Western History 30: Who were some of the great Ancient Greek Mathematicians?

While the Greeks borrowed heavily from the Mathematics rich cultures of Egypt and Babylonia their own contributions as outlined in the table below are significant.

Table 7 Greek Mathematicians

Name of Mathematician	Key Contribution
Apollonius of Perga	Geometer – Famed for work on conic sections – ellipse, parabola, hyperbola
Archimedes of Syracuse	One of the greatest minds of antiquity. Areas of mathematical concern include – area of a circle, anticipation of calculus, surface area and volume of a sphere, approximation of pi and the area under a parabola.
Diophantus of Alexandria	Father of Algebra. Work centred on Algebraic Equations.
Eratosthenes	Besides inventing the discipline of geography he was the first person to make use of Geometry to determine the circumference and diameter of the Earth. Was also involved in developing a method to identify prime numbers.
Euclid of Alexandria	Father of Geometry. Author of the Great work – The Elements – which deduces the Principles of Geometry from several axiomatic principles.
Hipparchus of Nicacea	Cofounder of Trigonometry. Discovered the Precession of the Equinoxes, developed trigonometric tables and solved several problems in spherical trigonometry.
Pythagoras of Samos	Although he is best known for his famous hypotenuse squared formula (that every student at one time or another has been forced to come to terms with) he did not derive this expression himself but merely popularized its usage (the Babylonians beat him to the punch). Pythagoras did however elucidate some of the mathematics that make the mathematics of music harmonics possible.
Thales of Milletus	Besides being the Father of Western Philosophy, Thales was a renowned Geometer who showed amongst other proofs that the diameter of a circle subtends a triangle with a right angle at the circumference (arguably the oldest proof in Geometry).

Western History 29: What was the contribution of the Athenian trio?

Perhaps no single group of philosophers have influenced Western Thought more than Socrates, Plato and Aristotle. In fact one could argue that the foundation of our education system rides on the bedrock of this trio of Athenian intellects.

Socrates, who words are primarily portrayed in external sources (such as Plato’s dialogue), stressed the importance of ethics in philosophy, questioning arguments to elucidate their strength and challenging one’s assumptions.

Plato, like his mentor Socrates focused on several themes that included justice, friendship and piety. His work on government outlined in the Republic serves as the bedrock for any study of political philosophy and his outlining of the ideal is still central to most thought.

In Aristotle we witness a methodical breakdown of academics into its component parts, a formalization of logic (through syllogisms) and a greater focus on relativism in both the abstract and the here and now.

Western History 28: How did philosophy develop in Ancient Greece?

The Milesian thinker and mathematician Thales is considered to be one of the fathers of the Western Philosophical tradition. While many of his contemporaries were running around blaming natural events on the ongoing strife of the gods Thales believed that such phenomena could be BEST understood by rationally unraveling the structure of matter that he believed was centred around water as the originating principle. In doing so Thales helped take explanation beyond the scope of the supernatural and so galvanized the earliest school of philosophy named after the Ionian City in which he resided (Miletus).

In addition Thales was well versed in deductive reasoning and goes down in history as the first person ever to be identified with a mathematical principle (Thales’ theorem of the diameter of a circle subtending a right angle triangle).

Now Thales was not the only philosopher to emerge from this school. Following closely in his wake, and continuing with the notion of the structure of matter were :

• Anaxgoras – Felt that material was ordered by the cosmic mind and that there was an infinite number of primary substances
• Anaximander – argued for an endless, unlimited mass not restricted by age
• Diogenes of Apollonia – Rationalized that air was the primary substance
• Empedocles – Favoured the four element makeup of matter – the four elements were water, earth, air and fire – Also spoke of forces within matter

·         Heraclitus – Believed that all of matter is made up of fire and that change is real – he also argued that everything is in a state of flux ("No man can cross the same river twice, because neither the man nor the river are the same.")

·         Hippo – extended basic matter concepts into the biological realm – thought to be one of the earliest atheists.

·         Parmenides – Philosopher from Italian Greek colony of Elea who argued that reality is one, existence is timeless and change is impossible. Antithesis of Heraclitus.

Worldohistory Going Forward

My intention is that Worldohistory will become my principal blog. I plan to shut down Worldoreason but will migrate some material over to Worldohistory as is necessary.

Posts in Worldohistory will be of three types

a. General writing on various historically relevant topics (includes Quizzes)
b. The Western World in 300 Events (An Ongoing chronicle of key facets that shaped Western Civilization)
c. Reflections on topics not necessarily related to history - includes writing on Deism, Skepticism and Judaism.

The Western History 27: How did Democracy develop in Athens?

The common wisdom is that the liberal western democracy has its roots in the democratic structure of Ancient Greece and to some extent that is true. Athens was easily Greece’s most influential city, even if its prowess as evident in the Peloponnesian War did not always translate to military success. Yet the democracy of the Athenian’s was on a level far removed from that what we see today in the west and had origins which were less than glorious.

Like most ancient cities Athens was ruled by a king who was the head of the land-owning aristocrats (Eupatridae). A council of government called the Areopagus was charged with the day-to-day running of the city that expanded as Athens came to dominate the region of Attica in a process known as synoikismos. However unrest caused by disparities in income undermined the status quo and the Areopagus, through its go-to-guy Draco (whose name provides the root for the draconian adjective) drafted stringent codified laws to curtail these unwelcome developments. Predictably they failed and the Areopagus was forced to carry out an ‘about face’ with the appointment of the reformer, Solon (whose bas-relief can be found in the US House of Representatives).

Solon (aka the Lawgiver)  is credited with laying the foundations for the Athenian model of democracy. He reduced the economic power of the aristocracy, lessened restrictions on trade and commerce and restructured Athenian society into four groupings. Wealth and military service were to guide such division but what was most important is that the poorest of all these classes, the Thetai, were given political rights for the first time.

True power still resided with the Areopagus and initially class unrest was not curtailed. However the system would continue under the tyrant (a name given to somebody who takes power by force) Peisistratus (Solon’s cousin).

The true hero though of Athenian democracy was Cleisthenes, who further weakened the power of the aristocracy and introduced a system of ostracism (whereby citizens deemed to be a threat to the democracy could by a vote of 6,000 citizens be exiled from the city for ten years).

Cleisthenes filled positions in his government using a random selection process known as sortition (setting up the Council of 500). He also transformed the four traditional tribes system of order into a system of ten tribes based on area of residency. These new structures were known as demes.

Despite the successes Athenian Democracy was a far cry from the democracy we have today (although it was revolutionary in its break from the political structures of its time). Only free, male citizens above the age of 18 could vote with the exclusive citizenship criteria greatly restricting the electorate base. Consequently at the height of its power it is believed that only 10-20% of the population of 310,000 has any say whatsoever in the running of the Athenian polis. Nevertheless it was an important start that would pave the way for later reforms and therefore should be judged favourably as a valuable milestone in the development of the western political structure.

Western History 25: Who were the Dorics?

The Doric Greeks originated in the mountains of Epirus and Macedonia in what is now known as Northern Greece. The expansion of the Dorians southwards from 1150 BC appears to have hastened the fall of the earlier Mycenean culture. However it was the Dorians that would eventually provide the basis for the a more coherent Greek civilization that would dominate the peninsular in the 5^th and 4^th centuries BCE.

Extremely adept colonists the Dorians would also set up settlements in Asia Minor (Modern Turkey) that would develop into the Ionian realm of Greek civilization This  expansion seems to have been motivated by plague and famine in the Greek heartland. The Dorians introduced several dialects to Greece that include Delphic, Locrian, Elean, Northwest Greek Koine and Epirotic.  However they did not have a written language and much of what we know about them comes from a legacy of storytellers that specialized in myths and fables - a tradition that would carry through into the collective literature of western civilization.

The fabulist Aesop lived around the period of Doric domination although it is commonly believed that his origin comes from Thrace (modern day European Turkey).

Western History 24: How did Persia impact the World?

While the Egyptian Civilization was defined in a sense by its longevity (it survived for over three thousand years), the Persians Achaemenids were the great acquirers of territory so much so that at its height the Persian Empire covered 8.5 million km².  This made the Empire the largest of the Ancient World (Yes…. it was bigger than the Empires of Alexander the Great and Rome which covered 5.2 and 5.0 million km² respectively). Over 40% of the World’s population at the time is believed to have lived under the domain of the Achaemenids.

The Achaemenid Empire was centred in the Iranian Plateau but spread throughout Asia and encompassed much of what we now know as the Middle East. Libya, Egypt, Bulgaria, Afghanistan, parts of China and Thrace-Macedonia, Pakistan. Georgia,  Armenia, Abkhazia and Azerbaijan. .It was Cyrus who defeated the Kingdoms of Media and Lydia and the Babylonian to build establish the Achaemenid legacy that would dominate the geo-political arena from 550 to 330 BCE.

Table 5 lists some of the most important Achaemenid Emperors, their period of reign and the key events of their respective eras of rule.

Emperor	Key Events of Reign
Cyrus the Great aka Cyrus II (559-530 BCE)	Established the Achaemenid after defeating the Medes, Lydia and Babylonia. Champion of Religious Freedom. Allowed the Jews to return to the Holy Land. Occupied Cyprus. Father of the First Persian Empire. Solidified Zoroastrian religion in the Empire.
Cambyses II (530-522 BCE)	Conquered Indus Valley Takok the city of Pelsium, defeated and brought Egypt into the Persian domain.
Darius I (Darius the Great) (522-486 BCE)	Linked the Nile to the Red Sea by Canal (early version of Suez Canal). Wages war against the Scythians (people from the European Steppes) Fought against the Greeks during the Ionian rebellion. Lydian city of Sardis was burnt to the ground. Persians are defeated by the Greeks at the Battle of Marathon. But Darius will go on to capture the island of Rhodes.
Xerxes I (486-465 BCE)	Destroyed Babylon. Defeated Greeks (albeit at a high cost ) at the Battle of Thermopylae but lost the key naval battle of Salamis (480 BCE). His ambition to invade mainland Greece came to an end at the Battle of Plataea (479BCE). He did however build the Gate of All Nations, the Hall of 100 Columns and the Grand Palace of Xerxes.
Artaxerxes I (465-424 BCE)	Negotiated a peace settlement with the Greeks (Peace of Callias). Ionian Greek cities gain autonomy.
Darius III (336-330 BCE)	Adversary of Alexander the Great. His defeat hastened the end of the Achaemenid collapse.

While the Persian made many contributions to Western Civilization their greatest legacy arguably lies with the religion of Zoroastrianism – one of the earliest attempts at monotheism and the dualism of good and evil as forces in nature. The Abrahamic religions – Judaism, Christianity and Islam – have all placed considerable emphasis on these notions within their respective theological philosophies.

The Achaemenid Empire would eventually fall to the sweeping force of Alexander the Great in c. 330 BC but it would resurrect itself in various forms under the later Parthian (247 BCE- 224 CE), Sassanian (224-651 CE) and Safavid (1502-1736) Empires. While none of these later Empires would aspire to the global dominance of the Achaemenid, they certainly carried much of the cultural wealth of the Achaemenids, who through their great building projects, road design, postal service and system of Satraps (governors) provided the foundation model that the Greeks, Romans, Ottoman and British would adopt in their later version of Empire.