It was fairly easy for me to identify at exactly which point in "Zero: A Biography of a Dangerous Idea" (by Charles Seife) I surpassed my mathematical comfort zone. Up til we get into truly modern physics I found myself nodding along thinking 'well, that's obvious.' Until all of a sudden, it wasn't so obvious, and while I understand the concepts to a degree, I couldn't conceptualize them. I suppose some people can think in 10-dimensions of space/time, but I ain't one of them.
This is no fault of Seife's, who writes with wit and clarity, but rather reflects the intellectual paradigm in which I've grown up. Not just educationally, but experientially. I can't understand the posited fifth through tenth dimensions because I have lived in 3 (and with consideration, 4. "Time" fits in quite well with length, width and depth. If you think about it, you take it into account everday, whether it's driving, crossing the street to avoid traffic, or running to catch a flyball playing softball) and am perhaps only physiologically capable of seeing the world in those terms. (I may be splitting the logicial hair here, but the fact that humans cannot observe something does not mean it is necessarily unobservable.)
So while it's easy to ridicule the anti-Copernicans, or the Greeks who refused to even countenance the existence of 'zero,' to them, the concept of a void and/or infinity (the book is particularly excellent in discussing the infinity/zero duality) seemed as bizzare, counter-inutitve and frankly looney as something like String Theory might seem to me.
There's a generalizable principle at work here, I think, but I'm not sure I can spell it out just right, any suggestions?
Pooh's View: informative, educational, and most importantly digestable even for those who are terrified by derivatives, limits and Zeno's Paradox.