Zero | Charles Seife

Summary of: Zero: The Biography of a Dangerous Idea
By: Charles Seife

Introduction

Dive into the intriguing world of ‘Zero: The Biography of a Dangerous Idea’ by Charles Seife, as we embark on a captivating journey through the origins and repercussions of zero. This fascinating read explores the absence of zero in primitive mathematics, its conception in ancient Babylonia, and the subsequent controversy among ancient civilizations. Uncover the critical role zero played in shaping Indian and Arabic mathematics, and how they made crucial strides. Be prepared to delve into the complicated Western reception of zero, and witness the revolutionary impact it sparked in the realm of calculus. Finally, the book intricately weaves these concepts into the fabric of physics, revealing the undeniable power and mystery that surrounds zero, even today.

The Birth of Zero

Back in the Stone Age, there was no need for the concept of zero. But over time, the ancient Babylonians realized that something – or rather, nothing – was missing. The Babylonian counting system, which was sexagesimal, had just two symbols. At 60, they’d just start again with the “1” symbol. Sixty and 1 were represented by the same symbol. 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. 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.

The Ancient Greeks and Zero

The ancient Greek’s philosophy of numbers and their rejection of zero despite its usefulness led to Zeno’s paradox, which questioned conventional beliefs. Aristotle’s influence on banning zero led to a lack of understanding of infinity until later.

The ancient Greeks had a unique view of numbers, considering them a whole philosophy rather than mere tools for counting. They saw a harmony of numbers within every shape, with mathematician-philosophers such as Pythagoras at the forefront of this philosophy. However, while the Greeks had much insight into numbers, they vehemently rejected zero, considering it non-existent. Aristotle, one of the most influential philosophers in history, declared that zero was merely a product of man’s imagination.

This rejection of zero had significant consequences, leading to Zeno’s paradox, a mind-bending concept that questioned conventional wisdom. The paradox explored whether Achilles could overtake a tortoise that had a one-foot head start in a race. While Achilles could make up the one-foot advantage, the tortoise would have already moved a little bit further. This cycle could repeat infinitely, making it impossible for Achilles to overtake the tortoise. However, we know that in reality, this is not the case, as the gap between Achilles and the tortoise becomes zero.

The Greeks’ mathematical system couldn’t explain Zeno’s paradox because it did not account for zero. Aristotle taught that zero and the infinite did not exist, making everything finite. However, this assumption raised questions, such as what happened before time began, which either leads to the answer of nothing at all or an infinite starting point. By excluding zero and infinity from their system, the Greeks and, later on, the Western world lacked an understanding of these concepts until much later.

While zero was excluded from the ancient Greek belief system, this was not the case in the East, where Aristotle’s influence was not as significant. In conclusion, the ancient Greeks’ philosophical approach to numbers and rejection of zero led to a lack of understanding of infinity until later.

The Indian Concept of Infinity and Zero

The ancient Indian belief system held that the universe was created from nothingness, and it was believed to be infinite. This belief allowed ancient Indian mathematicians to embrace zero as a number and led to significant mathematical advancements. Unlike ancient Greek mathematicians, who made sense of numbers in terms of proportions and shapes, Indian mathematicians conceived numbers in abstract terms. They used zero as a separate number and found that it fit neatly between the positive and negative integers. However, they also found that some of its properties, like multiplication and division, were strange. These new mathematical concepts were initially challenging to the worldview of Muslim, Jewish and Christian thinkers, who were heavily influenced by Aristotle. Eventually, they all adopted the Arabic system of counting, which included the digit for zero, in favor of the cumbersome Roman system.

The Theological Implications of Zero

This book summary delves into the theological complexities of zero and how embracing its mathematical significance led to the development of calculus. The Cartesian coordinate system introduced by René Descartes necessitated the existence of zero, but Descartes, influenced by Aristotle’s teachings, would not fully accept its existence. However, later mathematicians like Isaac Newton and Gottfried Leibniz realized the importance of zero and used it to develop calculus. While this was a significant mathematical advancement, the concept of zero and infinity in calculus raised theoretical questions, which were eventually resolved by Jean Le Rond d’Alembert’s explanation of limits.

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