I read Evelyn Waugh's Men at Arms this past week with 50% enjoyment. Just after reading Lorna Doone with all its unusual words and obscure topical references, I assumed that in reading a book about the Second World War I would be in more familiar territory. But once again I found myself surrounded by the unfamiliar: slang, military cant, and casually mentioned references to people and events unknown to me. And yet I liked the story and the characters and the few jokes that I got.
The plot has very little to do with actual warfare. As the book starts, it's September, 1939, and England goes to war with a Germany that has not backed out of Poland. But by the last page, the main character, Guy Crouchback, does little but join the Royal Halberdiers and then train. The only actual action the unit sees, in the last pages, involves one death: that of a man who may or may not have been an enemy. Instead, Men at Arms tells about every aspect of army life during wartime except for fighting: bad drill instructors, meals, military pay, confusing networks of authority, sudden changes of deployment, and so on. The commander shows his total detachment from the realities of battle by insisting that the men find and count all spent cartridges on the firing range to make sure all supplies have been accounted for. The lack of battle action seems to me so much a part of the theme of the novel that thinking of it as the first entry in a trilogy changes my sense of the book. For Guy, war is not about fighting, and his experience in this novel confirms his understanding. Maybe in the next two books he learns some hard lessons.
The book also treats the power of words to sustain a false sense of glory. None of the Halberdiers, for instance, does anything like holding a halberd. And their predecessors may not have actually done so, either. Part of Guy's training, along with learning to march and to shoot, involves learning the stories that make one proud to be a Royal Halberdier. The regiment is also known as the Applejacks, and Guy must learn a catechism in which he can explain the origin of that nickname in the group's use of apples as weapons in one historical battle; the story suggests a group of musketeers, not halberdiers, who have run out of shot or powder. To take another example, Guy has an ancestor revered as a saint in one town in Italy, and yet this ancestor did nothing of note during his life except die in his first battle -- against his neighbor's castle. Rarely in the book does the worth of people, things, and events match that of their names and titles and slogans. Guy even questions the sincerity of Churchill and the meaning of the phrase "Spirit of Dunkirk." No sacred cows here.
But Waugh also shows us the military's predilection for other questionable symbols of rank and pride. Guy purchases a monocle at one point because he thinks it makes him look more like an officer. The regiment has a ceremonial horn of snuff with silver spoons and brushes that each member must use in a prescribed way. They toast a deposed (and perhaps deceased) princess of prerevolutionary Russia as their "Colonel-in-Chief." And the officers dine with silver candlesticks that they understand to represent battles of World War I. No, war is not a matter of silver snuff spoons. But without these accoutrements, how many previously comfortable civilians would stick with their determination to go to war?
The best character is Guy's companion Apthorpe, who tries to keep with him several chests of secret supplies that he thinks he will need to stay comfortable during his time as a soldier. These include several bottles marked "poison" -- supposedly drugs for the diseases he fears -- and a portable toilet. I don't understand that last item, but it must be valuable because he ends up fighting over it with the second-best character, the brigadier general. Brigadier Ben Ritchie-Hook craves violent action. He has only one eye and uses a hand with only two fingers and a half of a thumb, but he wears his eyepatch and waves his glove-covered stump of a hand with great pride in the incidents that caused his losses -- incidents that, perhaps tellingly, he never describes. His wounds may be no more badges of courage than Apthorpe's, who suffers injury "in his rears" when Ritchie-Hook blows up the portable toilet at an opportune time.
But, as I said, in between the parts I enjoyed, I went through a lot I simply didn't understand. I found a book of contemporary critical reviews of all of Waugh's novels, and I found some comfort in reading the ones dealing with Men at Arms. One reviewer called the book "uneven." Another said he didn't understand half of it either, feeling as if he'd walked in on the telling of an inside joke. But all seemed to agree with a third who said that, while the book was one of his weakest, Waugh at his worst still writes "ten times better" than many popular authors at their best. I agree. I think Brideshead Revisited is among the great novels, and Scoop is one of the funniest twentieth-century novels I've ever read. So I'll keep coming back to Waugh. But maybe I should read more of the reviews and pick one of the better books for my next visit.
Sunday, July 31, 2011
Saturday, July 30, 2011
The Good, the Bad, and the Unfounded
Somewhere in The Everlasting Man, Chesterton takes on a common tendency of some academic types to infer a spiritual meaning in prehistoric artifacts and then to teach their theory as if we had direct, primary evidence of the religious tenets of the people involved. Some have said, for instance, that the cave dwellers of Lascaux worshiped the animals they painted on their walls and that rooms with more paintings than others functioned as sanctuaries. Maybe, counters G. K., they simply admired the beauty of the animals they hunted, and perhaps the rooms where animal pictures abound served as nurseries.
I see bold declarations of the inner motivations of prehistoric people disturbingly often. My son's high-school American history text taught that the first Americans crossed a land bridge between Asia and Alaska in order to find food. I'm sure that they hoped to find food, because all members of the animal kingdom share that need. And I'm sure that they found food, because their descendents live today in testimony to their survival. But I'm not sure at all that we can know that finding food provided their sole motivation for migration. Humans move for many reasons. Maybe the original immigrants were trying to get away from an aggressive enemy. Maybe they were searching for furs. Maybe they just liked the look of the mountains. That history book did nothing to teach young people about these possibilities based on observations of human nature. And, by the way, it certainly didn't teach young people about the nature of history since, without primary documentation, the historical method can make no conclusions whatsoever about human motivation.
This kind of confident but unfounded speculation lies near the center of Spengler's approach in The Decline of the West. Spengler's main thesis is that Europe and the Americas have seen many cultures rise and fall -- not just one "Western Civilization" -- and that the arc always follows the same trajectory. But I haven't encountered anything like an argument for the thesis with which I can either agree or disagree. He often draws his comparisons between cultures by simply mentioning, for instance, the Baroque era in Classical Civilization or saying that Napoleon and Alexander were alike; explanations of these intriguing turns of phrase appear rarely. At least he's consistent with his own vision, since he says that the true spirit of a civilization can not be explained, only felt. I guess I don't feel it. In any case, having convinced some readers by intuition that all cultures rise and fall in the same way, Spengler sometimes describes prehistoric cultures based only on his theory that they must be like all the others.
Spengler says in fact that all cultures begin without history. So he rules out the very possibility of documentary evidence for the conditions of early cultures and doesn't offer any other basis for his observations beyond his idea that Destiny determines that early cultures be the way he says they were. According to Spengler, one of those destined features of prehistorical cultures is an original lack of religion. (The cave dwellers of Lascaux, we must suppose, had advanced beyond this stage.) He also claims to know the way that language started and how grammar developed. Anyone watching a man converse with a dog, he says, can see how it must have been.
I have trouble agreeing with many of the points he makes about historical times, too. I became very intrigued (at last!) when Spengler started talking about the tendency of western religion and philosophy of the last 1000 years toward expecting their standards of everyone, or even of imposing those standards. I agreed when he suggested that demonstration taught better than force. But he lost me again when he said that no western religion before 1000 AD would have dreamed of imposing itself on others. I don't understand what he thinks he can achieve by saying something so revolutionary without any explanation. Islam spread extremely rapidly in the century after Mohammed, and common understanding says this expansion benefited from both words and swords. Millions suddenly became nominal Christians when the Empire became officially Christian at the end of the fourth century. And I seem to remember something about a pagan emperor or two forcing everyone within reach of the legions to sacrifice to Caesar as a god. Now maybe some big change of attitude happened around 1000 AD that Spengler has discovered. But he doesn't help me see it simply by rewriting the prior thousand years of documented history in a single, unexplained, unsupported sentence.
Again, I'm puzzled when Spengler says the Classical (i.e. ancient Greek) person had no sense of the importance or influence of past and future. His evidence is the Greek statue, which captures and preserves, he says, a single, undifferentiated moment. Because of this extreme version of "living in the now," the protagonist in a Greek drama is simply a victim of the present whims of the gods and the coincidental circumstances of the moment. Nothing in the character or history of Oedipus makes any difference to the story of his unwitting patricide and incest, he says. It could just as well have been anyone.
I read this section constantly thinking of counterexamples. I don't buy his interpretation of Greek sculpture to begin with. Don't many of those statues suggest an awful lot of gymnastic exercise prior to the captured moment? Doesn't Poseidon have a future target in mind for that missing trident? And doesn't that beautiful split second of rest at the top of the discus thrower's upswing clearly suggest both a past and a future? My confusion continues as I think about Greek drama and epic. Of course Oedipus' past matters. He's received a prophecy that warns him of his fate. And in the sequel, Oedipus at Colonus, the plot makes no sense without the past (i.e., the events shown in Oedipus the King) and the courage of his daughter, Antigone. Agamemnon is all about the wicked character of Clytemnestra and Agamemnon's history as a general in the Trojan War. "It could just as well have been anyone"? Substitute Shakespeare's Portia and Falstaff for Clytemnestra and Agamemnon, and theater-goers won't see a play about a woman killing her husband.
So what about "the good" that the title of this post promises? Spengler proves accurately prescient when, in 1922, he reports his vision of our era:
I see bold declarations of the inner motivations of prehistoric people disturbingly often. My son's high-school American history text taught that the first Americans crossed a land bridge between Asia and Alaska in order to find food. I'm sure that they hoped to find food, because all members of the animal kingdom share that need. And I'm sure that they found food, because their descendents live today in testimony to their survival. But I'm not sure at all that we can know that finding food provided their sole motivation for migration. Humans move for many reasons. Maybe the original immigrants were trying to get away from an aggressive enemy. Maybe they were searching for furs. Maybe they just liked the look of the mountains. That history book did nothing to teach young people about these possibilities based on observations of human nature. And, by the way, it certainly didn't teach young people about the nature of history since, without primary documentation, the historical method can make no conclusions whatsoever about human motivation.
This kind of confident but unfounded speculation lies near the center of Spengler's approach in The Decline of the West. Spengler's main thesis is that Europe and the Americas have seen many cultures rise and fall -- not just one "Western Civilization" -- and that the arc always follows the same trajectory. But I haven't encountered anything like an argument for the thesis with which I can either agree or disagree. He often draws his comparisons between cultures by simply mentioning, for instance, the Baroque era in Classical Civilization or saying that Napoleon and Alexander were alike; explanations of these intriguing turns of phrase appear rarely. At least he's consistent with his own vision, since he says that the true spirit of a civilization can not be explained, only felt. I guess I don't feel it. In any case, having convinced some readers by intuition that all cultures rise and fall in the same way, Spengler sometimes describes prehistoric cultures based only on his theory that they must be like all the others.
Spengler says in fact that all cultures begin without history. So he rules out the very possibility of documentary evidence for the conditions of early cultures and doesn't offer any other basis for his observations beyond his idea that Destiny determines that early cultures be the way he says they were. According to Spengler, one of those destined features of prehistorical cultures is an original lack of religion. (The cave dwellers of Lascaux, we must suppose, had advanced beyond this stage.) He also claims to know the way that language started and how grammar developed. Anyone watching a man converse with a dog, he says, can see how it must have been.
I have trouble agreeing with many of the points he makes about historical times, too. I became very intrigued (at last!) when Spengler started talking about the tendency of western religion and philosophy of the last 1000 years toward expecting their standards of everyone, or even of imposing those standards. I agreed when he suggested that demonstration taught better than force. But he lost me again when he said that no western religion before 1000 AD would have dreamed of imposing itself on others. I don't understand what he thinks he can achieve by saying something so revolutionary without any explanation. Islam spread extremely rapidly in the century after Mohammed, and common understanding says this expansion benefited from both words and swords. Millions suddenly became nominal Christians when the Empire became officially Christian at the end of the fourth century. And I seem to remember something about a pagan emperor or two forcing everyone within reach of the legions to sacrifice to Caesar as a god. Now maybe some big change of attitude happened around 1000 AD that Spengler has discovered. But he doesn't help me see it simply by rewriting the prior thousand years of documented history in a single, unexplained, unsupported sentence.
Again, I'm puzzled when Spengler says the Classical (i.e. ancient Greek) person had no sense of the importance or influence of past and future. His evidence is the Greek statue, which captures and preserves, he says, a single, undifferentiated moment. Because of this extreme version of "living in the now," the protagonist in a Greek drama is simply a victim of the present whims of the gods and the coincidental circumstances of the moment. Nothing in the character or history of Oedipus makes any difference to the story of his unwitting patricide and incest, he says. It could just as well have been anyone.
I read this section constantly thinking of counterexamples. I don't buy his interpretation of Greek sculpture to begin with. Don't many of those statues suggest an awful lot of gymnastic exercise prior to the captured moment? Doesn't Poseidon have a future target in mind for that missing trident? And doesn't that beautiful split second of rest at the top of the discus thrower's upswing clearly suggest both a past and a future? My confusion continues as I think about Greek drama and epic. Of course Oedipus' past matters. He's received a prophecy that warns him of his fate. And in the sequel, Oedipus at Colonus, the plot makes no sense without the past (i.e., the events shown in Oedipus the King) and the courage of his daughter, Antigone. Agamemnon is all about the wicked character of Clytemnestra and Agamemnon's history as a general in the Trojan War. "It could just as well have been anyone"? Substitute Shakespeare's Portia and Falstaff for Clytemnestra and Agamemnon, and theater-goers won't see a play about a woman killing her husband.
So what about "the good" that the title of this post promises? Spengler proves accurately prescient when, in 1922, he reports his vision of our era:
Even now the world-cities of the Western Civilization are far from having reached the peak of their development. I see, long after A.D. 2000, cities laid out for ten to twenty million inhabitants, spread over enormous areas of countryside, with buildings that will dwarf the biggest of today's and notions of traffic and communications that we should regard as fantastic to the point of madness.It's curious that the one point that Spengler admits might sound mad is the point that proves the most sane.
Monday, July 25, 2011
Things I Didn't Know
I learned a number of remarkable facts today from Oswald Spengler's Decline of the West:
• Stained-glass windows work admirably as expressions of the West's primary symbol -- empty space -- because they are translucent and therefore bodiless. I have thought previously that these tangible, colored, lead-lined artifacts, often depicting the bodies of humans, plants, and animals, lit as they are from behind, convey a message that the corporeal things all around us receive being, energy, and meaning from their spiritual Source. But now I know that they serve only as deliberate gaps in a wall, indicators of emptiness.
• Blue-green is a Catholic color. I might have picked cardinal red, but I would have picked incorrectly. It also seems that blue-green appears in the music of Couperin, Haydn, and Mozart.
• Brown is a Protestant color. It also is the color of the sound of stringed instruments, especially when playing the music of Beethoven. (I'm unclear as to whether Haydn's string music is brown or blue-green, but it's Catholic string music, so I'm guessing the latter.)
• Brown, as the only real color not in the rainbow, is less tangible than the others. If any color were tangible, I might have supposed that the color of dirt, tree bark, and leather were more tangible than, say, sky blue. In fact, I have never thought that the rainbow represented anything tangible, its end being famously unreachable. But again, I find myself corrected. Apparently, besides being the primary color of Protestantism and fiddles, brown is also the color of stained-glass windows (another fact new to me), and since they are bodiless (see above), so is the color brown.
• Not only counterpoint (see yesterday's post) but also all "orchestrally conceived" genres such as oratorio, cantata, and opera, represent longing for infinite extension in space. I admit that Wagner's Ring of the Nibelungs seems to extend itself infinitely in time. But now I know the true purpose of Messiah and The Marriage of Figaro: all cultures begin their declines by attempting extension in space as a response to fear of death, and it's clear to me now how those two musical masterworks fit right in with the pattern.
• The color gold does not appear in nature.
• Red and yellow are colors of nearness and popularity, while blue is cold and distant. Perhaps election-night television programs should consider a change of color for the Democrats.
• The timbre of trumpets and trombones is red and yellow and consequently near, popular, and vulgar. (I actually knew that trumpets and trombones were vulgar, but now I know why.)
• Classical-era music represents cultural decline in its rigid adherence to older forms and methods. I have taught the appearance of sonata form and of the symphony and string quartet as innovations of the late eighteenth century, but I will now have to rethink my pedagogy.
• Romantic-era music falls even lower than mere stagnation and indulges in imitation of a past imitation. I don't know as of p. 133 of Spengler what past it imitates, but I'm sure that if I look hard enough, I'll find its chromatic-third relations, rich orchestration, extended forms, and predilection for programmatic music in an earlier, already moribund era of music history.
I'm happy to be able to share these finds with my readers, who will no doubt begin to feel colors and hear timbres differently from now on. . . . Hang on a minute. . . . I seem to remember now reading about some occasions on which John Lennon felt colors and saw timbres. I've always read that LSD brought on these experiences, but perhaps Lennon had just been reading Spengler.
• Stained-glass windows work admirably as expressions of the West's primary symbol -- empty space -- because they are translucent and therefore bodiless. I have thought previously that these tangible, colored, lead-lined artifacts, often depicting the bodies of humans, plants, and animals, lit as they are from behind, convey a message that the corporeal things all around us receive being, energy, and meaning from their spiritual Source. But now I know that they serve only as deliberate gaps in a wall, indicators of emptiness.
• Blue-green is a Catholic color. I might have picked cardinal red, but I would have picked incorrectly. It also seems that blue-green appears in the music of Couperin, Haydn, and Mozart.
• Brown is a Protestant color. It also is the color of the sound of stringed instruments, especially when playing the music of Beethoven. (I'm unclear as to whether Haydn's string music is brown or blue-green, but it's Catholic string music, so I'm guessing the latter.)
• Brown, as the only real color not in the rainbow, is less tangible than the others. If any color were tangible, I might have supposed that the color of dirt, tree bark, and leather were more tangible than, say, sky blue. In fact, I have never thought that the rainbow represented anything tangible, its end being famously unreachable. But again, I find myself corrected. Apparently, besides being the primary color of Protestantism and fiddles, brown is also the color of stained-glass windows (another fact new to me), and since they are bodiless (see above), so is the color brown.
• Not only counterpoint (see yesterday's post) but also all "orchestrally conceived" genres such as oratorio, cantata, and opera, represent longing for infinite extension in space. I admit that Wagner's Ring of the Nibelungs seems to extend itself infinitely in time. But now I know the true purpose of Messiah and The Marriage of Figaro: all cultures begin their declines by attempting extension in space as a response to fear of death, and it's clear to me now how those two musical masterworks fit right in with the pattern.
• The color gold does not appear in nature.
• Red and yellow are colors of nearness and popularity, while blue is cold and distant. Perhaps election-night television programs should consider a change of color for the Democrats.
• The timbre of trumpets and trombones is red and yellow and consequently near, popular, and vulgar. (I actually knew that trumpets and trombones were vulgar, but now I know why.)
• Classical-era music represents cultural decline in its rigid adherence to older forms and methods. I have taught the appearance of sonata form and of the symphony and string quartet as innovations of the late eighteenth century, but I will now have to rethink my pedagogy.
• Romantic-era music falls even lower than mere stagnation and indulges in imitation of a past imitation. I don't know as of p. 133 of Spengler what past it imitates, but I'm sure that if I look hard enough, I'll find its chromatic-third relations, rich orchestration, extended forms, and predilection for programmatic music in an earlier, already moribund era of music history.
I'm happy to be able to share these finds with my readers, who will no doubt begin to feel colors and hear timbres differently from now on. . . . Hang on a minute. . . . I seem to remember now reading about some occasions on which John Lennon felt colors and saw timbres. I've always read that LSD brought on these experiences, but perhaps Lennon had just been reading Spengler.
Sunday, July 24, 2011
Recent Disappointments
In each of the first five years of my ten-year plan, I've scheduled what seem like the tougher things mostly in the first half or two-thirds of the year, leaving stuff I know I love for the end of the year. I do this partly for the sake of delayed gratification and partly because my fall semester is much busier than my spring or summer. But this annual plan runs the risk of putting me in a Slough of Despond if I end up with too many books I don't enjoy in the first six or seven months.
And that's just what happened this last week. My interest in Lorna Doone waned as I read more of it (or never fully waxed, perhaps), and Spengler's Decline of the West has not captured my sympathy at all. By the end of Lorna Doone, it seems that the virtues Blackmore rewards are physical strength, rage, beauty, money, and ownership of weaponry. I had hoped that John Ridd's humility, wisdom, or love of Shakespeare might play a part in the climax, but that hope was disappointed. In the end, John kills all his enemies, making sure to get a valuable necklace from one first, and then lives happily ever after with his beautiful wife.
I thought of the Slough of Despond a minute ago because a slough plays a part at the end of Lorna Doone. John drops his gun and wrestles with his last enemy, literally tearing his muscles off his bones, until they find themselves in a bog. John jumps out in time and then watches his nemesis sink "joint by joint" without a thought of helping him. I just saw Harry Potter and the Deathly Hallows Part 2 a couple of days ago and watched Harry risk his life to save the life of his supposedly mortal foe, Draco Malfoy, and I was reminded that acts such as these are what make me root for Harry. But by the end of Lorna Doone, I no longer had any reason to root for the character I had spent three weeks with. Mark Twain said that, while in a good book the reader wants to see the good characters rewarded and the bad characters punished, he wanted to see all the characters of The Last of the Mohicans drowned together. And I must confess that I thought of Mark Twain while I watched John Ridd standing by that bog letting the other man drown alone.
Spengler actually seems a little crazy so far. He calls the West a "Faustian" culture, but only explains that term on page 97. By that expression he means a culture that has adopted empty space as its chief symbol. He finds empty space in gothic cathedrals, Bach's counterpoint, Rembrandt's colors, Descartes's geometry, Newton's physics, and Kant's philosophy. Nevermind the common understanding that the spaces of gothic cathedrals were filled with light, that Kant denied the concept of empty space, or that the system of abstract spatial coordinates that Descartes and Newton and other in the seventeenth century used seemed like innovations at the time; Spengler says our declined culture is all about empty space.
I was willing to go along with his idea and his manic, ill-organized presentation of it to see if it helps make any sense of history even if not totally accurate. But I read something Friday that pulled the rug out from under my generous intentions. In the service of some argument I didn't quite follow about vision and extension and fear of death (or something), Spengler said that form in western music was based entirely on variation and that expansions and contractions of time had absolutely no place in music. Here Spengler has stumbled onto a subject I know a little bit about, and I can say that he's quite simply wrong. The Bach whose music he says represents empty space often manipulates a motive or even an entire theme in such a way that it takes twice as long to unfold. This kind of temporal expansion (and correlate methods of contraction) pop up all throughout the "Faustian" period of music history: in the twelfth-century compositions of Notre Dame, in the fifteenth-century proportional motets of Ockhegem, and in the nineteenth-century hemiolas of Brahms and Chaikovski, to name just three other examples. Theme-and-variation form, on the other hand, never played the prominent role he claimed for it in the Classical period of Haydn and Mozart, not to mention the rest of the Faustian Era.
The bright side of my situation carries both short-term relief and long-term hope. For the present, I'm finished with Blackmore, and I can kick my reading speed of Spengler into a higher gear. I'd rather skip some of the words all the way through the rest of the book than give up and skip all the words of the second half. And then after I finish Decline of the West, I have nothing left to read this year but books I know I love -- Plutarch, Durant, Boswell, Catton, Lewis, and others among my favorites -- and then I end the year with the Great Man himself.
And that's just what happened this last week. My interest in Lorna Doone waned as I read more of it (or never fully waxed, perhaps), and Spengler's Decline of the West has not captured my sympathy at all. By the end of Lorna Doone, it seems that the virtues Blackmore rewards are physical strength, rage, beauty, money, and ownership of weaponry. I had hoped that John Ridd's humility, wisdom, or love of Shakespeare might play a part in the climax, but that hope was disappointed. In the end, John kills all his enemies, making sure to get a valuable necklace from one first, and then lives happily ever after with his beautiful wife.
I thought of the Slough of Despond a minute ago because a slough plays a part at the end of Lorna Doone. John drops his gun and wrestles with his last enemy, literally tearing his muscles off his bones, until they find themselves in a bog. John jumps out in time and then watches his nemesis sink "joint by joint" without a thought of helping him. I just saw Harry Potter and the Deathly Hallows Part 2 a couple of days ago and watched Harry risk his life to save the life of his supposedly mortal foe, Draco Malfoy, and I was reminded that acts such as these are what make me root for Harry. But by the end of Lorna Doone, I no longer had any reason to root for the character I had spent three weeks with. Mark Twain said that, while in a good book the reader wants to see the good characters rewarded and the bad characters punished, he wanted to see all the characters of The Last of the Mohicans drowned together. And I must confess that I thought of Mark Twain while I watched John Ridd standing by that bog letting the other man drown alone.
Spengler actually seems a little crazy so far. He calls the West a "Faustian" culture, but only explains that term on page 97. By that expression he means a culture that has adopted empty space as its chief symbol. He finds empty space in gothic cathedrals, Bach's counterpoint, Rembrandt's colors, Descartes's geometry, Newton's physics, and Kant's philosophy. Nevermind the common understanding that the spaces of gothic cathedrals were filled with light, that Kant denied the concept of empty space, or that the system of abstract spatial coordinates that Descartes and Newton and other in the seventeenth century used seemed like innovations at the time; Spengler says our declined culture is all about empty space.
I was willing to go along with his idea and his manic, ill-organized presentation of it to see if it helps make any sense of history even if not totally accurate. But I read something Friday that pulled the rug out from under my generous intentions. In the service of some argument I didn't quite follow about vision and extension and fear of death (or something), Spengler said that form in western music was based entirely on variation and that expansions and contractions of time had absolutely no place in music. Here Spengler has stumbled onto a subject I know a little bit about, and I can say that he's quite simply wrong. The Bach whose music he says represents empty space often manipulates a motive or even an entire theme in such a way that it takes twice as long to unfold. This kind of temporal expansion (and correlate methods of contraction) pop up all throughout the "Faustian" period of music history: in the twelfth-century compositions of Notre Dame, in the fifteenth-century proportional motets of Ockhegem, and in the nineteenth-century hemiolas of Brahms and Chaikovski, to name just three other examples. Theme-and-variation form, on the other hand, never played the prominent role he claimed for it in the Classical period of Haydn and Mozart, not to mention the rest of the Faustian Era.
The bright side of my situation carries both short-term relief and long-term hope. For the present, I'm finished with Blackmore, and I can kick my reading speed of Spengler into a higher gear. I'd rather skip some of the words all the way through the rest of the book than give up and skip all the words of the second half. And then after I finish Decline of the West, I have nothing left to read this year but books I know I love -- Plutarch, Durant, Boswell, Catton, Lewis, and others among my favorites -- and then I end the year with the Great Man himself.
Wednesday, July 20, 2011
Watching the Sunset
We have a large bush in the front garden that I have to trim back every fall. I go outside, usually on one of the first cool Saturday mornings, grab the shears and the stepladder, and start on the front. The trimming here usually goes quickly and smoothly. Evenly distributed, leafing branches have sent out shoots during the spring and summer, and these thin additions come off without much effort, leaving a full, symmetrical, rounded body of green. But then I move to the back, and eventually to the top. In these places, the foliage on the old surface is sparser, making room for thick limbs that have thrust through to steal the light. I don't know just how this works: many of these massive runners come from near the bottom of the central trunks, passing without branch or leaf through many feet of the core before exploding at the surface. Apparently these interlopers don't know and don't care that the thinner twigs can expand in these areas with much less effort; the aggressors just see an opportunity and grab it.
Last Friday, I started Oswald Spengler's Decline of the West. I expected some kind of rather linear chronology of recent events in Europe, with praise for whatever epoch or structure Spengler saw as the pinnacle of history and blame for whatever trends he saw as causes for departure from the zenith. Instead, I found first an attempt to describe a new philosophy of history. But his new philosophy apparently includes the tenet that history can't be explained, only intuited. And so he can't really explain it and instead just talks around and around it. His language reminds me of the wild, self-promoting branches in my holly. With seemingly little regard for order or traditional definitions of words and little respect for the risks of unbroken streams of abstract statements, Spengler's prose finds one idea after another bursting to the fore begging for what attention it can grab before its sudden eclipse. Here's an example, chosen completely randomly:
Despite the overwhelming effusion of abstract, unsupported statements, though, I'm enjoying the read so far. He seems to be saying that history does not proceed on a single, millennia-long path of progress, and I have no trouble agreeing. Rather, he says, the world teems with cultures that pursue a destiny, following a determined story arc told over and over again: cultures rise on a wave of creativity shaped by local relationships, then become civilized (by which he means both stultified and national or even imperial) and ebb. Every aspect of culture -- art, religion, politics, science, trade, technology, and so on -- works together to symbolize the culture. As a result of this view, Spengler's treatment races between topics and across eras. After the rather long introduction, which mentions each of the topics just listed, Spengler moves to a treatment of mathematics, which, he says, always represents a philosophy. The part of the chapter I've read so far makes reference to the Egyptian Ahmes, Pythagoras, Archimedes, Euclid, Aristarchus, Al-Khwarizmi, Descartes, Galileo, Pascal, Newton, and many others. Along the way, Spengler lights momentarily on architecture, religion, astronomy, painting, and musical instruments.
In an interesting coincidence, I just read today a passage in which Spengler talks about Euclid's dependence on natural numbers even though hypotenuses can't always be measured by them, a topic I blogged about recently. Spengler credits Euclid's view to a fear of the infinite. As with everything else in the chapter, Spengler doesn't say anywhere near enough to convince me he's right or even to suggest how I might decide whether he's right. But he sure has me thinking.
Given Spengler's firm belief in predetermined unfolding of history, I'm amazed by his slight of Hegel. But then maybe he saw Hegel as a rival claimant to his throne. Because, for all his insistence that truths are relative to culture, Spengler, like Hegel, declares himself the first to provide mankind with the right view of the universe. His book, he says, "is laden . . . with all the defects of a first attempt . . . . Nevertheless I am convinced that it contains the incontrovertible formulation of an idea which, once enunciated clearly, will (I repeat) be accepted without dispute." It's almost a self-parody. But, like Monty Python's soccer game between the ancient Greek philosophers and the modern Germans (most of which players Spengler mentions in the first thirty pages of the book), so far Decline of the West provokes thought even while it entertains.
Last Friday, I started Oswald Spengler's Decline of the West. I expected some kind of rather linear chronology of recent events in Europe, with praise for whatever epoch or structure Spengler saw as the pinnacle of history and blame for whatever trends he saw as causes for departure from the zenith. Instead, I found first an attempt to describe a new philosophy of history. But his new philosophy apparently includes the tenet that history can't be explained, only intuited. And so he can't really explain it and instead just talks around and around it. His language reminds me of the wild, self-promoting branches in my holly. With seemingly little regard for order or traditional definitions of words and little respect for the risks of unbroken streams of abstract statements, Spengler's prose finds one idea after another bursting to the fore begging for what attention it can grab before its sudden eclipse. Here's an example, chosen completely randomly:
Systematic philosophy closes with the end of the eighteenth century. Kant put its utmost possibilities in forms both grand in themselves and -- as a rule -- final for the Western soul. He is followed, as Plato and Aristotle were followed, by a specifically megalopolitan philosophy that was not speculative but practical, irreligious, social-ethical. This philosophy . . . begins in the West with Schopenhauer, who is the first to make the Will to life ("creative life force") the centre of gravity of his thought, although the deeper tendency of his doctrine is obscured by his having, under the influence of a great tradition, maintained the obsolete distinctions of phenomena and things-in-themselves and suchlike.This passage leaves me with more questions than answers: What makes a philosophy systematic? What are its utmost possibilities? How does Spengler know the utmost possibilities of philosophy? How can Kant give the final word when philosophers such as Hegel claim to build on Kant? If Kant is the last philosopher of the earlier school and Schopenhauer the first of the new, what is Hegel? How does Goethe, who lived between Kant and Schopenhauer and whom Spengler elsewhere calls a philosopher, fit in? What is a megalopolitan philosophy? How can he categorize Plato, Aristotle, and Kant as speculative philosophers in contrast to the supposedly ethical philosophies that followed them, when each wrote books on ethics? What is the deeper tendency of Schopenhauer's doctrine? What makes a tradition great? The only thing I actually understand in the passage is the "distinctions of phenomena and things-in-themselves," and they are declared obsolete. Yet how can the tradition be obsolete while Schopenhauer maintains it?
Despite the overwhelming effusion of abstract, unsupported statements, though, I'm enjoying the read so far. He seems to be saying that history does not proceed on a single, millennia-long path of progress, and I have no trouble agreeing. Rather, he says, the world teems with cultures that pursue a destiny, following a determined story arc told over and over again: cultures rise on a wave of creativity shaped by local relationships, then become civilized (by which he means both stultified and national or even imperial) and ebb. Every aspect of culture -- art, religion, politics, science, trade, technology, and so on -- works together to symbolize the culture. As a result of this view, Spengler's treatment races between topics and across eras. After the rather long introduction, which mentions each of the topics just listed, Spengler moves to a treatment of mathematics, which, he says, always represents a philosophy. The part of the chapter I've read so far makes reference to the Egyptian Ahmes, Pythagoras, Archimedes, Euclid, Aristarchus, Al-Khwarizmi, Descartes, Galileo, Pascal, Newton, and many others. Along the way, Spengler lights momentarily on architecture, religion, astronomy, painting, and musical instruments.
In an interesting coincidence, I just read today a passage in which Spengler talks about Euclid's dependence on natural numbers even though hypotenuses can't always be measured by them, a topic I blogged about recently. Spengler credits Euclid's view to a fear of the infinite. As with everything else in the chapter, Spengler doesn't say anywhere near enough to convince me he's right or even to suggest how I might decide whether he's right. But he sure has me thinking.
Given Spengler's firm belief in predetermined unfolding of history, I'm amazed by his slight of Hegel. But then maybe he saw Hegel as a rival claimant to his throne. Because, for all his insistence that truths are relative to culture, Spengler, like Hegel, declares himself the first to provide mankind with the right view of the universe. His book, he says, "is laden . . . with all the defects of a first attempt . . . . Nevertheless I am convinced that it contains the incontrovertible formulation of an idea which, once enunciated clearly, will (I repeat) be accepted without dispute." It's almost a self-parody. But, like Monty Python's soccer game between the ancient Greek philosophers and the modern Germans (most of which players Spengler mentions in the first thirty pages of the book), so far Decline of the West provokes thought even while it entertains.
Tuesday, July 19, 2011
Nothing New to Say
That title certainly won't excite anyone about reading today's post. I wish I had a more enticing hook, but it's time for an update on Lorna Doone, and I simply haven't found much new to report. In my third week now of reading the book, I continue to alternate between enjoyable passages of poetic descriptions or interesting observations on the one hand, and opaque or confusing narrative on the other.
I'm getting used to the dialect by this point; it still comes up regularly, if not quite so often as it did in the first chapters. A recent sample: "Whoy, dudn't ee knaw, Maister Jan," said Bill Dadds, looking at me queerly, "as Jan Vry wur gane avore braxvass." Of thirteen words in Bill's sentence, only one is spelled in the familiar way, and it's one that we would not use in contemporary construction. As I understand it, the original rendition represents local pronunciation and wording of this sentence: "Why, didn't you know, Master John, that John Fry was gone before breakfast?" Curiously, in one long story told by the John Fry just referenced, Blackmore has John Fry speak in unbroken dialect except where he quotes a man from London. So can John Fry imitate a London accent (supposedly represented by standard spelling), or did Blackmore just not think this scene through carefully enough?
The antiquated -- or at least unfamiliar -- rural vocabulary also continues. In the last several days I've come across besom, gamboge, hoggets, antre, sheppey, withy, linhay, and armiger. I actually knew besom (the only one Blogspot's spellchecker seems to know, as well), but it still seems to fit this category since it refers to a broom made of bundled sticks.
But many times I have trouble following a passage even when no unusual words or special spelling are involved. Blackmore has his first-person narrator, John Ridd, say something like "I can't remember if I've mentioned before that . . ." so often that I begin to wonder if Blackmore himself simply forgets to supply necessary details. In one conversation, government officer Jeremy Stickles says, "Not one word to your mother about this unlucky matter," to which John Ridd replies, "Do you suppose I can sleep . . . and all the time have it on my mind, that not an acre of all the land, nor even our old sheep-dog, belongs to us, of right at all!" I've gone back over the conversation three times now, and I can find no indication from Stickles about any end of the Ridds' rights to their property. The only "unlucky matter" referred to before this is the theft of a valuable necklace. Is there a line of dialog missing? This forgetfulness (whether it belongs to the narrator or to the author) is especially ironic since John often claims to remember details of events vividly even when he doesn't understand their significance until, perhaps, years later.
The examples go on and on. John hears that two militia forces have attacked the villainous Doones as planned, yet he concludes (apparently correctly) that they have attacked each other. A carriage is waylaid by highwaymen apparently in the middle of the woods only to be destroyed by a wave of the ocean -- and then later the carriage is said to have been on a mountain pass! I've been confused about the plot or character's motivations so often, I've started reading a different way. Instead of trying to figure things out or follow threads, I just let the events and dialog come as they may. I try to treat anything that doesn't make sense simply as a pleasant surprise. I don't know if the disconnect lies in Blackmore, his characters, or me, but it lies somewhere, so now every time it appears, I just wave at it and move on.
And Blackmore rewards my persistence. I enjoyed this observation by John about some overlooked colors of autumn:
I'm getting used to the dialect by this point; it still comes up regularly, if not quite so often as it did in the first chapters. A recent sample: "Whoy, dudn't ee knaw, Maister Jan," said Bill Dadds, looking at me queerly, "as Jan Vry wur gane avore braxvass." Of thirteen words in Bill's sentence, only one is spelled in the familiar way, and it's one that we would not use in contemporary construction. As I understand it, the original rendition represents local pronunciation and wording of this sentence: "Why, didn't you know, Master John, that John Fry was gone before breakfast?" Curiously, in one long story told by the John Fry just referenced, Blackmore has John Fry speak in unbroken dialect except where he quotes a man from London. So can John Fry imitate a London accent (supposedly represented by standard spelling), or did Blackmore just not think this scene through carefully enough?
The antiquated -- or at least unfamiliar -- rural vocabulary also continues. In the last several days I've come across besom, gamboge, hoggets, antre, sheppey, withy, linhay, and armiger. I actually knew besom (the only one Blogspot's spellchecker seems to know, as well), but it still seems to fit this category since it refers to a broom made of bundled sticks.
But many times I have trouble following a passage even when no unusual words or special spelling are involved. Blackmore has his first-person narrator, John Ridd, say something like "I can't remember if I've mentioned before that . . ." so often that I begin to wonder if Blackmore himself simply forgets to supply necessary details. In one conversation, government officer Jeremy Stickles says, "Not one word to your mother about this unlucky matter," to which John Ridd replies, "Do you suppose I can sleep . . . and all the time have it on my mind, that not an acre of all the land, nor even our old sheep-dog, belongs to us, of right at all!" I've gone back over the conversation three times now, and I can find no indication from Stickles about any end of the Ridds' rights to their property. The only "unlucky matter" referred to before this is the theft of a valuable necklace. Is there a line of dialog missing? This forgetfulness (whether it belongs to the narrator or to the author) is especially ironic since John often claims to remember details of events vividly even when he doesn't understand their significance until, perhaps, years later.
The examples go on and on. John hears that two militia forces have attacked the villainous Doones as planned, yet he concludes (apparently correctly) that they have attacked each other. A carriage is waylaid by highwaymen apparently in the middle of the woods only to be destroyed by a wave of the ocean -- and then later the carriage is said to have been on a mountain pass! I've been confused about the plot or character's motivations so often, I've started reading a different way. Instead of trying to figure things out or follow threads, I just let the events and dialog come as they may. I try to treat anything that doesn't make sense simply as a pleasant surprise. I don't know if the disconnect lies in Blackmore, his characters, or me, but it lies somewhere, so now every time it appears, I just wave at it and move on.
And Blackmore rewards my persistence. I enjoyed this observation by John about some overlooked colors of autumn:
On either bank, the blades of grass, making their last autumn growth, pricked their spears and crisped their tuftings with the pearly purity. The tenderness of their green appeared under the glaucous mantle; while that grey suffusion, which is the blush of green life, spread its damask chastity. Even then my soul was lifted, worried though my mind was: who can see such large kind doings, and not be ashamed of human grief?So Lorna Doone certainly hasn't become one of my favorite books or even one that I would recommend to anyone, but it has provided pleasant (if sometimes mystifying) entertainment on my daily walks for the past two weeks.
Friday, July 15, 2011
With a Little Help
How am I supposed to write about Kant? Synthetic a priori judgments. If you understand that phrase, you don't need me to explain anything. On the other hand, if you don't understand it . . . well, you still don't need me to explain it.
Kant is hard to read. His revolutionary ideas are difficult to grasp because they are so counterintuitive, and he didn't do himself any favors by couching them in such turgid language with so few illustrations. But having made it through his works once in the first ten-year reading plan, I wanted to go through them again after finally having something of a grasp on them -- a loose, greasy sort of grasp though it may be.
This year my assignment was to read a middle section of the Critique of Pure Reason, a part designated as the Analytic of the Transcendental Logic, by which Kant means the description of the fundamentals of thought. In the previous section, on Transcendental Aesthetic, Kant explained his view that everything we perceive seems to be in space and time only because our mode of perception uses space and time to sort out the objects we perceive. Space and time, he says, don't exist outside ourselves, at least not that we could ever tell. What things are in themselves, we don't know, but they seem to us to have locations in space and time because that's just the way our senses work. Space and time are in us, not in the outside world. Along the same lines, in the Transcendental Logic Kant says that categories such as causality, necessity, quantity, and so forth are also in our minds; they are the forms by which we must think thoughts and conceive conceptions and judge judgements, but we cannot know whether causality and the rest actually exist in the world.
Sometimes in reading Kant it becomes clear that I need help. An example: one of Kant's categories, these forms of pure understanding with no known basis in the outside world, is existence. Seriously? Existence is only a mode of thought? We can't know that anything exists? Not even, say, ourselves? It is very easy for me to read this kind of thing and wonder if I'm misinterpreting; I'm sure I'm not alone in having this feeling. It would help if I could travel through this reading list with a panel of expert teachers who could guide me and cut away the vines when I reach dense thickets such as this one. I don't carry my own faculty around with me, but I do consult expert teachers -- in other books. Yes, my list for any given year is larger than it looks, because it involves an implied list of books about the books.
This year, in order to boost my understanding and confidence while reading the Critique of Pure Reason, I've also been reading Peter Kreeft's Socrates Meets Kant, part of a series of imaginative dialogs in which the ancient sage meets up with various philosophers in an afterlife and puts them through his searching routine of questioning all assumptions. If you can get past that funny conceit and accept a Socrates that has kept up with the story of western philosophy, the book proves both entertaining and instructive. Kreeft's Socrates call Kant on several "self-contradictions" like saying both that various things exist and that existence is only a form of thought, or saying both that objects cause sensations and that causality is only a form of thought.
Another similar problem of inconsistency in Kant that I've noticed over the years involves his conception of human beings. One of the rules in his ethical system is that one should never treat another human being as a mere means to an end. Kant's reasoning involves his understanding of human nature, yet he claims that we can never know what the things we perceive in the world are really like in themselves. So how does he know that these beings he sees and hears are humans with the same nature he finds in himself? I agree with Kant's ethical rule. It's just that he says in one book that it is logically inescapable while saying in another that one of its premises (the nature of human beings) is absolutely unknowable to us.
I sat down this afternoon intending to explain briefly why I shouldn't write about Kant and then to spend most of the space on Kreeft's book and other guides. But now that I see that I've written several paragraphs about Kant, I'll close with just a brief mention of several books about books that I've found helpful in pursuing my plan.
• Also doing a great deal of the clarifying work that Kant didn't do for himself is Roger Scruton's Kant: A Very Short Introduction. All the other volumes I've tried from the Very Short series have been helpful, so I'm sure I'll look at more.
• For Shakespeare, I find Isaac Asimov's Guide to Shakespeare invaluable. His strength lies in historical, geographical, and mythological background, but his plot overviews and critiques of quality are also interesting to read.
• The Tragic Drama of the Greeks by Arthur Elam Haigh is available for free online and provides an excellent overview of every extant play by Aeschylus, Sophocles, and Euripides.
• Mortimer Adler, the godfather of my reading project, wrote a book called Aristotle for Everybody that serves as a perfect starting place for reading The Philosopher.
• As clear as Aquinas seems to me now, I would never have started making sense of him without Peter Kreeft's selective commentary, A Shorter Summa, and Kreeft's commentary on Pascal literally changed my life.
• The Oxford World's Classics series provides an expert introduction in every book, fiction or nonfiction, and every one I've read has helped a lot.
Well, now you've read my post about books that tell about books, including one by Kant that says that humans can never know what things are in themselves. If that seems to leave you a long way from any actual knowledge and suggests that today's post has very little value, remember that distance and value are both measured as quantities and that quantity is only a mode of thought.
Kant is hard to read. His revolutionary ideas are difficult to grasp because they are so counterintuitive, and he didn't do himself any favors by couching them in such turgid language with so few illustrations. But having made it through his works once in the first ten-year reading plan, I wanted to go through them again after finally having something of a grasp on them -- a loose, greasy sort of grasp though it may be.
This year my assignment was to read a middle section of the Critique of Pure Reason, a part designated as the Analytic of the Transcendental Logic, by which Kant means the description of the fundamentals of thought. In the previous section, on Transcendental Aesthetic, Kant explained his view that everything we perceive seems to be in space and time only because our mode of perception uses space and time to sort out the objects we perceive. Space and time, he says, don't exist outside ourselves, at least not that we could ever tell. What things are in themselves, we don't know, but they seem to us to have locations in space and time because that's just the way our senses work. Space and time are in us, not in the outside world. Along the same lines, in the Transcendental Logic Kant says that categories such as causality, necessity, quantity, and so forth are also in our minds; they are the forms by which we must think thoughts and conceive conceptions and judge judgements, but we cannot know whether causality and the rest actually exist in the world.
Sometimes in reading Kant it becomes clear that I need help. An example: one of Kant's categories, these forms of pure understanding with no known basis in the outside world, is existence. Seriously? Existence is only a mode of thought? We can't know that anything exists? Not even, say, ourselves? It is very easy for me to read this kind of thing and wonder if I'm misinterpreting; I'm sure I'm not alone in having this feeling. It would help if I could travel through this reading list with a panel of expert teachers who could guide me and cut away the vines when I reach dense thickets such as this one. I don't carry my own faculty around with me, but I do consult expert teachers -- in other books. Yes, my list for any given year is larger than it looks, because it involves an implied list of books about the books.
This year, in order to boost my understanding and confidence while reading the Critique of Pure Reason, I've also been reading Peter Kreeft's Socrates Meets Kant, part of a series of imaginative dialogs in which the ancient sage meets up with various philosophers in an afterlife and puts them through his searching routine of questioning all assumptions. If you can get past that funny conceit and accept a Socrates that has kept up with the story of western philosophy, the book proves both entertaining and instructive. Kreeft's Socrates call Kant on several "self-contradictions" like saying both that various things exist and that existence is only a form of thought, or saying both that objects cause sensations and that causality is only a form of thought.
Another similar problem of inconsistency in Kant that I've noticed over the years involves his conception of human beings. One of the rules in his ethical system is that one should never treat another human being as a mere means to an end. Kant's reasoning involves his understanding of human nature, yet he claims that we can never know what the things we perceive in the world are really like in themselves. So how does he know that these beings he sees and hears are humans with the same nature he finds in himself? I agree with Kant's ethical rule. It's just that he says in one book that it is logically inescapable while saying in another that one of its premises (the nature of human beings) is absolutely unknowable to us.
I sat down this afternoon intending to explain briefly why I shouldn't write about Kant and then to spend most of the space on Kreeft's book and other guides. But now that I see that I've written several paragraphs about Kant, I'll close with just a brief mention of several books about books that I've found helpful in pursuing my plan.
• Also doing a great deal of the clarifying work that Kant didn't do for himself is Roger Scruton's Kant: A Very Short Introduction. All the other volumes I've tried from the Very Short series have been helpful, so I'm sure I'll look at more.
• For Shakespeare, I find Isaac Asimov's Guide to Shakespeare invaluable. His strength lies in historical, geographical, and mythological background, but his plot overviews and critiques of quality are also interesting to read.
• The Tragic Drama of the Greeks by Arthur Elam Haigh is available for free online and provides an excellent overview of every extant play by Aeschylus, Sophocles, and Euripides.
• Mortimer Adler, the godfather of my reading project, wrote a book called Aristotle for Everybody that serves as a perfect starting place for reading The Philosopher.
• As clear as Aquinas seems to me now, I would never have started making sense of him without Peter Kreeft's selective commentary, A Shorter Summa, and Kreeft's commentary on Pascal literally changed my life.
• The Oxford World's Classics series provides an expert introduction in every book, fiction or nonfiction, and every one I've read has helped a lot.
Well, now you've read my post about books that tell about books, including one by Kant that says that humans can never know what things are in themselves. If that seems to leave you a long way from any actual knowledge and suggests that today's post has very little value, remember that distance and value are both measured as quantities and that quantity is only a mode of thought.
Sunday, July 10, 2011
New Wor(l)ds
A week ago, all I knew about Richard Blackmore's Lorna Doone was that the book shares a name with a cookie and that Deep Purple's guitar player shared a name with the author. As it turns out, I didn't even know the book's general date, since I put it under "18th-century novels" in my overall plan and, as I learned on the first page of the book, it was published in 1869.
But I had even more to learn as I kept turning the pages (or, actually, pressing the Kindle button). In starting Lorna Doone, I entered a strange new world: the Exmoor region in Devon and Somerset of southwest England, where I've never been and know very little about. As with Henry Esmond, coincidentally, this nineteenth-century book sets its tale in the seventeenth century, which adds to the alien atmosphere of the book: when first-person narrator John Ridd tells of the arrest of Lord William Russell and Mr. Algernon Sidney, he assumes I know who they are, but I don't. Then there's the antiquated vocabulary of English farming and trade: chapman, wether, peat rick, and so on. (My spell checker puts a wavy line underneath "wether" and "chapman," so it doesn't know these words either.) And he often uses outmoded meanings of familiar words: "factor" as a trader in goods, for instance, and "tell" to mean "count." (The last example survives in our culture with the bank teller.) And on top of it all, some of the characters speak in a local dialect whose accent (also unknown to me before this) Blackmore indicates by respelling almost every word. A sample:
Poor Lorna grows up in this perilous world among a family of heartless marauders. She acknowledges the evil of her clan's ways, but she believes herself doomed never to escape. "Is it any wonder," she says to John, "that I cannot sink with these, that I cannot so forget my soul, as to live the life of brutes, and die the death more horrible because it dreams of waking? There is none to lead me forward, there is none to teach me right; young as I am, I live beneath a curse that lasts for ever." (Her last words reminded me of A Tale of Two Cities and Charles Darnay's disgust with the aristocratic heritage that has, he says, left him "bound to a system that is frightful to me, responsible for it, but powerless in it." I wonder if John Ridd will have to make a Sydney Carton-esque sacrifice in order to free Lorna.)
Lorna says she takes some comfort from little, everyday "signs" of goodness. "Whether from the rustling wind," she says, "or sound of distant music, or the singing of a bird, like the sun on snow it strikes me with a pain of pleasure." Much of the theme of the book, in fact, seems to revolve around observation of the poetry in things. Like Duke Senior in the comedy by John's favorite poet, John might say he and Lorna find "tongues in trees, books in the running brooks, sermons in stones," although they may have trouble finding "good in everything." John says "God can never charge him" for being a poet, but within a couple of pages of taht denial, he notices remnant patches of snow left on the hills "like a lady's gloves forgotten." He claims that in remembering a scene, he notices details that made no impression at the time, so perhaps we're to take it that John simply has a natural poetic gift without realizing it -- or at least without the cultural freedom to admit it.
John's first-person narrative wanders aimlessly through this dangerous, mysterious world. Characters come and go quickly, and he cannot report even the briefest event without tangents upon tangents about the situation, the way he felt, and other similar events. Explanations for these side-excursions always come later rather than sooner. Sometimes he tells the reader that explanations will come later, as when he says one man came "a foot below the Doone stature (which I shall describe hereafter)." Why didn't he just say then that the Doone's were normally quite tall? Overall, the unfamiliar details and the tangled presentation of context makes for difficult reading.
But don't I read a novel partly to learn about a world I'm not familiar with? Maybe a lack of narrative organization is just part of John's character. When he starts to tell Lorna's background, in fact, he admits that writing gets him confused and decides to let her tell her story in her own words. Then, he says, "If ye find it weariness, seek in yourselves the weariness." John Ridd really is wiser than he lets on or admits to himself; he knows that slow reading might be due to the book and might be due to the reader. I'm enjoying the parts I understand of Lorna Doone and even some of what I don't understand, so I'll credit my weariness to the reader and keep going.
But I had even more to learn as I kept turning the pages (or, actually, pressing the Kindle button). In starting Lorna Doone, I entered a strange new world: the Exmoor region in Devon and Somerset of southwest England, where I've never been and know very little about. As with Henry Esmond, coincidentally, this nineteenth-century book sets its tale in the seventeenth century, which adds to the alien atmosphere of the book: when first-person narrator John Ridd tells of the arrest of Lord William Russell and Mr. Algernon Sidney, he assumes I know who they are, but I don't. Then there's the antiquated vocabulary of English farming and trade: chapman, wether, peat rick, and so on. (My spell checker puts a wavy line underneath "wether" and "chapman," so it doesn't know these words either.) And he often uses outmoded meanings of familiar words: "factor" as a trader in goods, for instance, and "tell" to mean "count." (The last example survives in our culture with the bank teller.) And on top of it all, some of the characters speak in a local dialect whose accent (also unknown to me before this) Blackmore indicates by respelling almost every word. A sample:
"Plaise ye, worshipful masters," he said, being feared of the gateway, "carn 'e tull whur our Jan Ridd be?"This mysterious world of Lorna Doone is full of all kinds of danger. I've seen floods and rapids threaten or even take life several times already in the first quarter of the book. Highwaymen plague the crude roads, but John Ridd and his family consider them gentlemen in comparison to the Doone family, who rob and kill neighbors sometimes randomly for sport. The people of Exmoor apparently just grow up learning to accept the danger and deal with it. John says at one point that he is "feared of being afraid; a fear which a wise man has long cast by, having learned of the manifold dangers which ever and ever encompass us." And the danger may not be all material: an uncanny moan floats through the woods every few months or so. "It mattered not whether you stood on the moor, or crouched behind rocks away from it, or down among reedy places; all as one the sound would come, now from the heart of the earth beneath, now overhead bearing down on you. And then there was rushing of something by, and melancholy laughter, and the hair of a man would stand on end before he could reason properly."
"Hyur a be, ees fai, Jan Ridd," answered a sharp little chap, making game of John Fry's language.
"Zhow un up, then," says John Fry poking his whip through the bars at us; "Zhow un up, and putt un aowt."
Poor Lorna grows up in this perilous world among a family of heartless marauders. She acknowledges the evil of her clan's ways, but she believes herself doomed never to escape. "Is it any wonder," she says to John, "that I cannot sink with these, that I cannot so forget my soul, as to live the life of brutes, and die the death more horrible because it dreams of waking? There is none to lead me forward, there is none to teach me right; young as I am, I live beneath a curse that lasts for ever." (Her last words reminded me of A Tale of Two Cities and Charles Darnay's disgust with the aristocratic heritage that has, he says, left him "bound to a system that is frightful to me, responsible for it, but powerless in it." I wonder if John Ridd will have to make a Sydney Carton-esque sacrifice in order to free Lorna.)
Lorna says she takes some comfort from little, everyday "signs" of goodness. "Whether from the rustling wind," she says, "or sound of distant music, or the singing of a bird, like the sun on snow it strikes me with a pain of pleasure." Much of the theme of the book, in fact, seems to revolve around observation of the poetry in things. Like Duke Senior in the comedy by John's favorite poet, John might say he and Lorna find "tongues in trees, books in the running brooks, sermons in stones," although they may have trouble finding "good in everything." John says "God can never charge him" for being a poet, but within a couple of pages of taht denial, he notices remnant patches of snow left on the hills "like a lady's gloves forgotten." He claims that in remembering a scene, he notices details that made no impression at the time, so perhaps we're to take it that John simply has a natural poetic gift without realizing it -- or at least without the cultural freedom to admit it.
John's first-person narrative wanders aimlessly through this dangerous, mysterious world. Characters come and go quickly, and he cannot report even the briefest event without tangents upon tangents about the situation, the way he felt, and other similar events. Explanations for these side-excursions always come later rather than sooner. Sometimes he tells the reader that explanations will come later, as when he says one man came "a foot below the Doone stature (which I shall describe hereafter)." Why didn't he just say then that the Doone's were normally quite tall? Overall, the unfamiliar details and the tangled presentation of context makes for difficult reading.
But don't I read a novel partly to learn about a world I'm not familiar with? Maybe a lack of narrative organization is just part of John's character. When he starts to tell Lorna's background, in fact, he admits that writing gets him confused and decides to let her tell her story in her own words. Then, he says, "If ye find it weariness, seek in yourselves the weariness." John Ridd really is wiser than he lets on or admits to himself; he knows that slow reading might be due to the book and might be due to the reader. I'm enjoying the parts I understand of Lorna Doone and even some of what I don't understand, so I'll credit my weariness to the reader and keep going.
Thursday, July 7, 2011
"Our" History
In finishing Eusebius, I ended a wonderful, eye-opening experience. Paul L. Maier's translation made the reading very easy and, in its modern, streamlined English, made Eusebius sound like a person and not like a textbook. I wish that Maier had not apologized, though (as he did several times), for certain passages that would sound, he thought, distasteful to the twenty-first century reader. Any living person reading a Church History written in the fourth century knows that tastes in writing style change over the ages and needs no warnings or apologies.
Eusebius surprised me by casting something of a critical eye on his sources. Although not engaging in the aggressive scrutiny of current scholarship, and certainly not acting on the skepticism of some criticism that rejects miraculous accounts out of hand, Eusebius still knows that his sources may be mistaken or exaggerate or lie for various reasons, that authorship is not always as clear as it seems, and that he must defend the authority of some documents against detractors. His basic recognition that not everything in black and white is true blue probably came naturally to him as a scholar interested in examining and comparing a great many manuscripts. His mentors Origen and Pamphilus apparently assembled an extensive library in Caesarea, and Eusebius seems to have become a master of the whole lot since he refers to apocryphal gospels, letters, state documents, translations, theological tracts, and more. He cites several sources, for instance, on the identity of the writer of the Revelation. His conclusion is that the author's name was truly John but that he was not the Son of Zebedee who wrote the gospel and at least one of the letters bearing that name. His reasoning involves both subject matter and Greek style, and Maier says that most current scholars agree with his conclusions and for the same reasons. He defends the book's place in the canon as well as that of most of the other New Testament books (although he's skeptical about 2 Peter, 2 John, and 3 John). It was news to me that already in the fourth-century critics challenged the authenticity of the first and third gospels because of their divergent genealogies for Jesus; apparently this kind of thing is not the product of the modern Age of Doubt. Eusebius' solution, by the way, is that Joseph had two fathers, being the biological son of a man who married his dead half-brother's widow, according to the Law, and had children in the dead man's name.
Eusebius wrote his book just after Constantine made Christianity legal in the Roman Empire, and he saw the history having a neat resolution: after centuries of periodic persecution, the Church now enjoyed protection thanks to the servant of God, Constantine. His detailed, gory renditions of the persecutions, especially in Lyons and Alexandria, were chilling. But throughout the descriptions, Eusebius' identified with the martyrs: he often spoke of "our" courage or "our" problem, even with regard to events from before the time he was born. He reminded me that I, too, belong to that "we" and that his story was also partly my tragedy and my triumph.
Soberingly, he called the last great persecution, under Diocletian and Galerius, the just chastisement by God of a worldly Church -- and he called the sin "our worldliness." Just as he brought me back to the fourth century with the word "our," he forecast his concerns into the twenty-first century. The Church History proves relevant to current times with its examination of critical issues; might it also have something to say about today's Church, its condition, and its relation to the world?
One of the motivations of my reading program is the idea that there are books out there that I've been missing. Sometimes I get to classic books that I haven't read before and they end up tasting dry; I finish those thinking, "Well, I wanted to say I've read that book, and now I can say it." But others confirm my suspicion that juicy feasts await me. This book joins Wordworth's poetry at the top of that second list so far this year.
Eusebius surprised me by casting something of a critical eye on his sources. Although not engaging in the aggressive scrutiny of current scholarship, and certainly not acting on the skepticism of some criticism that rejects miraculous accounts out of hand, Eusebius still knows that his sources may be mistaken or exaggerate or lie for various reasons, that authorship is not always as clear as it seems, and that he must defend the authority of some documents against detractors. His basic recognition that not everything in black and white is true blue probably came naturally to him as a scholar interested in examining and comparing a great many manuscripts. His mentors Origen and Pamphilus apparently assembled an extensive library in Caesarea, and Eusebius seems to have become a master of the whole lot since he refers to apocryphal gospels, letters, state documents, translations, theological tracts, and more. He cites several sources, for instance, on the identity of the writer of the Revelation. His conclusion is that the author's name was truly John but that he was not the Son of Zebedee who wrote the gospel and at least one of the letters bearing that name. His reasoning involves both subject matter and Greek style, and Maier says that most current scholars agree with his conclusions and for the same reasons. He defends the book's place in the canon as well as that of most of the other New Testament books (although he's skeptical about 2 Peter, 2 John, and 3 John). It was news to me that already in the fourth-century critics challenged the authenticity of the first and third gospels because of their divergent genealogies for Jesus; apparently this kind of thing is not the product of the modern Age of Doubt. Eusebius' solution, by the way, is that Joseph had two fathers, being the biological son of a man who married his dead half-brother's widow, according to the Law, and had children in the dead man's name.
Eusebius wrote his book just after Constantine made Christianity legal in the Roman Empire, and he saw the history having a neat resolution: after centuries of periodic persecution, the Church now enjoyed protection thanks to the servant of God, Constantine. His detailed, gory renditions of the persecutions, especially in Lyons and Alexandria, were chilling. But throughout the descriptions, Eusebius' identified with the martyrs: he often spoke of "our" courage or "our" problem, even with regard to events from before the time he was born. He reminded me that I, too, belong to that "we" and that his story was also partly my tragedy and my triumph.
Soberingly, he called the last great persecution, under Diocletian and Galerius, the just chastisement by God of a worldly Church -- and he called the sin "our worldliness." Just as he brought me back to the fourth century with the word "our," he forecast his concerns into the twenty-first century. The Church History proves relevant to current times with its examination of critical issues; might it also have something to say about today's Church, its condition, and its relation to the world?
One of the motivations of my reading program is the idea that there are books out there that I've been missing. Sometimes I get to classic books that I haven't read before and they end up tasting dry; I finish those thinking, "Well, I wanted to say I've read that book, and now I can say it." But others confirm my suspicion that juicy feasts await me. This book joins Wordworth's poetry at the top of that second list so far this year.
Tuesday, July 5, 2011
More on Proportion
A couple of days ago, I said that Euclid talks about ratios of line segments without using numbers to measure them. So how does he define ratios of line segments if he doesn't use numbers? Definition 5 of book 5 gives his method, an abstract method of imagination: The ratio of segments A and B is equal to that of C and D if, when A and C are each multiplied by the same arbitrary number and B and D are each multiplied by another arbitrary number, the "equimultiples" of A and C are both greater than or both equal to or both less than the equimultiples of B and D, respectively.
Yeah. I didn't get it at first, either. Trying to understand the significance, I thought about two pairs of line segments, each pair in a ratio of 1:2. Maybe the first pair measured 6 inches and 12 inches, while the second pair measured 5 and 10. Multiply each of the first pair by 5 and each of the second pair by 6, and you come up with 30 and 60 in each case: the two pairs are equal. Why bother with less-than and greater-than?
Only partway through book 5 as Euclid used this definition did I understand that it meant that if you performed this operation using every imaginable pair of multipliers (an infinity of possibilities) the results would always come out equivalent: both greater than or both equal to or both less than. Anachronistically using decimal fractions to measure segments, let's imagine a unit square and its diameter, whose length is the square root of 2: 1.4142135623. . . . Now imagine a square built on a side twice as long. Its diameter is also twice as long: 2.8284271247 . . . . Knowing as we do that the lengths of the diameters are irrational, we can never find a pair of integers to use as multipliers that will make the results equal. But imagine multiplying the sides (1 and 2) by 14 (results: 14 and 28), and imagine multiplying the diameters each by 10 (results: 14.1421. . . and 28.28427 . . . ). Each of the first numbers is less than its corresponding number in the second pair. Now try multiplying the sides by 141 (141 and 282) and the diameters by 100 (141.421 . . . and 282.842 . . . ). The first pair is still less than the second pair, but the difference is proportionally less. We could go on and on, getting the two pairs as close as we like to each other, but they will never be equal. That wording of our situation reminds me of what I've learned at the beginning of several calculus books. (I've never made it very far in any of them.) So Euclid doesn't exactly anticipate Descartes's geometry on a measurable grid, but definition 5 does give hints of the theory of limits.
Imagining an infinite number of monkeys multiplying two numbers by an infinite combination of integers over an infinite amount of time makes for a fun thought experiment (and probably reproduces Hamlet), but it hardly provides a practical way to reproduce a given ratio. Fortunately, Euclid offers a quick, practical method. If you have one line segment (A) divided at some point (P) and you want to divide another line segment (B) by the same ratio, make any triangle out of those two lines and a third (C), and draw a new line (D) parallel to C going through point B. The point at which line D intersects line B divides B into the desired ratio.
Forgive this ludicrous post. No one wants to read about geometry with no pictures. I could learn to insert graphics into my blog, or I could just apologize, and I'm much better at the latter. I'm just recording the things I've been thinking about prompted by my reading, and recently, this is it, I'm afraid. And on top of all these problems with today's post, I could be totally wrong. Music theorists don't usually have to count higher than 12, so my math skills are rusty -- although not as rusty as they would be if I didn't read Euclid every year and try a calculus book every once in a while.
Since I'm close to the end of book 6, I peeked ahead yesterday at the beginning of book 7 (next year's assignment) and saw immediately that I was wrong about one thing in my last post. Book 7 starts with definitions about numbers and primes and such, and the proofs all use line segments to represent the numbers, something I thought Euclid never did. My new guess is that while he thought any sets of numbers (by which he meant counting numbers: 1, 2, 3, and so on) could be represented by corresponding line segments, he knew that not every set of line segments could be assigned to numbers, since some line segments (like the diameter of the square) could not be measured by integers.
I have now exceeded all proper proportions and will stop for the day.
Yeah. I didn't get it at first, either. Trying to understand the significance, I thought about two pairs of line segments, each pair in a ratio of 1:2. Maybe the first pair measured 6 inches and 12 inches, while the second pair measured 5 and 10. Multiply each of the first pair by 5 and each of the second pair by 6, and you come up with 30 and 60 in each case: the two pairs are equal. Why bother with less-than and greater-than?
Only partway through book 5 as Euclid used this definition did I understand that it meant that if you performed this operation using every imaginable pair of multipliers (an infinity of possibilities) the results would always come out equivalent: both greater than or both equal to or both less than. Anachronistically using decimal fractions to measure segments, let's imagine a unit square and its diameter, whose length is the square root of 2: 1.4142135623. . . . Now imagine a square built on a side twice as long. Its diameter is also twice as long: 2.8284271247 . . . . Knowing as we do that the lengths of the diameters are irrational, we can never find a pair of integers to use as multipliers that will make the results equal. But imagine multiplying the sides (1 and 2) by 14 (results: 14 and 28), and imagine multiplying the diameters each by 10 (results: 14.1421. . . and 28.28427 . . . ). Each of the first numbers is less than its corresponding number in the second pair. Now try multiplying the sides by 141 (141 and 282) and the diameters by 100 (141.421 . . . and 282.842 . . . ). The first pair is still less than the second pair, but the difference is proportionally less. We could go on and on, getting the two pairs as close as we like to each other, but they will never be equal. That wording of our situation reminds me of what I've learned at the beginning of several calculus books. (I've never made it very far in any of them.) So Euclid doesn't exactly anticipate Descartes's geometry on a measurable grid, but definition 5 does give hints of the theory of limits.
Imagining an infinite number of monkeys multiplying two numbers by an infinite combination of integers over an infinite amount of time makes for a fun thought experiment (and probably reproduces Hamlet), but it hardly provides a practical way to reproduce a given ratio. Fortunately, Euclid offers a quick, practical method. If you have one line segment (A) divided at some point (P) and you want to divide another line segment (B) by the same ratio, make any triangle out of those two lines and a third (C), and draw a new line (D) parallel to C going through point B. The point at which line D intersects line B divides B into the desired ratio.
Forgive this ludicrous post. No one wants to read about geometry with no pictures. I could learn to insert graphics into my blog, or I could just apologize, and I'm much better at the latter. I'm just recording the things I've been thinking about prompted by my reading, and recently, this is it, I'm afraid. And on top of all these problems with today's post, I could be totally wrong. Music theorists don't usually have to count higher than 12, so my math skills are rusty -- although not as rusty as they would be if I didn't read Euclid every year and try a calculus book every once in a while.
Since I'm close to the end of book 6, I peeked ahead yesterday at the beginning of book 7 (next year's assignment) and saw immediately that I was wrong about one thing in my last post. Book 7 starts with definitions about numbers and primes and such, and the proofs all use line segments to represent the numbers, something I thought Euclid never did. My new guess is that while he thought any sets of numbers (by which he meant counting numbers: 1, 2, 3, and so on) could be represented by corresponding line segments, he knew that not every set of line segments could be assigned to numbers, since some line segments (like the diameter of the square) could not be measured by integers.
I have now exceeded all proper proportions and will stop for the day.
Sunday, July 3, 2011
Out of Proportion
I have an intelligent friend who says she's "bad at math." She has a sad case of arithmophobia, but she's so smart, I sometimes wonder if she wouldn't have had strong skills with numbers if she just hadn't developed the fear. But in any case, there it is: she can't do math. This problem became known to me early in our acquaintance when, for one reason or another, our conversation hit upon geometry and I sad something about similar triangles or parallel lines or something of that sort. My friend said she didn't know what I was talking about. "You took geometry in high school, didn't you?" "Sure, everyone took geometry, but I never learned that." "You must have just forgotten, because this subject comes up early in any geometry course." "No," she insisted, "we never studied this."
I assumed she didn't even remember what she had forgotten until one day a few years later when I was helping another friend's son with his homework. He asked the group of adults a question about an equation to express a series, and they all looked at me, so I looked at his book to see what I could contribute. But the book gave no instructions on how to find the equation; we were left to the mercy of trial and error. Frustrated, I looked at the cover so I could at least know the names of the authors I was angry with, only to receive a shock upon seeing the title: Modern Geometry. I flipped through the book looking for axioms, for proofs, for inscribed polygons, but I found none of these things. One chapter gave the formulas for areas of various plane figures, but otherwise, the book had nothing to do with the noble ancient art of Earth Measuring or its classic logical method. Such is public education in our times. At least my innumerate friend was right about never having studied it; she went to the same high school and probably studied the same book.
Somewhere in some defense of the Great Books program, Mortimer Adler uses Euclid as his prime example: why study geometry from anyone but the classic master? Not foreseeing our local school district's advanced policies, Adler didn't know he had to defend the study of geometry itself. But assuming that I want to study actual geometry rather than guessing at equations, Adler's advice isn't all bad. For a high-school class or a first introduction to the subject, Euclid's Elements would need a little page-layout makeover, some extra notation on the diagrams, and a workbook of exercises, but otherwise it would work perfectly. Its topics are immaculately organized, and the presentation is almost always crystal clear, although Thomas Heath's century-old translation could use a little polishing and updating.
Reading Euclid gives me an audience in the court of brilliance. He nimbly juggles a variety of ways of approaching a problem, for instance. Some proofs he conducts by straight deduction from the premises, some by first making a construction and then making deductions. At other times, he poses a counterhypothesis and then argues the reductio ad absurdum. If you're in the mood for it, the slowly building procession of theorems can have the exciting effect of a mystery novel's plot: some parts may at first seem random (although entertaining), but by the end of any given book, each element plays its part in the drama of the whole. The first time I read book 1, as I reached the last demonstration, proving the Pythagorean Theorem, I had the feeling the classic philosophers speak of when they say that contemplating such truths gives us a glimpse of God's mind -- the most powerful instance of this sensation I've ever experienced. For a moment I saw the whole edifice, from its foundation in a handful of axioms to its cupola of right triangles and squares, and I felt my mind lifted from some earthly burden I hadn't even noticed before.
The portion on my schedule for this year, bk. 6, deals with similar triangles and other similar polygons. Similar figures have equal angles and proportional sides, so before dealing with these figures, Euclid had to cover proportionality of line segments, the subject of book 5. Last year, I went a long way through that book writing my notes in something like algebraic notation (If a > b, a:c > b:c and c:b > c:a, for instance) and wondering why it took Euclid so many words and pictures to say the same thing. I'll have to check with my friend Kerry, a science historian, but I think I only got it right when I finally realized that Euclid "measured" (at least mentally and abtractly) these line segments as magnitudes, not as quantities, in other words, not as numbers in the way we'd think of them. I think it was Descartes who first worked geometry by numbers and arithmetic.
If anybody can help me out on this, please share. Right now, I understand just a few differences between Euclid's view and ours. First, I think of ratios as convertible with fractions: a:c > b:c is true if and only if a/c > b/c. But I don't believe Euclid had knowledge of fractions or worked with them. From my study of the history of music theory, I know writers dealing with string lengths use only ratios of whole numbers until the seventeenth century. In ancient thinking, 1 cannot be divided. It is unity, an atom. How can you have half of a person or half of a hole? Numbers start with 1 and go up. Magnitudes, on the other hand, can be divided, perhaps indefinitely. Another difference is that without thinking of the magnitudes as represented by some particular number, Euclid can have "ratios" involving sides of "irrational" length, as for instance between one side of a square and its diagonal.
My high school may have done English and history all wrong, but they did mathematics right. I loved learning geometry, and I've often made use of both its content and its logical method ever since. Now I enjoy studying it all over again with Euclid. This year, I'm again inspired by Euclid's creative intelligence and by the beauty of the material, yet I'm also thankful again for Descartes and fractions.
I assumed she didn't even remember what she had forgotten until one day a few years later when I was helping another friend's son with his homework. He asked the group of adults a question about an equation to express a series, and they all looked at me, so I looked at his book to see what I could contribute. But the book gave no instructions on how to find the equation; we were left to the mercy of trial and error. Frustrated, I looked at the cover so I could at least know the names of the authors I was angry with, only to receive a shock upon seeing the title: Modern Geometry. I flipped through the book looking for axioms, for proofs, for inscribed polygons, but I found none of these things. One chapter gave the formulas for areas of various plane figures, but otherwise, the book had nothing to do with the noble ancient art of Earth Measuring or its classic logical method. Such is public education in our times. At least my innumerate friend was right about never having studied it; she went to the same high school and probably studied the same book.
Somewhere in some defense of the Great Books program, Mortimer Adler uses Euclid as his prime example: why study geometry from anyone but the classic master? Not foreseeing our local school district's advanced policies, Adler didn't know he had to defend the study of geometry itself. But assuming that I want to study actual geometry rather than guessing at equations, Adler's advice isn't all bad. For a high-school class or a first introduction to the subject, Euclid's Elements would need a little page-layout makeover, some extra notation on the diagrams, and a workbook of exercises, but otherwise it would work perfectly. Its topics are immaculately organized, and the presentation is almost always crystal clear, although Thomas Heath's century-old translation could use a little polishing and updating.
Reading Euclid gives me an audience in the court of brilliance. He nimbly juggles a variety of ways of approaching a problem, for instance. Some proofs he conducts by straight deduction from the premises, some by first making a construction and then making deductions. At other times, he poses a counterhypothesis and then argues the reductio ad absurdum. If you're in the mood for it, the slowly building procession of theorems can have the exciting effect of a mystery novel's plot: some parts may at first seem random (although entertaining), but by the end of any given book, each element plays its part in the drama of the whole. The first time I read book 1, as I reached the last demonstration, proving the Pythagorean Theorem, I had the feeling the classic philosophers speak of when they say that contemplating such truths gives us a glimpse of God's mind -- the most powerful instance of this sensation I've ever experienced. For a moment I saw the whole edifice, from its foundation in a handful of axioms to its cupola of right triangles and squares, and I felt my mind lifted from some earthly burden I hadn't even noticed before.
The portion on my schedule for this year, bk. 6, deals with similar triangles and other similar polygons. Similar figures have equal angles and proportional sides, so before dealing with these figures, Euclid had to cover proportionality of line segments, the subject of book 5. Last year, I went a long way through that book writing my notes in something like algebraic notation (If a > b, a:c > b:c and c:b > c:a, for instance) and wondering why it took Euclid so many words and pictures to say the same thing. I'll have to check with my friend Kerry, a science historian, but I think I only got it right when I finally realized that Euclid "measured" (at least mentally and abtractly) these line segments as magnitudes, not as quantities, in other words, not as numbers in the way we'd think of them. I think it was Descartes who first worked geometry by numbers and arithmetic.
If anybody can help me out on this, please share. Right now, I understand just a few differences between Euclid's view and ours. First, I think of ratios as convertible with fractions: a:c > b:c is true if and only if a/c > b/c. But I don't believe Euclid had knowledge of fractions or worked with them. From my study of the history of music theory, I know writers dealing with string lengths use only ratios of whole numbers until the seventeenth century. In ancient thinking, 1 cannot be divided. It is unity, an atom. How can you have half of a person or half of a hole? Numbers start with 1 and go up. Magnitudes, on the other hand, can be divided, perhaps indefinitely. Another difference is that without thinking of the magnitudes as represented by some particular number, Euclid can have "ratios" involving sides of "irrational" length, as for instance between one side of a square and its diagonal.
My high school may have done English and history all wrong, but they did mathematics right. I loved learning geometry, and I've often made use of both its content and its logical method ever since. Now I enjoy studying it all over again with Euclid. This year, I'm again inspired by Euclid's creative intelligence and by the beauty of the material, yet I'm also thankful again for Descartes and fractions.
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