walkingshadow (![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png)
walkingshadow) wrote2005-11-11 05:33 am
walkingshadow) wrote2005-11-11 05:33 am
Entry tags:
tell sir thomas more we've got another failed attempt
today i sprawled out on the couch in the living room with the dog and the cat and finished the man who loved only numbers: the story of paul erdős and the search for mathematical truth. the title is apt. i once took a personality and aptitude test that asked me to rank facts, people, ideas, and things from one to four according to personal relevance and importance and inclination. for me, people are at the very bottom of the list, while the other three jostle for first place. for paul erdős, mathematics reigned supreme, conflating ideas and facts; people came in second; and things weren't even on the radar. he lived to be eighty-three years old and he was itinerant for most of it, living out of a suitcase and a plastic bag while he bounced around the world visiting mathematicians: stimulating them, collaborating with them, and relying on their hospitality for shelter, transportation, cooking, temperature control, and shoe-tying.
it sounds ghastly, but everyone adored him—you just had to accept the fact that the material world meant very little to him and he couldn't be bothered with it. he didn't think anything about splashing water all over his host's bathroom (germphobic; didn't like towels) or asking someone to clip his toenails; but he loved people and was always attuned and solicitous where people were concerned. he especially loved children and always remembered names and ages and past illnesses; he comforted and challenged friends who were going through upheavals in their lives, or crises of confidence with themselves and their work. he was a genius and astoundingly prolific (he published a total of 1,475 papers, "many of them monumental, and all of them substantial"), but everyone who knew him confirmed that his greatest contribution to the field was his way of pushing his colleagues (anyone with that spark of mathematical genius, he didn't discriminate) to greatness by asking them questions and posing the perfect problems, exactly right for them at just that time. he collaborated with more people—485—than any other mathematician in history.
the book is composed almost entirely of quotes and anecdotes from family and friends and colleagues and erdős himself, bound up with a mini-history of hungary, the tracking of erdős's movements, and mathematical exposition. he was celibate all his life and uninterested in sex or romantic relatinships (he had some form of erectile dysfunction, i can't remember the name of the exact condition; john selfridge: "He told me that when blood started flowing into his penis, it caused him great pain" (139)). he was attached to his mother (and vice-versa) in a way that had me humming tom lehrer's oedipus rex; and he breathed and lived for mathematics:
he had heart trouble eventually—tachycardia, bradycardia, they had to install a pacemaker—though curiously the author never blames the amphetamines.
more excerpts:
okay, hoffman briefly mentions euler's magic equation eπi + 1 = 0 (recently featured in![[livejournal.com profile]](https://www.dreamwidth.org/img/external/lj-userinfo.gif)
basingstoke's adorable euler's jewel) which i still can't quite suss out. i know that eπi has to equal -1, which means the natural log of -1 has to equal πi; and one of the rules of logarithims is that you can't take the log of a negative number, but i understand that's going to have something to do with the i; i just can't quite see how we get there from here. [ETA: aha, that's what wikipedia is for! that's AWESOME.]
i somehow feel that numbers like π and e were introduced wrong in school. we come to them initially in specific contexts, especially π, which is usually defined first as the ratio of a circle's circumference to its diameter. but they're constants, which are just numbers, numbers that are fascinating and important because they're transcendental and because they pop up everywhere! learning specifics first means backtracking and retconning later, so when you get to trigonometry or infinite series, you're confused because suddenly π has nothing to do with circles anymore.
i'm just happier when i begin at the point of origin, the closest to the beginning that i can get, and then i feel completely confident in moving up and out. and i think i was like, absent the day we first started logarithms, or i dozed off for five minutes or something, because suddenly we were just doing them, and i had no idea where they came from; this was especially bad when we came to natural logs, and i was like, wait, what's a natural log again? and they answered, "a log whose base is e! and i was like, right, sure, of course, and what's e? and they kinda looked at me funny and said, it's the base of the natural log. which didn't tell me anything. i swear, i have never not grasped a concept like i didn't understand exponential growth and decay. i'd have been better off with the "isn't it cool?" explanation: generating e from a series, defining it as transcendental, and then showing that it happened to be central to growth and decay, compound interest, and the distribution of things like prime numbers—and isn't that cool?
it sounds ghastly, but everyone adored him—you just had to accept the fact that the material world meant very little to him and he couldn't be bothered with it. he didn't think anything about splashing water all over his host's bathroom (germphobic; didn't like towels) or asking someone to clip his toenails; but he loved people and was always attuned and solicitous where people were concerned. he especially loved children and always remembered names and ages and past illnesses; he comforted and challenged friends who were going through upheavals in their lives, or crises of confidence with themselves and their work. he was a genius and astoundingly prolific (he published a total of 1,475 papers, "many of them monumental, and all of them substantial"), but everyone who knew him confirmed that his greatest contribution to the field was his way of pushing his colleagues (anyone with that spark of mathematical genius, he didn't discriminate) to greatness by asking them questions and posing the perfect problems, exactly right for them at just that time. he collaborated with more people—485—than any other mathematician in history.
the book is composed almost entirely of quotes and anecdotes from family and friends and colleagues and erdős himself, bound up with a mini-history of hungary, the tracking of erdős's movements, and mathematical exposition. he was celibate all his life and uninterested in sex or romantic relatinships (he had some form of erectile dysfunction, i can't remember the name of the exact condition; john selfridge: "He told me that when blood started flowing into his penis, it caused him great pain" (139)). he was attached to his mother (and vice-versa) in a way that had me humming tom lehrer's oedipus rex; and he breathed and lived for mathematics:
Erdős first did mathematics at the age of three, but for the last twenty-five years of his life, since the death of his mother, he put in nineteen-hour days, keeping himself fortified with 10 to 20 milligrams of Benzedrine or Ritalin, strong espresso, and caffeine tablets. "A mathematician," Erdős was fond of saying, "is a machine for turning coffee into theorems." (7)
he had heart trouble eventually—tachycardia, bradycardia, they had to install a pacemaker—though curiously the author never blames the amphetamines.
more excerpts:
Only one mathematician in history managed to publish more pages than Erdős did. In the eighteenth century, the Swiss wizard Leonard Euler, who fathered thirteen children, wrote eighty volumes of mathematical results, many reportedly penned in the thirty minutes between the first and second calls to dinner. (42)
Erdős's forte was coming up with short, clever solutions. He solved problems not by grinding out pages of equations but by constructing succinct, insightful arguments. He was a mathematical wit, and his shrewdness often extended to problems outside his areas of specialty. "In 1976, we were having coffee in the mathematics lounge at Texas A & M," recalled George Purdy, a geometer who began working with Erdős in 1967. "There was a problem on the blackboard in functional analysis, a field Erdős knew nothing about. I happened to know that two analysts had just come up with a thirty-page solution to the problem and were very proud of it. Erdős looked up at the board and said, 'What's that? Is it a problem?' I said yes, and he went up to the board and squinted at the tersely written statement. He asked a few questions about what the symbols represented, and then he effortlessly wrote down a two-line solution. If that's not magic, what is?" (49)
Erdős's ability to think about disparate things simultaneously was legendary. Michael Golomb, who wrote a joint paper with Erdős in 1955, recalled a time in the 1940s when he came across Erdős playing chess with a local master named Nat Fine, "whom Erdős could only beat rarely, usually by psychological warfare. . . . I saw Nat with his head between his hands, deep in thought considering the next move, while Erdős seemed to be engrossed in studying a voluminous encyclopedia of medicine. . . . I asked him, 'What are you doing, Paul? Aren't you playing against Nat?' His answer was, 'Don't interrupt me . . . I am proving a theorem.'" (50)
(Ron Graham, long-time friend and colleague of Erdős:) "My father stepped in and offered to contribute to my tuition if i switched from the 'dangerous, leftist' University of Chicago to 'an All-American school' he knew like the University of California at Berkeley." (150)
[Unit fractions] are fractions that are the reciprocals of positive integers, like 1/5, 1/8, and 1/127, fractions in which the numerator is 1. Such fractions were prized by the ancient Egyptians, who refused to deal with any fractions that weren't unit fractions (with the sole exception of 2/3, which had its own special hieroglyph). (153)
"This is the remarkable paradox of mathematics," observed commentator John Tierney. "No matter how determinedly its practitioners ignore the world, they consistently produce the best tools for understanding it. The Greeks decide to study, for no good reason, a curve called an ellipse, and 2,000 years later astronomers discover that it describes the way the planets move around the sun. Again, for no good reason, in 1854 a German mathematician, Bernhard Riemann, wonders what would happen if he discards one of the hallowed postulates of Euclid's plane geometry. He builds a seemingly ridiculous assumption that it's not possible to draw two lines parallel to each other. His non-Euclidean geometry replaces Euclid's plane with a bizarre abstraction called curved space, and then, 60 years later, Einstein announces that this is the shape of the universe." (162-3)
When the interests of Erdős's colleagues drifted away from pure mathematics, he made no secret of his disapproval. "When I wasn't sure whether to stay a mathematician or go to the Technical University and become an engineer," Vázsonyi recalled, "Erdős warned me: 'I'll hide, and when you enter the Technical University, I'll shoot you.' That settled the matter." (163)
Euler, though capable of making mistakes, was the greatest number theorist of the eighteenth century. And in Erdős's eyes, he deserved credit for doing mathematics up until the bitter end. On September 18, 1783, after calculating the orbit of the recently discovered planet Uranus, Euler paused to play with his grandson and sip a cup of tea. Pipe in hand, he suffered a fatal stroke, getting out the last words, "I die."
"I told this story once at a lecture," said Erdős, "and some wise guy shouted out, 'And another conjecture of Euler's is proven.' I want to leave like Euler. I want to be giving a lecture, finishing up an important proof on the blackboard, when someone in the audience shouts out, 'What about the general case?' I'll turn to the audience and smile. 'I leave that to the next generation,' I'll say, and then I'll keel over." (201)
Many people who go into mathematics are seeking refuge from the world. "I believe with Schopenhauer," said Einstein, "that one of the strongest motives that lead men to art and science is to escape from everyday life with its painful crudity and hopeless dreariness, from the fetters of one's own ever-shifting desires. A finely tempered nature longs to escape from the personal life into the world of objective perception and thought." (266)
okay, hoffman briefly mentions euler's magic equation eπi + 1 = 0 (recently featured in
basingstoke's adorable euler's jewel) which i still can't quite suss out. i know that eπi has to equal -1, which means the natural log of -1 has to equal πi; and one of the rules of logarithims is that you can't take the log of a negative number, but i understand that's going to have something to do with the i; i just can't quite see how we get there from here. [ETA: aha, that's what wikipedia is for! that's AWESOME.]i somehow feel that numbers like π and e were introduced wrong in school. we come to them initially in specific contexts, especially π, which is usually defined first as the ratio of a circle's circumference to its diameter. but they're constants, which are just numbers, numbers that are fascinating and important because they're transcendental and because they pop up everywhere! learning specifics first means backtracking and retconning later, so when you get to trigonometry or infinite series, you're confused because suddenly π has nothing to do with circles anymore.
i'm just happier when i begin at the point of origin, the closest to the beginning that i can get, and then i feel completely confident in moving up and out. and i think i was like, absent the day we first started logarithms, or i dozed off for five minutes or something, because suddenly we were just doing them, and i had no idea where they came from; this was especially bad when we came to natural logs, and i was like, wait, what's a natural log again? and they answered, "a log whose base is e! and i was like, right, sure, of course, and what's e? and they kinda looked at me funny and said, it's the base of the natural log. which didn't tell me anything. i swear, i have never not grasped a concept like i didn't understand exponential growth and decay. i'd have been better off with the "isn't it cool?" explanation: generating e from a series, defining it as transcendental, and then showing that it happened to be central to growth and decay, compound interest, and the distribution of things like prime numbers—and isn't that cool?
you can't spell imaginary without the letter 'i'
Re: you can't spell imaginary without the letter 'i'
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p.s. The whole "isn't it cool?" thing is exactly the way my mom teaches math. She is all about showing where the formula or concept came from instead of just making her students memorize it. She is famous for presenting a problem and working it out the "long" way, and then saying, "shouldn't there be an easier way to do this?" and introducing the concept or formula and showing why/how it came to be. She used to drive her professors crazy with all kinds of questions they could never answer because the answer wasn't in the textbook. I sometimes wish we hadn't fought so much when I was in high school, because I know I could have learned a lot more from her if I had been able to listen to her...
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well, that's because your mom is awesome! (and honestly, it's never too late to learn lots of things from her, though the math appeal is probably gone. in re: the fighting and not being able to listen? i so hear you on that.) my calc professor freshman year was this man who was SO HAPPY to be teaching us calculus and always showed us everything, all the proofs, all the stuff that was going on in the background of what we were doing and how we got there. and then you knew why.
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I don't know if it was just that I was never taught it in an interesting way in school or what but trig and calc etc were my worst nightmares at school - I sat my gcse maths exam twice. I love the formulas and how they look but half the time they make no sense to me without a context or I don't remember learning them at all.
I had a bit of maths related yay recently though - we had a guest lecturer in my web design class who was talking about the Golden Ratio and how it's used in design and I was sitting there thinking 'hey..that sounds like the rule of thirds in photography' and then he went 'and if you've ever done a photography course, you'll know it as the rule of thirds' and I was all 'yay! maths! that I understand!')
Maybe I should look into doing gcse maths again once I graduate.
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and they say cheesy sci-fi television isn't educational! *g* the fanon surrounding john sheppard's math talent is a little perplexing, but i don't care when i'm reading a story about it. i love the way the fandom is embracing math for its own sake.
the more books i read about math the more i wonder why we aren't taught more about the practical, mundane applications of math in the real world. because that's really the cool thing about it—that these things crop up all over, in the strangest places! your rule-of-thirds story is a perfect example. i think of it like software code running underneath a UI skin, that if you peeled away the surface of the world you'd find math describing it all.
(though i have to admit that the practical applications of calculus are mostly physics, and since i had a horrifying year in physics with a terrible teacher, i tended to like calculus for its own sake.)
Maybe I should look into doing gcse maths again once I graduate.
sure! some things are like crossword puzzles, you leave them alone for a while when you can't figure them out, and when you come back they're suddenly solvable.
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I enjoyed Physics, I had an excellent teacher but because by that point Maths and I were no longer speaking, it never really clicked. My dad's a scientist though, so I end up getting odd bits and pieces that make sense - like cos, sin and tan are used in building, which I never knew! That would have been so much easier, if I'd had a maths problem I could have related to rather than just cos over tan = x what is sin or whatever.
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I'm curious about the meta and fanon of sg:a now - do you know if there's any good meta/discussion comms? I've seen some interesting discussions on various character comms about things like Rodney's education and the probablity of Zelenka having military training ( highly probable as it was compulsory until 2004 in the czech republic) and the differences between scottish and british schooling etc but I don't want to sign up to all those communities and then have to scroll through pages of fic (man, sg:a fic ranges from fantastic to 'I have never seen the show but I have read enough fic!') for the odd bit of meta.
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no, no, you have not missed it: it isn't there. this is one of the things that really surprised me too when i started watching, because i was ready for it! but it never came. i think part of it stems from an early, (un?)official bio on the website and part of it comes from some people not knowing what constitutes high-level mathematics; there's a good discussion of it here (http://www.livejournal.com/users/perian/282581.html). personally, i see john as an extremely *well-rounded* person, intellectually, and i'd expect his degree(s) to be in something closer to engineering than pure math, what with the flying contraptions he loves so much. he can do math just fine, but he's not a mathematician.
as for centralized meta, i'd check out
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Right. Ok, so I am clearly not cracking up or anything. I mean, there's the one bit in Rising when he calculates the range of stargate addresses they have to look up to find the Wraith pretty quickly but that's still not maths genius. (although, Rodney's face when John answers him then is *great*). I'd assume he'd be pretty quick at doing some maths - trajectories etc when he's flying but I'd be more on the side of 'he's learnt to do 'em like that' as aposed to 'is a maths genius'.
Engineering is more than likely what his degrees are in. I could see physics but not as a complete degree - maybe a minor at undergrad level? Maybe he did maths as a minor. Heh.
Meta etc:
Excellent - I have both sga_newsletter and sga_flashfic and do a similar thing to what you do. Shall add ship_recs.