Zero: The Biography of a Dangerous Idea | Book Review
Zero: The Biography of a Dangerous Idea by Charles Seife is an engaging book that will change the way you view the universe. I first read Zero twenty or so years ago, and I loved it! So, I decided to reread it for my blog’s recent theme of 0. Seife’s writing style is easy to read as he breaks down complicated mathematical and scientific ideas into simple understandable language and illustrations. I also like the fact that he writes it in the style of a biography for us right-brained people. It’s a must read for anyone who is interested in mathematics or mathematics education!
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Summary
Zero has been and continues to be a divisive figure. Seife takes us on journey through history, and we learn about how different cultures embrace or reject the number 0; the consequences are steep. As embracing zero may destroy one’s current worldview but rejecting it impedes progress and discovery. For better or worse zero continually entangles itself with theology and philosophy.
Zero has the power to reveal more knowledge but simultaneously throws up roadblocks to impede progress. This is especially true as zero seems to be always intertwined with its twin: infinity. Every time the scientific and mathematical communities think they have zero figure out a new challenge emerges.
Caveat
This book was first published in 2000 which is over 20 years ago. There may be new discoveries since this book was originally published. Since I am not up-to-date in the most recent scientific developments, this blog post is going to assume that the information is still current.
Theology
Although I am a math (and ELA) educator, my true passion is God’s Word. One of the things I loved about this book is how it challenged me theologically. I believe that it issues a stark warning for Christians. Although the East embraced zero, the West rejected it because it didn’t align with their theological/philosophical beliefs. However, zero wasn’t a problem from a Biblical perspective it was a problem from an Aristotelian perspective. Over the years catholic theology became so intertwined with Greek philosophy (especially Aristotle) that they couldn’t distinguish one from the other. Aristotle like his predecessor Pythagoras rejected zero.
Pythagoras
Pythagoras thought that the entire universe was governed by ratios and shapes, and the planets traveled in concentric spheres that made music. Since the ratio of anything to zero can destroy logic, he rejected it as it didn’t fit into his nice, neat theory of the universe. (He also did the same with irrational numbers. Legend has it he killed one of his disciples that disclosed the existence of irrationals.)
Aristotle
Like Pythagoras, Aristotle believed the earth was the center of the universe surrounded by beautiful spheres. Aristotle declared that infinity did not exist in reality, and it was just a construct of the human mind. Since in Aristotle’s world, infinity didn’t exist there were only a finite number of spheres. The universe was contained in a giant sphere as there was no infinite or void, and God was the prime mover of the spheres. Because his philosophy was so entrenched into the church, questioning Aristotle was equated with questioning God.
Renaissance and Reformation
However, during the Renaissance, zero started making a comeback. Originally, it didn’t pose a threat to the church, because it started out as an artistic tool. However, once the protestant reformation occurred the Catholic Church became touchy about change. Therefore, they doubled down on Aristotle’s philosophy even more heavily than before, and zero became a heretic.
My Response
Throughout the book, Seife discusses the constant struggles between mathematician and theology. With every new discovery, especially related to infinity and zero, people tend to contemplate and mediate on God. Just as many people feel the majesty of God when they view the sunset over the ocean, I suspect thinking about infinity provides mathematicians with a similar experience.
Although, I’m a math teacher, it’s been a long time since I’ve studied Calculus, and even then I was no expert. Reading Zero: The Biography of a Dangerous Idea allows and provokes me ponder on the infinite nature of God and his creative powers. It’s why I really love the book!
Interesting Fact: Leibniz, who invented binary numbers (numbers that can be written in a string of ones and zeroes) considered them to be creation ex niho (creation out of nothing). He stated that the creation of the universe is God/1 and void/0. He used this information to try to convert the Chinese to Christianity. Math as a missionary tool. Ha! He also thought that imaginary numbers, i, was a mix of existence and nonexistence where 1 equaled God and 0 equaled the void. He decided that i was the Holy Spirit.
Application
As time progressed, people could no longer refute the existence of zero (and infinity), yet the reason for so much resistance was misplaced theology on heathen Greek philosophers instead of on our Holy Scriptures. Yet, the church was so entrenched in a secular worldview that they didn’t even recognize it contradicted Scripture. They may have had good motives, but their theology was misplaced, and so grave errors occurred.
I think that is a good lesson for us as Christians. It’s often hard to see our own biases as we are entrenched in the culture in the world around us. That’s why it’s important to test everything against Scripture (God’s only revealed truth) to see if it stands. Otherwise, it’s so easy to go awry without even knowing it. What parts of the world’s and our knowledge base have we unknowingly accepted? Do we know Scripture even well enough to detect errors in our culture?
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Transformational Power of Zero
Zero at times acts crazy and defies logic, but embracing it has transformational power. Using zero in the Arabic numerals allowed banking and trade to advance, since it was easier to do complex equations. Putting zero on a number line helped create a more accurate calendar and allowed for the invention of the Cartesian plane. The Cartesian plane allowed for the intersection of algebra and geometry. Figures and shapes could be turned into equations. Algebra and Geometry were the same thing represented differently.
Without zero calculus could not be invented. Calculus is the combination of differentiation and integration. It allowed scientists to discover the laws that govern the universe. Calculus seems to be the language of nature; nature seems to speak in differential equations, and you need calculus to solve them. Without zero, there is no Calculus, and therefore our ability to understand nature is much more limited.
Mathematics as a Language
In college, I never had to take a foreign language, because the college I attended considered mathematics as a language. With the acceptance of zero, the world discovered that the language of nature is equations, but not just any equations—Differential equations. In a normal linear or quadratic equation, if you substitute a number into an equation, another number or set of numbers comes out. However, in a differential equation, you substitute an equation into the differential equation and another equation comes out.
Zero in Art
Those that know me know that I occasionally dabble in art (although, it’s been quite a few years now as life got busy.) Three out my four grandparents and my mother were all professional artists at one time or another, so I also appreciate the book’s connection to art.
Zero made its appearance in the West via Filippo Brunelleschi who used a vanishing point in his paintings. Mathematically, a point is 0 since it has no dimensions; it has no length, width, or height. A line is one-dimensional, and a shape is two dimensional. (Flatland by Edwin Abbott is also a fun book to read for math educators or theologians/philosophers.)
The vanishing point represents a spot on the canvas that is an infinite distance away from the observer. As objects recede into the distance they get farther and farther away from the observer and get closer and closer to the vanishing point. Everything in the painting that approaches the vanishing point gets smaller as well. Once again zero and infinity are linked.
This idea transformed the art world as suddenly paintings that used a vanishing point seemed three-dimensional and lifelike. And now zero was the center of every painting (or centers if they used multiple vanishing points).
For you educators out there, these art ideas connect to the mathematical concept of a dilation and similarity.
Zero and Infinity
Another thing that fascinated me about this book is the connection between zero and infinity. Infinity, zero, and the idea of limits are all bound together. For one thing, there is an infinite amount of zeroes. This can be demonstrated to students using the mystery box featured in Engaging Math Lesson: Zero Zebras and Infinity and A Mathematical Journey through Zero and Infinity Part 1: A Mystery Box, Some Books, and a Contest blog posts.
Once calculus was invented people could add infinite sums and get a finite result. Not only can you add an infinite number of sums and get a finite number, but some summations approach zero. At other times, as the terms in a sequence approach zero the summation approaches infinity. As Seife puts it, “An infinite sum of zeroes can equal anything at all—and everything at the same time.” Zero and infinity together defy all logic! 0/0 can be any number that you want it to be! Although Calculus is the language of nature, it has zeroes and infinities woven through it. Hence, the eventual invention of the limit.
When Reimann merged projective geometry with complex numbers, lines became circles, circles become lines, and zero and infinity are the poles of the sphere. In his sphere, infinity and zero are equal and opposite, and they are locked in a struggle to consume all other numbers like a black hole.
Scientific Applications
The author then delves into other science-related applications of zero and infinity throughout history. Here are some examples:
- An object gives off an infinite amount of high-energy light as its wavelength approaches 0. Zero wavelength equals infinite energy.
- There is an infinite amount of nothingness in a black hole. A black hole takes up no space at all, but still has mass.
- If a spaceship traveled the speed light, every second in space would equal an infinite amount of time on the earth.
- The electron is a zero-dimensional object, but it has an infinite mass and charge. String theory started treating particles as loops of string (one-dimensional objects) instead of dots (0-dimensional objects) to get around this problem.
Greater Representation in Calculus
As a female Calculus was always boring to me. It’s also the first math class where I struggled. It was hard for me to pay attention and would start daydreaming when my Calculus teacher filled the board with equations with all sorts of fancy notation. Additionally, it was about motion. Velocity and acceleration which has to do with cars, and balls, and rockets. I don’t really care how fast things move. Cars and trucks have always been boring to me, and I tend to tune out to that kind of talk right away. I’m sure many females feel similarily.
But if Calculus were framed as solving the mysteries of the universe—not just the mechanical questions of how, but the metaphysical questions of why? Or the theological questions about the character of God? I think more females would be interested in Calculus.
I know there has been a lot of work trying to get more diverse representation into the hard STEM careers, but possibly reframing Calculus would help. I know it would have intrigued me. That’s why I think all Calculus students (and perhaps pre-Calculus and maybe even Algebra 2 students) should read this book. Instead of talking about cars and rockets, what if Calculus teachers talked about black holes, and an infinite God who created the universe out of the void, or how calculus allows the possibility of space/time travel. Reframing Calculus may lead to higher engagement for underrepresented populations in the hard STEM careers.
Educators
Every middle school and high school math teacher needs to read this book! I believe it’s especially true for Christian educators. The more I dwell on zero and infinity, the more it makes me ponder the infinite majesty of God and his creation. It so remarkable and unfathomable and awesome! Although, awesome doesn’t do enough to describe the emotion.
I would probably share some of the information from this book with middle schoolers and early high schoolers in a very abridged form, but I definitely think it’s a must-read for Calculus students the same way that Flatland is a must read for Geometry students.
Note For my Christian educator readers out there: I imagine that the author is not a creationist as I think he subscribes to the Big Bang theory, but it is such a small mention toward the end of the book. Most of the book is filled with a history of theology, and so it’s worth the read even if you disagree with his world view!
Cross-Curricular Collaboration
Sparking kids imagination could cause greater student engagement. This is why cross-curricular lessons and collaboration are so important. To encourage students in Calculus (especially underrepresented populations), it may be beneficial to collaborate with an English teacher to write science fiction stories based on Calculus. Additionally, there’s a section in Appedix E of Zero: The Biography of a Dangerous Idea on how to Make Your Own Wormhole Time Machine which could engage students.
Disclosure: I only recommend products/books that I think would be helpful to you in your journey as an educator. All opinions expressed here are my own. I am NO longer participating in Amazon’s affiliate link program (8/28/25). Read my full privacy policy here.
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