David's Reviews > Zero: The Biography of a Dangerous Idea

Zero by Charles Seife
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Feb 01, 09

bookshelves: history-of-science, non-fiction

This book made me want to actually learn calculus. At least until the brain fever wore off. :)

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Terran Calculus is beautiful! Unfortunately, they lie to you about why it works. You have to take analysis to find out the truth. (And point set topology and measure theory wouldn't hurt.) [sigh:] So much beautiful math; so little time to study it...


David This book made me see, if only distantly, how beautiful it is. Seife has a rare ability to communicate the wonder of difficult to grasp subjects to laypeople.

I do actually wish I knew calculus.


Terran I agree. I really enjoyed this book. Writing about science and math is hard enough when you're writing to experts. (And, sadly, all too often, scientists are lazy bastard writers themselves and don't even bother to try to make it accessible to experts in the field. E.g., my review of Spline Models for Observational Data.)

When you get away from all of the formalities and symbols and gunk, the core ideas of calculus are (IMNSHO) fairly accessible. In a lot of ways, it's just the study of infinity and continuity -- to hold infinity in the palm of your hand, and eternity in an hour, if you will.

What happens when you add up a bunch of very small things? What happens if you make those small things effectively infinitely small, but make infinitely many of them? Can we think of funky-shaped things as being a bunch of such tiny widgets glued together cleverly? What happens when you look at points that are almost infinitely close together on a shape? What's the difference between a straight line and a curve? If you look extremely close, is there a difference at all?


David "just" the study of infinity - ah, how jaded you are! ;)


Terran I guess what I mean is that all of the crazy notation and formality, while important to get everything really right and to use calculus for applications, mostly just gets in the way of the core understanding. I think a lot of people are daunted by the formality and abstractness of the notation, but would find the ideas accessible if they were presented in the right way.

Infinity itself is a strange idea, but not too hard of one (at least, for most people). It's usually sufficient to think of "something bigger than you've ever imagined", or in the case of infinitesimals, "something smaller than you've ever imagined". Or even just "something really, really big" and "something really, really tiny". When I think about most infinitesimal quantities in calculus, I usually actually visualize tiny, but still nonzero bits. Calculus is mostly about how those tiny bits go together to make up "normal sized" things.


David I think a lot of people are daunted by the formality and abstractness of the notation, but would find the ideas accessible if they were presented in the right way.

I think you're absolutely right. I was teasing about the jadedness - but there's just something amazing (I find) about pondering these sorts of ideas that are really about some fundamental aspects of the world as we know it.


Terran Yeah, that's a lot of what I find beautiful and powerful about math. And also that it describes worlds that never were, so it can be a playground for the imagination. (Banks makes this point in Excession, IIRC.)


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