We like his way of explaining it so much we’ll transcribe it for you:
There are many realities out there. There is, of course, the physical reality we find ourself in. Then there are those imaginary universes that resemble physical reality very closely, such as the one where everything is exactly the same except I didn’t pee in my pants in fifth grade, or the one where that beautiful dark-haired girl on the bus turned to me and we started talking and ended up falling in love. There are plenty of those kinds of imaginary realities, believe me. But that’s neither here nor there.
I want to talk about a different sort of place. I’m going to call it “mathematical reality.” In my mind’s eye, there is a universe where beautiful shapes and patterns float by and do curious and surprising things that keep me amused and entertained. It’s an amazing place, and I really love it.
The thing is, physical reality is a disaster. It’s way too complicated, and nothing is at all what it appears to be. Objects expand and contract with temperature, atoms fly on and off. In particular, nothing can truly be measured. A blade of grass has no actual length. Any measurement made in this universe is necessarily a rough approximation. It’s not bad; it’s just the nature of the place. The smallest speck is not a point, and the thinnest wire is not a line.
Mathematical reality, on the other hand, is imaginary. It can be as simple and pretty as I want it to be. I get to have all those perfect things I can’t have in real life.
(Quoted from page 1 of Measurement, by Paul Lockhart. Harvard University Press, 2012.)
For a brief biography of Paul Lockhart, click here. For images of or relating to Paul Lockhart, click here.
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