Felix, Qui Potuit Rerum Cognoscere Causas

Lucky Is He Who Can Understand the Causes Of Things

By Amy Barr at The Lukeion Project

In a brighter and better world, October would mean most of us would now be finishing the chores of harvesting. Moods would brighten as temperatures drop. Communities come together to enjoy the celebration of a good harvest and the promise of a well-earned winter rest with well-stocked larders.

The virtues of various agrarian cycles seem a bit dreamy (at least if you are wired like I am) but I get to experience this ancient autumn ritual, albeit vicariously. I live close to Amish communities and have several Amish friends whose skilled planting, harvesting, and preserving make my attempts utterly incompetent. In early October, most fields have been put to bed for the winter except for a few beds of cabbage and collards. Everyone pulls together for last harvest chores which, about now, includes boiling down this season’s sorghum syrup while the final hay cuttings are tucked into barns. If families are too busy to cook during this final autumn rush, there are shelves and shelves of home preserves that make for fast feasts.

There’s a brilliant tango of tasks, chores, habits, rituals, and celebrations connected with an agrarian life. The deep satisfaction over successfully navigating the caprice of weather, animal health, and a zillion other challenges of growing things for oneself. Having a deep understanding of the causes of things—from what it takes to grow great tomatoes, to knowing when is best to harvest, to figuring out when is best to plant again—that is the very substance of a deeply satisfying life.  

One of the earliest pieces of Greek poetry was composed by Hesiod around the same time that Homer was composing his Iliad and Odyssey (roughly 750 B.C.). His Works and Days extols the virtues of the human relationship with the land and the importance of hard work. Philologists describe his poetry as didactic (educational). If you’ve never read this poem for yourself, it may be because few today are attracted to poems teaching you how to farm!

Hesiod and other poets inspired the Roman writer Vergilius (aka Virgil) who composed a 4-part (4 seasons) poem called Georgics, named from the Greek word γεωργικά, "agricultural things." Vergil expounds on the beauty of an agrarian life and then, as they say, he gets real. After extolling the virtue of hard work and the satisfaction of success in book 1, he describes a massive storm that brings all of man's efforts to nothing. I’m sure there are some citrus farmers in Florida that can relate right now.

In book 2 Vergil focuses on seemingly mundane things like grafting, growing vines, and the beauty of spring, all while describing agriculture as man's struggle against a hostile natural world (much like goats eating what he’s so carefully planted). He soothes his readers with assurances that despite the challenges, there’s certainly more to offer in the country vs. corrupt and filthy cities.

After book 3, when Vergil addresses the issues of taking care of animals, the poet compares the habits of bees to the lives of humans in book 4. Bees suggest many applicable virtues but “lack love and the arts.” The poet impactfully compares the fragility of a colony of bees to human civilization which may buzz along with much success until suddenly it does not.

There are many other poets drawn to this subject including Nicander, Aratus, Aristotle, Theophrastus, Callimachus, Lucretius, Ennius, and others now lost to us. Vergil patterns his efforts on the neoteric poets who adored intimate personal themes expressed in a learned (well-informed) style. Think in terms of a textbook on agriculture written as a lofty poetic philosophical piece.

Vergil ties his poetic passion for all things agricultural to politics. In case you aren’t up to date on all the happenings of Rome in 29 B.C., suffice it to say that Roman politics make ours seem fairly tame. Rome had been rocked by civil war for a good part of a century and had only recently found small respite after the battle of Actium in which Octavian established the premise and groundwork to throw out the Roman Republic to better manage the “emergency” of a war that Rome picked with Egypt. Vergil even refers to a recent plague in book 3.

Though mixing didactic agrarian poetry, philosophy, politics, and bees seems like a strange mix, you’d be surprised. Vergil is in touch with the perils of losing everything to sudden storms or shifts in world events or the loss of loved ones due to illness. Though he’s known as one of Rome’s best poets in his war-focused work Aeneid, his first and best delight was in his little plot of land and a villa in the country.  "How lucky, if they know their happiness, are farmers, more than lucky, they for whom, far from the clash of arms, the earth herself, most fair in dealing, freely lavishes an easy livelihood."

Why Study Philosophy?

Make an Investment in Clear Thinking and Logic

By Regan Barr, philosophy instructor with The LukeionProject

Plato has preserved a humorous anecdote about the “first” Greek philosopher, Thales of Miletus. As the story goes, Thales was walking along staring up at the sky and pondering the mysteries of the heavens. He was so oblivious to his immediate environment that he failed to notice a well in his path and fell in. A Thracian servant-girl was nearby to observe his misfortune, laugh at him, and spread the word abroad. Presumably, she also called for help to get him out.

The point of this short story was to poke fun at the Pre-Socratic philosophers, whom many Greeks stigmatized as being more interested in the stars and the heavens than in the path right in front of their feet. They believed that philosophy (the love, or pursuit, of wisdom) was both impractical and a waste of time. Some people today still believe that.

So is there any practical benefit to studying philosophy? I would argue there are many, but I’ll just mention three.

1. The study of philosophy helps develop critical thinking and problem-solving skills

“It’s easier to fool people than to convince them that they’ve been fooled.” This quote is often attributed to Mark Twain, and while we have several similar quotes from him, there isn’t definitive evidence that he ever said or wrote it. Nevertheless, it’s certainly true. Humans are proud creatures, embarrassed and unwilling to accept that they’ve been duped. In fact, many people will continue to cling to a belief even when confronted with irrefutable evidence that these beliefs are based on falsehoods and mythology rather than fact.

Our society is experiencing a crisis in critical thinking. Students are often taught to believe and obey rather than to question, think, and evaluate. They are taught that “authority figures” should not be questioned, even if there is evidence that their statements are untrustworthy. Essentially, students are taught to place blind faith in these figures.

As students engage with the great thinkers of the past and of our own time, they sharpen their skills in research, logic, and evaluation. They come to understand the rules of logical argumentation and learn to identify errors in reasoning. By observing how philosophers have carried on a dialectic through the centuries, one arguing for one position and another responding with a counterargument, they can begin to identify and correct problems in their own thinking and in the arguments of others. The study of philosophy is one of the best antidotes to blind trust, and a catalyst for independent reasoning.

2. The study of philosophy helps develop logical and persuasive methods of communication

The Austrian philosopher Ludwig Wittgenstein wrote, “To convince someone of the truth, it is not enough to state it, but rather one must find the path from error to truth.”  His message is clear: to change someone else’s mind, one must not only be correct, one must also be persuasive. The student who studies Plato’s Socratic dialogues will appreciate not only Socrates’ civility in the face of sometimes confrontational adversaries but also the way that he gently guides his debate partners to recognize their own inconsistencies in reasoning.

A group of ancient philosophers called the Sophists claimed that they could defend either side of an argument equally well. They were rightly criticized when they used their oratorical skills to convince people to believe untruths (“making the weaker argument seem stronger”), but their mastery of the art of persuasion is undeniable. Many ancient orators and statesmen, including the famous Athenian Pericles, sought out the Sophists to teach them how to move their audience to action. They were persuasive because they combined carefully crafted arguments with an understanding of their audience.

Today accusing someone of “sophistry” is an insult, but now more than ever, individuals must be prepared to defend their beliefs with persuasive arguments, AND to know when they are being manipulated by sophistry and demagoguery. In 2004, Desmond Tutu famously said, “Don’t raise your voice, improve your argument.” The ability to improve one’s argument and persuasively deliver a defense of one’s position, whether written or spoken, requires well-organized thoughts, clarity of expression, and an understanding of the audience. This is one of many important benefits of studying philosophy.

3. The study of philosophy moves one to consider the bigger, but oft-neglected, questions of life

Many students enter an ancient philosophy course expecting the ideas of the ancients to be somewhat unsophisticated. After all, hasn’t the human race progressed so far over the intervening centuries that the early philosophers will seem fairly simple-minded by comparison? Nothing could be further from the truth.

It is true that our understanding of our physical world has moved far beyond what the ancient philosophers could have even imagined. But some of the questions they grappled with remain unanswered. For example, how can we “know” anything? This is the question of epistemology. Can we be certain that our brains are interpreting stimuli correctly? In fact, how can we be sure that we’re not laying in a coma somewhere and everything around us is an illusion?

Then there is the question of ethics, to which Socrates turned our attention. Is there a difference between “good” and “evil”? If so, how do you defend your definition of “doing what is right”? Does the definition of bad or good behavior change depending on our circumstances? Do we have any obligations to our fellow-humans? To our planet? To other creatures with whom we share our world? And if so, from where do these obligations come? Are they based entirely on tradition, or is there some source we should consider authoritative in the realm of ethics?

Grappling with questions like this are not only mind-expanding, they are life-preparing. They move us past the mundane trivia that consumes much of our daily lives. When we are faced with difficult decisions about family, government, or health, on what principles will we make our decisions? If we have consistently lived our lives in accordance with a set of principles that we’ve chosen intentionally, perhaps the correct choice will be more apparent, even if it’s not the easiest one.

If you’re still reading, you know my answer to the question posed in the title of this blog, and I’ve only scratched the surface. Studying philosophy is an investment in clear thinking and logic, and it’s always worth it!

Here’s Lookin’ at Euclid

Why was Euclid so Great?

Dr. Kim Johnson at The Lukeion Project

Educators at The Lukeion Project include some great Classical authors in their courses: Cicero, Plato, Tacitus, Sophocles…the list goes on! But one Classical author stands above them all. More versions of his work have been published than any work other than the Bible. He’s been read almost continuously for more than 2,000 years. Knowledge of his work has been considered the mark of an educated person in Rome, Baghdad, London, and Athens. When Abraham Lincoln would enjoy circuit rides through the Illinois countryside, he would bring two books: the Bible and this work. This author was a topic of one Edna St. Vincent Millay’s sonnets. Who is this celebrated author?

He was a mathematician!  Euclid of Alexandria (Εὐκλείδης, which means "renowned, glorious"), 325-265 BC, wrote The Elements. This work not only changed the course of mathematics, but it also changed the way people think of logic and argument forever afterwards.

Who was Euclid, and what were The Elements?

The truth is that we don’t really know much about the personal life of Euclid. He came to work in the library at Alexandria around the time Ptolemy II, Hellenistic monarch of Egypt, was expanding it. We don’t know where he was originally from, although he is possibly one of the few Alexandria natives who came to fame at the library.

We have a few stories written many years after Euclid’s life. When he was teaching Ptolemy geometry, the king asked if there was a shorter way. Euclid responded scornfully, “There is no royal road to mathematics.” When one of his students asked, “When will I ever use this?” (a cry common to modern mathematics students), Euclid responded, “Give the boy some money, for he has to see some profit come from this work.”  Mostly, we have Euclid’s masterwork, The Elements.

The Elements is a collection of 13 books (really chapters) collecting most of the Greek knowledge of geometry up to Euclid’s time. Euclid himself did not discover most of the theorems in this book. He simply collected and organized them but the way he organized them was unique.

Previously, Greek mathematicians who wanted to prove something would list the assumptions they were making. They ran into the problem experienced by modern geometry students: what you can assume, and when? After all, you wouldn’t want to prove that the angles in a triangle add up to 180 degrees while inadvertently assuming that very thing. This would be circular reasoning and a fallacy. Euclid’s method avoided such problems by starting with almost nothing and assuming only things that he had previously proven.

The Elements’ starting point included definitions, common notions, and postulates. Definitions are important for any practitioner of logic: Before statements and arguments, one must make the terms precise. Common notions were meant to be clear without proof. For example, things which are equal to the same thing are also equal to each other. Postulates were slightly more complicated but self-evident. After making clear his assumptions, Euclid cataloged much of Greek mathematics. Each theorem was based on the theorems stated before. He included the steps of the proof and diagrams (including labels) to make his reasoning clear. He began with theorems about triangles and parallel lines (precisely where modern geometry students start) and ended proving that there are exactly 5 platonic solids, the primes are infinite, and some numbers are irrational.

This is not to say that Euclid was perfect in 200 BC. Over the years his proofs were corrected, and some of the corrected proofs became part of the canon. His postulates were not enough to prove all his theorems so in the 19th century more postulates and notions were added. The most stunning change came in 1832, when Janos Bolyai and Nicolas Lobachevsky proved that if you change the 5th postulate you get an entirely new geometry. Over all his theories held, and The Elements spread far and wide.

What came before Euclid?

Certainly, people did math before Euclid and without Euclid. The Babylonians had a number system in 2000 BC which would not be surpassed in Europe until after the 1200s when place value and the use of zero started overtaking inefficient Roman numerals. The ancient Egyptians clearly had a solid grasp on geometry. Just look at the pyramids which are still a wonder of the world! Indian mathematics predating Euclid were very advanced and included negative numbers, complicated computations, and zero was considered a number. Chinese mathematicians worked out theories of solving systems of equations, solving polynomials, Pascal’s triangle, and the Pythagorean theorem all without Euclid.

Although these mathematicians made great advancements, Euclid still stands out. These other mathematicians weren’t interested in making their mathematics accessible to the public. Perhaps they didn’t think it was necessary. Perhaps they wanted to keep their secrets to guarantee their future employment or the exclusivity of the scribe and priest class. But most of their work was published with the problem, the solution, and perhaps a method for solving it. Euclid was accessible to anyone willing to put in the work.

The other characteristic of mathematics in other cultures without Euclid was that they were interested in showing solutions to specific problems. Although an intelligent reader could generalize, the writings of mathematicians before and without Euclid would use specific values for the lengths of sides, radii, and other calculations. They did not show the general solution.

What changed after Euclid?

First, most of the old geometry books were destroyed. It’s hard to find any geometry books written before Euclid. Euclid’s work is the only one cited for basic theorems about geometry.

Euclid’s The Elements spread everywhere. For example, there are potsherds with references to his work found at a military outpost found near the Nile plus copies of his book from personal libraries in Babylon and Constantinople. Euclid’s work spread to Baghdad in the 700s, England in the 1000s, and eventually to India and China. Euclid’s work was not a secret but something that anyone could work through and discover for himself. Judging by the computations written in the margins of many ancient copies, some readers were more successful than others.

Euclid’s method was adopted for many other mathematical, scientific, and philosophical efforts. Think about the other variations on The Elements that have been written over 2000 years, including the Elements of Theology by Proclus in the 5th century AD to the Elements of Style by Strunk and White in the 20th century. When Descartes wrote “I think, therefore I am,” he was using Euclid’s method of eliminating all extraneous assumptions to reach the most basic statements we can affirm.

Reading Euclid and learning to think logically came to be one of the cornerstones of a good education. From when it became one of the four liberal arts in the Middle Ages until every schoolchild in England had to pass the “pons asinorum.” Knowing Euclid was essential to training one’s brain to think logically. This is why Lincoln studied Euclid and used his reasoning as an example in a debate against Stephen Douglas. This is why Edna St. Vincent Millay wrote, “Euclid alone has looked on beauty bare.”  Anyone who builds or measures, who makes arguments from first principles, or uses science built on any mathematics that came after Euclid, is ultimately referring to Euclid. That’s why Euclid is so great.

The Elements concentrated on building knowledge up from the smallest possible number of assumptions. He wasn’t just interested in knowing what was true, but how you could be sure that you knew it. In addition, Euclid didn’t just solve one problem, he solved them all. One of the previous mathematicians might notice that 3^2+4^2=5^2. Euclid proved that for all right triangles, the square of the hypotenuse was equal to the sum of the squares of the other two sides.

In The Lukeion Project course Counting to Computers: Math from the Dawn of Time to the Digital Age, we investigate the connections between the great mathematicians of the past and the mathematics we learn today. Whether you love, hate, or are indifferent to the standard course of math study, if you are interested in learning more about why we do things the way we do them today, how they were invented in the first place, and the people who were involved, come join us Wednesday afternoons this fall!