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| Saturday, May 18th, 2013 | | 1:40 pm |
Third run of 2013
I went for a pleasant run this morning, but my performance is flat. Once a week is just not enough to make any progress. I did seven miles in 83:01, essentially exactly what I did two weeks ago. I have to get out more often. | | Sunday, May 12th, 2013 | | 10:12 pm |
First and second runs of 2013
Last Sunday (May 5) I did my first full outdoor run of seven miles this year at Paul Bartlett Track. (The commemorative sign is gone, so perhaps the track is becoming anonymous.) A week before that, I had done a trial run, but various bits of muscle soreness prompted me to keep it to six miles, and I didn't post about it. Last Sunday I felt much better, and was able to finish the run in 83:00, a poor time for me but typical of first runs after a furlough. Yesterday morning I did my second run. I had waited six days, still being cautious about my back and knee, but I still had a modest improvement to 81:47. I'll keep monitoring the soreness to decide when to run next. | | Sunday, April 28th, 2013 | | 9:15 pm |
More Les Misérables blogging
I'm still plugging away a Victor Hugo's Les Misérables. I shouldn't say it that way, because I am enjoying the novel, but ma-a-a-an is it lo-o-o-o-ong. I should have realized that Father Madeleine was Jean Valjean way earlier. Almost every mysterious male character in the novel turns out to be Jean Valjean. Hugo is still writing like he has all the time in the world. An entire book, nineteen chapters, about 50 pages, is devoted to a careful, detailed recounting of the events of the Battle of Waterloo. I now know more about the battle than I did, but I can't say that it forwarded the plot. The single incident that ties the battle to the story is told briefly in (Volume 2, Book 1) Chapter XIX, and could have been told with much less background. But Hugo wanted to talk about Waterloo. He reminded me of Tolstoy, who was similarly obsessed with Napoleon, and had to natter on about him endlessly, inflating War and Peace by about 40%. All that having been said, the stuff Hugo had to say about Waterloo was interesting, so I think I'm just complaining because it's fun to complain. | | Saturday, April 13th, 2013 | | 3:04 pm |
Les Misérables blogging
I've been reading Victor Hugo's Les Misérables for about six days, and I have a few comments. The book is long because Hugo is an extremely self-indulgent author. As long as he has your attention, he feels free to write in a fashion that I may call "generous" or "expansive"; it is written, as it were, in extremely low gear, spending enormous amounts of ink to advance the story very, very slowly. As when a car is in low gear, it moves slowly but irresistably, the story is accumulating a certain amount of glacier-like force. It's hard to tell whether it will pay off. The book is divided into parts, which are divided into books, which are divided into shortish chapters. I am still in the first part, and have just started the fifth book. So far, only the second book has been devoted to Jean Valjean, who I understand is supposed to be the main protagonist. The first book is pure character development for Monseigneur Bienvenu, whose function in the second book was only to be a moral safety net for Jean. Then that story is set aside, and the third book is completely devoted to introducing Fantine and getting her into difficulty; the short fourth book just gets her in deeper. So far, the fifth book is mostly about yet another character, a philanthropic business genius who sets up shop in Fantine's home town, and revitalizes the whole place. I assume that we will get back to Fantine soon, but as self-indulgent as Hugo is, we may spend the entire fifth book on Father Madeleine. Hugo loves to set the scene by describing things that are happening in history that are contemporary with the story (which so far has taken place mostly in the years 1815-8, not counting flashbacks). But his descriptions are allusive. "This was the summer that so-and-so was the talk of Paris." Unless I already know what so-and-so was famous for, this technique does nothing for me -- and I usually don't. The book would really benefit from a bit of scholarly apparatus: an introduction explaining the major events of the relevant piece of French history, and footnotes explaining who various offhandedly-mentioned personalities were. It is lucky for me that most of this historical detail isn't necessary for understanding the story, but I'm sure I would understand it better if I had the background. I'm just under an eighth of the way through. | | Saturday, April 6th, 2013 | | 2:07 pm |
Venus re-enters the evening sky, in theory
On March 28, Venus slipped behind the sun, moving from west to east, and became the Evening Star again. I think I missed blogging the last time this happened, about 583 days ago. I haven't seen the planet yet; it's still very close to the sun. Probably at sea in very clear weather somebody with sharp eyes who knew exactly where to look might be able to spot it. It would be very close to the horizon, just to the left of the sunset point. I'll be looking for a glimpse over the next few weeks. | | 2:01 pm |
Project Gutenberg etext #134: Maria: or, The Wrongs of Woman
The day before yesterday I finished reading Mary Wollstonecraft's incomplete didactic novel Maria, published in 1798 after the author's death. Her husband, William Godwin, edited the manuscript and prepared it for publication. We have about half the novel, plus very sketchy notes about the conclusion, but the didactic work seems complete. I would like to know more about what happens to the characters, I suppose. The structure of the novel is interesting. We find Maria unjustly imprisoned in a private insane asylum; she manages to gain the confidence of her keeper, an embittered woman named Jemima. The bulk of the narrative consists of stories told by the characters to each other about their various pasts. Jemima tells Maria her story; then Maria reciprocates, but embedded in Maria's story, one of Maria's landladies tells Maria hers. All these stories are about how men take advantage of women, and all are horrible but plausible. Wollstonecraft's style is quite similar to her daughter Mary Shelley's. In particular, Jemima's story has a texture that closely resembles the monster's narrative that forms the core of Frankenstein. In the mother's novel, though, women are the wronged, outcast monsters. I've started in on the next etext, and again I know what I will be reading for the next month or so: Victor Hugo's Les Misérables. Perhaps I will give "progress reports" on this one. | | Saturday, March 30th, 2013 | | 6:18 pm |
Project Gutenberg etext #133: The Damnation of Theron Ware
Until I started reading it, I had never heard of either the 1896 novel The Damnation of Theron Ware or its author, Harold Frederic, who seems to have been an interesting character himself. I found the novel confusing (at first) for a reason that is actually a little embarrassing; I didn't know at first what I was supposed to think about its eponymous protagonist. Ware is a young, married Methodist minister, who is dismayed to be assigned to a rural New York congregation. He starts out as very idealistic and devout, but he has a weakness of character that allows him to be absurdly easily corrupted; his soft spot is his desire to seem admirable to people he admires. He meets some intellectual free spirits in his assigned town, and is so taken by them that he remakes his entire personality on a model which he imagines (mistakenly) that they would approve. In doing so he tries to betray his blameless wife, and only misses doing so because his would-be mistress slaps him down. She is one of the people he had remodeled himself for. For the whole novel one gradually comes to hate the man more and more, though he is shown as sympathetically as possible; when he finally gets humiliated near the end, it's hard not to cheer. It must be a difficult authorial task, to write a non-virtuous protagonist like that. We happily and without conflict cheer the victories and mourn the setbacks of virtuous protagonists, but with a book about a cad the reader's situation is more confused. If the author makes the character too unsympathetic, the reader will just root for the protagonist's failure, and thus not be very invested in the story. Frederic, I think, errs on the other side, so the reader sometimes doesn't know whether the author wants the reader to consider Ware's actions vicious. This problem goes away as the book becomes less ambiguous in its second half, but it did make a rocky start for me. One throwaway comment did catch my attention: Dr. Ledsmar tells Rev. Ware of a book Ledsmar wrote about serpent-cults; Ware asks to read it but Ledsmar disappoints him by explaining that the book is in German. There was an English translation, but the tiny printing was sold out to "collectors who bought it for its supposed obscenity, like Burton's Arabian Nights". I don't doubt such collectors existed, but I suspect they would have been disappointed by Burton's Nights; imagine buying sixteen hefty volumes just for a dozen or so pages of not-very-arousing porn. I blushed a little when I read Frederic's characterization, even though that's not why I bought my copy of the Nights. Etext #134 is Mary Wollstonecraft's Maria; or the Wrongs of Woman, an unfinished novel published in 1798 after the author's death. I was confused between Mary Wollstonecraft and her daughter, Mary Wollstonecraft Shelley, the author of Frankenstein; I mention this so you won't be. Wollstonecraft was an influential "zeroth-wave" feminist, of whom I had never heard. Project Project Gutenberg is making me fractionally less ignorant. | | Saturday, March 16th, 2013 | | 10:51 am |
Project Gutenberg etext #132: The Art of War
The Art of War is a document purportedly from about 500 B.C., written by the military advisor to the king of one of the many small states that tiled China at that period. There is an enormous amount of folklore surrounding Sun Tzu (modern spelling Sunzi) and his famous work; The Art of War has accreted the usual layers of learned commentary from all periods of history from its composition to the present. As is usual with ancient documents, the text itself is corrupted in places, and a lot of the commentators came to differing conclusions about some of the difficult passages. I wrongly asserted that the translation was by Herbert Giles; it was by Herbert's son Lionel, and was published in 1910. The core text itself is very brief, but it is "Fisked" with the translator's comments, including translations of a lot of the traditional commentary; this surrounding material is often more interesting than the gnomic central content. In particular, the commentators often give anecdotes from Chinese history that illustrate the validity or correct interpretations of Sun Tzu's dicta. These stories are refreshingly human and humane, in contrast to the old general's dry strategic advice. The main impression left with me is how ignorant I am of Chinese history. I could probably entertain myself for the next thirty years studying this monumental subject. However, etext #133 is not more Chinese literature, but rather a novel I've never heard of, The Damnation of Theron Ware, by an author I've never heard of, Harold Frederic. Apparently it dates from 1896, and at least so far, it is about a young Methodist minister. | | Sunday, March 10th, 2013 | | 4:16 pm |
Screen ding on my digital reader
Sometime in the last couple of days my Nook electronic reader suffered an impact of a small hard object (a belt buckle? a coin?) against the screen, and there is now an unremovable defect there, a little gray smudge. I don't think it's so annoying that the machine is unusable, but Dr. Wife warns me that such defects can spread. This reader is about eight months old; I think it was purchased in mid-June of 2012. | | Wednesday, March 6th, 2013 | | 10:46 pm |
Project Gutenberg etext #131: The Pilgrim's Progress
John Bunyan's The Pilgrim's Progress was published in 1678. It was followed by a sequel in 1684, which in some editions is included as a second part; but this etext has only the original work, not the extension. As far as I can tell, Project Gutenberg didn't get around to the Second Part until it published an edition of Bunyan's collected works as etexts 6046-6049, so it's unlikely that I will read it as part of Project Project Gutenberg. The Pilgrim's Progress is an early, seminal example of English allegorical literature, but as allegory it struck me as clumsy and amateurish. An allegory teaches its readers about some set of concepts by representing those concepts as characters, places, or things, whose interactions parallel the way the real-world concepts interact. So an allegory has two distinct levels: the conceptual "payload", and the dramatic representation. In The Pilgrim's Progress, the concepts are the principles of Christianity, the obstacles to salvation, various states of human existence, and so on. The characters and places in the story are mostly given transparent names which serve as a key to the representation scheme: Christian, Hopeful, Talkative, Despair, and the like. The clumsiness comes from not keeping the levels clear. The later dialogues between Christian and Hopeful are just sermons, without any allegorical dramatizations at all. The last third of the book also suffers from an odd change in Christian's character; he turns from a seeker into a preacher, and the change isn't gradual or motivated by anything, but it's just as if one Christian was replaced by another. It's not consistent; the two personalities jostle through the whole lead-up to the end. A lot of the middle of the book is taken up with the "works versus grace" issue, which I've talked about in these pages before, when I was reading the New Testament. Bunyan presents characters who profess extreme sides of the debate, and tries to draw a medium between them, but to my mind he favors grace and scants works. Anyway, it was an interesting thing to read, and another little window on a fascinating period of history. Now I have started etext #132, a translation of Sun Tzu's Art of War by one of the founding Western sinologists of the modern era, Herbert Giles. I've never read any Chinese literature before, and I'm wondering what it will be like. | | 9:41 pm |
Even more Dr. Wife health adventures
About two weeks out from her appendectomy, Dr. Wife's trend of slow improvement reversed, and she started feeling less comfortable. It was hard for her to describe exactly what she was feeling, but there was definitely something not right, and she had one episode of fairly intense pain. We didn't call in, because she was coming up on her two-week followup appointment with the surgeon. That happened yesterday, and the surgeon sent her right back to the ER for another scan. The scan revealed a fluid-filled pocket which they thought at first was an abscess (filled with pus), but when they actually stuck a tube into her to drain it, they discovered that it was a hematoma (same thing, but filled with blood). All the blood was old, probably from internal bleeding immediately after the operation. In hindsight we know when that was, because she was displaying some symptoms of anemia over those first few post-op days. After they put in the drain, and as soon as she shook off the effects of the contrast fluid and the painkillers, she felt much better, and is home again after a night in the hospital. We expect an uneventful recovery, this time for sure. | | Tuesday, February 26th, 2013 | | 10:31 pm |
Two epigraphs from A Pilgrim's Progress
As I've explained, I've just started reading John Bunyan's Christian apologetic allegory, A Pilgrim's Progress. The body of the book is in prose, but the book opens with a verse prologue, The Author's Apology for his Book. (It might help some to be reminded that the word apology used to mean something a lot closer to the modern excuse or defense.) This prologue supplied two very different authors with epigraphs for two very different books, both of which I have read, and I remembered the excerpts; it was amusing and interesting to see them in their original context. The one my readers are more likely to have seen was used by the quirky author Mervyn Peake to raise the curtain on his very weird gothic fantasy, Titus Groan, the first book of the Gormenghast trilogy. It is from near the end of Bunyan's apology, where he is encouraging (or shaming) his reader to choose spiritual over worldly reward (and, incidentally, to read his book): Dost thou love picking meat? Or wouldst thou see
A man in the clouds, and hear him speak to thee? (In Bunyan's defense I must note that "in the" was, in his time, often pronounced as one syllable, as "i' th'", rhyming with "with". In this case, the scansion requires this pronunciation.) I've always liked the couplet, though I'm still puzzled at what Peake thought its application to Titus Groan was; the book is pretty much all meat-picking, with no cloud-men to be seen. When I was getting to know Dr. Wife, I was charmed to learn that she had used this as her epigraph in her high-school senior yearbook; she also saw it in Titus Groan, and like me, had not read Bunyan. The other epigraph was chosen by the quirky mathematician John Horton Conway; at least one of my readers will have heard of him because he invented the cellular automaton called "The Game of Life", not to be confused with the board game about suburban domesticity. Conway has done a lot of cool work. The book he was introducing described a breakthrough in combinatorial game theory, not to be confused with the probabilistic game theory worked out by beautiful mind John Forbes Nash, among others. Conway's book was called On Numbers and Games; it's famous enough to be commonly acronymized as ONAG. It's as entertaining as a scholarly math book gets, idiosyncratic, dense, and full of creative notation and nomenclature, as well as deeply original content. It's an unusual enough work that the epigraph Conway lifted from Bunyan has exactly the same meaning in its new application as in its old: Some said, John, print it; others said, Not so;
Some said, It might do good; others said, No. | | 6:00 pm |
Project Gutenberg etext #130: Orthodoxy
I have never read anything by G. K. Chesterton before, but I've been reading his name in other works for my whole reading life. Martin Gardner admired Chesterton's work, and produced a couple of his classic "annotations" for Chesterton originals. Chesterton lived from 1874 to 1936; H. G. Wells and George Bernard Shaw were contemporaries. Orthodoxy appeared in 1908. I'm fairly conflicted about Orthodoxy. There is no question that Chesterton is engaging, interesting, and inventive. I think the best adjective for him is "jovial". I enjoyed the actual reading process thoroughly; I liked Chesterton's word-sense, his playful tone, his clear and deep humanity. On the other hand, Chesterton wrote Orthodoxy to explain why he is a Christian, something I emphatically am not. Was he going to succeed in converting me? I hardly thought so (and indeed, in the event, he didn't), but I wondered where such an evidently intelligent and able thinker would part company from me. Chesterton provided part of the answer at the very beginning. The book is not, he insists, an "argument" intended to convince someone who isn't a Christian to become one. Rather, it's a spiritual autobiography, an account of how he came to believe as he did. In this it succeeds admirably, and in fact I can now point to the difference in personality between me and Chesterton that adequately explains how two reasonably intelligent people living in the same world can come to two such very different conclusions about it. Perhaps it was, then, my fault that I found Orthodoxy so infuriating. I came in with a chip on my shoulder. I would love some publisher to pay me to quit my job and write a Gardneresque "annotation" of Orthodoxy. Every single page had something that I was itching to answer. I will try to keep this post to a reasonable length, but the urge is strong to go back to the beginning and start Fisking the entire thing in detail. The majority of the text boils down to, "If we got to choose which cosmos to live in, the Christian cosmos is the best." People who disagree with Christian tenet W, you see, must believe X and Y instead, from which it is inescapable to conclude Z, and how unbearable life would be if Z were the case! There are a lot of ways such a line of reasoning can fail, but the central problem here is that unpleasant, undesirable, unbearable are, none of them, synonyms for false. Even were I to grant what Chesterton presents as the necessary dreadful and nightmarish psychological sequelae to, say, skepticism about free will, that would not constitute a demonstration that free will exists. Chesterton, to give him credit, does get around to addressing this problem in his last chapter, but the positive arguments he makes about why it is reasonable and rational to believe in miracles and the supernatural are both obsolete and naive. They are obsolete because the book was written in the middle of an unfortunate period in the history of science, in which a small number of charlatans had succeeded in convincing some influential scientists that certain supernatural phenomena (most often, communication with the dead) were possible. It took a painful couple of decades for science to catch up and realize that it had been duped, and Orthodoxy was written exactly in this retrospectively-embarrassing window, the only time it was at all tenable to claim that Science as a whole was moving toward the supernatural rather than away from it. Chesterton's pro-miracle arguments are naive, on the other hand, because his evidence is completely composed of people's claims to have had supernatural experiences. I find it easy to believe that 100% of such accounts are explained by outright deception, desire for attention, delusion, misinterpretation, and ignorance; Chesterton thinks my view insulting to a vast majority, and is willing to stand by the common man as the common man describes his encounter with the ghost of Aunt Sally. In fairness, even if my explanations only explain 99% of putative miracles, Chesterton still wins. I would probably need to write a book at least the length of Orthodoxy to explain why I'm so confident that I can dismiss all such claims. I referred above to a lot of places that Chesterton's preferred dialectic can fail. The most notable is the straw man argument. Chesterton repeatedly constructs opposing views in order to knock them down, but he frequently makes his opposition, I couldn't help thinking, purposely weak and idiotic. This was most enraging when he was attacking Darwin's theory of evolution. He never engages with the theory proper, and even gives the central core of it a brief pat on the back in an early chapter, saying that's not the part he's at odds with. But for the rest of the book, evolution surfaces repeatedly as a stalking-horse, and always as a distorted one. If one believes in evolution, one must believe X, except, I found over and over, I do believe in evolution and don't believe X. Maybe Darwinists believed X in Chesterton's time, but I think it more likely that Chesterton was engaged with some distorted popularizations and not with the thing itself. I am glad Project Project Gutenberg had me read Orthodoxy, and look forward to reading more Chesterton, especially the famous Father Brown mysteries. I think I get some of those in the early 200s. Apparently February is Christian Apologetics Month here at Project Project Gutenberg, and I have now begun John Bunyan's renowned Pilgrim's Progress. I think I tried and failed to read this once when I was a kid. The English is much more modern than I remembered; it even seems noticeably more modern than Milton, and Paradise Lost is a bare decade older. Bunyan definitely belongs to the period of intellectual ferment in England surrounding the Interregnum and the Restoration; Isaac Newton, John Milton, and Andrew Marvell are some other names from this era. | | Sunday, February 17th, 2013 | | 10:06 pm |
Project Gutenberg etext #128: The Arabian Nights
Project Project Gutenberg is not my first ambitious and silly reading project. Some time in the late 1980's I was visiting my older sister in Ithaca, New York, and took a chance to browse used bookstores. I wound up making a purchase that was much more extensive than I expected: around $400 for a complete set of Richard Francis Burton's famous translation, The Book of a Thousand Nights and a Night, subtitled Alf Laylah Wa Laylah. This translation was reprinted several times, mostly in private subscription runs (because Burton refused to expurgate sexual and scatalogical content), and the publication info is not well-marked, but I think I have the 1900-1901 American edition. In the summer of 2001 I decided that if I owned them I might as well read them, and found, from the fact that I had to slit lots of uncut pages, that I was this copy's first reader. Getting through all sixteen volumes took about eleven months. Burton was a quirky guy, and his translation was intended to give the English-speakers a real feel for Arabic storytelling prose. His own English is fairly elaborate, and when trying to convey the flowery narrative style of the original Nights, he really went overboard, ransacking archaic vocabulary so that he could provide alliterative phrases wherever there was alliteration in the Arabic. (One I remember is "cark and care" to express extreme anxiety.) Some of it was tedious but overall I enjoyed the experience. The Nights themselves are almost more of a genre than a unitary work. I've written about this kind of thing before, when I read Aesop's Fables. The outer formal structure of the Nights is perfect for framing almost arbitrary anthologies of tales. The framing-story seems to have been borrowed into Arabic in the early 8th century, and in the centuries following, this gripping story of Princess Sheherazade telling stories by night, literally to save her life, became a set of bookends for an ever-growing, ever-more-comprehensive collection of stories, until there really was enough material that it became plausible that it represented a thousand and one nights of storytelling. Furthermore, this initial device of stories nested inside stories is repeated throughout the Nights, so that at one point there are as many as half-a-dozen different layers of stories "on the stack". Burton conveys this structure into English exactly as he found it in the manuscripts he worked with. The Nights were introduced to Western Europe in the early 1700s, with Antoine Galland's French translation. Galland didn't try to be comprehensive, and he left out material he thought would be considered objectionable. The 200-page version I just read was compiled by Andrew Lang in the 1890s, mostly from Galland; I don't know how much of the wordsmithing is actually Lang's. I have already noted that the Aladdin translation was done by Violet Hunt. Lang's Nights sacrifices many stories and a lot of the nested structure, never going more than two layers deep, and drops all the sex and the dirty jokes. Many framing-stories, including the main one, retain only their beginning; the triumphant ending of the Sheherazade story is completely missing, leaving us hanging about Sheherazade's fate. Lang's English is much easier and more familiar than Burton's though. Etext #129 is a million digits of the square root of 2, which I am passing on. Now I have started etext #130, G. K. Chesterton's Christian apology, Orthodoxy. I've never read any Chesterton before. | | 8:40 pm |
More Dr. Wife health adventures
On Friday Dr. Wife started to complain about abdominal pain; she thought she was constipated. But the pain kept her up almost all of Friday night, and Saturday morning we called the health center. The fact that the pain was now focused on the right side of the lower abdomen was absolutely classic appendicitis sign, and the weekend triage nurse at the clinic said we should go straight to Mt. Auburn Hospital's ER. We got to the ER at about 10, and were seen by a triage nurse within the hour and given a room in the emergency part. Dr. Wife had to drink a contrast liquid, and then after about two more hours she got a CAT scan. Sure enough, it looked like the appendix. The next few hours were very unpleasant for her, because the contrast liquid is fairly vile stuff once it's inside you, and in addition to vomiting and diarrhea it gave her a bad headache. Weirdly, the IV Dilaudid they gave her knocked the belly pain right out, but did almost nothing for the headache. The day dragged on very slowly. We sat around in the ER roomlet playing smartphone games (though Dr. Wife had to stop when the headache got bad), and after receiving several visits from medical persons and answering exactly the same history questions every time, we finally got to talk to a surgeon who said she would take out Dr. Wife's appendix sometime Saturday evening. Then they checked Dr. Wife into a real hospital room, and we waited for our turn. It was a very busy day there, and they only got Dr. Wife into the operating room at about 10 pm, but after that things went fast; the surgery was over in about an hour, and went completely perfectly; they were able to complete it laparoscopically, with three tiny incision-holes; there won't be that classic vertical scar. Dr. Wife spent the night at the hospital, and this morning her blood pressure was low enough that she had trouble standing up, so they kept her the rest of the day and boosted her with IV fluids and two meals. Finally she was discharged around 6, and we came home. Pain is already less than it was before the surgery. We're glad she's home. | | Sunday, February 10th, 2013 | | 10:15 pm |
The number e
For some reason I find myself in a math-splainy mood. I mentioned the mathematical constant "e" in my previous post, and decided to give an account for laypeople of this famous number. Because it's overshadowed by the even more famous pi, many people haven't heard of it. I'll put the rest of the explanation behind a cut to save space on your friends-page.
Most high-school graduates can give the first few digits of pi (3.14159...), and many can even say what this famous number means: you take a circle one meter in diameter, and when you measure the circumference you will get exactly pi meters. Although pi seems to be "about" circles, it turns up in bizarre places in math that, at first glance, seem to have no circle-ness about them whatsoever. This spooky pervasiveness is what makes pi so interesting.
But very few people who haven't particularly studied math can even say approximately how big e is, even though this number, like pi, turns up all over the place in mathematics. I won't keep you in suspense: e is between 2 and 3, rather closer to 3 than to 2; to five digits accuracy it's 2.71828....
Pi and e have many things in common: they are both irrational numbers, which means that they are not exact integer fractions; no matter how big you make the denominator, you cannot capture either pi or e as a fraction. This is equivalent to saying that when written in decimal notation, pi and e both go on forever without repetition: in fact, the digit strings for both look completely random. Both numbers are known to be transcendental, which is a kind of super-irrationality. (Rational numbers are the solutions of first-degree integer polynomial equations; algebraic numbers are the solutions of polynomial equations of any degree; and transcendental numbers fail to be algebraic.)
OK. If pi is about circles, what is e about? It's a little hard to answer, partly because e, like pi, turns up in so many unexpected places. But one possible answer is that e is about exponential growth. The easiest way to think about this is to consider compound interest.
Suppose you have a bank account earning 4% interest per year. (I know, dream on.) If you deposit $100 on your birthday in 2013, and then empty the account on your birthday in 2014, you'll have $104; the bank is paying you four cents on the dollar for the privilege of getting to invest your money for a year. But what if you take your money early? Do you get any extra money? It depends on the exact rules of the account. If it says, "interest compounded yearly", then you get no interest until the bank has had your money for a whole year. But many accounts say "interest compounded quarterly", which means that instead of giving you your four cents on the dollar at the end of the year, they give you one cent on the dollar every three months.
This is a better deal for you than yearly compounding. Not only do you get some gain if you have to take your money out early, but after a year you have more money with quarterly compounding. To see why, we have to run the numbers. You deposit $100 on your birthday. Three months later, the bank pays you one cent on the dollar; this comes out to a whole extra dollar, so now you have $101. Three months after that, the bank again gives you one cent on the dollar. Since you now have $101 dollars, the bank pays you 101 cents, or $1.01. So after six months you have $102.01. Three months after that, the bank again gives you a cent per dollar; neglecting fractional cents this comes to $1.02, so you now have $103.03. Finally, on your birthday in 2014, they pay you $1.03, and you finish the year with $104.06. I know that was a lot of arithmetic to go through, but the bottom line is that quarterly compounding got you an extra six cents over the whole year. What they call the effective interest rate is 4.06% instead of only 4%.
Quarterly compounding is also fairer than annual compounding. Even having your money for one day benefits the bank; the world of high finance is full of things like enormous overnight loans, and the prices of financial assets fluctuate from day to day, so a canny trader is trying to make money constantly, from hour to hour. Maybe it would be fairer for the bank to pay you one 365th of the yearly interest every day? How much benefit would that give you? I just did the math so you don't have to: daily compounding would turn your $100 into $104.08 in a year. You get eight cents extra on a hundred dollars with daily compounding; the advantage over quarterly compounding is two cents on a hundred dollars. Maybe it's not as much as you expected. Even compounding every second gives only a tiny extra advantage over that.
Now we have to make a leap, and without making you sit through several weeks of class you'll have to take my word for it that the leap is justified. With the magic of calculus, we can create an account in which interest is compounded continuously. You would think that this would get you an infinite amount of interest: after all, the interest is paid to you an infinite number of times. But fighting with this is the fact that the amount of interest given with each award has shrunk to an infinitesimal amount. Who wins, the infinity, or the infinitesimal?
To make matters simpler mathematically, imagine that the interest rate is a whopping 100% per annum. Again you deposit $100 on your birthday. With annual compounding, you walk away next year with $200. With quarterly compounding, you would get $244.14. With daily compounding, $271.45. And with continuous compounding ... will it be infinite? No. The answer is perhaps counterintuitive, but with continuous compounding you walk away with $271.83 minus a couple of tenths of a cent.
We have set up a situation where we have a quantity whose growth rate is equal to the quantity itself. After one time unit has passed, such a growing quantity will always be found to have increased by exactly the same ratio: 2.71828... to 1. This ratio is the number e. It is one greater than the effective interest rate of a bank account that pays 100% per year, compounded continuously. (The effective interest rate is 171.828...%, but you get back your original investment too, so your money has grown by a factor of e.)
Continuous exponential growth is a situation that comes up frequently in mathematics, and every time it does, you can expect e to turn up in the analysis. (The effective interest rate of an account paying 4% per annum, compounded continuously, is e raised to the power of 4%, minus 1.)
Computing e is surprisingly easy. The classic procedure is to start with 1, add 1, add 1/2, add 1/6, add 1/24, and so on: the denominators of those fractions is calculated by starting with 1 and multiplying by 2, 3, 4, and so on, so the next fraction to add is 1/120, because 24 times 5 is 120. This procedure gives a very close approximation to e after very few steps. It is intriguing that nobody has been able to find a procedure that is so inexpensive for calculating pi; e seems to be intrinsically easier to calculate than pi, though no one has succeeded in proving this; it's an open mathematical question and if you could settle it you would be famous in the mathematical world.
I mentioned that e comes up in surprising places, so I'd like to conclude with a little story to illustrate the weird places that e tends to hide. The story is true in outline, though I never knew most of the details, so I will have to tell it vaguely. There was a television program on which a man who was skeptical of astrology issued a challenge to an astrologer. The astrologer would be presented with a panel of twelve volunteers, each of which was born under a different sun sign, so the panel would contain one Aries, one Taurus, one Gemini, and so on around to Pisces. The astrologer claimed that the birth sign affected the personality in ways that a trained astrologer could detect; he thought that given time to interview the panel, he could correctly assign each panelist to their proper sign. This was a very strong claim, and the skeptic agreed that if the astrologer could do that without chicanery, the skeptic would have to admit that there was something to astrology. (The claim was strong because the odds of getting all twelve signs right by blind chance is a smidge better than 1 in 480 million.)
The astrologer was given all the time he wanted to interview the panel, and finally wrote down his guesses on cards which were handed face down to the panelists. The panelists were instructed to turn over their cards and stand up if the astrologer's prediction was correct. With appropriate dramatic flourish, the panelists turned over their cards and every one remained seated. The astrologer had failed as badly as it was possible to fail, assigning every single panelist to the wrong sign.
That's the end of the story proper, but any moderately curious person might think, "Hey, getting every single one wrong is sort of unlikely too, isn't it? Wouldn't one expect the astrologer to have gotten one or two right, just by luck?"
If there were only two people on the panel, the odds of getting both signs wrong would be 1 in 2. If there were three people on the panel, the odds would be 1 in 3. If there were four people, the odds would be 3 in 8, or about 1 in 2.667. As the number of people goes up, the odds settle very quickly to about 1 in 2.718; some mathematical sleight-of-hand reveals that the limiting odds are exactly 1 in e. (For twelve panelists, the odds differ from this ideal by only a few parts per billion.)
So yes, it's a bit unlikely to get them all wrong, but no supernatural explanation is needed for something that would happen about one time in three by chance. (If an astrologer could get them all wrong for, say, ten successive panels, then I would have to agree that maybe there was something weird going on.) But I think you will agree that it is odd to see e pop up in this question about probability. And that's just the beginning, but the deeper ubiquity of e (and the utterly gobsmackingly beautiful deep connection between e and pi) are way beyond my scope.
| | 11:33 am |
Project Gutenberg etext #126: The Poison Belt
Arthur Conan Doyle introduced Professor Challenger in his 1912 novel The Lost World. 1913's The Poison Belt is the second Challenger story. Although Challenger was clearly intended to contrast with Sherlock Holmes, there are points of similarity as well. Both are formidable intellects, with poorly-disguised disdain for the lesser minds that surround them, and Challenger's condescending manner of speech reminded me a lot of Holmes's. The contrasts are mostly material: Challenger is a big, hairy, powerful guy, living in luxury with his wife in the country, while Holmes is urban, solitary, thin, and mostly ascetic in his habits. I found the story itself a bit bizarre. It has a deep narratological defect that made the whole thing seem somewhat pointless. The Poison Belt describes a global catastrophe, which the central characters manage to survive almost by chance, thanks to the forethought of Professor Challenger, who is the only person to have predicted it. But then, when the catastrophe is past, it turns out that they would have survived anyway. Challenger and his little team provide nothing except a point to view the catastrophe from. The catastrophe itself, a change in the local quality of the ether, was already of dubious plausibility when Conan Doyle wrote The Poison Belt. The Michelson-Morley experiment cast serious doubt on the existence of the hypothetical tenuous medium that was thought to pervade space; the absence of ether was one of the major influences on Einstein's 1905 theory of relativity. All of this was in the air in 1913; Conan Doyle must have heard about it. Maybe I'm too crusty, but it bothers me when science-fiction authors lie about science. This report is so crabby that I have to mention that the story isn't uninteresting. The premise is an intriguing fantasy, and the characters are entertaining. The next etext, #127, is around a million digits of the mathematical constant "e". I can't make myself read it, because I already know how it ends ... that is, it doesn't. Admittedly, this allows for an unending series of million-digit sequels that would have been the envy of Robert Jordan. So the next etext I'll read is #128, Andrew Lang's version of The Arabian Nights. I've read the Nights in Burton's slightly overexalted translation, so I'll be interested to read the version that inspired Burton to think he could do better. | | Friday, February 8th, 2013 | | 10:43 pm |
Project Gutenberg etext #125: A Girl of the Limberlost
I think I would call Gene Stratton-Porter's A Girl of the Limberlost (1909) the American Anne of Green Gables. It's a loose sequel to Porter's Freckles (1904), and came out just a year after Lucy Maud Montgomery's more famous work. The book belongs firmly in a genre, or maybe it's a trope, in which the young protagonist's inner strength and virtue allows him or her to triumph despite a difficult environment: further, the protagonist's healthy example and influence redeems one or more secondary characters. Anne and Freckles are two more exemplars. The theme seems to have been wildly popular from the latter part of the nineteenth century well into the twentieth, but then people started perceiving it as trite or saccharine, and later examples are somewhat thin. I rather regret its demise; I'm a softy, as I've mentioned many times, and I eat this stuff up. The eponymous girl, Elnora Comstock, manages to redeem at least three people around her; the last is the real triumph, and gives the book its climax. The Limberlost swamp itself (a real place in western Indiana) is sort of a tragic figure, much diminished since Freckles. Most of the story takes place near the swamp but not as much in it as the earlier novel. But the climax happens far away, on Mackinac Island in northern Michigan. While the Limberlost is a degraded wild paradise, Mackinac is a tame place, already a tourist trap in 1908 (when the story takes place); I was intrigued because I was there several times as a child. It was still a tourist trap. The domestication of the landscape brings the human drama into sharper focus: it's useful for dramatic purposes that Elnora is not on her home ground, and I thought the whole thing rather deftly handled. Now I have started etext #126, a 1913 science-fiction novel called The Poison Belt, by Arthur Conan Doyle. It's a sequel to The Lost World, which I read as a child and barely remember. As sometimes happens in Project Gutenberg, the sequel was digitized first, probably because somebody liked it better than the original. Anyway, I know nothing about The Poison Belt, and am having fun reading it. | | Tuesday, February 5th, 2013 | | 10:03 pm |
Finishing the Apocrypha (Project Gutenberg etext #124)
I finished the Apocrypha last night, as I expected I would. The prayer of Manasseh was pretty pedestrian. "Oh, God, I am a really awful person, and don't deserve forgiveness, but you're going to forgive me anyway because us Jews are your chosen people and you don't want us to look bad. Thanks, bro." The only remaining book was "Bel and the Dragon". It's another Daniel story, with three parts. The first part is a detective story. Daniel deprecates the Babylonian god Bel (probably Ba'al), saying that the idol is just an inanimate object. "But then how does Bel eat all those offerings we leave for it?" asks the King. Daniel makes a wager: if he cannot demonstrate that Bel does not eat the offerings, Daniel will be put to death for blasphemy against Bel, but if he can show that Bel is a fraud, the priests of Bel will be killed. Daniel uses a clever stratagem and succeeds. The Babylonians also worship a dragon god; this story is a little less coherent. In particular, it is bizarrely unclear whether the dragon is an actual living creature, a mechanical simulacrum, or another idol. Daniel "feeds" it some bizarre mixture and it bursts, showing that, whatever it was, it wasn't a god. Still, deicide wasn't condoned. The third part is a retelling of the famous lion's den incident; this time Daniel is thrown to the lions for wrecking the dragon, while in the Book of Daniel proper it's for refusing to stop praying to God and pray to King Darius instead. It's the Daniel story that was so nice, they told it twice. Now I get to read the Gene Stratton-Porter's sequel to Freckles. The sequel is more famous than the first book; it's The Girl of the Limberlost. | | Monday, February 4th, 2013 | | 1:24 pm |
Monday Apocrypha blogging: Baruch, Susanna, and the Prayer of Azariah
I read the brief Book of Baruch, a conventional piece of Captivity prophecy, which for some reason includes as its last chapter the Epistle of Jeremy (the Greek form of Jeremiah), and finished them last night. All the remaining books in this collection of apocrypha are short. The next two, Susanna and the Prayer of Azariah, are less canonical parts of the Book of Daniel. Susanna is a "Daniel story", this one from Daniel's youth. Susanna is a virtuous young wife; two old lechers try to convince her to have sex with them, and when she refuses they publicly accuse her of having sex with an unidentified young man, a capital offense. But before she can be killed, young Daniel intervenes and cleverly demonstrates that the old men have fabricated the charge. The Prayer of Azariah belongs to the episode in Daniel when three Jewish children are thrown into a fiery furnace, but are miraculously preserved. Azariah is one of the children, and he delivers this long prayer from the midst of the flames. The prayer is followed by a hymn sung by all the children, which is sometimes presented separately as the Song of the Three. I'm about to start the Prayer of Manasseh; I'm sure I'll finish the Apocrypha tonight. |
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