Fra Verus

Next up is Epictetus' Discourses and the Handbook. Epictetus is yet another Stoic author. Unlike our previous two Stoic authors, Marcus Aurelius and Seneca, Epictetus was neither wealthy nor powerful. Rather, he was a freed slave he strove to live simply. His explanation of Stoic principles is the most rigorous and best-organized of the three authors. His "handbook" is actually a concise compilation of Stoic ideas created by one of his students. It is so concise that I could easily imagine it as a pamphlet. Maybe as the modern Stoicism movement continues growing it will become one. However, his rigor does come at a cost. His writings feel like lectures. This is probably because they originally were lectures. They lack the intimacy of Seneca's Letters or Marcus Aurelius' Meditations. For this reason, many modern proponents of Stoicism recommend leaving him for last. I think I would have been happier had I started with Epictetus but I can see how leaving him for last may be beneficial for most people.

Epictetus brings clarity to a number of issues for me. For example, Seneca and Marcus Aurelius speak of the Stoic observance of duty. But one's duty is never clearly defined. Epictetus offers some crucial guidance here. He argues that one's duties are defined by one's social relationships. In other words, your duties are primarily to your family and friends. You have a duty to be a good son or a good father and a duty to be a good friend. And then less immediately one has a relationship to one's community, city, and country. This clarity also presents a challenge for me. I am semi-estranged from my own family and I have a hard time feeling a patriotic duty to a country that has allowed itself to be consistently mismanaged my entire life. In short, Epictetus brought me one step forward on the matter of duty only to present me with a new problem to solve.

Epictetus also clearly avoids the fallacy of believing that perception determines reality, which Marcus Aurelius seems to argue for. Instead, the Handbook says, "It is not the things themselves that disturb men, but their judgments about these things." In other words, perception determines one's emotional state. This says nothing about objective reality. The change is only within ourselves. I am much more comfortable with Epicetus' framing of the issue than that of the other two authors.

Epictetus also makes the point that allowing one's judgment of another person's actions to affect one's emotional state gives that person power. And such an action is irrational in a way. Why should we reward those who cause us harm with further power over us? He cites an example of a man who is easily upset by his slave's incompetence. If the slave can shatter his owner's emotional composure effortlessly, who is really in control?

There is plenty more to Epictetus but much of it is just a more direct explanation of things covered by Seneca and Marcus Aurelius. For example, the need to accept fate, the need concentrate on living one's philosophy rather than merely thinking about it, or the need to detach one's happiness from external things. But his brevity and clarity mean that he is the author I will most likely reread when I feel the need for reinforcement.

Backtracking a little after Meditations, I bit the bullet and read Lucretius' De Rerum Natura. This title is and can be translated a number of different ways, owing to the broadness of the Latin word res. The most literal translation would probably be "About the nature of things". However, in this context "things" encompasses the entire universe. It is a first-century BC Latin Epicurean poem, physics textbook, philosophical treatise, and personal letter all rolled into one. The linked translation is pretty standard for Loeb editions. In other words, there's Latin on the left and fairly literal English on the right with a moderate number of footnotes and a scholarly introduction. You may want to consider other options if you have no interest in the Latin on the left-hand side.

Epicureanism is a curious thing. While other ancient schools of thought like Platonism, Aristotelianism, and even Stoicism still hold some currency in the present day, Epicureanism is largely forgotten in the mainstream. And when it is remembered, it is used as a synonym for hedonism. And the thing that makes this strange is that Epicureanism actually more closely aligns with the modern Western world view than these other philosophies in many ways. For example, Lucretius argues that either the gods do not exist or that they have no reason to care about the affairs of mortals and are therefore irrelevant. He also champions atomism, the idea that matter is made from atoms rather than the classical elements. He even concludes that other planets must exist. While he still argues largely through logic, much in the way that Aristotle and Plato did, he also pushes the Epicurean idea of the reliability of the senses. In other words, Epicureans rejected the Platonic notion of a shadow world and instead accepted the idea of an objective and observable universe. This belief in the senses, incidentally, is the root of the insistence that Epicureans are hedonists. The form of argumentation is very familiar but the conclusions are completely different. It is like looking in a mirror version of the Western tradition.

So given the strong parallels to modern thinking and the empirically-verified truth of that thinking, why did Epicureanism die off rather than catch on? I think Epicureanism had problems with both the medium and the message.

By "medium", I mean the style of argumentation. Argument by logic alone is fraught with peril. It only takes one faulty assumption or one fallacy to turn an entire, seemingly logical, worldview into a useless house of cards. And in worse instances, Plato accuses some "philosophers" of spinning logic with no regard for truth simply because it was an easy way to get students and their fees. To varying degrees, ancient philosophers were aware of the limitations of their epistemological approach. However, most were certain of the rigor of their own methodology. The end result is that logic alone lacked sufficient persuasive force. Even if the conclusions were true, it was too difficult to discern complex and true logic from complex and false logic. You can see similar problems in our modern statistical approaches. One mistake and "overwhelming" statistical evidence can become completely meaningless. Empiricism, in contrast, lends itself to physical demonstrations. And in a way that worried Plato but likely pleased the Epicureans, people believe what they can see. But lacking that, philosophies could come and go like fashions, regardless of how accurately they described the world. Truth alone was not sufficient and often not even required.

And by "message", I mean that some of the claims of Epicureanism are extremely inconvenient. For example, the essential atheism of Epicureanism made it impossible for many political figures to openly endorse it. Roman paganism was the de facto state religion and many government ceremonies and practices were essentially religious. Lucretius even warns his intended reader, the praetor Gaius Memmius, that pursuing the truth of Epicurean philosophy may not always be compatible with his official duties. Contrast this with Stoicism. Some argue that Stoicism tends toward monotheism. Others reject this. But in either case, it is compatible with the general idea of deism. And even if it were not, Stoics would argue that duty obliged Stoic politicians to perform the necessary state rituals with at least seeming earnestness. In other words, Emperor Marcus Aurelius could function both as a Stoic and as Emperor openly without any real philosophical conflict and without turning popular opinion against him. An Epicurean Emperor would have been in a much more difficult position. And this would have been true, to varying degrees, of anyone with any office in the Roman political system. In other words, Epicureanism was likely at a patronage and advocacy disadvantage. Religions and philosophies benefit immensely from the conversion of political figures. And Epicureanism could never realistically compete on that front.

In a similar vein, many people likely had issues with the Epicurean view that even though the soul exists, it is mortal. In other words, there is nothing after death. And this has never been a popular point of view. People take comfort in the notion of an immortal soul, whether it is Aristotle or the Pope preaching the idea. The survival instinct in humans, like all animals, is strong and the thought of utter annihilation makes our blood run cold. Fighting such instinctual preferences requires more evidence than Epicurean methods could muster.

In short, if you are going to push a new philosophy or religion, it helps to make it convenient and appealing. Impossible-to-prove promises that feel good can often win more converts than truth. Lucretius was somewhat aware of this fact that. It is the whole reason De Rerum Natura is a poem. He thought that a beautiful form would make uncomfortable truths easier to digest.

My next reading will probably take me back to the Stoics with the letters of Seneca, assuming Amazon ever ships me the third volume in the set.

Completing the set of early-modern satires is Jonathan Swift's Gulliver's Travels. This book has seen a ton of editions and you can't go wrong with most of them. I mostly chose this edition because it comes in hardcover and it has original illustrations by Jon Corbino. It is a solid and comfortable size. The Corbino illustrations are interesting at times. My only complaint would be that the Corbino illustrations rarely show up very close to the related scene. Pick it up if you want a nice hardcover with some weird art as a bonus or just stick with the Dover edition otherwise. Either option is amazingly cheap.

The story of Gulliver's Travels is one of those stories that is "well-known", largely through numerous adaptations, e.g. movies and cartoons. But like many popular stories known primarily through adaptations, many details and themes have gone missing over the years. In that way, it reminded me a lot of H.G. Wells' Time Machine. For example, many adaptations focus on Lilliput and Brobdingnag, the land of tiny people and the land of giants, respectively. Gulliver's time in those lands makes up only half the book. This still leaves the land where they have floating islands powered by lodestone and adamant and the land of noble, intelligent horse people. It was also a bit racier than the child-friendly adaptations. For example, I do not remember ever seeing a version as kid where Gulliver whips his dick out to extinguish a fire, as he does in the book. They also leave out the complications of clothing and defecation in differently-scaled lands. This process has, over the years, shifted the story from a feeling of science fiction foreshadowing works such as Sir Arthur Conan Doyle's Lost World to a kind of fantastic fairy tale. Literary adaptation is simultaneously both a creative and a destructive force.

While I say the book had the feeling of science fiction, it is primarily intended to be a satire. These things are not mutually exclusive. Swift is broadly attempting to criticize the politics and culture of his own age. In particular, there is something noted in various ways in each of the lands that remains true even in our own modern American society: we really do not put much thought in to selecting leaders. For example, we really do not seem to care all that much if our leaders are even remotely virtuous. One need only look at the products of our presidential elections. In your everyday life, what would you entrust to a former coke-head, a serial adulterer, or even a self-proclaimed pussy-grabber? If you have any sense, the answer is, "Not much." And yet these things are not stumbling blocks to the most important job in the country. After the fact, we are often astounded by the lies and crimes of our leaders. How do we not see that immoral people will continuing being immoral once we elect them? How do we still not see it when they engage in the predictable bad behavior and we are offered a chance to reelect them? It is a madness born out of a society that can not even say "virtue" as anything other than a sexual euphemism. This was as much as problem in Swift's day as it is in our own. It seems to have weighed heavily upon him. And his gift to posterity is to share this burden with us. It is strange how hard it can sometimes be to be grateful for a useful and necessary thing.

The ending of the book provides a sort of warning for those who gaze too long into the abyss of humanity's flaws. Gulliver spends so much time away from flawed humanity that, when he finally returns home for the last time, he can not even see his own family as anything other than a bunch of ugly and disgusting beasts. Strangely, I have not fallen into this trap because, when push comes to shove, I am nearly as resigned as I am cynical. While I see humanity as very flawed, I do not really expect anything else. I hope for more from myself but I do not really have any inclination to hold people in my everyday life to any real standard. I just accept their faults as normal. Christianity also has its own way of framing and resolving this conflict: While we are all born with original, we are also still made in the image of God and we each have a shot at redemption. If you find yourself going down Gulliver's path, grab one of these sorts of logical lifelines as soon as possible. Otherwise, only misery can follow.

On other reading fronts, Aquinas' Summa is still on-going. I took a bit of a break for a while and so progress stopped for a while. I am now trying to get back in to it with a little over half of it to go. I have the nugget of at least one more post on that kicking around in my brain. On the French front, I have picked up the complete works of Pascal but it is an incredible amount of text without the crutch of a dual-language edition. I am also reading Nassim Nicholas Taleb's Incerto. It isn't usual Great Books material but I may write something about it anyway.

Next up is the first part of St. Thomas Aquinas' Summa Theologiae. This edition is fantastic. Physically, the volumes are as beautiful as they are sturdy. The English translation is solid. There are not really really any footnotes but Aquinas designed the Summa to be able to serve as a first introduction to scholastic theology and philosophy. Some familiarity with Aristotle and Plato helps a lot but not absolutely necessary. That said, Aquinas' language is sometimes quite complicated in a way that English just doesn't handle very well. Even with my so-so Latin, I find it much easier to follow the flow of logic in the Latin original than in the faithful English translation.

One of the first things a reader of the Summa notices is that unusual system of argumentation. While many ancient and medieval forms of argumentation remain familiar to modern readers, the so-called summa style is mostly dead. The style has the following form: First a question is asked, usually conceptually linked to the previous question, if there is one. Then arguments against the author's view are given, usually representing varying schools of thought and methods of argumentation. Then the author's response to the question is given. Finally, each earlier argument that had opposed the author's view is given its own individual refutation. Both the author's own view and the imagined critics cite a broad range of respected sources. Nearly all the works are cited equally by both sides. Normally I would expect this style of argumentation to be an endless string of strawmen. But Aquinas, for the most part, has the humility to represent the opposing views fairly and with citations as worthy those he gives his own arguments. That said, given that he argues against such heavyweights as Aristotle, Augustine, Boethius, and countless others, it is unlikely that serious strawmanning these figures would have endeared him to the Church or the rest of the scholastic community. But you can't go wrong with humility seasoned by pragmatism. It is, however, a lot of work. And the sheer amount of work involved is likely the biggest factor in this style's unpopularity.

The first part of the Summa contains what are known as Aquinas' five arguments for the existence of God. This popular description is somewhat misleading and yet it is the thing the Summa is most known for. It seems only right that I address it. While it is an argument for God's existence, it is also clearly stated to be a definition, e.g. "this is what we call God". The arguments are largely Aristotelian. First, there is classic unmoved mover argument. This is based on the Aristotelian observation that nothing moves unless moved by something else. And if one logically follows the chain back, it seems necessary that there must be some strange thing that does not have this same constraint. Otherwise, how would anything in our present universe be moving at all? The second argument is about "efficient cause". This is logically much the same as the unmoved mover argument except that the chain of movement is replaced with the chain of cause and effect. The third argument is also similar, instead being about a chain of existence, i.e. you can't create something from nothing therefore there must be an original and necessary thing. The fourth argument is about gradation. In other words, we live in a universe of greater or lesser and better or worse. It is assumed that these things are intrinsic properties of the universe and not merely the product of the human mind. And it is then supposed that in such a system there must be a greatest and best being. The final argument is that our universe has a level of complexity but also order and seeming purpose that would suggest that it was deliberately designed in some way.

The first three arguments are perhaps the most persuasive, even if they are all basically a single argument. We have no real answer for the ultimate origin of the universe. Sure, we have the Big Bang. And where'd that matter come from? Maybe it all came from photons. Where did all those photons come from? With better tools, we have peeled back the onion a lot more than Aristotle ever could but we still seem to have a logical dead end. Logic would seem to suggest that somehow either the rules changed, there was a thing that could violate the rules, or there is something entirely external to the system of our universe as we know it. These do not necessarily imply the popular contemporary notion of what God is, but they are what Aquinas means when he says God. He is not some bearded sky wizard. He is either the physics changer, the physics breaker, or the simulation programmer.

I find the argument from gradation pretty fascinating from a Platonist perspective. But it is hard to prove that it is not either a human construct or a simple happy byproduct of how the universe works. And while some things are said to be better than others, it is often situational. There is no magical perfect chair, for example. There could, however, be a perfect chair for a given person in a given situation. God would probably make a bad chair though.

The final argument kind of falls apart when one realizes that complexity and order are largely relative terms and we have no other universes for comparison. Maybe our universe, on some imaginary absolute scale, is a total chaotic shitshow. Or maybe our universe is, relatively speaking, ordered perfection. As for its seeming purpose, I think it would be pretty lame to have all this for no reason. But the universe probably does not care much about my feelings on the subject

Given all these things, I think I am firmly in the camp of believing that atheism is irrational because it denies the clearly possible. On the other hand, theism is unable to definitely prove its case. Agnosticism would seem to be the most rational path. However, theism can also be rational just by acknowledging its own optimism.

On some funnier notes, Aquinas will occasionally refute arguments that cite the Old Testament by simply saying that the ancient Hebrews were simply too primitive to fully grasp God's or Moses' true meaning. In a later part, he argues against the idea of astrology in part by saying that though "necromancers" believe that the movements of the planets and stars is important for the invocation of demons, it is not actually true. Instead, demons just like necromancers believe that it is true because demons are great fun-loving trolls like that.

I have also finished Rameau's Nephew and should be writing something short about that soon. And there will likely be at least one more Summa post before I finish reading it.

Next up in my French reading is Molière's Le Tartuffe. This is a no-frills Dover dual-language paper edition, much like my copy of Candide. However, the translation of Tartuffe is a lot less literal than Candide. In fact, some of the translation choices are simply bizarre. This is perplexing because literalness is supposedly part of the Dover dual-language edition philosophy. I do not recommend the translation as anything other than an aide for reading the French. The footnotes, though few, explained everything that I would otherwise have had to look up. For someone just starting out with the French language of today, Molière's French provides a significantly greater challenge than the language of Voltaire. I would not recommend it to another beginner like myself.

Molière himself was an early modern playwright of the mid-17th century, only a few decades after Shakespeare's time. Partly due to the temporal proximity, Molière is often referred to as the French Shakespeare. However, unlike Shakespeare, Molière only dabbled in the genre of comedy. And his comedies are quite different from Shakespeare's due to a much greater influence of the Italian commedia dell'arte on Molière's work. While Shakespeare borrowed elements from commedia once in a while, Molière strongly adheres to the style. His characters are largely the stock characters of commedia with little to distinguish themselves from other characters in other plays adhering to the same archetype. And, true to commedia, the action is largely driven by simplistic and petty emotions most at home in the most lizard-like part of the human brain. It is theatre designed for popular and common appeal. Even the metrical style of Molière relies heavily on rhyming couplets that would appeal even to a child. It seems to me that Molière's comedies have more in common with the old Greek satyr plays than Shakespeare.

The play Tartuffe itself did not appeal to me. Much of the earlier action is a family fighting. On stage, I'm sure all this bustling anger plus a little slapstick would probably elicit a chuckle or two. On paper, however, the characters just seem like jerks. The title character himself is a psychopathic conman out to swindle the head of the household by charming him with his false piety. He does not actually show up until the second half of the play. And until then, half the family thinks he is a living a saint and the other half suspects that he is a fraud. After reading Candide, I was already feeling burnt out on the perennial French trope of the holy hypocrite. Tartuffe did not help at all. In short, every single character in this play lacked depth and thus had little appeal to me.

The ending is perhaps the worst of part of the play. I am not reluctant to spoil because it is absolute garbage. Tartuffe manages to steal some papers incriminating the head of the household. He then uses these papers to get an audience with the king and permission to basically steal the family's house and put the head of the household in prison. When all this is revealed to the family, they are in utter despair. But then, out of nowhere, it is revealed the the king is such a great soul that he can immediately see through the lies of any conman and get at the truth of the matter. From these magical powers, he deduced that Tartuffe is a fraud and family is really a bunch of nice people. Thence Tartuffe is taken to prison just when he thought he won. This is such a blatant example of deus ex machina that it is literally used as one of Wikipedia's examples in the article on deus ex machina. This ending is bad and Molière should feel bad.

Next up on the list will be Molière's Le Bourgeois Gentilhomme or The Bourgeois Gentleman. Since it's more Molière and the bulk of its humor derives from outdated class expectations, I am not particularly excited. But maybe Molière will surprise me. And, if nothing else, it will further allow me to empathize with the plight of French secondary school students forced to read Molière.

Squaring off the Greek math section is Nicomachus of Gerasa's Introduction to Arithmetic. Sadly, this work is long out of print. You can scrounge Amazon or Abe Books for a copy. There are some paperback versions floating around that are just the translation without any of the introductory material. They tend to be a lot cheaper. However, they were intended only for internal use at St. John's College and the publisher did not give permission for the resale of those books. I went for original hardcover version. The notes in this edition are truly exceptional. Most of Nicomachus' explanations and proofs are paired with alternate versions, often from other Greek authors, in the footnotes. So if Nicomachus loses you, the footnotes can often put you back on track. The notes also provided references to a number of other very interesting Greek mathematical works that I think I would like to check out the next time around.

Nicomachus starts off from a very defensive position. In essence, he tries to explain why anyone should care about arithmetic at all. His very philosophical about it. And the basis of his argument is that the study of "real things" is essential to understanding reality and the universe. From there, he argues that arithmetic is among the things that are truly real. While we moderns would say that a deer in front of us is more real than an abstract concept like "animal", Nicomachus disagrees. A deer can die. However, the idea of "animal" could potentially outlive the existence of animals. In other words, qualities, quantities, and forms exist uniformly throughout all of time, while mere objects and creatures exist for only a slice of time. Therefore, in the grand scheme of the universe, these more abstract things spend more time being real than the seemingly concrete things. And should not the thing that exists for the entire life of the universe be considered more real than the thing that exists for a relative blink of an eye? It is certainly an interesting way of looking at things.

Nicomachus, shortly thereafter, addresses an issue I raised in a previous post: numbers can fill completely different, e.g. counting versus measuring, without us giving much thought to that fact. Nicomachus expands on that. He explains that arithmetic is the study of numbers, particularly numbers of the countable kind, i.e. integers. While arithmetic enables other types of math, it is conceptually prior to them all. He argues that the children of arithmetic are those types of math which study objects, motion, and ratios. These three types of math Nicomachus says we call geometry, astronomy, and music. While this may seem like mere word play, I think there is something to it. We easily become constrained by notions of what math is. But the whole system sometimes needs radical modification to deal with news problems. The classic example is Newton's physics requiring the development of Calculus. On the other side of the coin, Descartes unified geometry and algebra and effectively destroyed the classical/medieval conception of geometry. Meanwhile, music and its study of ratios has managed to soldier along largely without numbers and without being regarded as properly math. And I think there are seriously conceptual revolutions to be made. I once again point to D'arcy Thompson's On Growth and Form. There you can see how poorly our math copes with measuring a three-dimensional object's change over time. The problem demands some sort of calculus of geometry.

Though Nicomachus probably did not see such a division, after his philosophical expositions comes his purely mathematical ones. He dedicates himself primarily to figuring out the properties of numbers. He starts with evens and odds. He then goes into concepts like "even-times even", which we would call powers of two. Likewise, he goes into all the variants of the even and oddness of a number's divisors. Prime numbers and the sieve of Eratosthenes are explained. The list of classifications of numbers is long and fascinating. I can not really capture its breadth here. Though I am tempted to write a program that can detect all of Nicomachus' proposed classifications. Going beyond the properties of single numbers, Nicomachus also covers the 10 classic proportions in detail, including a bit about their history. Apparently in Pythagoras' day only first three, arithmetic, geometric, and harmonic, had yet been discovered. I once again recommend Matila Ghyka's The Geometry of Art and Life for exploration of those proportions in, well, art and life.

The road forward gets trickier from here. Per a friend's advice, I will be tackling the Latin authors in reverse order from Thomas Aquinas. The reason is that his Latin is quite easy to read and it provides a good follow-up to the Vulgate, both conceptually and linguistically. Unfortunately, Aquina's Summa in Latin is eight volumes. It will take quite a while for me to finish. However, there is some good news. I have recently put effort into expanding my ability to read academic French to also read literary French. I have started with Voltaire's Candide and, at the current pace, should be able to write a review of that in a month or so. I will likely continue with other French authors in the Great Books set. Hopefully this will keep the posts flowing while I tackle the Summa.

Next up on the list are The Works of Archimedes. This Dover edition is basically your only option these days. Sir Thomas Heath's translation is the only game in town and Dover's edition is the only edition still in print. If you are desperate for a better quality binding, Cambridge University Press put out Heath's original translation in hardcover in 1897. I opted to track down a copy of that. The downside is that Archimedes' The Method would not be rediscovered for nearly another decade after the CUP edition came out. They released a pamphlet supplement of The Method also by Heath. Unfortunately, I only discovered this after reading all of the 1897 edition. The supplement is quite rare now but I found exactly one copy in the hands of a Latvian book dealer. It was surprisingly cheap. Unfortunately, it will probably take several weeks to arrive so I may need make an addendum to this post if anything really interesting crops up in there. So, while I have not seen the Dove edition in person, it is probably the best of bet for any sane reader who does not want to spend a lot of time and cash with antiquarian book dealer listings.

Archimedes' work greatly resembles that of Euclid, from a modern perspective. So, a lot of what I said about the eye-opening experience of Euclid could also easily apply to Archimedes, if Archimedes is the reader's first introduction to Greek mathematics. However, I think Euclid would be easier on the first time reader. Euclid's Elements describes a system of geometry with enough detail that one can just start on the first page with no prior knowledge and make it all the way through to the end. Archimedes is not so forgiving. While Euclid's work can and did (even still does, in certain corners) serve as a textbook, most of Archimedes' works were simply problems that he wanted to tackle. His intended audience was fellow mathematicians, such as Dositheus of Pelusium, Conon of Samos, and other members of the illustrious Alexandrian crowd. Further, Archimedes' surviving works make reference and depend on other works that do not survive. Since we have a full-blown system of geometry and mathematics of our own to rely on, filling in the missing pieces is not too difficult. However, these things together mean that Euclid is going to provide a smoother first hit for a prospective student of Greek mathematics.

Archimedes has a lot of very Euclid-like proofs on spheres, cylinders, circles, conoids, and spheroids. But Archimedes is at his best when he tries to tackle specific and concrete problems. This is why, despite his great purely mathematical achievements, he is considered the father of engineering; while he was a great mathematician, he was the greatest engineer. I will give a few examples of my favorites.

Archimedes, like many mathematicians of the centuries, sought to figure out the ratio of a circle's circumference to its diameter, i.e. pi. There is an age-old philosophical question about whether or not there is a difference between a circle and a polygon with an infinite (or simply extremely high) number of sides. An ideal circle is certainly different has no sides. But maybe in the real universe of Planck measurements there is no difference. Ultimately, for Archimedes' purposes, and most purposes involving pi, the answer does not really matter. The length of the sides of a polygon are very easy to measure. And a polygon drawn hugging the inside or outside of a circle will more closely approximate the circle as the number of sides goes up. Therefore, a polygon with a high number of sides can give a good approximation of pi. And the more sides one adds, the closer one gets. Archimedes chooses to go up to 96 sides, one polygon hugging the outside and one hugging the inside of a circle. This gives a lower bound for pi at 3 10/71 and an upper bound at 3 1/7. If these two values are averaged, it gives pi accurate up to 3.141. Further sides could be used to produce infinitely more values. Christoph Grienberger, an Austrian mathematician, pushed Archimedes' approach all the way to 39 digits of accuracy. Interestingly, Wikipedia is very misleading on this topic. Archimedes stopped at his 96-sided polygon proof because it was more than sufficient and smashed the accuracy of all existing estimates. Extending it further was an obvious practice left up to the reader. He had solved pi.

Archimedes also has a fascinating work where he describes the process of calculating how many grains of sand it would take to fill up the universe. He does this in response to the notion that there is no number big enough to count the grains of sand on Earth. His numbers for the size of the Earth and the universe are wildly off. His estimation for the size of the Earth is off by an order of magnitude and he dismisses the approximations of his own day which were actually fairly accurate. Still, while his methodology is bogus, he comes up with the same basic idea of our modern scientific notation of large numbers to represent the number of grains of sand it would take to fill the universe. In a sense, he fumbles the theoretical but nails the practical here.

I was always fascinated by the mechanics of seesaws as a child, particularly the "trick" of moving along the seesaw to allow children of different sizes to still play with one another. He describes the math behind this process, along with a few methods for figuring out the center of gravity of common shapes, in his On the Equilibrium of Planes. The math here was surprisingly simple and a real personal joy for me.

Archimedes also describes the mechanics of hydrostatics, i.e. how things float, sink, and/or displace liquid. In other words, Archimedes knows what floats your boat. Given that we have already established that he also knows what tilts your seesaw, I think you are in for a good time. The math to solve the famous problem of how much gold is really in a crown is all laid out here, though he does not actually recount the story. It is possible that he came up with the method and wrote it down before discovering that particular practical use. It is also possible that the story of Archimedes and the gold crown was merely an illustrative story that later came to be treated as history by Vitruvius.

Heath, in his introduction, argues that Archimedes was fairly close to giving us Calculus. And I think he is right. Archimedes' section on spirals describes them both in geometric terms, i.e. moving along a circle and a line at the same time, and in terms of a change in magnitude over time. He also tackles the problem of calculating the area of these spirals. Elsewhere, he deals with calculating the area under many rather complicated curves. Combined with his fascination with mechanics, who knows what could have been, if only more interest had been given to Archimedes, more of his works preserved, or the scholarly community in Alexandria not hobbled over the years?

Way after than promised, I have finished reading the New Testament, also known as Bible II: The Adventures of God Junior. For details about the edition I chose, see my previous post: Antiquum Testamentum.

While it should come as no surprise to readers with a Christian background, the New Testament is radically different from the Old Testament. Rather than tales of the previously-mentioned endless warfare in the meat-grinder of civilization, the New Testament covers a time of relative peace in the Middle East, the so-called Pax Romana or Roman Peace. The God of the New Testament is less about crushing your enemies, adhering to a long list of rules, and wrecking false idols than he is about loving one's fellow man, forgiveness, and "faith".

I put faith in quotes because the Latin word for faith, fides, has a broader meaning than the typical modern English usage. When we say faith, we tend to mean belief, or even blind belief. But the sense of the Latin equivalent is more a reciprocal relationship of loyalty and honesty. Fides is the same word we see show up in variant forms in phrases like bona fide and semper fi. It is the faith of "good faith". And it's interesting to see this contrasted with what we tend to translate as "works". The Latin opus (plural opera) is fairly translated as work or works. When I consider what Paul says in the larger context of Jewish law, one of the things he seemed to be saying was that it is important to follow Jesus and God's teachings honestly rather than simply going through the motion. I can think of two good examples of what I believe is meant by works rather than faith. First, consider the issue of the disciples picking wheat on the Sabbath or Jesus healing the sick on the Sabbath. Technically this is against the rules since the Sabbath is a day of rest. However, as Jesus says, "The Sabbath was made for man, and not man for the Sabbath." What rest is there in hunger or illness? These things may violate the letter of the old law, but not the spirit of it since a starving or sick man can have no rest. To take another example, among modern Jews, there are certain people who believe in a long list of things that should not be done on the Sabbath. One of these things not to be done on the Sabbath is dialing a telephone. To overcome limitations like this, less faithful Jews have developed various devices and tricks. For example, I saw a video once of a man who had bought a fake hand on a stick that he would use to dial his phone. He argued that the hand dialed the phone, not him. Therefore he claimed that he had no broken any rule. That is not a faithful adherence to God's old law. Thus it is easy to see the point of the argument that works without faith mean nothing.

Non-Christians may find it odd that I make reference to the "old law". By that I mean the laws given in the Old Testament, the ones Jews adhere to in varying degrees to this day. These laws were superseded with Jesus' arrival. When asked about what laws people should adhere to, it is said in the gospels that Jesus only explicitly listed a few things: do not murder, do not steal, do not commit adultery, do not give false testimony, honor your mother and father, and love thy neighbor. Acts and the epistles of Paul further clarify that dietary restrictions and circumcision definitely do not apply to converts. This is important to keep in mind when common criticisms about the "hypocrisy" of Christians are thrown around. The majority of such criticisms depend on citations from Leviticus in the Old Testament. Aside from those things which also appear in the New Testament, nothing in Leviticus is prohibited to Christians. And many things in Leviticus are, arguably, not even prohibit to non-priestly Jews. Take for example homosexuality. In Leviticus, death is the punishment for homosexuality. In Romans, it is said to be a sin but it is in a list of sins so broad that all of us our guilty. Paul's point, a point commonly reiterated in the modern Catholic church but less so in Protestant churches, is that we are all sinners and our only potential redemption is through God's grace. In other words, homosexuals are just like the rest of us: forgiven through Jesus and damned without him. This difference between Romans and Leviticus is not a contradiction for Christians. The rules of Leviticus simply do not matter anymore. Thus there is no hypocrisy or contradiction here. Let he who is without reading comprehension go back to getting stoned.

On the topic of inconsistency and contradiction, there is some truth to the fact that the gospels do not all tell the same story of Jesus' life. However, having studied both medieval manuscript transmission, oral transmission, and history more generally, parallel accounts like this almost never have this level of consistency. The differences are primarily in the level of detail. For example, if I'm not mistaken, the story of Lazarus shows up in both Mark and John but only John goes into enough detail to actually give Lazarus' name. Faithfully recording the gospels must have been very serious business in the early church and that seems only natural given the obvious importance of God's son showing up, delivering the new law, raising the dead, healing the sick, and then coming back from the dead himself. Similarly, the idea that there is "no evidence" that Jesus ever existed is farcical unless one arbitrarily decides that the Bible somehow does not count. I think most people would be surprised how little evidence we have for people and events in antiquity. It is not that rare to know of something from a single manuscript copy of a single work. And yet we accept those things as historical fact. If you want to start saying that Jesus did not exist at all, you need to start questioning half of the things you think you know about the ancient world.

More generally, most of the criticisms of Christianity that I personally had or had read that lead me to become an atheist as a teenager simply fall apart with a single honest reading of the Bible as a trained historian. It really comes down to a few simple questions, which correspond very nicely with the affirmations in the Nicene Creed. Do you believe there is a God who created the universe? Do you believe that he became man in the form of Jesus? Do you believe that Jesus was killed and came back from the dead? Do you agree with his teachings that we should probably not murder, steal, and so on? Most people can agree to the last question easily. A lot of people have no problem with the first question, though it is quite the sticky wicket. It is those middle two questions that I find the most difficult. Did the apostles and disciples really see what they think they saw? Was human incarnation really the best method God could come up with? If one accepts that we live in a created universe with some driving force behind it, these things certainly seem possible. Unfortunately, without witnessing them, I can not, thus far, come up with an ironclad argument for why these things would be so. Still, this is progress. When reading the Great Books, I am often left with more questions than I started with. I think the Bible is the first time where I have read something and eliminated more questions than I gained. And I have definitely vastly narrowed down the doubts I may have about the Christian faith.

In any case, next up should be Euclid, as I had originally planned. Stay tuned.

Next up is Galen: On the Natural Faculties (Loeb Classical Library). It's another Loeb but aside from the original Great Books volume, it's just about the only translation available. The remarks in my previous post about Hippocrates and the respective Loeb editions more or less apply equally to this volume of Galen. The only thing I would add is that this volume of Galen has a very extensive introduction and many useful footnotes, even compared to the Loeb norm. A.J. Brock is to be commended for his thorough work.

Galen was a Greek born in the 2nd century AD, well after the Roman conquest of Greece. His father was well-educated and reportedly virtuous architect. His mother, on the other hand, was said to be an irrational and angry woman who caused no end of grief for Galen's father. Learning by example and counter example, Galen sought to emulate his father as much as possible and to shy away from the behaviours of his mother. As a young man, he wandered the major hubs of learning in the Eastern Mediterranean. After returning home and working as a surgeon for gladiators, he eventually made his way to Rome. He did not like what he found.

Much like the days of Plato, the best wisdom of those that had gone before was often ignored in Rome in favour of novel theories peddled by the reigning sophists of the day. Galen pitted his knowledge of Hippocrates, supplemented by his own experiments, against these sophists with limited results in his own day. In one instance, he argued against a prevailing notion that the bladder was a useless organ. Galen attempted to argue that he had seen the bladder swell with urine in animals and further that Aristotle says that nature does nothing without reason. His opponent remained unconvinced. Galen resorted to literally slicing open some poor animal right in front of the man. He then tied something around the animal's penis to keep it from urinating. He patched the animal back up and then reopened it later to show that the bladder was now swollen. He then untied the animal's penis and urine immediately came forth. The animal's bladder deflated. Galen's opponent was still not convinced.

Supporting arguments with evidence from vivisections was a favored tactic of Galen's. Empiricism, however, is not a foolproof method against certain types of minds. Galen persisted in his arguments. He won great favor among some. He even became the personal physician of the great Emperor Marcus Aurelius, whom we will read a work of later. It is hard not to strongly believe in truths one has witnessed first hand and can reproduce on command, provided a dog can be found quickly. And yet some people will always remain immune to reason. It was a case of an unstoppable force meeting an unmovable object. The expected social catastrophe ensued and Galen was forced to flee for his life from the other medical practitioners in Rome. Marcus Aurelius would later beg him to come back but he refused.

So, the moral of the story is that while you can lead a sophist to a dog's piss-filled bladder, but you can't make him drink believe that it plays a role in dealing with urine. And adherence to the truth can be so enraging for the indoctrinated that not even the protection of one of the greatest Roman emperors can be counted on to preserve truth's advocate.

Ps. The title is actually a pun when translated to Swedish.