Cloying Calculus

This is a short rant.

I started off liking David Berlinski’s A Tour of the Calculus. Then, his syrupy, metaphor-ridden, simile-mangled, history-bending style of describing math began to slowly grate on my nerves. If you want to make math accessible, by all means, cut through the jargon. Elucidate, present the concept in easier language, or in terms of easier concepts that we understand. But, don’t obfuscate math by comparing it with the human condition. As much as you like to appeal to the poets within us, a mathematical limit is not like romantic love – and describing it as such leaves the concept just as blithely amorphous as before. At best, such strategies can (temporarily) engage the attention of the non-mathematical within us;  they will not teach us any math at all.

Needless to say, I hated the book and hated myself for being impressionable enough to read all but the last three chapters. From the encomiums on the jacket, you find that The New York Times called it “Playful, witty, highly literate”. It is all of those. It is also a lot of bullshit.

There. I have exhausted my vitriol. Now I need some fresh air.

5 thoughts on “Cloying Calculus”

  1. I own it, and also failed to finish it. I couldn’t quite tell if there was some majesty nuanced into what read like a self-loving caricature of math, or if it really did suck. It’s sad, and maybe I’ll end up finishing; I kind of pride myself on finishing even the dreck (ahem, Chalker). But Berlinski is no Derbyshire.

    At least you made it further than me. I guess. )

  2. Daniel, I would love to read Derbyshire. I see that he has written about Riemann in Prime Obsession, so that looks like a nice place to start.

    About Berlinski, I can’t help getting worked up. At some point, after all the flowery description, I wished he had communicated that, ultimately, math has its own abstract, crystalline beauty and the practice of math for its own sake is wonderful enough. But no, he is obsessed with analogy and story-telling. The dangerous thing about communicating math through analogy is that the analogy, especially human analogy is extremely subjective while the meanings of mathematical definitions are not. Who is to say what aspect of love (“so near yet so far”) I associate with a limit?

    I recently finished Paul Lockhart’s Mathematician’s Lament, and he did a much better job at communicating the magic of math in two chapters than Berlinski did in fifteen. Also, if you haven’t yet looked up Simon Singh’s book on Fermat’s Last Theorem, I’ll recommend it heartily.

  3. I’ve read both Lockhart’s and Singh’s pieces, and enjoyed them both. The only Derbyshire I read was Unknown Quantity: The History of Algebra, which I found fascinating. He manages to humanize the subject and uses a punchy wit, as opposed to a rhapsodic, lilting, bard-like approach Berlinksi might, while only making algebra more enticing for it.

    It’s actually quite pertinent, as I consider what to do with a (recently completed) math (undergrad) degree. That’s a pretty pedestrian attitude, and I certainly won’t regret doing nothing directly mathematical, at least not much (a part of me would question taking from 1998 through 2010 to complete the degree program); but at the same time, I’d like to reap some fruit from the effort.

    One consideration is to enter some kind of pedagogical endeavor, e.g., working in local home-schooling networks to help develop solid mathematical resources, contributing to local or regional policy discussions, applying all these social-network appendages to creating or contributing to a grassroots educational organization, etc. All of which, notwithstanding the meandering narcissism, is to say that the divide between Singh, Lockhart, Derbyshire on one hand, and Berlinski on the other, might align with the divide between inviting pedagogical methodologies, and those that serve institutional preservation over student enrichment.

    With any luck, that babble makes some sense. There isn’t much place for the Berlinski school of trite, self-aggrandizing blathering, not in a popular treatment of mathematics, and not in anything resembling a classroom. It’s a stretch, I guess, to indict Berlinski as a symptom of anything more than his ego, much less of a defeatist educational institutionalism, but I’m going to try anyway.

    “Learners should not be forced to submit to an obligatory curriculum, or to discrimination based on whether they possess a certificate or diploma. Nor should the public be forced to support, through regressive taxation, a huge professional apparatus of educators and buildings which in fact restricts the public’s chances for learning to the services the profession is willinig to put on the market. It should use modern technology to make free speech, free assembly, and a free press truly universal and, therefore, fully educational.” Illich, Deschooling Society, 1971

    I can’t help getting worked up, either, it appears.

  4. Daniel, yes – math education needs some new teaching methods urgently, not just to do justice to math-as-art, but also to make it understandable and less intimidating to a larger audience. I was giving a talk recently, and in the middle of the presentation, felt like apologizing for showing what would be the only 2 slides with equations in a whole day of presentations. I was worried that the listeners – very few of whom were academics – would just look at the equations and shut down their receptors. In the case of this particular audience, I needn’t have worried, but there is definitely a less-than-cheerful attitude toward math among many people.

    It never occurred to me that social networking can help in the respect; How cool would that be!

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