Zero Book Summary - Zero Book explained in key points

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Zero summary

Name: Zero
Rating: 4.4 (339 reviews)
Author: Charles Seife

Charles Seife

The Biography of a Dangerous Idea

4.4 (339 ratings)

22 mins

Brief summary

Zero by Charles Seife is a fascinating exploration of the concept of 'zero,' its history, and its profound impact on mathematics, science, and human understanding.

Topics

Mathematics Physics Change & Evolution Ancient History

Table of Contents

Zero
Summary of 6 key ideas

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Key idea 1 of 6

What’s in it for me? Discover the history of a heretical number.

Zero is a curious sort of number. It’s not much like 4, or 32, or 83.

When you add zero to other numbers, nothing happens. When you multiply other numbers by zero, you always get zero back. And when you divide by zero, all hell breaks loose.

It’s such a strange number, in fact, that back in the ancient world many great mathematicians denied its existence altogether. And, in modern times, even the philosopher René Descartes claimed it wasn’t real.

But since its eventual acceptance, it’s been found at the heart of pretty much every breakthrough in math or physics. How so? You’re about to find out.

In these blinks, you’ll learn

why the Babylonians invented zero;
why Aristotle banned it; and
why infinity is zero’s twin.

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.

Philosophically minded ancient Greeks rejected zero despite its usefulness.

For many ancient civilizations, numbers were merely tools for counting and dividing up land. For the ancient Greeks, however, numbers were a whole philosophy. Mathematician-philosophers like Pythagoras saw a harmony of numbers within every shape.

But the ancient Greeks were not on board with zero – not at all. In fact, Aristotle declared that it simply didn’t exist; it was merely a product of man’s imagination. And his views on this subject, as on so much else, resounded through the centuries – to the detriment of math in the Western world.

Ancient Indian and Arabic mathematicians embraced zero and made huge mathematical strides.

In ancient India, there was nothing to fear about infinity or zero. While Aristotle rejected these concepts altogether, they were a key part of the Indian belief system. Ancient Indians believed the universe was created from a void of nothingness, and that it was infinite – but that because the world came from nothing, it would one day return to nothingness.

Ancient Indian mathematicians realized that zero deserved a place among the numbers. And that realization opened all sorts of doors.

Embracing zero in the West was theologically tricky, but it yielded a mathematical revolution: calculus.

René Descartes was born in 1596. Like so many great thinkers before him, including Pythagoras, he was both a mathematician and a philosopher. But even he didn’t totally embrace zero.

Descartes lends his name to the Cartesian coordinate system – the x and y axes we learn about in high school. Those two axes have a zero in the bottom left corner by necessity. If you started with 1, you’d soon end up with errors.

Mathematicians soon discovered that zero and its opposite, infinity, had a complex but enthralling relationship.

Quadratic equations are a mainstay of high school math classes. But that doesn’t mean they’re straightforward. Far from it.

Take a seemingly simple one, for instance: x2 + 1 = 0. What’s x?

Zero and infinity aren’t just mathematical concepts – they abound in physics too.

We’ve just been talking about imaginary numbers – but zero and infinity are so real that they make themselves felt in the real world in all manner of important ways. In fact, they underpin many of the advances made in physics over the past hundred or so years.

One example goes back even before that. In the 1850s, physicist Lord Kelvin discovered that it was literally impossible to cool an object below around -273 degrees Celsius. In other words, he discovered absolute zero.

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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.

Zero Review

Zero (2000) delves into the world of mathematics, science, and history to uncover the significance of 'zero.' Reasons to read this book:

It offers a unique perspective on the development of human knowledge and understanding.
The book combines history, philosophy, and science in an engaging and accessible manner.
Readers will gain a newfound appreciation for the power of zero and its influence on our world.

Expand your horizons by reading Zero and uncover the mysteries behind this intriguing concept.

Who should read Zero?

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

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.

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