Math Thoughts of a Young Mathematician

I specifically recall two mathematical ideas from my early school days:

When we were in the 2nd or 3rd grade, my friends and I would spend our time writing down integers, one after another, starting from 1 and going into the thousands. This task had no goal other than producing a really mammoth set of sheets of numbers, higher and higher, to dizzying heights. What were we thinking??!
I believe that I began to come to grips with the concept of infinity by this futile effort.
When it came to contemplating the universe, I would sometimes worry that our world was actually contained within a shoebox in another boy's room, and that he might shake it and send us careening around the place. Worse than that, his world might also be contained within a shoebox in another boy's room, and so on, ad infinitum, and if any shoebox should be shaken up the line, why all would be lost. It led to a certain vertigo, a sense that nothing was really as stable as it seemed....

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Updated on 01/14/2008 06:01:12