"Introduction to Arithmetic": Math As Evidence of Natural Laws

 It's been longer than usual since I've posted on this blog. Part of the reason is that my library didn't have Introduction to Arithmetic and I had to read it as a PDF file. I much prefer reading an actual book than reading on a screen, so consequently I wasn't as motivated to keep reading as I normally am. That, and I recently went through an emotionally painful experience, and honestly learning about abstract arithmetic didn't always seem all that important to me.

Overall I enjoyed this book more than I thought I would and I also found it easier to understand than I thought it would. Nicomachus is always careful to repeat statements and give examples.

The thing that struck me the most about the Introduction to Arithmetic was the elegance of mathematics. The way numbers fit together into patterns is really amazing… and none of it is man-made. The patterns are inherent! It’s darn good evidence for an ordered, lawful universe. It was interesting how Nicomachus sometimes took a “mystical” (for lack of a better word) approach to mathematics. It seems strange coming from what is basically from a math textbook, but given the inherent elegance of mathematics, it’s easy to see why he would.

I've disliked math from an early age (and have struggled with it due to my math block i.e. my inability to calculate in my head), but I remember having one teacher in Grade 11 who actually made math interesting for me. Like Nicomachus, he emphasized the patterns and elegance of math. Nicomachus brought me back to that interest.

"Ethics" [Book II; Book III, Ch. 5-12; Book VI, Ch. 8-13]

Ever since Meno I've been taking point form summaries of the Great Books I've been reading and I've found it very beneficial. Writing ideas down helps me to comprehend them and it's handy to have the main ideas from these books easily available (rather than re-reading the entire thing).

The reading of Aristotle's Ethics consisted of Book 2 in its entirety, chapters 5-12 of Book 3, and chapters 8-13 of Book 6. I greatly enjoyed Book 2 and the selected chapters from Book 3 complimented it. However, the selected chapters from Book 6 came across as a little random to me and I didn't comprehend it as much as I did the other chapters.

In Book 2, Aristotle defines a virtue as the mean (i.e. the correct amount) of a quality between excess and defect. For example courage is the mean between cowardice and rashness and temperance is the mean between self-deprivation and over-indulgence. Aristotle also said that virtue is acquired through practice, and that a virtuous disposition cannot simply be willed to happen, it must be put into action. At first you might not like doing virtuous acts; do them anyway and what you imitate will become reality. Eventually, a truly virtuous person will take delight in doing virtuous acts. Ultimately, Aristotle says that a virtuous man "must have knowledge of virtue, must chose to do the acts for their own sake, and the action most proceed from a firm and unchangeable character."

In the selections from Books 3 and 6 Aristotle delves deeper into the virtues of courage and temperance and then talks about intellectual virtue (as opposed to moral virtue), but it was Book 2 that really struck me.

I found this book very practical and good for self-improvement (I'll take Aristotle over a modern self-help book any day!). I've recently been re-reading Mere Christianity and, this time around, I really notice the Aristotelian influence on it. This might seem silly, but one of the initial reasons I wanted to read the Great Books was to gain a better understanding of Lewis's writings. So far it's worked.

Ethics is probably my favourite book on the second list so far, over-taking Herodotus' Histories. I think I still like Herodotus' writing better, but I love Aristotle's ideas.

"Poetics": Tragedy and Epic Poetry 101

Poetics is Aristotle's classification of poetry. He classifies the different types of poetry and goes over various conventions of poetry and how it can be done well and how it can be done poorly.

"Poetry", as Aristotle defined it, referred both to what we would think of as poetry (i.e. written verse) and also plays, mainly tragedy and comedy. Poetics deals mainly with tragedy and epic poetry. Aristotle wrote a second book about the remaining forms of poetry (e.g. comedy), but it has been lost. Aristotle wrote that poetry is primarily a mode of imitation, which is different, I think, from modern views of poetry. We would probably say poetry, or art in general, is primarily self expression. We tend to shy away from calling art "bad" by saying things like "beauty is in the eye of the beholder" and "to each his own", but in ancient Greece, art either hit the mark (was a good imitation) or it didn't (was a bad imitation). Like a lot of Greek thought, I find these ideas refreshing and I would be inclined to agree with them. I would love to see an ancient Greek philosopher like Plato or Aristotle walk into a modern art gallery and debate with modern artists and critics. It would make my day.

Even though this book was aimed at tragedies and epic poetry, much of the guidelines Aristotle sets out could be readjusted to fit modern movies or novels. For example Aristotle's listing of the six components of a tragedy (Spectacle, Character, Plot, Diction, Melody, and Thought) seem like they could be applied, with some adjustment, into most forms of story-telling.

I prefer epic poetry to tragedies, but I have to admit, Aristotle gave really good reasons for tragedies superiority. He said that tragedies can be enjoyed being watched or being read, while epics can only be read and tragedies relative short length make them pithy while the length of epics can make them diluted and less unified. I think I still prefer epics to tragedies, but I can really see Aristotle's points. Interestingly though, of the epic poetry I've read, my favourites (e.g. Paradise Lost and the "Divine Comedy") were non-Greek; I think I enjoyed the plays of Aeschylus and Sophocles more than The Iliad. It will be interesting to see what I think of The Odyssey when I get to it on the reading list.

"Meno": The Nature of Arete

Meno opens with Meno asking Socrates whether or not "virtue" can be taught. The word "virtue" is translated from the Greek word arete. My history teacher taught me that arete means "excellence". Now, having read Meno and seeing arete being used many times in context, I think both definitions are a little lacking. For example when Meno attempts to define arete as ruling over others, our word "virtue" doesn't seem to fit; "excellence" seems a better fit. However, Socrates then replies that Meno should add ruling "justly and not unjustly", making "excellence" alone a poor fit. It seems that arete covers both the English words "virtue" and "excellence".

After being given the question, Socrates responds with another question: what is arete? Most of the following dialogue is concerned with defining this elusive word. Socrates makes Meno realize that he doesn't know what virtue is, not to mess with him, but to make him wise. Socrates firmly believes that it is better to know that you know nothing than to think that you know anything when you really don't.

Meno attempts to define arete by saying that it differs from person to person, depending on their role or nature. He says that men run cities and women run homes, and therefore different people have different virtues. Socrates defends universal morality by comparing the virtues to bees. Bees have different features, but they are all bees. Similarly, although men and women have different jobs to do (in ancient Greece), they are compelled to do those jobs with the same qualities (e.g. justice and moderation). Justice and moderation are virtues for all of humanity.

Socrates also said that no man desires evil for its own sake. Rather men desire evil things thinking they are good things or with good things as the ends. 

One quote I particularly liked: "We will be better men, braver and less idle, if we believe that one must search for the things one does not know, rather than if we believe that it is not possible to find what we do not know and that we must not look for it".  This quote really speaks to the post-modern idea that there is no objective truth and also agnosticism.

Interestingly Socrates argued that human rationality comes from our pre-birth existence, either as a past life or elsewhere. He tells an uneducated servant boy to figure out a math problem. The servant boy answers the math problem by answering questions asked by Socrates, not be being taught by him. This proves that rationality is inborn and not taught. Socrates goes on to say that "learning" is merely recollecting from past existence. Cool stuff.

It was only towards the end that Socrates' argument lost me. Socrates asserted that arete is caused by neither nature nor nurture, but is a gift from the gods, after refuting that arete is a kind of knowledge. Socrates said that arete isn't knowledge, because there are no teachers. He used the example of good men having bad sons. If arete could be taught certainly the good men's sons would have turned out good as well. I don't know if I completely agree though. If not for my parent's correcting I don't know if I would have the same morals I do today. I don't even know if I would have the same morals if I hadn't grown up watching and reading stories about heroes. Of course lessons can fall on deaf ears, so there seems to be a combination of nature and nature. And isn't everything, to an extent, a gift from the gods (God)?

Overall, though, I thoroughly enjoyed getting back to Plato, my favourite Great Books author. I find his philosophy of eternal forms so refreshing in my relativistic culture. I think we can learn a lot from him.

"The History" [Book II: Euterpe]: The Ancient Egyptians

Near the beginning of Book II of The History, Euterpe (named after the Muse of Music), Herodotus speculates about what lies south of Egypt and where the Nile's source is and what is the case of the rising and falling of the Nile. The speculation of uncharted territory filled me with a numinous awe that I don't think I've ever gotten from reading non-fiction before. I don't know if Herodotus intended it, but the thoughts of the mysterious unknown gave me the chills. The fact that we now know what lies south of Egypt, what the source(s) of the Nile is (Lake Victoria and Lake Tana), and what causes the flooding of the Nile (an increase in rain at the Niles sources), did nothing to dampen the mood.

Ancient Egypt is one of my favourite historical subjects, because it is so mysterious. Herodotus said that "there is no country that possesses so many wonders, nor any that has such a number of works which defy description" and my history teacher described Ancient Egypt as "intoxicating".

Interestingly, the Egyptians are familiar with the story of the Trojan War, but they told it differently. The Egyptians said that Paris, after he had taken Helen, made a stop in Egypt, and the Egyptians, realizing that Paris had taken another man's wife took Helen away from Paris. Paris went back to Troy without Helen and Menelaus retrieved her from the Egyptians. The Trojan War was still fought, but Helen was not at Troy during it. Herodotus thought that the Egyptian story was more historically credible than Homer's version, because he didn't think that Priam would risk his country by allowing Paris to keep Helen. Herodotus thought that Homer wrote The Iliad the way he did, because the Egyptian version is "less adapted for epic poetry."

Also interestingly, Herodotus refused to mention the name of Osiris. It reminded me of Voldemort.

After going over the animals, culture, and religious customs of Egypt, Herodotus repeated stories of various pharaohs that he he had learned from the priests of Egypt. Two of the most interesting were the stories of Mycerinus and Sethos:

Mycerinus (the Latin name for Menkaure), pious son and grandson of two impious pharaohs (the famous pyramid builders Chephren and Cheops respectively), was told by an oracle that his life would draw to a close prematurely. Upset, Mycerinus asked we he should have a short life, while his wicked father and grandfather had long lives. The oracle replied that Mycerinus had to do precisely because of his goodness. "Egypt was fated to suffer affliction one hundred and fifty years - the two kings who preceded thee upoun the throne understood this - thou hast not understood it."

Sethos, formerly a priest, neglected the warrior class, and when Sennacherib, King of the Assyrians, invaded, the warriors refused to fight for Sethos. He pleaded to the gods for deliverance and, because he was pious and favoured of the gods, they sent mice to nibble at the bowstrings of the Assyrian soldiers during the night. Because of this, the Assyrians were driven from Egyptian territory and Egypt was saved from invasion. A statue of Sethos with a mouse in his hand was raised, with the inscription "Look on me, and learn to reverence the gods".

Overall, I thoroughly enjoyed Herodotus and I think he is now my second favourite of the Great Books authors, under Plato.


Old Map: http://mathildasdiary.files.wordpress.com/2008/07/herodotus-map.jpg

Menkaure: http://en.wikipedia.org/wiki/File:Menkaura_Bust_Closeup.jpg

"The History" [Book I: Clio]: The Lydian Empire and Cyrus the Great

The first book of The History, "Clio" (named after the Muse of History) is mainly concerned with the rise and fall of the Lydian Empire and the rise of the Persian Empire under Cyrus the Great, with numerous rabbit trails on related subjects.

I really enjoyed Herodotus and I think he is my second favourite Great Books writer after Plato. History is one of my favourite subjects as it is and Herodotus' writing style only made it more enjoyable. Although I've greatly enjoyed the Great Books so far, I often feel the need to push myself forward in my reading, but that wasn't the case with Herodotus. I was never bored while reading "Clio" and everything Herodotus wrote about was relevant and interesting. I've also heard that Herodotus is quite historically accurate. I felt like Herodotus was more objective than Gibbon. Herodotus' love of and bias towards Greece was apparent, but Herodotus made no effort to hide it and didn't let it control his writing. Gibbon on the other hand almost seemed to be writing with an agenda (e.g. discrediting Judeo-Christian religion). I would describe Herodotus as skeptical, but not cynical, whereas I thought Gibbon was heading towards cynicism.

I found Herodotus' descriptions of different nations' customs very interesting, especially Persia. I've heard of the Persian practice of having a drunken debate followed by a sober debate before, but I still think it's brilliant. I don't think passion should be ignored, but I do think it should be controlled by reason.

I find the Ancient Persian religion endlessly fascinating. It seems to have connections with the Judeo-Christian tradition: they had no images of gods, they didn't believe the gods had the same nature as men (as the Greeks did), the Magi that visited Christ were thought to be the Persian priests described in Herodotus, and Zoroastrianism, a monotheistic religion that is thought by some to have influenced post-Exilic Judaism, was also founded in Persia. I believe that the divine light shines the brightest in the Judeo-Christian tradition, but I'm not against the idea of the divine light shining in other traditions albeit not as brightly or clearly. The Persians also worshipped the four elements (or personifications of them): water, earth, fire, and air. Unlike the Jews, but like the Christians, the Persians had no temples.

There were a couple of references to other books I've read in the Great Books series. Helen's abduction by Paris is described at the beginning of the book, Lycurgus, the law-giver of Sparta is mentioned, and the bones of Orestes son of Agamemnon are mentioned.

Unlike most modern historians, Herodotus seemed to have arranged his history into a narrative, with recurring themes and ideas. One of the main "themes" is the fickleness of fortune. Croesus, the King of Lydia, asks Solon, a Greek, who the happiest man on earth is. Croesus is expecting Solon to say that he, Croesus, is the happiest man, because of his wealth and power, but Solon names a few deceased Athenians as the happiest men on earth. Solon explains that a man shouldn't be called happy until he is dead, because his fortunes could change dramatically (this idea is similar to Aristotle's ideas in Book I of Ethics). Solon's words turn prophetic as Lydia is conquered by Cyrus and Croesus is on his way to execution. However, Cyrus spares Croesus because he is impressed by the wisdom he learned from Solon and Croesus becomes Cyrus's advisor. Solon's words once again become relevant when Cyrus the Great is killed by Tomyris, an enemy he underestimated, because of his overconfidence.

"Antigone": Rebel with a Cause

Of the past five plays I've read this month, Antigone was my favourite. It was the most thought-provoking and I thought it had the best characters.

Oedipus' sons, Eteocles and Polyneices, die on opposing sides in a struggle for the throne of Thebes. Creon, now King of Thebes, decrees that Eteocles will be honoured with a proper burial but that Polyneices will not be buried, but left to be carrion for animals. Creon will execute any who bury Polyneices. Antigone decides to bury her brother Polyneices, out of love and respect for her brother but also out of direct disobedience to her stepfather the king. Creon finds out that Antigone has buried Polyneices and Antigone does not deny that she has disobeyed the king by burying her brother out of reverence for the dead. Ismene, who earlier opted out of Antigones' plan out of fear of the king now wishes to be on trial with her sister. Antigone isn't keen on Ismene's support, because of her earlier cowardice. Antigone and Ismene are imprisoned. Creon's son and Antigone's lover, Haemon, the blind prophet from Oedipus the King, Tiresias, and finally the Chorus of Theban Elders try to defend Antigone. Eventually the Chorus persuades Creon to acquit Antigone of her "crimes"when it is discovered that Antigone has hanged herself and Haemon has stabbed himself at the sight of Antigone dead. Eurydice, Creon's wife and Haemon's mother, kills herself at the news. Creon is horrified, because he realizes that his decisions were the cause of Antigone's, Haemon's, and Eurydices' death.

The dialogue in this play was excellent. The debates between Creon and Antigone and her defenders was the highlight of the play. The Iliad got me thinking about war as a necessary evil and now Antigone has gotten me thinking about disobedience as a necessary evil. Obedience seems to me to be a good thing in itself, if for no other reason than that it preserves order, but obeying a wrong or immoral order also seems very foolish to me. It wasn't Antigones' disobedience that makes her sympathetic; it is her obedience to a higher law (reverence for the dead) that makes her a martyr. Antigone seemed to view disobeying her king as the lesser of two evils.

Creon reminded me of Agamemnon a little, because of how he can't take any disobedient act against himself and seems characterized by pride. I did find Creon a lot more sympathetic though, especially because he saw the error of his ways by the end of the play.