
Without zero, mathematics as we know it would not exist. And without mathematics our understanding of the universe would be vastly impoverished. But where did this nothing, this hollow circle, come from? And what, exactly, does it mean? For Kaplan, the history of zero is a lens for looking not only into the evolution of mathematics but into very nature of human thought. He points out how the history of mathematics is a process of recursive abstraction: how once a symbol is created to represent an idea, that symbol itself gives rise to new operations that in turn lead to new ideas. The beauty of mathematics is that even though we invent it, we seem to be discovering something that already exists. The joy of that discovery shines from Kaplan's pages, as he ranges from Archimedes to Einstein, making fascinating connections between mathematical insights from every age and culture.--From publisher description.
The interpretation of the concept that been different over time. See perhaps The Nothing That Is: A Natural History of Zero by Kaplan:
Charles Seife's "Zero: The Biography of a Dangerous Idea" (http://www.amazon.com/Zero-Biography-Dangerous-Idea-ebook/dp...)
Robert Kaplan's "The Nothing That Is: A Natural History of Zero" (http://www.amazon.com/Nothing-that-Natural-History-ebook/dp/...)
Both were great reads and left me energized. Neither had much to do with technology or startups. But I felt more prepared and motivated to solve problems after I read them.
"""A Roman idiosyncrasy about counting reinforced this avoidance. The 360 degrees of longitude, for example, were always measured from the vernal equinox, which lies in the zodiacal sign of Aries. This should be zero degrees, 0°. It was common, however, to call it instead 'the first degree', Aries 1°, as Pliny did around 60 AD, upsetting his calculations and those of many who followed him. It amounts to this: if you lay out four marks on the ground and step from the first to the last, have you taken three paces or four? Clearly three; yet four marks were involved. To get the right answer it helps to call the starting-line 'zero'; then the number at the mark you step on will correspond to the number of your steps. But the Romans counted so that three days after Sunday was Tuesday; the Italian for the fifteenth century is the quattrocento — and all of us still call the two steps in music from C to E a major third, taking the number from the three tones involved."""
I wouldn't say that the set that has one element, labeled 0, _has_ zero elements; it has one element with the label 0. Right?
