline of a pan in ashes; don’t wipe up a mess with a torch; don’t piss towards the sun; don’t walk on the highway; don’t offer your right hand too easily; don’t share your roof with swallows; don’t keep clawed birds; don’t piss or stand on your cut nails and hair; turn sharp blades away from you; when abroad, don’t turn back at the border

This is what these sayings mean: “don’t mix a fire with a knife” means not inciting the rage or swollen anger of people in power. “Don’t step over a balance beam” means don’t transgress equality and justice. “Don’t sit on a bushel” means keep both today and the future in mind since a bushel is a daily ration. “Don’t eat your heart” clearly means not wearing away your mind with troubles and grief. By saying “Don’t turn around when going abroad” Pythagoras advises people when they are leaving life not to cling to it desperately nor to be overcome by its pleasures. The logic of the rest of the sayings are similar to this and would take a while to go through.”

[Diogenes Laertius, Pythagoras 17–18]
[Source]

• Friday, January 29, 2021
  ancient Hellenic culture Diogenēs Laertios Diogénes Laértios Pythagoras

Artist reconstructs faces of famous ancient Greeks

Italian artist Alessandro Tomasi has reconstructed the faces of ancient Greek and Roman philosophers and statesmen using as reference statues and busts kept in various museums around the world.

Tomasi, who is based in Florence, has gained thousands of followers on social media around the globe for his painstaking work of bringing the past back to life.

• Thursday, December 31, 2020
  Alexander the Great Antisthenes Aristotle current affairs Demostenes herodotos Hómēros Plato Pythagoras Socrates Thales of Milete

Ten ancient Hellenic writers you should know (and five more)

Listverse released a list of ten ancient Hellenic writers you should know. It's a good list, and the reasoning why these were chosen is a great read in and of itself. The ten who made the cut are:

10. Hómēros -- writer of the Iliad and the Odysseia
9. Sophocles -- the tragedian who wrote (amongst others) Antigone, Oedipus the King and Electra
8. Herodotos -- whose book The Histories is considered the first work of history in Western literature
7. Euripides -- the tragedian who wrote (amongst others) Alcestis, Medea and The Bacchus
6. Hippokrátēs -- who fathered modern medicine, mostly with his Hippocratic Corpus
5. Aristophanes -- the comic playwright who wrote (amongst others) The Clouds, The Wasps and Lysistrata
4. Plato -- one of the fathers of Western philosophy
3. Aristotle -- the last of the great Hellenic philosophers 
2. Euclid -- a mathematician and the father of geometry, whose main work--The Elements--is still used as a textbook in mathematics 
1. Archimedes -- a mathematician, engineer, inventor, physicist and astronomer whose ideas are as the basics of all these disciplines

I most certainly concur that this list lists some of ancient Hellas' most influential writers, but the list is far from complete. Today, I want to add five more to it, and most of my picks will no surprise you.

5. Sappho
Sappho (Σαπφώ) was a Hellenic lyric poet, born on the island of Lesbos (Λέσβος) around 620 BC, although the exact date is unknown. She wrote beautiful and highly romantic poetry that comes and goes straight to the heart. One of the most famous of her works is her Hymn to Aphrodite.

4. Aeschylos
As the original list includes both Sophocles and Euripides, it seems only fair to include Aeschylos. Aeschylos (Aiskhulos, Αἰσχύλος) was the first of the three Hellenic tragedians whose plays can still be read or performed. According to Aristotle, he expanded the number of characters in plays to allow for conflict amongst them, whereas previously characters had interacted only with the chorus. Aescholos' most famous works are undoubtedly the Seven against Thebes, the Supplicants and the Orestia. 

3. Pythagoras
Pythagoras of Samos ( Πυθαγόρας ὁ Σάμιος) was an Ionian Hellenic philosopher, mathematician, and the father of the religious movement called Pythagoreanism. He lived from about 570 BC to about 495 BC, and made influential contributions to philosophy, religious teaching, math, ethics, and science. His most famous work is, undoubtedly, the Pythagorean theorem (a^2 + b^2 = c^2), that's standard in every math textbook. Interestingly enough, not a single bit of writing has been preserved--if he ever wrote anything down to begin with. His works are mostly quoted by his students, or known through critiques by Aristotle.

2. Plutarch
Plutach (Ploútarkhos, Πλούταρχος) was an ancient Hellenic historian, biographer, and essayist who lived between 46 and 120 AD. He is known primarily for his Parallel Lives and Moralia, but much of his work is lost to us. Plutarch's writings are full of details about people and places, and are therefor a true treasure trove.

1. Hesiod
Hesiod (Hesiodos, Ἡσίοδος) was a Hellenic oral poet who lived between 750 and 650 BC, around the same time as Hómēros. I would dare say that his work--especially 'Works and Days' and the 'Theogony'--has shaped the way scholars and practitioners of Hellenismos view ancient Hellenic society, religion and way of life. This is why I strongly feel that anyone who feels drawn to the Theoi, might benefit from investing some time in reading his words.

• Saturday, November 21, 2020
  ancient Hellenic culture Aristophanes Aristotle current affairs Euripides Hellenismos 101 herodotos Hesiod Hippokrátēs Hómēros Plato Plutarch Pythagoras Sappho Sophocles

Four astronomical truths the ancient Hellenes got right

The Histories by Herodotus (484BC to 425BC) offers a remarkable window into the world as it was known to the ancient Greeks in the mid fifth century BC. Almost as interesting as what they knew, however, is what they did not know. This sets the baseline for the remarkable advances in their understanding over the next few centuries – simply relying on what they could observe with their own eyes.

Read the full article here.

1. The planets orbit the Sun
Aristarchus of Samos (310BC to 230BC) argued that the Sun was the “central fire” of the cosmos and he placed all of the then known planets in their correct order of distance around it. This is the earliest known heliocentric theory of the solar system.

Unfortunately, the original text in which he makes this argument has been lost to history, so we cannot know for certain how he worked it out. Aristarchus knew the Sun was much bigger than the Earth or the Moon, and he may have surmised that it should therefore have the central position in the solar system.

Nevertheless it is a jawdropping finding, especially when you consider that it wasn’t rediscovered until the 16th century, by Nicolaus Copernicus, who even acknowledged Aristarchus during the development of his own work.

2. The size of the Moon
One of Aristarchus’ books that did survive is about the sizes and distances of the Sun and Moon. In this remarkable treatise, Aristarchus laid out the earliest known attempted calculations of the relative sizes and distances to the Sun and Moon.

It had long been observed that the Sun and Moon appeared to be of the same apparent size in the sky, and that the Sun was further away. They realised this from solar eclipses, caused by the Moon passing in front of the Sun at a certain distance from Earth.

Also, at the instant when the Moon is at first or third quarter, Aristarchus reasoned that the Sun, Earth, and Moon would form a right-angled triangle.

As Pythagoras had determined how the lengths of triangle’s sides were related a couple of centuries earlier, Aristarchus used the triangle to estimate that the distance to the Sun was between 18 and 20 times the distance to the Moon. He also estimated that the size of the Moon was approximately one-third that of Earth, based on careful timing of lunar eclipses.

While his estimated distance to the Sun was too low (the actual ratio is 390), on account of the lack of telescopic precision available at the time, the value for the ratio of the size of the Earth to the Moon is surprisingly accurate (the Moon has a diameter 0.27 times that of Earth).

Today, we know the size and distance to the moon accurately by a variety of means, including precise telescopes, radar observations and laser reflectors left on the surface by Apollo astronauts.

3. The Earth’s circumference
Eratosthenes (276BC to 195 BC) was chief librarian at the Great Library of Alexandria, and a keen experimentalist. Among his many achievements was the earliest known calculation of the circumference of the Earth. Pythagoras is generally regarded as the earliest proponent of a spherical Earth, although apparently not its size. Eratosthenes’ famous and yet simple method relied on measuring the different lengths of shadows cast by poles stuck vertically into the ground, at midday on the summer solstice, at different latitudes.

The Sun is sufficiently far away that, wherever its rays arrive at Earth, they are effectively parallel, as had previously been shown by Aristarchus. So the difference in the shadows demonstrated how much the Earth’s surface curved. Eratosthenes used this to estimate the Earth’s circumference as approximately 40,000km. This is within a couple of percent of the actual value, as established by modern geodesy (the science of the Earth’s shape).

Later, another scientist called Posidonius (135BC to 51BC) used a slightly different method and arrived at almost exactly the same answer. Posidonius lived on the island of Rhodes for much of his life. There he observed the bright star Canopus would lie very close to the horizon. However, when in Alexandria, in Egypt, he noted Canopus would ascend to some 7.5 degrees above the horizon.

Given that 7.5 degrees is 1/48th of a circle, he multiplied the distance from Rhodes to Alexandria by 48, and arrived at a value also of approximately 40,000km.

4. The first astronomical calculator
The world’s oldest surviving mechanical calculator is the Antikythera Mechanism. The amazing device was discovered in an ancient shipwreck off the Greek island of Antikythera in 1900.

The device is now fragmented by the passage of time, but when intact it would have appeared as a box housing dozens of finely machined bronze gear wheels. When manually rotated by a handle, the gears span dials on the exterior showing the phases of the Moon, the timing of lunar eclipses, and the positions of the five planets then known (Mercury, Venus, Mars, Jupiter, and Saturn) at different times of the year. This even accounted for their retrograde motion – an illusionary change in the movement of planets through the sky.

We don’t know who built it, but it dates to some time between the 3rd and 1st centuries BC, and may even have been the work of Archimedes. Gearing technology with the sophistication of the Antikythera mechanism was not seen again for a thousand years.

Sadly, the vast majority of these works were lost to history and our scientific awakening was delayed by millennia. As a tool for introducing scientific measurement, the techniques of Eratosthenes are relatively easy to perform and require no special equipment, allowing those just beginning their interest in science to understand by doing, experimenting and, ultimately, following in the foot steps some of the first scientists.

One can but speculate where our civilisation might be now if this ancient science had continued unabated.

• Tuesday, June 9, 2020
  ancient Hellenic culture archeology Aristarchus of Samos Eratosthenes herodotos Posidonius Pythagoras

A woman to know: Theano of Krotone

The ancient Hellenic writers were dedicated historians, but they often neglected to mention the achievements of ancient Hellenic women. Now it so happens that I am a woman and I quite like having a few female heroes to look up to, so I want to introduce you to them. Today: Theano of Krotone.

Little is known about the life of Theano (Θεανώ), and the ancient sources are confused. According to one tradition, she came from Krete and was the daughter of Pythonax, but others said she came from Krotone and was the daughter of Brontinos of Metapontum (Βροντῖνος) a Pythagorean philosopher, and a friend and disciple of Pythagoras himself. She was said by many to have been the wife of Pythagoras, although another tradition made her the wife of Brontinos. Iamblichus, in an attempt to resolve the confusion, refers to Deino as the wife of Brontinus. She is said to have given Pythagoras at least three daughters (Damo, Myia, and Arignote) and a son, Telauges.

The writings attributed to Theano were: Pythagorean Apophthegms, Female Advice, On Virtue, On Piety, On Pythagoras, Philosophical Commentaries, and Letters. None of these writings have survived except a few fragments and letters of uncertain authorship. Attempts have been made to assign some of these fragments and letters to the original Theano (Theano I) and some to a later Theano (Theano II), but it is likely that they are all pseudonymous fictions of later writers, which attempt to apply Pythagorean philosophy to a woman's life. The surviving fragment of On Piety concerns a Pythagorean analogy between numbers and objects; the various surviving letters deal with domestic concerns: how a woman should bring up children, how she should treat servants, and how she should behave virtuously towards her husband.

From the Gnomologium Vaticanum, a Byzantine collection of sayings and anecdotes of ancient Hellenic philosophers and other celebrities, come the following words of wisdom:

- "Theano used to say “It is shameful to be silent on matters about which it is noble to speak and noble to be silent on those shameful to mention'."
- "Theano the Pythagorean philosopher was asked how a man and woman might live together and said ‘if they learn to bear each other’s moods'."
- "Theano suggested that a woman coming to her husband should strip off her shame along with her clothes and put them all back on again when she left'."
 - "Theano, when asked what number of days a woman was clean from her husband and is was right for her to go to the temple, said ” ‘on the same day from her own husband, but never from another'."
- "Theano said ‘It is better to trust onself to an unbridled horse than an illogical woman'."
 - "While Theano was walking she showed her forearm and some youth when he saw it said 'Nice skin'. She responded, 'it’s not communal''."
- "When Theano the Pythagorean philosopher was asked what eros is, she said 'the passion of a soul with spare time'."

• Thursday, August 10, 2017
  a woman to know series ancient Hellenic culture Pythagoras

Suicide prevention week: suicide and Hellenismos

This week is suicide prevention week. This is an important week because suicide is a serious issue in modern life. As long time readers know, suicide is something I am intimately familiar with. Not because I considered it myself but because I have lost friends to it and I have grown up under the threat (and attempt) of it. I am ambivalent about suicide. I understand the urge and reasoning. I understand the desire for the pain, or loneliness, or all other crippling emotions to end. Yet, on the other hand, suicide forces others to carry that burden for you. And the constant threat of suicide is a yoke upon the necks of loved ones. For me, it was a yoke that nearly broke me.

Don't commit suicide. If you will listen to me on anything, if you are contemplating suicide, don't do it. Reach out. Reach out to loved ones, reach out to professionals, reach out to friends or trusted third parties. Depression lies and suicide is not the answer. Life has a lot to offer--you might not see it right now, or feel it right now, but it does. I have seen many suffer through the deepest, darkest, valleys in their lives. not commiting suicide even though they really, really wanted to, and realizing after all that time that life gets better. That it's worth it. So reach out, okay?

Personal (and very conflicted) feelings aside, Hellenismos, in general, does not condemn it. I find that comforting. In general, suicide was an accepted form of death and it even became an accepted form of capital punishment. Athenian philosopher Socrates, for example, was condemned to death for 'refusing to recognize the Gods recognized by the state' and for 'corrupting the youth.' He died by drinking down a cup of poison hemlock.

In Hellenic myth, suicide has different causes for males than for females. Males often take their own lives out of shame, fear of disgrace, self-sacrifice, grief or the loss of honor. Women kill themselves mostly out of grief over the death of a male child or husband, out of shame or through self-sacrifice although their self-sacrifice is often for different reasons and by different means than that of males. I have written a lot more about suicide in mythology, which you can find here.

Stepping away from mythology, suicide became a more frowned-upon practice as time went by. Pythagoras and Aristotle, for example, were against the practice. Pythagoras believed there were only a finite number of souls so suicide upset the balance. Aristotle was against suicide because he felt that the community suffered a loss. A lot later, with the arrival of the Christians, suicide became an act of the Devil.

Hellenists have not reached a consensus about condoning or not condoning suicide yet. We might, in the future, but for now our societies, our personal experiences and our own (political) preferences influence our views more than our Reconstructionistic practices.

Some may call suicide hubris. I can see where this idea comes from. I used to agree with this but I'm not so sure now.  The idea was that you have taken yourself from the Olympians, taking the decission of your death out of Their hands. But the Gods don't always judge over the time of our deaths. And who am I to say that suicide was not a choice the Gods made for this person? And who am I to pass judgement anyway?

I feel Hades would welcome the soul of someone who has committed suicide. I feel this very, very strongly. I don't think He would judge a person at all on committing suicide. That having been said, please read the part of this post about not committing suicide again. Once you're dead, you're dead and although the Underworld isn't that horrible a place, no one should wish to leave the sunlight before their time, no matter how hard life can get.

In the spirit of suicide prevention week, take look at how open you are for being talked to about suicide. Take a loot at your friends and family and see if anyone needs help. Ask if they need help. Suicide can be prevented, if those around the person are willing to intervene. So be willing, please. We're all special. We're all valuable. And we should all stay here as long as wel can, to live life, to enjoy the good things, to make an impact... and to honor the Theoi.

• Friday, September 9, 2016
  ancient Hellenic culture Aristotle current affairs personal Pythagoras Socrates suicide

A woman to know: Aesara of Lucania

The ancient Hellenic writers were dedicated historians, but they often neglected to mention the achievements of ancient Hellenic women. Now it so happens that I am a woman and I quite like having a few female heroes to look up to, so I want to introduce you to them. Today: the poet and warrior Aesara of Lucania.

Aesara of Lucania (Αἰσάρα, Aisara) was a Pythagorean philosopher, who lived in the 4th or 3rd century BC. Nothing is known about her life; she is known only from a one-page fragment of her philosophical work entitled 'On Human Nature' preserved by Stobaeus.

Joannes Stobaeus (Ἰωάννης ὁ Στοβαῖος) lived in the 5th century CE. He hailed from Stobi in Macedonia and was the compiler of a valuable series of extracts from Hellenic authors. The work was originally divided into two volumes containing two books each. The two volumes became separated in the manuscript tradition, and the first volume became known as the Extracts (also known as 'Eclogues') and the second volume became known as the Anthology (also known as 'Florilegium'). Modern editions now refer to both volumes as the Anthology. The Anthology contains extracts from hundreds of writers, especially poets, historians, orators, philosophers and physicians. The subjects covered range from natural philosophy, dialectics, and ethics, to politics, economics, and maxims of practical wisdom. The work preserves fragments of many authors and works who otherwise might be unknown today.

All we really know about Aesara is that she came from Lucania, an ancient district of southern Italy and part of Magna Graecia where many Pythagorean communities existed. On Human Nature, her famous work from which only a fragment remains, is written in the Doric prose characteristic of the 3rd century BC or earlier, although that doesn't exclude the possibility that it was written later in an archaic style. Aesara argues that it is by studying our own human nature (and specifically the human soul) that we can understand the philosophical basis for natural law and morality. She divides the soul into three parts: the mind which performs judgement and thought, the spirit which contains courage and strength, and desire which provides love and friendliness. These things, being divine, are the rational, mathematical, and functional principles at work in the soul. Aesara's theory of natural law concerns three applications of morality, concerning the individual, the family, and social institutions.

The Pythagoreans were notable for including women in their ranks. This did not necessarily equate to modern ideas of equality; they believed that women were responsible for creating harmony and justice in the home, in the same way that men had the same responsibility towards the state. Seen in this context, Aesara's theory of natural law is fundamental to justice and harmony in society as a whole.

It's not easy to find the full text of Aesara's exposition, so I have typed it out from 'A History of Women Philosophers: Volume I: Ancient Women Philosophers, 600 BC - 500 AD by M.E. Waithe.

"Human nature seems to me to provide a standard of law and justice both for the home and for the city. By following the tracks within himself whoever seeks will make a discovery: law is in him and justice, which is the orderly arrangement of the soul. Being threefold, it is organized in accordance with tripple functions: that which effects thoughtfulness is [the mind], that which effects strength and ability is [high spirit], and all that effects love and kindliness is desire. These are all so disposed relatively to one another, that the best part is in command, the most inferior is goverend, and the one in between holds a middle place; it both governs and is governed.

The god thus contrived these things according to principle in both the outline and completion of the human dwelling place, because he intended man alone to become a recipient of law and justice, and none other of mortal animals. A composite unity of association could not come about from a single thing, nor indeed from several which are all alike. (For it is necessary, since the things to be done are different, that the parts of the soul als be different, just as in the case of the body [the organs of touch] and sight and hearing and taste and smell differ, for these do not all have the same affinity with everything.)

Nor could such a unity come from several dissimilar things at random, but rather, from parts formed in accordance with the completion and organization and fitting together of the entire composite whole. Not only is the soul composed from several dissimilar parts, these being fashioned in conformity with the whole and complete, but in addition these are not arranged haphazardly and random, but in accordance with rational attention.

For if they had an equal share of power and honor, though being themselves unequal--some inferior, some better, some in between--the association of parts throughout the soul could not have been fitted together. Or, even if they did have an unequal share, but the worse rather than the better had the greater share, there would be great folly and disorder in the soul. And even if the better had the greater and the worse the lesser, but each of these not in the proper proportion, there could not be unanimity and friendship and justice throughout the soul, since when each one is arranged in accordance with the suitable proportion, this sort of arrangement I assert to be justice.

And indeed, a certain unanimity and agreement in sentiment accompanies such an arrangement. This sort would justly be called good order, whichever, due to the better part's rulling adn the inferior's being ruled, should add the strength of virtue to itself. Friendship and love and kindliness, cognate and kindred, will sprout from these parts. For closely-inspecting mind persuades, desire loves, and high spirit is filled with strength; once seething with hatred, it becomes friendly to desire.

Mind having fitted the pleasant together with the painful, mingling also the tense and robust with the slight and relaxed portion of the soul, each part is distributed in accordance with its kindred and suitable concern for each thing: mind closely inspecting adn tracking out things, high spirit adding impetuosity and strength to what is closely inspected, and desire, being akin to affection adapts to the mind, preserving the pleasant as its own and giving up the thoughtful to the thoughtful part of the soul. By virtue of these things the best life for man seems to me to be whenever the pleasant should be mixed with the earnest, and pleasure with virtue. Mind is able to fit these things to itself, becoming lovely through systematic education and virtue."

• Wednesday, August 31, 2016
  a woman to know series ancient Hellenic culture Pythagoras

Happy birthday to me!

Well, yesterday. As you know, I don't really celebrate my birthday, but I had a little brunch, my parents and my girlfriend's parents visited, and my girl made me a lovely dinner last night. It was quiet and easy going, and I enjoyed it. I didn't get a chance to write, though, and today, I am starting my new job, so I don't have the time to get anything up. So, until tomorrow, how about I leave you with a little something about the influence of the ancient Hellenes on mathematics?

"Often called the "birthplace of civilisation", Ancient Greece heralded numerous advances in philosophy, science, sport and also mathematics. Over six centuries from 600 BC a group of revolutionary thinkers -- from Thales, Pythagoras, Democritus and Aristotle to Euclid, Archimedes and Hypatia of Alexandria -- formalised the rules and language of modern mathematics.

For Greek thinkers, maths wasn't simply a means of calculating amounts but a way of testing reality and understanding the true nature of the world around them. Indeed, Pythagoras is believed to have coined both the words "philosophy" ("love of wisdom") and "mathematics" ("that which is learned"). In turn, Euclid came to be known as the "father of geometry".

At the heart of this new understanding, was the concept of "the proof", developed by Euclid in what is commonly regarded as the most important and successful mathematical textbook of all time -- the "Stoicheion" or "Elements". Built upon the axiomatic method, mathematical proofs were a way of testing assumptions by building up a mathematical argument using self-evident or assumed statements (or, "axioms").

It is this methodology that formed the foundational language and logic of modern mathematics throughout the world. Indeed, Euclid's Elements was widely used as the seminal maths textbook right up until the start of the twentieth century."

• Monday, August 25, 2014
  Aristotle Pythagoras this is not a real post videos

The Golden Verses of Pythagoras

Yesterday I was asked if the Golden Verses of Pythagoras have a place in my practice. For those of you unfamiliar with the Golden Verses, they are a collection of moral exhortations and comprise 71 lines written in dactylic hexameter verse. Traditionally, they are attributed to Pythagoras, although the exact origins of the verses are unknown. It appears that the verses may have been known as early as the third century BC, but their existence as we know them cannot be confirmed prior to the fifth century AD.  Neoplatonists used the golden verses as part of their preparatory program of moral instruction. The verses are:

1. First worship the Immortal Gods, as they are established and ordained by the Law.
2. Reverence the Oath, and next the Heroes, full of goodness and light.
3. Honour likewise the Terrestrial Daemons by rendering them the worship lawfully due to them.
4. Honour likewise your parents, and those most nearly related to you.
5. Of all the rest of mankind, make him your friend who distinguishes himself by his virtue.
6. Always give ear to his mild exhortations, and take example from his virtuous and useful actions.
7. Avoid as much as possible hating your friend for a slight fault.
8. Power is a near neighbour to necessity.
9. Know that all these things are just as what I have told you; and accustom yourself to overcome and vanquish these passions:--
10. First gluttony, sloth, sensuality, and anger.
11. Do nothing evil, neither in the presence of others, nor privately;
12. But above all things respect yourself.
13. In the next place, observe justice in your actions and in your words.
14. And do not accustom yourself to behave yourself in any thing without rule, and without reason.
15. But always make this reflection, that it is ordained by destiny that all men shall die.
16. And that the goods of fortune are uncertain; and that just as they may be acquired, they may likewise be lost.
17. Concerning all the calamities that men suffer by divine fortune,
18. Support your lot with patience, it is what it may be, and never complain at it.
19. But endeavour what you can to remedy it.
20. And consider that fate does not send the greatest portion of these misfortunes to good men.
21. There are many sorts of reasonings among men, good and bad;
22. Do not admire them too easily, nor reject them.
23. But if falsehoods are advanced, hear them with mildness, and arm yourself with patience.
24. Observe well, on every occasion, what I am going to tell you:--
25. Do not let any man either by his words, or by his deeds, ever seduce you.
26. Nor lure you to say or to do what is not profitable for yourself.
27. Consult and deliberate before you act, that you may not commit foolish actions.
28. For it is the part of a miserable man to speak and to act without reflection.
29. But do the thing which will not afflict you afterwards, nor oblige you to repentance.
30. Never do anything which you do not understand.
31. But learn all you ought to know, and by that means you will lead a very pleasant life.
32. in no way neglect the health of your body;
33. But give it drink and meat in due measure, and also the exercise of which it needs.
34. Now by measure I mean what will not discomfort you.
35. Accustom yourself to a way of living that is neat and decent without luxury.
36. Avoid all things that will occasion envy.
37. And do not be prodigal out of season, like someone who does not know what is decent and honourable.
38. Neither be covetous nor stingy; a due measure is excellent in these things.
39. Only do the things that cannot hurt you, and deliberate before you do them.
40. Never allow sleep to close your eyelids, after you went to bed,
41. Until you have examined all your actions of the day by your reason.
42. In what have I done wrong? What have I done? What have I omitted that I ought to have done?
43. If in this examination you find that you have done wrong, reprove yourself severely for it;
44. And if you have done any good, rejoice.
45. Practise thoroughly all these things; meditate on them well; you ought to love them with all your heart.
46. It is those that will put you in the way of divine virtue.
47. I swear it by he who has transmitted into our souls the Sacred Quaternion, the source of nature, whose cause is eternal.
48. But never begin to set your hand to any work, until you have first prayed the gods to accomplish what you are going to begin.
49. When you have made this habit familiar to you,
50. You will know the constitution of the Immortal Gods and of men.
51. Even how far the different beings extend, and what contains and binds them together.
52. You shall likewise know that according to Law, the nature of this universe is in all things alike,
53. So that you shall not hope what you ought not to hope; and nothing in this world shall be hidden from you.
54. You will likewise know, that men draw upon themselves their own misfortunes voluntarily, and of their own free choice.
55. Unhappy they are! They neither see nor understand that their good is near them.
56. Few know how to deliver themselves out of their misfortunes.
57. Such is the fate that blinds humankind, and takes away his senses.
58. Like huge cylinders they roll back and forth, and always oppressed with innumerable ills.
59. For fatal strife, natural, pursues them everywhere, tossing them up and down; nor do they perceive it.
60. Instead of provoking and stirring it up, they ought to avoid it by yielding.
61. Oh! Jupiter, our Father! If you would deliver men from all the evils that oppress them,
62. Show them of what daemon they make use.
63. But take courage; the race of humans is divine.
64. Sacred nature reveals to them the most hidden mysteries.
65. If she impart to you her secrets, you will easily perform all the things which I have ordained thee.
66. And by the healing of your soul, you wilt deliver it from all evils, from all afflictions.
67. But you should abstain from the meats, which we have forbidden in the purifications and in the deliverance of the soul;
68. Make a just distinction of them, and examine all things well.
69. Leave yourself always to be guided and directed by the understanding that comes from above, and that ought to hold the reins.
70. And when, after having deprived yourself of your mortal body, you arrived at the most pure Aither,
71. You shall be a God, immortal, incorruptible, and Death shall have no more dominion over you.

As for the answer to the question: the short answer is ‘no’, but that is only if you stick to the ditchotomy of ‘yes’ and ‘no’. As much as I admire Pythagoras and his views, I feel far more drawn to the older ethical guidelines, like the Delphic Maxims and the tenets of Solon.

I am a follower of the Classical period, a period where the popularity of scholars and poets increased, but had not yet overtaken the minds of the followers of the Theoi in any major way. Pythagoras’ views on the Theoi do not overlap entirely with mine… so yes, I enjoy reading the Golden Verses and many of them overlap with older ethical guidelines I completely agree with… but I can’t agree with all of them.

• Tuesday, March 18, 2014
  ancient Hellenic culture ethics Hellenismos 101 personal Pythagoras

The characters of Atlantis

It's a sad day today: no new Atlantis episode on Saturday, so no new recap on Monday. Atlantis will be back next Saturday after a brief hiatus to make room for a special Doctor Who event, and we will get to see the boys travel to the Underworld in good, oldfashioned, hero style. To leave you with something today that may at least fill the void a little, I have taken my cue from last week's mini-breakdown of the real Pythagoras and will bring you a few character portraits of the characters and the mythological or actual people they were based upon.

Jason (Jack Donnelly)

Jason, obviously, is going to be the one without a counterpart in Hellenic mythology. That said, he is reflective of all the great heroes: he is strong, athletic, noble and shrewed. He has a keen mind, sharp senses and a drive to do good. Like any good mythological hero, he has daddy issues and he's taken over many a hero's role so far, but mostly Theseus comes to mind, who took down the Minotaur in the original Hellenic myth--and temporarily snatched up Ariadne, I should add. He also took Iásōn's name, the hero who commanded the ship Argo and led the Argonauts to the Golden Fleece and back.

Jason combines the best aspects of Hellenic heroism: a convoluted background, a sharp mind, a trained body, and a kind heart. Jason in the series also acts as the eyes of the audience as he came over from our world to Atlantis, and is still getting the hang of the ancient Hellenic culture as portrayed by the BBC.

Hercules (Mark Addy)

Hercules in the series is perhaps not the epithomy of human achievement--and a far cry from the hero we respect and worship--but he's a good guy at heart. That much is clear. I will be the first to admit that watching Atlantis' Hercules is often a bit difficult: to see arguably the greatest of Hellenic heroes avoid doing the right thing as long as he can because all other options are simpler/easier/cost less energy or money is a bit unsettling. That said, Heracles is still an intelligent man, with a good heart, who cares deeply for his friends. He would go to hell and back for them--and in the coming episode, it looks like he will do exactly that.

The ancient Hellenic Hēraklēs is a child (and great grand child) of Zeus. Hēraklēs was conceived by Zeus upon Alkmene, as He disguised Himself as her husband, returning early from war. Alkmene accepted Him in her bed gladly, as she was happy to see her husband again. When The real Amphitryon did return later that night, Alkmene realized what had happened, and told her husband. Amphitryon accepted her in his bed, regardless, and so she became pregnant with twins, one fathered by Zeus, and one by her mortal husband.

Hera, hearing of the affair, took an instant disliking to the unborn child. When it became time for Alkmene to give birth, Hera made Zeus swear a vow that a child born in the line of Perseus on this day would become King. Zeus agreed, and Hera hurried off to delay the birth of Hēraklēs and Iphikles, and hurry along the birth of Eurystheus (Εὐρυσθεύς), grandson of Perseus. Due to Hera's jealousy, he was stricken mad and killed the five sons he had by his wife. When he was released from his madness by a hellebore potion--provided by Antikyreus--and realized what he had done, he cried out in anguish, and went on a long journey to cleanse himself of the miasma caused by these killings. In the end, Hēraklēs became a God and ascended to Olympus where he became one of the primary heroes prayed to by the ancient Hellenes and  worshippers today.

Pythagoras (Robert Emms)

Pythagoras iss actually not a person from myth but an actual person. Pythagoras of Samos (Πυθαγόρας ὁ Σάμιος) was an Ionian Hellenic philosopher, mathematician, and founder of the religious movement called Pythagoreanism. He was an influential voice in philosophy, religion, mysticism and science in the late 6th century BC, and is best known for the Pythagorean theorem which bears his name. Because almost everything we now know about Pythagoras was written down centuries later, it may very well be that the theorem as well as anything else attributed to Pythagoras was discovered by his colleagues, students, successors, or even his mother.

Pythagoras in the series could very well resemble a young Pythagoras who has a penchant for triangles. He's very smart, analythical, and would do anything for his friends. He is incredibly loyal and while he would prefer to handle everything with words, he's not above taking out a butter knife in defense.

Medusa (Jemima Rooper)

I miss you, Medusa, please come back! Okay, with that out of the way: Medusa. It might be obvious, but the Medusa from the series is a far cry from the mythological one. She is obviously based off of Ovid's version of the myth, where she was a human woman--possiby a priestess to Athena--who was raped by Poseidon (within the temple walls) and punished by Athena for her transgression.

The link above leads to a long and detailed account of the varying myths of Médousa, and it's perhaps best to suffice here by saying that the snake-haired Gorgon known from mythology is mostly a Roman invention; in the Hellenic era, the head of Médousa brought protection and was thus placed on shields and armors, but also on ovens to keep children away from them.

Medusa from the series is kind-hearted, funny, independant and doomed to have something horrible happen to her--as predicted by the Oracle, at least to Jason. If the show sticks with Ovid, that terrible someting is not something I want to watch (thank you very much) and also doesn't fall into the age bracket of the show, so we will see if Medusa ends up with snakes for hair or not.

Pasiphaê (Sarah Parish)

As the Evil Queen, Parish is currently only riveled by Lana Parrilla's Regina Mills on Once Upon A Time when it comes to milti-layered depictions of an evil caricature. Pasiphaê is the wife of King Minos and stepmother to Ariadne, love interest of Jason. She is a true 'evil' Queen; plotting to further the agenda of her husband and manipulating said agenda so she gets the best out of it. Her plans were recently thwarded by Jason and mostly Ariadne, who called off the wedding between her and Heptarian--Pasiphaê's puppet. Pasiphaê's redeeming features lie in the scenes where she comforts and counsels Ariadne and shows that--whatever she is doing--she believes it to be for the best of the Royal House and the citizens of Atlantis; as misguided as that may be.

Pasiphaê is part of the Myth of the Minotaur. Minos, king of Krete, requested Poseidon raise a bull from the sea, which the King promised to sacrifice; but when Minos refused to do so, Poseidon caused his wife Pasiphaê to fall in love with the bull. The child that came from this union was deformed in such a way that he had the head of a bull and the body of a man. I am fairly certain the original Pasiphaê did not have magical powers, but the series version definitely has.

Ariadne (Aiysha Hart)

Ariadne is the daughter of King Minos. When Theseus came to the island of Krete, she fell for him and offered him a ball of yarn so he would be able to find his way out off the labyrinth that housed the Minotaur. Theseus defeated the Minotaur and took Ariadne and her sister Phaedra from their home in thanks for their help. That night, they slept on the beach but Athena woke up Theseus and told him to sail out now, and to leave Ariadne and Phaedra behind. He did, although it pained him greatly.

Ariadne was devastated but was found by the God of wine, Dionysos, and He took her as His wife. Ariadne gained immortality and is still married to her God, being a Goddess in her own right now.

Ariadne in the series is not quite there yet. Our Theseus-substitute has declared his love but there is no running away or actual cordship involved. Set up as the show's One True Pairing, I doubt Jason is going to leave her in the end so she can be snatched up by a God. Ariadne is developing into one fo the most interesting of the series--from the myth's lovesick young woman to a strong princess who would do anything to protect the people she loves and the subjects of Atlantis, whom she cares about as well. In her youthful ignorance, she has managed to antagonize her stepmother Pasiphaê who retaliated by having Ariadne's friend and servant killed, and thus, Ariadne is currently getting a steady dose of reality shoved her way. I, for one, hope she comes out of it stronger on the other side and that Korinna's death can serve as a catalist for this proccess.

How to you feel about the re-imaging of these classical characters? Is there anything you would change back or anything that stands out as a good writing choice for the creators? How do you feel about Atlantis in general, ad are you happy it will be back on Saturday? Let me know!

Image property: character portraits by BBC ONE, classical art by Wikipedia Commons.

• Monday, November 25, 2013
  Ariadne Atlantis Dionysos Hēraklēs Iásōn Médousa Minos Pasiphaê Pythagoras Theseus

"Atlantis" recap (1.01): The Earth Bull

BBC One has a new 13-episode TV series set in a hollywood version of ancient Hellas--namely Atlantis. If you liked 'Merlin', this show will certainly fit your tastes. The show is about Jason, a strapping young man who ends up traveling to the--previously believed to be mythical--city of Atlantis in search for his father. Here, he ends up in a world of adventures, trying to find out who he is and who his father was. As we get very few regular series set in ancient Hellas, I decided to recap the episodes, starting a bit late as the second episode has already aired and the third will be broadcasted Saturday.

I think this part is obvious but this post contains spoilers.


We start the series looking out over the waters of the (what I assume to be) Mediterranean Sea with Jason (Jack Donnelly). He is on a hunt for his father, who took a submarine down under the surface after leaving his son a necklace with bull horns, and never came back up. He is about to take a submarine down himself and look for his dad, something the boat captain does not find a comforting thought.

 

The boat captain turns out to be right; Jason reaches the bottom of the sea and shines his one person submarine light on a piece of metal with the words 'the oracle' on it in funky typeface. I am assuming this is a part of his father's submarine as well as a major dose of foreshadowing.

As soon as Jason's light hits the metal, another light appears, speeding towards him with such force that it cracks the window of the submarine. Jason realizes his life is over and shields his face with his arms as the water rushes in.

When Jason wakes up on a beach, he seems to have misplaced his clothes, but he still has his necklace. That is never how it works for me in the swimming pool, but whatever, right? Jason does not care: he is still alive, so while covering his manhood, he tries to wave over some fishermen for help.

It seems the fishermen fish in the nude because when Jason reaches the place their boat left, there is a pile of (what I assume to be the hollywood version of) Hellenic clothing. Naturally, Jason takes the clothes and heads off to find civilization.

Civilization comes in the form of a huge city just past the dunes, which definitely does not look modern. It does, however, look pretty and the music swells in an impression of Greek music to set a mood that reminds me most of Xena: The Warrior Princess.

Once he wanders into the city, Jason finds himself in a market place where there are actually people who wear something resembling ancient Hellenic clothing (although most aren't) and are selling everything from chickens to fruits, to more fruits, and even more fruits. In the shade is something that finally seems to convince Jason that he is not in Kansas anymore: a two-headed lizard that I am assuming to be a Hydra. He tries to pet it and the Hydra snaps at him before chasing him through the market square. As a note, this scene had so many shots of fruit--either remaining stationary or rolling about after Jason knocks them over--that I figured there must be some hidden meaning or other relevance to it. Sadly, I have not been able to find out what.

 

After a long chase from the Hydra and then the city guards wherein Jason shows he was a gymnast in a (past) life, he ends up danging from a building and being pulled up by a scrawny young man so adorable, I immediately end up shipping Jason and the young man, who--it turns out--is Pythagoras (Robert Emms). Yes, that one. Pythagoras--like everyone in Atlantis--speaks posh English, and while I had not expected otherwise, it still irks me a little.

 

 

At any rate, Pythagoras is quite smitten with his guest, but his housemate isn't. Much to Jason's surprise, Pythagoras' housemate is no other than Hercules (Mark Addy, whom I know best from 'The Full Monty'). I really want to type 'Herakles' here, but it seems that is a bit too difficult for the common watcher, so 'Hercules' it is. Hercules is not exactly as he might have been portrayed in ancient Hellenic art, and I am quite sure he is supposed to be the comic relief, but I chuck any hope of authenticity out of the window just to be sure.

 

 

Jason shares a bit of his story with his new sidekicks and they wisely tell him to visit the temple of Poseidon and ask the Oracle his many questions. Pythagoras also tells Jason that his necklace represents the bull horns of Poseidon. To the show's credit, the temple is beautiful. It does, however, house the statue of a bull instead of a statue of Poseidon. As far as I am aware, Poseidon's only link to bulls is the myth of the Minotaur. Minos, king of Krete, requested Poseidon raise a bull from the sea, which the king promised to sacrifice; but when Minos refused to do so, Poseidon caused his wife Pasiphaê to fall in love with the bull. The child that came from this union was deformed in such a way that he had the head of a bull and the body of a man. Why the enormous link with bulls in Atlantis exists, I do not know.

 

At any rate, Jason sees Hercules leave the temple with a heavy heart and doesn't seem too happy to look for the Oracle now. He does, however, and the Oracle turns out to be the wonderful and underrated Juliet Stevenson for whom I am very happy she got another acting gig. In the most un-Hellenic thing of the episode, a chicken is slaughtered, its blood added to a bowl of water, and the Oracle tells Jason that his father 'walks amongst the dead'. She also hints that Jason is actually from Atlantis, and so was his father. She also hints that his destiny will cause a lot of danger to him. People want him dead; it seems only Jason can 'bring an end to the people's fear and suffering'.

 

After Jason leaves, the Oracle's helper asks her why she witheld information from Jason. She tells him she did it to keep Jason safe. In all my years reading books, watching TV, and playing games, never, ever, has witholding information led to a safer situation for the person involved, but we'll see what happens next.

 

 

Pythagoras meets Jason on the steps of the temple and the two bond over the message the Oracle had for Jason. Pythagoras then tells Jason to come home with him as there is a curfew tonight. Tomorrow, lots will be drawn amongst all Atlantians to see which seven citizens will be shipped off to be sacrificed to the Minotaur (Ah! Now the bull thing makes sense! (sort of)). Anyone caught outside tonight will be shot on sight, as it will be assumed they are trying to flee the will of Poseidon.

 

Later that night, Hercules begrudgingly allowes Jason a place to sleep in the house he owns, but Pythagoras helped him keep by paying his gambling debts, and then tries to sneak out of the house. Jason wakes up and wakes Pythagoras. The two sneak out after Hercules and manage to catch up to him before he climbs down the city wall, which would make him an exile for life. It seems he was fleeing because the Oracle predicted he would draw a black rock tomorrow and be shipped off to the Minotaur.

 

The trio manages to get back home safely, despite being discovered by the guards and being hunted by hunting lions. Jason shows the two some spectacular gymnastics and seems to be clueless as to how he suddenly developed this talent.

 

The next day, king Minos--played by Alexander Siddig whom I only know as Dr. Julian Bashir in 'Star Trek: Deep Space Nine' but who has done a lot of acting afterwards--oversees the drawing of lots after a half-assed speech about honor in sacrifice. Hercules draws a white stone and is thus safe, as is Jason who cares a lot more about the king's daughter Ariadne (Aiysha Hart) than the stone. Pythagoras, however, draws a black stone and is stunned.

 

 

That night, Pythagoras babbles about triangles to hide his fear of dying and the trio makes plans to save his life that never go anywhere. It isn't until the morning that a brilliant idea comes to Jason: take the stone and take Pythagoras' place, never mind that he can't handle a sword, nor any other weapon available in Atlantis. So said and done. No one seems to mind--or realize--that Jason took Pythagoras' place. The only one who does notice that Jason is not a scrawny, curly haired, math geek is Ariadne, who has fallen head over heels for our strapping hero and thus offers him her locket, which holds an unbreakable and/or unending chord of marvelous awesomeness which will lead him out of the labyrinth she used to play in as a kid.

 

 

Fast forward to the entrance to the labyrinth where Pythagoras and Hercules show up to bring weapons to their newfound friend at Pytrhagoras' insistance. They get found out, obviously, and end up taking the place of two of the women who drew black stones. Now they are all in a world of hurt.

 

Seven people enter the labyrinth and only one gets a name--a girl named Helena (Faye Brooks)--so I figure the others are Minotaur food. In the end, I think I'm right as I counted at least two (completely bloodless) deaths amongst the tributes. It takes a while of waving torches around and looking past the camera with fear on their faces, but eventually Jason ends up in the lair of the Minotaur who--as it turns out--was a man, turned into a Minotaur, and is a beautiful feat of CGI, especially as he turns back into a man after a bit of a lackluster fight where Jason only needs to hold out a sword to let the Minotaur run into.

 

It seems the man was turned into a Minotaur by the Gods as punishment for doing 'a great wrong' that 'betrayed his [Jason's] father', and was told that one day a kid named Jason would come along to lift the curse. I wonder if the dying part was included in the prophecy, but at least the man dies in the form of a man, and in the arms of a young stud. Before he dies, though, the Minotaur-man tells Jason that Minos must never know who he is, and that 'this is just the beginning' of his great destiny.

 

 

Outside of the labyrinth, the Oracle sees her prophecy come true as Jason slays the Minotaur. She and her sidekick see their faith in Jason rewarded and start plotting the next steps to Jason's greatness and their end goal, of which we are most certainly not certain. They also spell more doom for Jason.

 

Once the tributes are recovered from the labyrinth and presented to the king, queen, and princess, king Minos makes another speech which is just about as sincere as the previous one. He congratulates Jason, Pythagoras and Hercules for their efferts and Hercules gladly takes the credit for the kill. Jason lets him for now, but teases Hercules about his very limited help--it seems Hercules ran in the other direction when the Minotaur fell upon the group and never even saw the beast--once they are outside of the palace.

 

Jason returns Ariadne's necklace, which her mother--Queen Pasiphaê (Sarah Parish)--sees and does not seem to approve of. Watch out for that one, Jason. Pasiphaê looks like a woman who could pose a problem, and not just to your love life.

 

 

Next time on Atlantis: Jason goes to see the Oracle again to ask why she is hiding the truth from him, Jason has more innocents to protect at the bottom of a well (or the end of a chasm, I'm not sure), and we are introduced to Medusa.

 

Despite the glaring inaccuracies, I like 'Atlantis'. It's an adventure with Hellenic influences, and while the acting is not as strong across the board and the dialogue is a bit stunted, I look forward to the next mythological reference and to see where the prophecy goes. What did you think of Atlantis? And would you like to see recaps of the remaining episodes? Let me know!

• Tuesday, October 8, 2013
  Ariadne Atlantis Hercules Minos Mythology 101 Pasiphaê Pythagoras recaps

The Pythagorean theorem

Today, like with Plato's allegory of the cave, I want to discuss one of the major developments in thinking contributed to the ancient Hellenes. When I was in high school, I was terrible at math. Especially geometry was a huge problem for me. I had nightmares about the Pythagorean theorem even years after high school--I understood the overall theory, but then my teacher dragged in a lighthouse or tent pole and I was lost. It took my brain a good couple of years to understand that those lighthouses and tent poles didn't have anything to do with math and were just an overlay intended to make math easier for people whose brain was wired differently than mine. For me, it made me hate anything connected to mathematics. In a roundabout way, I was eventually reintroduced to math in a way that made a lot more sense to me, and looking back now, the Pythagorean theorem is really not that difficult anymore. If I have readers who are struggling with this in school, trust me, it gets better.

Back to Pythagoras. Pythagoras of Samos (Πυθαγόρας ὁ Σάμιος) was an Ionian Hellenic philosopher, mathematician, and founder of the religious movement called Pythagoreanism. He was an influential voice in philosophy, religion, mysticism and science in the late 6th century BC, and is best known for the Pythagorean theorem which bears his name. Because almost everything we now know about Pythagoras was written down centuries later, it may very well be that the theorem as well as anything else attributed to Pythagoras was discovered by his colleagues, students, successors, or even his mother. That said, I'm just going to assume that Pythagoras was brilliant and came up with one of the most basic fundaments of geometry, that in any right-angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle). Gods, that sounds complicated when posed like this. The Pythagorean theorem is better known as the formula used to solve it: a² + b² = c².

The easiest form of the Pythagorean theorem

We often call the ancient Hellenes the founders of modern thinking, and although the theorem was very influential even then, it had been discovered before. What Pythagoras did--and which man other Hellenic scholars did in their time--was proof why the theorem works. Instead of simply going with it, they struggled to find proofs of the theories. To prove the Pythagorean theorem, we must realize that it does not actually concern the triangle depicted above; it concerns the squares that you can connect to them. In the example above, there will be a square with a value of 3 on all sides to the left of the shortest side (a), a larger square with a value of 4 on all sides tagged to the bottom line (b), and an even larger square with a value of (in this example) 5 on all sides tagged to the hypotenuse (c). You can see this in the image to the left, below. Pythagoras then realized that this theory works because the area encompassed by the outer square never changes, and the area of the four triangles is the same at the beginning and the end, so the black square areas must be equal, therefore a² + b² = c². Actually, we don't know if this is the proof Pythagoras used, but it sure is one that works.

 

Pythagoras's theorem has been at the core of mathematics and geometry ever since its discovery, and even though the discoveries by Pythagoras and his contemporaries at his school were supposed to be kept secret within the brotherhood that surrounded those who studied, lived, and worshipped with Pythagoras, many of them were leaked to the public eventually. This allowed those who were not part of Pythagoreanism to understand and develop the foundations Pythagoras had laid out. His influence could be seen in the work of the greats--like Plato--but the influence of his brotherhood can be found even as far down the line as Freemasonry and Rosicrucianism.

 

Pythagoras made many more brilliant discoveries in his time, many of which w will talk about at a later date. For now, I want to share with you this lengthy, but hugely interesting lecture by N.J. Wildberger at the University of New South Wales for the college course 'History of Mathematics'. In this first lecture (with two parts) a very rough outline of world history from a mathematical point of view is given, with a focus on the position the work of the ancient Greeks as following from Egyptian and Babylonian influences has in that timeline. It also introduces the Pythagoras' theorem in a very elaborate and understandable way. The disposition about Pythagoras starts at about 13 minutes in. Part b can be found here, and is equally interesting. Enjoy!

 



 

Image source: squares, Pythagorean proof

• Sunday, June 16, 2013
  ancient Hellenic culture Plato Pythagoras teachings video

Ten ancient Hellenic writers you should know (and five more)

Listverse, has recently released a list of ten ancient Hellenic writers you should know. It's a good list, and the reasoning why these were chosen is a great read in and of itself. The ten who made the cut are:

10. Hómēros -- writer of the Iliad and the Odysseia
9. Sophocles -- the tragedian who wrote (amongst others) Antigone, Oedipus the King and Electra
8. Herodotos -- whose book The Histories is considered the first work of history in Western literature
7. Euripides -- the tragedian who wrote (amongst others) Alcestis, Medea and The Bacchus
6. Hippokrátēs -- who fathered modern medicine, mostly with his Hippocratic Corpus
5. Aristophanes -- the comic playwright who wrote (amongst others) The Clouds, The Wasps and Lysistrata
4. Plato -- one of the fathers of Western philosophy
3. Aristotle -- the last of the great Hellenic philosophers
2. Euclid -- a mathematician and the father of geometry, whose main work--The Elements--is still used as a textbook in mathematics
1. Archimedes -- a mathematician, engineer, inventor, physicist and astronomer whose ideas are as the basics of all these disciplines

I most certainly concur that this list lists some of ancient Hellas' most influential writers, but the list is far from complete. Today, I want to add five more to it, and most of my picks will no surprise you.

5. Sappho
Sappho (Σαπφώ) was a Hellenic lyric poet, born on the island of Lesbos (Λέσβος) around 620 BC, although the exact date is unknown. She wrote beautiful and highly romantic poetry that comes and goes straight to the heart. One of the most famous of her works is her Hymn to Aphrodite.

4. Aeschylos
As the original list includes both Sophocles and Euripides, it seems only fair to include Aeschylos. Aeschylos (Aiskhulos, Αἰσχύλος) was the first of the three Hellenic tragedians whose plays can still be read or performed. According to Aristotle, he expanded the number of characters in plays to allow for conflict amongst them, whereas previously characters had interacted only with the chorus. Aescholos' most famous works are undoubtedly the Seven against Thebes, the Supplicants and the Orestia.

3. Pythagoras
Pythagoras of Samos ( Πυθαγόρας ὁ Σάμιος) was an Ionian Hellenic philosopher, mathematician, and the father of the religious movement called Pythagoreanism. He lived from about 570 BC to about 495 BC, and made influential contributions to philosophy, religious teaching, math, ethics, and science. His most famous work is, undoubtedly, the Pythagorean theorem (a^2 + b^2 = c^2), that's standard in every math textbook. Interestingly enough, not a single bit of writing has been preserved--if he ever wrote anything down to begin with. His works are mostly quoted by his students, or known through critiques by Aristotle.

2. Plutarch
Plutach (Ploútarkhos, Πλούταρχος) was an ancient Hellenic historian, biographer, and essayist who lived between 46 and 120 AD. He is known primarily for his Parallel Lives and Moralia, but much of his work is lost to us. Plutarch's writings are full of details about people and places, and are therefor a true treasure trove.

1. Hesiod
Hesiod (Hesiodos, Ἡσίοδος) was a Hellenic oral poet who lived between 750 and 650 BC, around the same time as Hómēros. I would dare say that his work--especially 'Works and Days' and the 'Theogony'--has shaped the way scholars and practitioners of Hellenismos view ancient Hellenic society, religion and way of life. This is why I strongly feel that anyone who feels drawn to the Theoi, might benefit from investing some time in reading his words.

• Wednesday, May 8, 2013
  ancient Hellenic culture Aristophanes Aristotle current affairs Euripides Hellenismos 101 herodotos Hesiod Hippokrátēs Hómēros Plato Plutarch Pythagoras Sappho Sophocles