Zero Book Summary - Zero Book explained in key points

Zero summary

Charles Seife

The Biography of a Dangerous Idea

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What is Zero about?

Zero (2000) is the fascinating story of a number banned by the ancient Greeks and worshipped by ancient Indians. Zero – as well as its twin, infinity – is a number that’s been at the heart of both mathematics and philosophy over the centuries.

About the Author

Charles Seife is a journalist and author who teaches at New York University. He studied mathematics at Princeton and Yale, and his other books include Proofiness, Alpha & Omega, and Decoding the Universe.

Table of Contents
    Key idea 1 of 6

    Zero didn’t exist in the earliest days of math; it first emerged in ancient Babylonia.

    Can you imagine a world with zero numbers?

    Back in the Stone Age, that was how things were – until some enterprising cavepeople started carving notches onto a wolf bone.

    What were they counting? We don’t know. But it must have been something practical, like animals or spearheads. Because prehistoric math was strictly functional, there was no need for the concept of zero. They didn’t need a special word for “zero” deer; there just . . . weren’t any deer.

    But, over time, math advanced, and people developed complex counting systems. And the ancient Babylonians eventually realized that something – or rather, nothing – was missing.

    This is the key message: Zero didn’t exist in the earliest days of math; it first emerged in ancient Babylonia.

    To understand why zero first appeared, you’re going to need to know how the ancient Babylonian counting system worked. So, here’s a quick breakdown.

    You probably know that our modern counting system is decimal, or in base 10: we group things into 1s, 10s and 100s. But back in ancient Babylonia, the system was sexagesimal – it was in base 60. And get this: it had just two symbols.

    Those two symbols represented “1” and “10.” The Babylonians just repeated those symbols however many times they needed – much like in the later, better known Roman system. Fifty, for instance, would be five times the “10” symbol; fifty-one would be the same plus a “1” symbol – and so on, until you got to 60.

    Here’s the confusing bit: at 60, they’d just start again with the “1” symbol. Sixty and 1 were represented by the same symbol. And so was 60 times 60, or 3,600.

    If you’re thinking that sounds ambiguous, you’re right. But it was especially ambiguous when it came to numbers like 61 and 3,601. Those were both represented simply by two “1” symbols, side by side. So how could you tell the difference between them?

    Eventually, the Babylonians found a solution: zero. To write 3,601, they wrote a totally new symbol in between the two “1” symbols; this made clear that the first number wasn’t 60, but a degree higher up. This was the birth of zero.

    But this still wasn’t quite our modern-day zero. Really, it was just a placeholder denoting an absence. It was only later on that the strange, mystical properties of zero would become fully apparent – to the amazement, and horror, of the ancient Greeks.

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    Who should read Zero

    • Popular science enthusiasts
    • History buffs curious about how concepts have evolved over time
    • Philosophers interested in everything . . . and nothing

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