Zero: The Biography of a Dangerous Idea

By Charles Seife

A New York Times Notable Book.

The Babylonians invented it, the Greeks banned it, the Hindus worshiped it, and the Church used it to fend off heretics. Now it threatens the foundations of modern physics. For centuries the power of zero savored of the demonic; once harnessed, it became the most important tool in mathematics. For zero, infinity's twin, is not like other numbers. It is both nothing and everything.

In Zero, Science Journalist Charles Seife follows this innocent-looking number from its birth as an Eastern philosophical concept to its struggle for acceptance in Europe, its rise and transcendence in the West, and its ever-present threat to modern physics. Here are the legendary thinkers—from Pythagoras to Newton to Heisenberg, from the Kabalists to today's astrophysicists—who have tried to understand it and whose clashes shook the foundations of philosophy, science, mathematics, and religion. Zero has pitted East against West and faith against reason, and its intransigence persists in the dark core of a black hole and the brilliant flash of the Big Bang. Today, zero lies at the heart of one of the biggest scientific controversies of all time: the quest for a theory of everything.

• Language: English
• Publisher: Penguin Books
• Release date: Sep 1, 2000
• ISBN: 9781101199602

Charles Seife

Charles Seife is the author of Decoding the Universe, Alpha & Omega, and Zero, which won the PEN/Martha Albrand Award for first nonfiction book and was named a New York Times Notable Book. An associate professor of journalism at New York University, he has written for Science magazine, New Scientist, Scientific American, The Economist, Wired, The Sciences and many other publications. He lives in New York City.

Book preview

Chapter 0 Null and Void

Zero hit the USS Yorktown like a torpedo.

On September 21, 1997, while cruising off the coast of Virginia, the billion-dollar missile cruiser shuddered to a halt. Yorktown was dead in the water.

Warships are designed to withstand the strike of a torpedo or the blast of a mine. Though it was armored against weapons, nobody had thought to defend the Yorktown from zero. It was a grave mistake.

The Yorktown’s computers had just received new software that was controlling the engines. Unfortunately, nobody had spotted the time bomb lurking in the code, a zero that engineers were supposed to remove while installing the software. But for one reason or another, the zero was overlooked, and it stayed hidden in the code. Hidden, that is, until the software called it into memory—and choked.

When the Yorktown’s computer system tried to divide by zero, 80,000 horsepower instantly became worthless. It took nearly three hours to attach emergency controls to the engines, and the Yorktown then limped into port. Engineers spent two days getting rid of the zero, repairing the engines, and putting the Yorktown back into fighting trim.

No other number can do such damage. Computer failures like the one that struck the Yorktown are just a faint shadow of the power of zero. Cultures girded themselves against zero, and philosophies crumbled under its influence, for zero is different from the other numbers. It provides a glimpse of the ineffable and the infinite. This is why it has been feared and hated—and outlawed.

This is the story of zero, from its birth in ancient times to its growth and nourishment in the East, its struggle for acceptance in Europe, its ascendance in the West, and its ever-present threat to modern physics. It is the story of the people who battled over the meaning of the mysterious number—the scholars and mystics, the scientists and clergymen—who each tried to understand zero. It is the story of the Western world’s attempts to shield itself unsuccessfully (and sometimes violently) from an Eastern idea. And it is a history of the paradoxes posed by an innocent-looking number, rattling even this century’s brightest minds and threatening to unravel the whole framework of scientific thought.

Zero is powerful because it is infinity’s twin. They are equal and opposite, yin and yang. They are equally paradoxical and troubling. The biggest questions in science and religion are about nothingness and eternity, the void and the infinite, zero and infinity. The clashes over zero were the battles that shook the foundations of philosophy, of science, of mathematics, and of religion. Underneath every revolution lay a zero—and an infinity.

Zero was at the heart of the battle between East and West. Zero was at the center of the struggle between religion and science. Zero became the language of nature and the most important tool in mathematics. And the most profound problems in physics—the dark core of a black hole and the brilliant flash of the big bang—are struggles to defeat zero.

Yet through all its history, despite the rejection and the exile, zero has always defeated those who opposed it. Humanity could never force zero to fit its philosophies. Instead, zero shaped humanity’s view of the universe—and of God.

Chapter 1 Nothing Doing

[THE ORIGIN OF ZERO]

There was neither non-existence nor existence then; there was neither the realm of space nor the sky which is beyond. What stirred? Where?

—THE RIG VEDA

The story of zero is an ancient one. Its roots stretch back to the dawn of mathematics, in the time thousands of years before the first civilization, long before humans could read and write. But as natural as zero seems to us today, for ancient peoples zero was a foreign—and frightening—idea. An Eastern concept, born in the Fertile Crescent a few centuries before the birth of Christ, zero not only evoked images of a primal void, it also had dangerous mathematical properties. Within zero there is the power to shatter the framework of logic.

The beginnings of mathematical thought were found in the desire to count sheep and in the need to keep track of property and of the passage of time. None of these tasks requires zero; civilizations functioned perfectly well for millennia before its discovery. Indeed, zero was so abhorrent to some cultures that they chose to live without it.

Life without Zero

The point about zero is that we do not need to use it in the operations of daily life. No one goes out to buy zero fish. It is in a way the most civilized of all the cardinals, and its use is only forced on us by the needs of cultivated modes of thought.

—ALFRED NORTH WHITEHEAD

It’s difficult for a modern person to imagine a life without zero, just as it’s hard to imagine life without the number seven or the number 31. However, there was a time where there was no zero—just as there was no seven and 31. It was before the beginning of history, so paleontologists have had to piece together the tale of the birth of mathematics from bits of stone and bone. From these fragments, researchers discovered that Stone Age mathematicians were a bit more rugged than modern ones. Instead of blackboards, they used wolves.

A key clue to the nature of Stone Age mathematics was unearthed in the late 1930s when archaeologist Karl Absolom, sifting through Czechoslovakian dirt, uncovered a 30,000-year-old wolf bone with a series of notches carved into it. Nobody knows whether Gog the caveman had used the bone to count the deer he killed, the paintings he drew, or the days he had gone without a bath, but it is pretty clear that early humans were counting something.

A wolf bone was the Stone Age equivalent of a supercomputer. Gog’s ancestors couldn’t even count up to two, and they certainly did not need zero. In the very beginning of mathematics, it seems that people could only distinguish between one and many. A caveman owned one spearhead or many spearheads; he had eaten one crushed lizard or many crushed lizards. There was no way to express any quantities other than one and many. Over time, primitive languages evolved to distinguish between one, two, and many, and eventually one, two, three, many, but didn’t have terms for higher numbers. Some languages still have this shortcoming. The Siriona Indians of Bolivia and the Brazilian Yanoama people don’t have words for anything larger than three; instead, these two tribes use the words for many or much.

Thanks to the very nature of numbers—they can be added together to create new ones—the number system didn’t stop at three. After a while, clever tribesmen began to string number-words in a row to yield more numbers. The languages currently used by the Bacairi and the Bororo peoples of Brazil show this process in action; they have number systems that go one, two, two and one, two and two, two and two and one, and so forth. These people count by twos. Mathematicians call this a binary system.

Few people count by twos like the Bacairi and Bororo. The old wolf bone seems to be more typical of ancient counting systems. Gog’s wolf bone had 55 little notches in it, arranged into groups of five; there was a second notch after the first 25 marks. It looks suspiciously as if Gog was counting by fives, and then tallied groups in bunches of five. This makes a lot of sense. It is a lot faster to tally the number of marks in groups than it is to count them one by one. Modern mathematicians would say that Gog, the wolf carver, used a five-based or quinary counting system.

But why five? Deep down, it’s an arbitrary decision. If Gog put his tallies in groups of four, and counted in groups of four and 16, his number system would have worked just as well, as would groups of six and 36. The groupings don’t affect the number of marks on the bone; they only affect the way that Gog tallies them up in the end—and he will always get the same answer no matter how he counts them. However, Gog preferred to count in groups of five rather than four, and people all over the world shared Gog’s preference. It was an accident of nature that gave humans five fingers on each hand, and because of this accident, five seemed to be a favorite base system across many cultures. The early Greeks, for instance, used the word fiving to describe the process of tallying.

Even in the South American binary counting schemes, linguists see the beginnings of a quinary system. A different phrase in Bororo for two and two and one is this is my hand all together. Apparently, ancient peoples liked to count with their body parts, and five (a hand), ten (both hands), and twenty (both hands and both feet) were the favorites. In English, eleven and twelve seem to be derived from one over [ten] and two over [ten], while thirteen, fourteen, fifteen, and so on are contractions of three and ten, four and ten, and five and ten. From this, linguists conclude that ten was the basic unit in the Germanic protolanguages that English came from, and thus those people used a base-10 number system. On the other hand, in French, eighty is quatre-vingts (four twenties), and ninety is quatre-vingt-dix (four twenties and ten). This may mean that the people who lived in what is now France used a base-20 or vigesimal number system. Numbers like seven and 31 belonged to all of these systems, quinary, decimal, and vigesimal alike. However, none of these systems had a name for zero. The concept simply did not exist.

You never need to keep track of zero sheep or tally your zero children. Instead of We have zero bananas, the grocer says, We have no bananas. You don’t have to have a number to express the lack of something, and it didn’t occur to anybody to assign a symbol to the absence of objects. This is why people got along without zero for so long. It simply wasn’t needed. Zero just never came up.

In fact, knowing about numbers at all was quite an ability in prehistoric times. Simply being able to count was considered a talent as mystical and arcane as casting spells and calling the gods by name. In the Egyptian Book of the Dead, when a dead soul is challenged by Aqen, the ferryman who conveys departed spirits across a river in the netherworld, Aqen refuses to allow anyone aboard who does not know the number of his fingers. The soul must then recite a counting rhyme to tally his fingers, satisfying the ferryman. (The Greek ferryman, on the other hand, wanted money, which was stowed under the dead person’s tongue.)

Though counting abilities were rare in the ancient world, numbers and the fundamentals of counting always developed before writing and reading. When early civilizations started pressing reeds to clay tablets, carving figures in stone, and daubing ink on parchment and on papyrus, number systems had already been well-established. Transcribing the oral number system into written form was a simple task: people just needed to figure out a coding method whereby scribes could set the numbers down in a more permanent form. (Some societies even found a way to do this before they discovered writing. The illiterate Incas, for one, used the quipu, a string of colored, knotted cords, to record calculations.)

The first scribes wrote down numbers in a way that matched their base system, and predictably, did it in the most concise way they could think of. Society had progressed since the time of Gog. Instead of making little groups of marks over and over, the scribes created symbols for each type of grouping; in a quinary system, a scribe might make a certain mark for one, a different symbol for a group of five, yet another mark for a group of 25, and so forth.

The Egyptians did just that. More than 5,000 years ago, before the time of the pyramids, the ancient Egyptians designed a system for transcribing their decimal system, where pictures stood for numbers. A single vertical mark represented a unit, while a heel bone represented 10, a swirly snare stood for 100, and so on. To write down a number with this scheme, all an Egyptian scribe had to do was record groups of these symbols. Instead of having to write down 123 tick marks to denote the number one hundred and twenty-three, the scribe wrote six symbols: one snare, two heels, and three vertical marks. It was the typical way of doing mathematics in antiquity. And like most other civilizations Egypt did not have—or need—a zero.

Yet the ancient Egyptians were quite sophisticated mathematicians. They were master astronomers and timekeepers, which meant that they had to use advanced math, thanks to the wandering nature of the calendar.

Creating a stable calendar was a problem for most ancient peoples, because they generally started out with a lunar calendar: the length of a month was the time between successive full moons. It was a natural choice; the waxing and waning of the moon in the heavens was hard to overlook, and it offered a convenient way of marking periodic cycles of time. But the lunar month is between 29 and 30 days long. No matter how you arrange it, 12 lunar months only add up to about 354 days—roughly 11 short of the solar year’s length. Thirteen lunar months yield roughly 19 days too many. Since it is the solar year, not the lunar year, that determines the time for harvest and planting, the seasons seem to drift when you reckon by an uncorrected lunar year.

Correcting the lunar calendar is a complicated undertaking. A number of modern-day nations, like Israel and Saudi Arabia, still use a modified lunar calendar, but 6,000 years ago the Egyptians came up with a better system. Their method was a much simpler way of keeping track of the passage of the days, producing a calendar that stayed in sync with the seasons for many years. Instead of using the moon to keep track of the passage of time, the Egyptians used the sun, just as most nations do today.

The Egyptian calendar had 12 months, like the lunar one, but each month was 30 days long. (Being base-10 sort of people, their week, the decade, was 10 days long.) At the end of the year, there were an extra five days, bringing the total up to 365. This calendar was the ancestor of our own calendar; the Egyptian system was adopted by Greece and then by Rome, where it was modified by adding leap years, and then became the standard calendar of the Western world. However, since the Egyptians, the Greeks, and the Romans did not have zero, the Western calendar does not have any zeros—an oversight that would cause problems millennia later.

The Egyptians’ innovation of the solar calendar was a breakthrough, but they made an even more important mark on history: the invention of the art of geometry. Even without a zero, the Egyptians had quickly become masters of mathematics. They had to, thanks to an angry river. Every year the Nile would overflow its banks and flood the delta. The good news was that the flooding deposited rich, alluvial silt all over the fields, making the Nile delta the richest farmland in the ancient world. The bad news was that the river destroyed many of the boundary markers, erasing all of the landmarks that told farmers which land was theirs to cultivate. (The Egyptians took property rights very seriously. In the Egyptian Book of the Dead, a newly deceased person must swear to the gods that he hasn’t cheated his neighbor by stealing his land. It was a sin punishable by having his heart fed to a horrible beast called the devourer. In Egypt, filching your neighbor’s land was considered as grave an offense as breaking an oath, murdering somebody, or masturbating in a temple.)

The ancient pharaohs assigned surveyors to assess the damage and reset the boundary markers, and thus geometry was born. These surveyors, or rope stretchers (named for their measuring devices and knotted ropes designed to mark right angles), eventually learned to determine the areas of plots of land by dividing them into rectangles and triangles. The Egyptians also learned how to measure the volumes of objects—like pyramids. Egyptian mathematics was famed throughout the Mediterranean, and it is likely that the early Greek mathematicians, masters of geometry like Thales and Pythagoras, studied in Egypt. Yet despite the Egyptians’ brilliant geometric work, zero was nowhere to be found within Egypt.

This was, in part, because the Egyptians were of a practical bent. They never progressed beyond measuring volumes and counting days and hours. Mathematics wasn’t used for anything impractical, except their system of astrology. As a result, their best mathematicians were unable to use the principles of geometry for anything unrelated to real world problems—they did not take their system of mathematics and turn it into an abstract system of logic. They were also not inclined to put math into their philosophy. The Greeks were different; they embraced the abstract and the philosophical, and brought mathematics to its highest point in ancient times. Yet it was not the Greeks who discovered zero. Zero came from the East, not the West.

The Birth of Zero

In the history of culture the discovery of zero will always stand out as one of the greatest single achievements of the human race.

—TOBIAS DANZIG, NUMBER: THE LANGUAGE OF SCIENCE

The Greeks understood mathematics better than the Egyptians did; once they mastered the Egyptian art of geometry, Greek mathematicians quickly surpassed their teachers.

At first the Greek system of numbers was quite similar to the Egyptians’. Greeks also had a base-10 style of counting, and there was very little difference in the ways the two cultures wrote down their numbers. Instead of using pictures to represent numbers as the Egyptians did, the Greeks used letters. H (eta) stood for hekaton: 100. M (mu) stood for myriori: 10,000—the myriad, the biggest grouping in the Greek system. They also had a symbol for five, indicating a mixed quinary-decimal system, but overall the Greek and Egyptian systems of writing numbers were almost identical—for a time. Unlike the Egyptians, the Greeks outgrew this primitive way of writing numbers and developed a more sophisticated system.

Instead of using two strokes to represent 2, or three Hs to represent 300 as the Egyptian style of counting did, a newer Greek system of writing, appearing before 500 BC, had distinct letters for 2, 3, 300, and many other numbers (Figure 1). In this way the Greeks avoided repeated letters. For instance, writing the number 87 in the Egyptian system would require 15 symbols: eight heels and seven vertical marks. The new Greek system would need only two symbols: π for 80, and ζ for 7. (The Roman system, which supplanted Greek numbers, was a step backward toward the less sophisticated Egyptian system. The Roman 87, LXXXVII, requires seven symbols, with several repeats.)

Though the Greek number system was more sophisticated than the Egyptian system, it was not the most advanced way of writing numbers in the ancient world. That title was held by another Eastern invention: the Babylonian style of counting. And thanks to this system, zero finally appeared in the East, in the Fertile

Reviews for Zero

[booktsunami · Rating: 4 out of 5 stars]

When my primary school teacher mocked me for saying that 1/0 was infinity......I felt very vexed. To me it was obvious. But he was the authority figure. He claimed it was meaningless. Strangely, I’ve never forgotten this so I’ve always been fascinated by the concepts of infinity and Zero. Hence my interest in this book. But I haven’t had the advantage of reading it in the original. I’ve only read it as the Blinkist summary version and undoubtedly, one misses a great deal by doing this. Still, I’ve learned some things and been reasonably impressed. I’ve included a few snippets below which capture the essence of the book for me.
“Zero didn’t exist in the earliest days of math; it first emerged in ancient Babylonia.....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.”....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....Really, it was just a placeholder denoting an absence.
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.....But one philosopher, Zeno, devised a paradox that questioned this accepted belief....Every time Achilles catches up with where the tortoise was, it’s already moved ahead. The gap between them becomes smaller and smaller . . . but Achilles can never quite get there. Right?....We all know that, in reality, Achilles would simply overtake the tortoise. That’s because the gap between Achilles and the tortoise has a limit: zero....But the Greek mathematical system couldn’t account for Zeno’s paradox–because it banished zero.
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. Here's the key message: Ancient Indian and Arabic mathematicians embraced zero and made huge mathematical strides.....Along with negative numbers, the ancient Indians were happy to include zero in their number system; it fit neatly between the positives and the negatives. But they still thought it was sort of strange.
How many Os are there in 1? The twelfth-century Indian mathematician Bhaskara realized the answer was infinity.....Incidentally, infinity had strange properties too; you could add or subtract any number, and it stayed exactly the same.
When these mathematical advances reached Muslim, Jewish, and Christian thinkers, it was a big deal.......Eventually, though, all three adopted them......The Christians were the last to accept zero
Embracing zero in the West was theologically tricky, but it yielded a mathematical revolution: calculus. ...Descartes lends his name to the Cartesian coordinate system....Yet Descartes would always insist that zero itself did not actually exist. Having been brought up on Aristotle's teachings, zero was just a step too far for him.....If we stay on a two-dimensional grid, things become pretty complicated so the mathematician Bernhard Riemann realized that it made more sense to visualize things on a sphere.
Imagine a sphere with i at one point on it, and -i directly across from it. Perpendicular to those two points are 1 and-1. And what goes at the top and bottom points of the sphere? Zero and infinity......The strange logic of math with complex numbers reveals that zero and infinity are equal and opposite poles, just like 1 and-1.
The Riemann sphere makes some previously problematic equations easier to understand. Take y = 1/x, for example. In two dimensions, it looks messy: the curve shoots out of the picture toward infinity as x approaches zero. But on the sphere, it makes perfect sense: the curve simply reaches the topmost point.
Zero and infinity aren't just mathematical concepts-they abound in physics too.....It's actually impossible to ever reach the temperature of absolute zero, because absolute zero is the state a gas reaches when it has zero energy at all. But absolute zero really is there, as a limit, in the natural world.......Another zero in physics was uncovered by the work of Albert Einstein: the black hole.........despite taking up zero space, it still has mass.
According to string theory, the universe exists in ten or possibly eleven dimensions, so what seems like zero to us may not really be zero when all the other dimensions are factored in.
Nothing can be created from nothing, the poet and philosopher Lucretius once said. But that nothing has strange, mystical properties. And we're still uncovering them today”.
What’s my overall take on the book? I though it was pretty good. Covered a lot of ground.....most of the concepts I was familiar with though I still struggle a bit with Zeno’s paradoxes. The solutions seem a little too glib for me. I also wonder whether we should treat both zero and infinity as concepts rather than as numbers. If numbers, then they are certainly very strange. And maybe dividing a finite number by zero makes as much sense as dividing it by “blue”. (Though blue doesn’t fit into a sequence neatly as zero does. Happy to give the book four stars but still feel I don’t really have a good grasp on what “nothing” is.

[tgraettinger_1 · Rating: 4 out of 5 stars]

This book started off slowly for my tastes and expectations, with a strong philosophical and cultural bent. For me, it picked up steam once the author got more into the mathematical and scientific aspects of the "bio". Even there, I found it surprising how much the religious and cultural overtones impacted the thinking about science and math.

[skid0612 · Rating: 2 out of 5 stars]

Really enjoyable opening few chapters after which the book became a chore to read. Life is too short......

[seriousgrace · Rating: 4 out of 5 stars]

No other number can do so much damage, so says Charles Seife. He tells you this as he is explaining the Golden Ratio, how Winston Churchill is equal to a vegetable, and how you can make your very own wormhole. Mathematics, religion, philosophy, art, engineering, history: they all connect to zero. Mathematics is a more obvious element, but take religion: Shiva, one of the three gods in the Hindu triumvirate, represents nothing because Shiva's role is to destroy the universe in order to perpetually recreate it. Seife goes deep to illustrate the importance of the zero and how, historically, it created as well as calmed chaos. Zero is historical and humorous, informative and even a little emotional.

[hefau-358932 · Rating: 5 out of 5 stars]

This book was entrancing from start to finish, filled with fascinating information on mathematics and history. Seife follows the progression of the idea of zero through human history, and he weaves this expertly with tales from many disciplines: art, philosophy, engineering and more. Well written and endlessly entertaining, I see myself rereading this over and over.

[tronella_1 · Rating: 3 out of 5 stars]

This is probably better suited to someone who hasn't read much about the history of maths/physics before, but it's a nice framing device, and I did like the parts about conflicts between religion and science. It covered a lot of old ground for me, but ymmv.

[danhammang · Rating: 5 out of 5 stars]

Great read, mathematics, history, humor. Just fine for the non-mathematician. It is a history of the number zero and the ideas behind it. They are large ideas that have had a big impact on culture that usually take backstage to our everyday use of the number. What a joy it is to read an accomplished mathematician who engages with history and culture, who can explain his profession to a broad audience. I highly recommend this short, fun read.

[joanaxthelm · Rating: 5 out of 5 stars]

A historical narrative of the evolution of the number Zero. The story starts before history starts and leads up to contemporary times. Written in a fascinating and engaging way - there are even a few illustrations!

Lexile: 980

[stef7sa-1 · Rating: 4 out of 5 stars]

Interesting read. Most surprising the representation of complex numbers as points on a globe. The physics part at the end seemed a bit far fetched.

[themulhern · Rating: 4 out of 5 stars]

Generally lively and fun book w/ a few flaws. The somewhat inaccurate historical asides as footnotes are a bit troubling, but sometimes they end up in parentheses instead, which is more annoying. The preface, about a division-by-zero error in some software on a US Navy ship is just too metaphorical to be anything but ridiculous to a practicing software engineer. The illustration enliven the book w/out generally contributing much to understanding. Chapter 1 discusses number systems and some of the arithmetic properties of 0. Chapter 2 discusses many aspects of Greek mathematics and also the fact that our calendar has no year 0. I tend not to celebrate arbitrary dates, so I never took any interest in the "when is the true millenium?" discussion, and I still don't. Chapter 3 gives credit to the Hindu mathematicians for actual inventing zero and our decimal number system and digits, talks about numerology, and the Fibonacci sequence, and gives an etymology for the word "stockholder". Chapter 4 discusses Copernicus and Ptolemy, the Cartesian coordinate system, the vanishing point in perspective drawing, atmospheric pressure, and Pascal's wager. Chapter 5 is mostly about the early stages of calculus, from Archimedes' method of exhaustion to Newton, Leibniz, Bishop Berkley, and L'Hopital's rule. The connection with zero is often tenuous, but a book that was actually just about zero would probably be very boring. There is some discussion about a connection between math and religion; I know about the Pythagoreans and their distress over irrational numbers...but the rest just seems goofy.

All in all, a fun read w/ some real math in it.

[le.vert.galant · Rating: 3 out of 5 stars]

The portion of the book dealing with post-Newtonian physics and mathematics is not terribly interesting or different than dozens of other popular science books; however, the earlier chapters on the dissemination of zero from the East to the West are quite engaging.

[pieterpad_1 · Rating: 2 out of 5 stars]

A little glib and concept-driven, linking such diverse topics as cosmology, calculus, and single-point perspective through a common dependence on the concept of zero. It's an attractive idea, but not pursued very consistently. The "danger" of the title, for example — that the idea of void (and its opposite, infinity) was just too weird and threatening to be accepted in many cultures — promises to offer insights into the history of ideas and knowledge, but the author is content to state his case and rarely enlarges on its historical significance. He's particularly sketchy on the ancient Greeks, but does write interestingly on Renaissance and early modern thinkers on the subject. The style is brisk, sometimes gee-whiz, and often repetitive, by no means up to such writers as George Gamow and James Gleick. There is an extensive bibliography and the book seems well indexed.

[kcshankd · Rating: 4 out of 5 stars]

Do they still have bookclubs? This was part of a set of books on numbers: pi, i, ln2, golden ratio that was an introductory offer in the early aughts. I've resolved to read them this year.

This is a great, readable account that starts with paleolithic counting sticks and ends up in string theory. I could mostly follow along, only giving up on Riemann spheres and the different sized infinities of real and imaginary numbers - there are apparently infinitely more imaginary numbers than the infinite set of real numbers. Um, okay math, I'll take your word for it.

There was one rambling two page section explaining Aristotle's idea of the cosmos and perfection that repeated the same points three times - it read as if a set of lecture notes were dropped on the floor and hastily retrieved. Otherwise well worth the effort.

[katiebrugger-1 · Rating: 5 out of 5 stars]

This book covers mathematics, history, philosophy, the history of science, and quantum physics. An interesting observation I learned from this book: the next time someone calls you “a zero” or you hear someone use zero as a pejorative term, you will know that person is ignorant of the true meaning of the word. Zero is an important number and is as big as infinity. To be zero is to be everything.

The book begins by exploring the beginnings of numerical symbols in the Middle East cultures of Greece, Egypt, and Babylonia a few hundred years before the beginning of the current era.

The history of zero (at least west of India, this book does not cover China) begins in the Babylonian civilization concurrent with ancient Greece. The Babylonians discovered how to write numbers using a place system, and this necessitated a placekeeper meaning “naught.”

The first half of the book traces the resistance to the idea of zero from the early Greeks and Egyptians to Aristotelian-influenced Christianity. None of these cultures’ belief-systems could allow for the concept of the void, of nothingness. Christianity had absorbed Greek philosophy and one of the elements of this philosophy was the aversion to the idea of nothing. The Greeks did not believe that nothing or infinity existed. Even though the Bible begins with God creating the universe out of the void, the Judeo-Christian tradition ignored this to follow the Aristotelian credo that there is no void and there is no infinity.

Zero was heretical to the Catholic church. Only with the Renaissance did zero become accepted in Europe. With the Reformation came the loosening of strictures against free thought, and the European mind opened up to new ideas. With the introduction of zero began the advances in mathematics and science that have led to the technological civilization of today.

But the concept of zero is a latecomer to our culture and we have not completely integrated it into our cultural paradigm. Look at a computer keyboard. Zero is not in its proper place before 1 where it belongs; it is dangling up above 9. Look at a telephone. Zero is stuck below the three-by-three keypad of numbers in a limbo symbol-land of asterisk and pound sign.

The author goes on to trace the development of science, using zero as the focal point, up to modern-day quantum physics. Quantum physics gives an understanding of zero analogous to white light. As white light contains all colors, zero contains all within it. There is no such thing as nothing. Vacuum is not nothing; it is everything.

[teenielee · Rating: 3 out of 5 stars]

Guess what? The Biography of Zero is just as awesome as you think it might be.

[lisamaria_c · Rating: 3 out of 5 stars]

Two stars represents on Goodreads "it was okay" and I think that's about right. Yet that feels too low, because I did get through this book, and that usually represents at least a three to me--that I liked it--unless I find an ultimate WTF moment. If I was tempted to mark it lower, I think it's that I found this book so uneven. I'm not sure exactly what kind of background in mathematics would be ideal to enjoy this book. I made it to differential calculus in college, and it didn't break me, but it's been a long time since then and at this point I doubt I could solve an equation beyond simple algebra. There were parts of this book where I felt absolutely lost, particularly Chapter Six "Infinity's Twin" on projective geometry, set theory and transfinite numbers, yet so much else, even in later chapters, felt too elementary for anyone with just a high school education--or at least too familiar. And really, I think he was pushing it in trying to embrace the science of everything through the lens of the concept of zero.

At the same time there were tidbits throughout I did find interesting--sometimes fascinating--such as the "Casimir effect" of Quantum mechanics that some speculate could be used to power starships. The thing is those familiar areas? I think Stephen Hawking and Carl Sagan explain and describe them better--and those things not familiar are I think due more to the fact this was published in 2000--so it has more recent findings included than Sagan's Cosmos (1980) or Hawking's A Brief History of Time (1988). So as a science book it didn't impress me--and I just don't find this in the running for a great history book either--where it felt superficial. It was cool to learn Arabic Numerals should actually be known as Indian--because that's where the Muslims got them from--and that the Indians got zero from the Babylonians who were using it in 500 BC--but I felt the history part of zero in the book could be encapsulated in a few pages, so much so the title is almost a misnomer. Neither as science or history did this rock my world.

[kaionvin · Rating: 4 out of 5 stars]

0
+ ( It's a book about math. And I read it. ) - ( It took me nine months. )
= 0

For three weeks after I finished Zero: The Biography of a Dangerous Idea, its central figure looked out ominously at me. In that way, Charles Seife was entirely successful in this piece of pop-nonfiction, weaving together the creation of the "zero", its place in history of mathematical theory, its religious controversies, its philosophical significance and ultimately, its . It's to Seife's credit that he manages to weave out of these eclectic approaches a coherent story that borders at times upon the epic... while never being too important not to include an irreverent tangent about Pythagoras's acute dislike of beans.

If anything, Seife trends too sprightly at times. Though I admire his stance in neither dumbing down the material nor making it intimidating for the casual reader, at some point, no matter how breezily one explains black holes or the Casimir effect- there's no disguising that there are some vast concepts being covered. As it is, I believe you definitely have to at least of heard of some of these ideas (particularly in the last third) to enjoy the new contexts he weaves for them in his narrative. Myself, I sort of managed alright with some first year Calculus and Physics schooling.

I can't say I ever turned down the chance for more trivia, and Zero delivered in spades. Also, know this: the first appendix details a mathematical proof on why Winston Churchill is a carrot.

[flexatone_1 · Rating: 3 out of 5 stars]

Zero is organized well enough, moving along history from its start as a placeholder to its linchpin in calculus. Following his explanation of calculus, though, the book descends into a rehashing of, say, A Brief History of Time and the narrative becomes diffuse. Throughout, Seife's data and research are compelling, even if his arguments (connecting Aristotle, faith, and the notion of zero) are not always convincingly conveyed.

[sarahfrierson · Rating: 4 out of 5 stars]

I recommend this book not because you will enjoy reading it. In fact, I guarantee you will not. But it is a book that everyone should read. Don’t get me wrong, it is a wonderfully well-written book and it will fly by from the moment you read the first chapter, but it is very painful have to experience even a moment of what Abdulrahman Zeitoun experienced during and after Hurricane Katrina. Eggers is able to masterfully tell this story that touches on family, faith and the responsibility of a government, all while giving the readers a chance to step into the shoes of one who lived it, if only for a moment.

[billhatfield_1 · Rating: 4 out of 5 stars]

Fascinating take on the history of ideas from the perspective of a mathematician. Argues that the exclusion of zero/infinity from the Western thought process (since Aristotle) limited and formed our philosophical and religious ideas and ultimately our early development in science. Seems like a stretch, but the author makes a convincing case. Also tracks the use of zero/infinity from India through the Islamic countries and ultimately into the West. The real joy of the book is in its sweep through history from this unique perspective. Lots of fascinating, little-known historical trivia tidbits throughout.

[crazybatcow · Rating: 4 out of 5 stars]

It's, err, about Math. Why on earth I'd pick this up considering I barely understand division is beyond me. It's not bad for a "layperson" to follow, really, though a lot of the examples were over my head (i.e. I still don't understand the concept of Zero being infinity...)

It's an interesting look at the evolution of math, and interesting in that I hadn't realized that Zero is a relatively new understanding for humankind. (I wonder if the aliens gave it to us?)

Anyway, it's good for what it is, but I won't be investing any time in mathematical research anytime soon... math is hard!

[m2campanella · Rating: 4 out of 5 stars]

An interesting little book which gives you an extraordinarily insightful look at the History of Mathematics, how it progressed in societies and how societies progressed with it. It is also a nice way to gage just how well you know the subject. I know mathematics at about the level of the Renaissance.

[rcgamergirl · Rating: 5 out of 5 stars]

I found the first part of this book interesting, as I had never realized how radical the idea of zero was considered. The rest of it I loved; it brought back many pleasant memories of my Philosophy of Science and Vistas in Astronomy courses. The only complaint I had was that I wanted more details about the topics (and that’s not bad for an introductory book)!

[pratchettfan · Rating: 4 out of 5 stars]

An intriguing look at the history of a special number, zero. Written in an easily digestible form it gives a great overview over the clash of philosophies which happened around zero and what effects of them we still face today. Not only for science and math buffs!

[_zoe__1 · Rating: 4 out of 5 stars]

I was initially skeptical about this book, because in the early chapters I felt like Seife sometimes presented questionable anecdotes as fact. Plus, for the chapters that I knew the most about, I lamented the lack of footnotes, which isn't really a fair criticism of a popular science work. The book quickly won me over, though, and I often found myself reluctant to put it down. The story presented here is about much more than math: there's history, philosophy, religion, and modern physics too. Much of the material was already familiar to me, but Seife brought it all together into a satisfying overview of the evolution of western thought. I would recommend this even to people who don't particularly like math; it's not very technical and is full of information that would be interesting to anyone.

[maowangvater · Rating: 4 out of 5 stars]

Starting with the Egyptian and Greek geometricians Seife relates the history of a number with very peculiar properties and its polar opposite, infinity. That makes this a book about nothing and everything. He uses it to mathematically prove that Sir Winston Churchill was a carrot and includes instructions on how to “make your own wormhole time machine.” For the most part he uses drawings rather than mathematical formulae to illustrate concepts, making this a very accessible book for the non-mathematicians among us.

[co_coyote · Rating: 4 out of 5 stars]

This is a most interesting book about the number zero. I don't believe I ever realized before what a radical idea it was, and what havoc it played with number theory, such as it was in Aristotle's day and for centuries to come in the West. Seife's ability to explain the role of zero, and its twin, infinity in conjunction with imaginary numbers and Riemann geometry was like an epiphany. Is it too late to become a mathematician? Highly recommended, especially if you are not a mathematician.

[kaelirenee · Rating: 4 out of 5 stars]

Not only has zero not always existed, numbers aren't quite as concrete as our math teachers would have us believe. Seife presents the entire history of counting and numbers before getting into the history, philosophy and theology surrounding the number zero (and frequently, infinity).
It helps to be somewhat comfortable with mathematical concepts, but it is not mandatory at all. Nor is it mandatory to know much about Greek philosophy-and the two get about as much attention.
This is an excellent and sweeping history of how religion has had to change itself because of the immutable idea of nothingness. This also goes into the history of physics, particularly quantum physics and string theory, and astronomy. This is because, in almost all situations, mathematical theorums work beautifully and explain nature and the cosmos-until you have to account for zero.

Well writen and researched. Highly recommended for any level reader-layman or expert.

[pw0327 · Rating: 5 out of 5 stars]

Charles Seife has written an excellent book on the concept of zero. An idea that had been taken for granted for years. No one really understand the meaning of the value of the concept of zero at first, but once contemplated, the concept is quite ingenious.

I thought Seife did a very admirable job introducing the concept, following along on the chronology and explaining why it was such a devious and subversive concept to the church and to philosophy in general. I found his explanations lucid and clear and the history is quite interesting. The chapter on projective geometry was particularly enlightening.

Where he really shines is when he coupled zero with infinity. I have always had a real problem with the relativity concept, even when I was studying physics. But Seife does an excellent job explaining all of the ideas. Where he falters is where he tries to make the connection between the numbers with the theories of modern physics, perhaps it is the problem with the concept of superstrings that bogs the narrative down into the morass of incomprehention, but the narrative does bog down when it enters this section. Since Brian Green has written a much bigger and thicker book on the subject of superstrings, I would hazard to guess that the fault does not lie with Seife but with the subject, which is, by the way, a sub-area of the book, so I wouldn't worry about it. Even if no one understands the connection between modern physics and zero, the book is a rewarding read.

[teaperson_1 · Rating: 2 out of 5 stars]

There's an adage of TV newswriting: tell 'em, tell 'em, and tell 'em again. Mr. Seife apparently belongs to this school. He tells us uncountably times (>0 but less than infinity) that zero was dangerous. Still, the book covers a lot of ground in an approachable manner. I just wished he would stop repeating himself.