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July 14, 2007

John Derbyshire Recommends ...

Michael Blowhard writes:

Dear Blowhards --

One of the reasons I'm wary of attributing too much significance to aptitude tests has to do with my own experience of math aptitude tests. As a student I always did well on them despite the fact that I have never had any actual aptitude for doing math. Year after year, I'd score well on a math aptitude test; I'd be assigned to a fast math class; I'd squirm out of it in two or three weeks; I'd just barely manage to squeak by in a slowish class ... And then I'd do well on another math aptitude test, and start the following year in a fast math class once again.

This cycle repeated itself over and over until the authorities finally allowed me to ditch math entirely. (I can't tell you how many little pep talks I endured about how I wasn't living up to my math potential. Earth to authorities: I had no math potential, I just wanted out.) So I was left wondering: Given my complete lack of any actual math gift -- and I'm not being coy about this, let alone asking to be contradicted or reassured -- what on earth were these tests measuring?

Still, despite my inability to do math, it seemed like an interesting field. All those brilliant mathematicians must have been up to something fascinating, no? What was it? I mean, roughly speaking. The many hours that I spent snoozing through conventional math classes I might well have spent happily indeed listening to someone talk about the history of math: what it was good for, how it worked, what the basic fields were, what the Larger Questions it raised were ...

Why didn't anyone want to tell me about any of this? I mean, without requiring any actual math of me?

But this line of thought may reflect a failing of mine: I was born with a deep-seated conviction that anything, no matter how complicated, can be turned into plain and vivid English. Further, I have the ego to be convinced that if I'm not following a line of discussion it isn't because I'm dim, it's because whoever is doing the presenting is falling down on the job. He / she isn't turning the material into accessible and enjoyable English.

Is it in fact true that anything can be turned into plain and fun English? I've run into specialists who claim that this isn't the case. The argument seems to be that, past a certain level of complexity, abstraction, and technicality, there's simply no way plain English can suffice.

Yet I've also read histories of thought that did what seemed to me to be bang-up jobs of presenting far-out ideas. I've lunched with philosophy profs who have made their interests and their fields of study clear and understandable to me. Hey: I once spent an afternoon with a scientist at the Jet Propulsion Laboratory who explained his black-holish, string-theory-ish studies and findings in ways that I could follow.

So while I could be wrong, I still cling to my conviction. Besides, can such first-class writers-about-science-for- the-interested-layman as Stephen Pinker, Paul Davies, Jeremy Campbell, Oliver Sacks, Richard Gregory, and Richard Feynman feel that they have done disservices to the fields they've presented? Hmmm: Perhaps what the "it can't be done" crowd really means is that they can't do it.

Anyway, if schools are going to insist that those who lack the math gene nonetheless learn something about -- if only a little respect for -- math-beyond-arithmetic, why don't they skip the equations and offer courses that present the material in straightforward English? I'll never be able to do calculus, let alone anything any tougher -- but surely there must be an explanation out there somewhere of what calculus is and why it matters that even I could follow.

Perhaps the situation is the fault of the professoriat. In the case of economics, I spent two semesters in college Intro-to-Econ classes sitting slack-jawed with bewilderment and boredom. I didn't begin to grasp the topic -- as in, I didn't begin to be able to start following the general conversation about econ -- until I stumbled across a few histories of economic thought written for the popular audience. No graphs, no equations, no technical language. Just good, rousing stories of intellectual adventure and speculation, accompanied by the explanations necessary to make these stories register.

(Timothy Taylor's audio history of economic thought for the Teaching Company -- now on sale for an absurdly good price -- is an excellent way for the math-averse to dip a toe in the econ waters. I raved about Taylor's Teaching Company courses here. Back in this posting, I mentioned a few other resources for lib-arts types curious about econ; visitors pitched in with many more suggestions.)

I've been musing about all this because of a posting-and-commentsfest at GNXP. The topic was: What are the good math textbooks? I meekly peeped up in the midst of that brainy, math-lovin' crowd and asked if anyone could recommend an accessible, plain-English history of mathematical thought. When no one responded, I slunk away. Ah, well, I thought: another field I'll never crack.

The next day I opened my emailbox to find an email from none other than The Derb, National Review columnist John Derbyshire. Derbyshire -- himself the author of two books about math for the popular audience -- passed along a link to a book about the history of mathematical thought. I haven't read it yet, though I have hit the One-Click button. Once I've read it, though, maybe I'll have acquired the knowledge and background it takes to enjoy Derbyshire's own books about math. I look forward to them.

Many thanks to John Derbyshire. Here's Derbyshire's own website, where he archives a lot of his writing.

Are you familiar with Derbyshire's work? He's best-known as a columnist for the National Review. I especially love his monthly Diary. I love the columnist's-diary as a form generally -- why doesn't anyone offer me such a gig? -- and Derbyshire seems at his best in it: fast, amusing, trenchant.

In any case, he's one of my favorite columnists. I love his brains, his precision, and his drollery. His work has a combo of the low-key and the exuberant that I find irresistable, as well as a joyous disdain for political correctness -- for political sentimentalities of all kinds -- that I find very congenial. Even when I disagree with Derbyshire, I smile at the writing, I enjoy the voice, and I get a lot out of wrestling with his arguments.

Derbyshire -- clearly one of the world's least-blocked writers -- is also a generous contributor to the National Review's blog, and he writes as well for The New English Review and its blog. Razib did an interview with Derbyshire for GNXP. Here's an interview with Derbyshire by Bernard Chapin.

Do you have any kind of math gift? If not, was your experience of math classes as painful as mine was? And what was your experience of math aptitude tests like?

Come to think of it, what on earth is the point of subjecting kids who lack the math gene -- and who have no math in their future -- to anything beyond basic arithmetic? It really does seem like academic sadism of the worst sort, doesn't it?

Steve Sailer points out a good new Charles Murray piece about the SAT.



posted by Michael at July 14, 2007


I would once have agreed with you that anything that can be understood can be put into plain English. Much of my job involves translating complex biomedical information into lay language. But there is one area that firmly resists such translation. That is genetics and proteomics. All lay accounts of -- say -- gene-based therapies for cancer, are by necessity simplified to the point of distortion and untruth. The word "genetics" itself is so broad as to be meaningless in regards to specific research. On the topic genes and such, there is very little shared vocabulary between researchers and persons outside of the field. When they penetrated the genome, they discovered a world of fathomless complexity, whose understanding requires total dedication of the intellect. You and I may be permanantly left out.

Posted by: faze on July 14, 2007 8:50 PM

I had a math prof so good in college that he convinced me to add math as a second major. Any class he taught, I had no trouble following. The more math prodigy types found his classes kind of slow though.

In other classes, their content would sink in when I was in the succeeding class. This didn't bother me, but some people got really hung up on needing to get it >right now

Nearly all of what I studied was theoretical math, so I spent a lot of time writing proofs. I think of math as another language, something like I suppose studying Russian or Arabic might be like. Not everything translates simply to English. E.g., I could explain the idea behind homeomorphisms to you more clearly with drawings than words.

I did well on aptitude tests, but never as well I did on practice tests. Testing always coincided with my seasonal allergy attacks which were quite severe when I was a teenager.

Oh, you might enjoy this: Imagining the Tenth dimension. I haven't read the book yet, but there's a neat flash demonstration of the concept on the site.

Posted by: claire on July 14, 2007 9:25 PM

This is an interesting post. As an engineer, I've been through my share of math, both simple and tricky. I never had much trouble with it, but its not a favorite. I think it helps if you consider math as a kind of language that is quite rigorous and logical. This appeals to some and befuddles others. To me, there seems to be some good parallels between regular language and math in this regard--that there are branches of math that are a lot more abstract, and some that are very concrete, which describe concrete phenomena. I always found the more abstract branches of this language harder than the concrete ones. Some people really excell at the abstract kind, and I think that these types would be what most of us consider the high-powered, pure mathmeticians--much like their intellectual peers in other disciplines.

I also think that the study of math for non-numbery types is little more than torture after a certain point. I guess the idea is to inculcate a bit of logical training because math is logical and rigorous, but I think the purpose would be better served with a class in logic or argumentative rhetoric. But somehow I'm not sure the free spirits would be so happy with that either. I wish I had spent more time goofing around in school. You're lucky you had trouble with it--nobody pressed you too hard to follow up. My curse was that I never had much trouble with any subject in school, so I got it all shoved at me full force (the better you are at something, the more work is thrown at you).

And as a general principle, we all have far more potential in many different areas than we will ever realize. What limits us is time and temperment. It makes the idea of choices and personality more important than talent, doesn't it?

Posted by: BIOH on July 14, 2007 10:49 PM

I think that many scientific topics can be explained in clear English, but that the more mathematical they are, the longer the explanations get (and the hard they become to write). Mathematical notation is an extremely compressed form of communication - the closest analog I can think of in English prose is reading a highly abstract philosophy text where every other noun is a specialized term that has been rigorously defined.

The concentrated bursts of meaning that math expressions deliver is the source, I think, of the belief that some things can be expressed no other way. What's meant is that such things can be expressed in no other way that is so complete, precise, and elegant.

A really good equation or proof is just perfect, in a way that language has a hard time conveying. Randall Jarrell, in a poetry review article, said that the poems under discussion could be heated red hot, beaten with hammers, and dropped into a bucket of water - and all that would happen would be that the hammers would break and the water would boil away. Mathematics is like that.

Posted by: Derek Lowe on July 14, 2007 10:59 PM

Try "Journey through Genius", a popular, plain-English history of some math proofs you should know. Of course, there's also the nerd tome Godel, Escher, Bach.

You should take a look at Calculus again; I assure you it's not difficult. There are two (quite related, by The Fundamental Theorem of Calculus) important questions in Calculus. First, how fast is something changing? This is the derivative. That is, the derivative of velocity is acceleration. Second, what is the area of an object? We've known since the Greeks (or earlier, in some cases) how to find the area of things like Circles and Pentagons. But what about the area of a sinuous Gehry-designed museum? For that, we need the integral.

Both of those concepts require an idea called a limit. At the heart of the limit is a "paradox" from Greek times: If it takes me finite time to walk some distance x, I can never walk across a room. First, I'll cross half the room in time x1. Then I'll cross half the remainder in x2. And so on. Of course, with the limit, we can easily show that some infinite sums are finite.

It's a bit strange, but this type of "background"/"nonapplied" math is covered in higher level courses such as Analysis at most universities.

Posted by: cure on July 15, 2007 12:25 AM

My fourth grade math teacher was the kind who said, "Put this number here, put that number there, draw a line under them and add. Don't forget to carry." I always forgot. I'd have done pretty well with "modern math" if I could have played around with those little sticks. I need to visualize in a concrete manner.

I took statistics three times and could NOT understand what was going on. Finally the third time I hit a master teacher. "Imagine a long shelf here," he'd say. "The middle apple is rotting. Which apples do you think are most likely to rot next." I could just "see" it in my mind. And, voila! Standard deviations! Then he retired. I changed my major from clinical psychology to ministry (no math).

But late in life I was actually employed as a cashier for a major city. I could NOT make that till balance, nor could the woman who previously had had the job. Along came a woman who LOVED numbers, said they had colors, talked to each other, danced in pairs. She also had been trained in a German bank. (Her husband was military.) She designed a worksheet for the end of the day and our till balanced to the penny every time.

I suspect that you are exactly right, Michael. There is a complex of kinds of thinking involved and since there are different kinds of math, it's like a lot of stuff -- looking for what fits.

Prairie Mary

Posted by: Mary Scriver on July 15, 2007 12:45 AM

Faze -- That's very interesting to learn, thanks. "Proteomics" -- even the word is scary. I wonder how people in the field are going to communicate the substance and importance of what they're up to to civilians ... A challenge, I guess.

Claire -- That's another great point, the way someone who lights your fire (or stirs your brain, or reaches your imagination) can affect you. I've sometimes wandered off learning things I never imagined I was interested in just because I was following a teacher (or writer) who really did it for me. It was more important to have that experience of being switched-on (and hungry and digesting it) than it was to follow my own interests, at least for a while. It can hit you hard. You snooze through courses or books on topics you think you adore, then suddenly someone's talking about something you didn't think you had much interest in, and you're awake and alert. How'd that happen?

BIOH-- I like your term "non-numbery". I can imagine that being good at it all could actually make you vulnerable - you'd think it would be a position of power, but it could also mean you could get pushed into all kinds of things that other people want, and not you. I'm with you on character vs. talent too. What the math aptitude tests I did pretty well at didn't measure (among other things) was motivaton and interest. How can you do something hard like math if the basic oomph to do so isn't there? Which means that the oomph is at least as important as the raw ability (not that I really had any). I picture it as being like an engine and a tank of gasoline. It might be a nice engine, but with no gas, or no connection to the gas, it's just a lump of useless metal.

Derek - That'a beautifully put. Why weren't you teaching science and math to me when I was a kid?

Cure -- That's a great explanation of "why calculus?" Which is about 90% of what I want to know about calculus. Actually it would be great to have a chance to line you and Derek and BIOH up and pepper you with my idiotic questions. Hmmm: I see the potential for a hit reality-TV show here ...

P. Mary -- Yeah, remembering to "carry" was always a tough one ... Funny how some people have such a nice relationship with numbers, isn't it? They always struck me as enemies, just as charts and equations always make me want to shake someone and say, "Would you put it in plain English, please?" All that said, I do love books and websites and such that mix up images and words in mutually-enhancing ways. I wonder if my problem, er, challenge (beyond the basic lack of talent, of course) might not have had to do with the precision thing. Derek's comment reminded me of Feynman, who went on once about how he felt comforted by numbers, and certainly a lot of people like math or science or even business because there's some hard reality there. My own main impulse isn't to nail things down, or probably even to build them up, it's to mess them up a bit, or at least mess with them a bit and see what happens ...

Hmm, disconnected thought coming ... I wonder if the translating-it-into-plain-English question might have to do with the difference between "someone determined to do something in the field" and "good enough for interested civilians." Certainly a good popular-science book, for instance, isn't going to transform anyone into a practicing scientist. Yet it might well convey whassup in the field in trustworthy, vivid, and helpful ways that interested outsiders would find useful and that maybe even insiders might not disapprove of.

Posted by: Michael Blowhard on July 15, 2007 1:03 AM

Math _is_ a language, and a very precise one. The problem of translating math into plain English is similar to translating poetry from one language to another - you can come close, but you can't quite capture the nuances and precise meanings. If you really want to "get" the poem, or master the mathematical argument, you gotta do the heavy lifting and master the language.

For me, I didn't figure out the "math language" stuff until I went to college and escaped the hell of "memorize all these formulas and don't ask where they came from". I had always been competent in math, but ended up majoring in it after I discovered the joy of proofs.

Posted by: Foobarista on July 15, 2007 1:16 AM

"Hmmm: I see the potential for a hit reality-TV show here ..."

...Or great fodder for a wildly entertaining and informative podcast?

Posted by: Cody on July 15, 2007 1:20 AM

We were introduced to differential calculus thus:- Imagine that you want to build a railway from town A to town B. The straight route has to pass through a wide swamp, where it costs much more per mile to lay railway line than on dry land. But the swamp is wedge-shaped, so that you need to cross less swamp if you make the route indirect. To get the cheapest railway, which route should we take? We had a quick discussion and were then asked to bear the problem in mind as we began the fundamentals. After a few weeks, someone asked "What about the railway, sir?" "Oh", says he, "you can all solve that one now, can't you?" And we realised that we could. Doesn't it help if your teacher knows how to reach!

Posted by: dearieme on July 15, 2007 6:15 AM

I'm lousy at math and yes, it does prove that I'm one of the myriads of semi - not truly - bright folks out there. :>[

Posted by: ricpic on July 15, 2007 11:04 AM

I had a friend who went into math in his early teens. I went in the other direction. This alone wouldn't have ended our friendship. What ended it was his use, his abuse I should say, of the word elegant. Elegant this. Elegant that. Elegant elegant elegant. Every aspect of math, every proof was elegant. It drove me batty. And ended the friendship. I've noticed this about the math and science crowd, especially physicists. They're fixated on the word. Biologists not so much since biology is messy, not elegant. Admittedly, a lot of math and science is elegant, but guys, think of another word, 'kay?

Posted by: ricpic on July 15, 2007 11:29 AM

Randall Jarrell, in a poetry review article, said that the poems under discussion could be heated red hot, beaten with hammers, and dropped into a bucket of water - and all that would happen would be that the hammers would break and the water would boil away.
Thank you, Derek, that's a WONDERFUL quote!

I'm like you Michael. I kept getting pushed into math courses that I didn't like and had little aptitude for. My private high school seemed to think if you could excel in history and English you should do just as well in math. Didn't work for me. It was a great relief to get to Tulane where all I had to take was simple statistics for anthropology. And I could take all the archaeology and history I wanted.

Posted by: Reid Farmer on July 15, 2007 12:09 PM

Dearieme -

A college math teacher of mine used a somewhat different version of the railway-line example you cited. Aware that he was teaching college undergraduates, with their interests being what they are, the example he used was how to design a beer can to minimize the cost of materials and keep the brewski's price as low as possible. If I recall correctly a square can actually would be the cheapest.

Posted by: Peter on July 15, 2007 12:36 PM

Math puts a huge strain on your visual-spatial skills, and those decline sharply starting about age 30. (BTW, that is the reason that math & science types tend to make their first big splash in their 20's -- not because they're trying to attract chicks, as suggested in the recent evolutionary psychology "10 un-PC truths" article.)

This is most easy to see in popular math media aimed at children vs. adults (as in, 30-somethings or older). Anyone remember Donald Duck in Mathmagic Land? It focused only on the math, using Donald Duck just to goof it up a bit.

Contrast that with A Beautfiul Mind (or any documentary on Nash), N is a Number (a doc on Erdos), or anything else really that's aimed at adults. They don't showcase math at all; it's all about biography, personality, drama, etc. Math occasionally enters the picture, but then quickly leaves, like a pop-out-of-the-closet moment in a horror movie to give the audience a good quick shock. Aaah, numbers and shapes! Oh OK, they're gone now, it's OK, it's OK, I'm fine, I'm fine...

This is odd: those watching A Beautiful Mind need more, not less, visual aid to help them picture what is going on mathematically. In fact, the author of the book A Beautiful Mind says that in interviews, mathematicians always told her that his results in game theory aren't his coolest. One of his more impressive results has a highly geometric flavor, and you can't talk about the basic problem efficiently in just words (even if the proof ends up containing only words and symbols).

Make sure that any book you buy has plenty of pictures if you don't have the math gene (that's true even if you do).

Posted by: Agnostic on July 15, 2007 12:53 PM

I also always did really well on math aptitude tests without, as far as I could tell, having any great aptitude for math. My senior year in high school I was persuaded to take a college math class, which I had to drop after a few weeks--too hard for me.

Whether or not you think anything can be explained in plain English is really just a question of how much detail and complexity you're willing to lose. If you won't settle for any simplification at all, then of course almost nothing in a field with a specialized vocabulary can be expressed in plain English, or at least not in a reasonable number of words. Whereas if you care about only the broadest outlines of something, most everything can be summarized in plain English. It's a question of your priorities.

At a certain point, though, it becomes easier to just teach people a little specialized vocabulary than to try to use "plain English." People can learn new words--they're smart!

Posted by: BP on July 15, 2007 3:18 PM

Here's a crack at explaining proteomics to a non-science readership. Let me know how it works - I hope to do more of these from time to time.

Posted by: Derek Lowe on July 15, 2007 4:58 PM

There's an old 4-volume set called "The World of Mathematics", ed. Newman. You can buy it for $25 or so, or find it in a library. A fair amount of it (perhaps 1/4) is readable English prose. I liked it, and in fact I'm thinking of buying it now.

My experience with math was about like yours. I done moderately well in math when interested, but I'm usually not. I regret this a lot.

Posted by: John Emerson on July 15, 2007 6:08 PM

I think the problem with communicating any complicated ideas is that usually the person doing the imparting of the wisdom has forgotten what it can be like to approach the ideas for the first time. When I was 5 or 6, I wondered why it was that if cars on the road all went the same speed, they didn't bang into each other. Surely the front one needs to go a little faster than the one behind, and so on, until we get to the last car which shouldn't be moving at all! I can laugh at this now, as a much older-year old. But really, what's so funny? Aristotle thought the velocity of objects in free fall depended on their mass and it took humans the better part of 1500 years to work out otherwise. To find out the truth about these intuitions takes a lot of education.

At school I was good at English, and therefore put into the upper math stream. I could never see the point in math or in physics, and consequently played up in class, failed physics and just scraped through in maths. When I was in my early 20s, I read the "nerd-tome" Godel, Escher, Bach, and a light came on somewhere. I had learned the piano as a child and I have always loved Bach, and I have always been intrigued by Escher's pictures - but now a connection had been made between all these things I had hitherto not associated. Not only did I understand the "point" of math, I understood why it was so difficult to explain that point to a teenage schoolboy. Now I wanted to learn all the maths I had tried to ignore at high school. I went back to university and studied maths and physics, and with the more recipe-based problems I found I had some aptitude. With more advanced think-outside-the-box math like analysis and differential geometry, though, I hit a wall. Although I can see what it is I want to understand, despite several years of trying in my spare time to learn more, my progress has been negligible. (At least I can get work doing more prosaic computational stuff now though.)

It may be that teaching maths is "academic sadism". How can any kind of real educating of free and wild young people not occasionally be accused of this? Maths develops the ability to think logically about abstract ideas. As such it hones generic skills that have application in areas outside maths itself. To me, this reason alone is sufficient to provide justification for continuing to inflict maths on all kids all through school. After school they need never do any more. The second thing is that maths teaches you the meaning of the old saying that Mohammed must go to the mountain when the mountain will not come to Mohammed. Grappling with mathematical problems can be irritating and soul-destroying. It can require hard work. But the reward is that solving the problem requires apprehending it in all its aspects -just exactly as it is. You see it in a new light. This extends to the rest of the world: it can lead to a new appreciation of nature. The new ideas don't come from anyone else: they are entirely your own. Developing this approach to problems also has application to the world outside mathematics.

My big lesson from all this is that teaching maths has the fundamental benefit of teaching kids that the world is as it is, and not necessarily as they would like it to be, and imparting skills that have the potential to give each student the ability to see life in new ways by their own agency. I don't think teaching maths is academic sadism so much as (done properly) teaching the virtues of a bit of academic masochism.

I really like John Derbyshire's maths writing and am very interested to see his column. And sorry if this comment is too long.

Posted by: peters on July 15, 2007 7:00 PM

You are aware of course that there is another class of people with precisely the reverse problem: they can deal with symbols and equations with ease, but for the life of them can neither read nor write good English prose on just about any subject. I knew a guy like that at Reed in 1962. He looked sort of like the unabomber, long-haired hermit in the mountains, and he was a kind of idiot savant in all things mathematical -- that, and rock climbing, he could climb anything, even brick walls. He flunked out of Reed for refusing to take the 2 year double-course humanities program. Ended up a meth addict in the Bay Area.

Posted by: Luke Lea on July 15, 2007 11:25 PM

what on earth were these tests measuring?

In my experience as test-taker and -teacher: largely the disposition not to care about the consequences of the test result, or at least not to freak out about them. To be in the moment, thinking about the question, not the status of the class you'll be placed in, college you'll go to, job you'll get, etc.

Posted by: J. Goard on July 16, 2007 5:30 AM

I figured out by sixth grade that I would never be able to make a serious go at math--and I was okay with that. I had no plans to ever deal with it beyond basic figuring, and the experience of sitting there in class and having no idea what was going on (as well as the experience of exasperating my parents and teachers) was proof enough that, for me, math was best avoided.

But come my first year at college I was still being forced to deal with math. I remember thinking, "Here I am paying for my education and looking to major in English or Art History, and I'm still wasting my time not understanding all this numbers crap."

I heard a lot about how math would contribute to making me "well-rounded," and blah and blah and blah. The people saying that generally didn't understand that any math that managed to sink into my feeble brain just dripped out as sludge about a week later. I was incapable of retaining anything.

I ended up taking a course called Symmetry, which, I took it, was intended to allow math dullards such as myself to fulfill the requirement relatively painlessly. It involved studying Escher prints and determining how many points of symmetry they had. Wow, I thought. Escher's cool! Right up my alley!

Wrong. While the course gave me a new appreciation for Escher's complexity, I'm not sure it's the sort of appreciation that can be considered a good thing. Because I now can't look at an Escher without getting that acid-rising-in-the-belly feeling that I experience whenever someone tries to explain something mathematical to me.

I also agree with Michael and several of the comments posters that the ability to present complex things like math in lucid, compact ways is a real talent--one that should be a goal of anyone concerned with helping people to understand and enjoy things. Teachers, in other words.

Later on in my college career, after my math travails were about over, I found myself forced to read a lot of books full of fancy modern art theory. Although I got the jist of what was being expressed in most caes, it was just about as bad as the math. Maybe worse, because in this case the manner of presentation was wringing all the fun out of something I actually started out enjoying. Art, namely.

I confronted my teacher about this. She told me that ideas can be complex, and that sometimes only compex, impossible-to-get-through writing was the only way to do such ideas full justice. The impenetrability (which she fully admitted) was a badge of honor, in other words.

This is a bit like saying that since the true nature of dentistry is cutting and extracting and drilling, the patient should therefore acknowldge it by, you know, actually feeling all that stuff.


Posted by: Ron on July 16, 2007 9:14 AM

I think the general concept of just about anything can be explained to a layperson, but the detailed workings of very complex and abstract mechanisms are probably beyond the English, or any, language.

Also, I was in the same boat as you in school, Michael. I'm a world-class test taker who always scored high on math aptitude tests, but would absolutely fail every advanced math class I was placed in. Test-taking skills and actual aptitude in a subject are very often two different things.

Posted by: the patriarch on July 16, 2007 10:04 AM

1) I call excessive modesty on Derbyshire. Unknown Quantity was an excellent easy read about the development of algebra from ancient times til recently. I'd pick it before his first, award winning, book which dealt with Hard Math. I also reccomend The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry by Mario Livio . He leaves the heavy math for the appendices.

2) Math, unlike many other disciplines, is largely a serial rather than parallel undertaking. If you don't get geometry, you're not going to get trig. If you get a bad math teacher in 3rd grade, you are screwed. I was comfortably on the A track, but senior year HS Calculus totally baffled me. (1979 SAT math 740) I've always felt the aloof Jesuit and I just didn't connect. I stepped down, with great shame and disgrace, to pre-cal. The next year, Calculus at UT was my favorite class. Michael Starbird was responsible for that ( teaching company link. ) Teachers matter. And there are perverse incentives in Math. Mathematicians live and die by "THE PROOF". Students of Math, unless they intend to become professors, live and die by cook-book memorization of "the formulas". What are the solutions to the quartic equation? couldn't tell you, but I could google it and solve any problem involving x^4.

Posted by: KevinM on July 16, 2007 10:42 PM

I've come to feel that testing is often less of a test for what the teacher thinks it is, and more of a test for how well you take a test, especially if it's multiple guess (err, choice). If you know how these tests are usually put together, you can do fairly well on most topics.

I once went to visit a friend still in college, and one morning he had to leave for a test in class. I thought, since it's one of those 200+ student classes, why couldn't I sneak in and take the test as well? Well, I did, and when the scores were posted, in a class that I had never been to, on a topic I knew little about, I made an 84. I started to wish I hadn't gone to a small private school so I could skip more classes!

Posted by: Mike on July 17, 2007 11:51 AM

I was just the opposite, a math whiz who didn't care about English. Thing is, I was good at English, actually, I had a good vocabulary and a reasonable prose style from reading all those damn books when I should have been chasing girls, but I had some idiotic idea that logic was the only thing that mattered and the humanities weren't logical enough. (Hey, I was 15.)

Eventually I came to my senses...

Posted by: SFG on July 17, 2007 6:24 PM


Derbyshire also wrote a really good novel called "Seeing Calvin Coolidge in a Dream." Very well written and entertaining and moving. With some modernist technique in presentation (all short divided paragraphs if I remember correctly) anyway very much worth looking at - DA

Posted by: doug on July 21, 2007 10:22 AM

I think "Mathematics: From the Birth of Numbers" by would be a very good fit for you. You can skim through (parts) of it through Google Books,
and check out the Amazon reviews. I remember tremendously emjoying going through it in high school, and the the little historical asides and cartoons really livened it up.

Posted by: Urijah on July 29, 2007 12:37 AM

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