New film from NOVA plunges to the extremes of our numerical consciousness, demonstrating the bounds of zero and infinity throughout time and history
BOSTON, MA; November 15, 2022—ZERO TO INFINITY, a new one-hour special from NOVA—a production of GBH—explores the stories behind the seemingly obvious and indispensable concepts of zero and infinity. This documentary examines how these relatively recent human inventions came to be—not just once, but over and over again as different cultures invented and re-invented them across thousands of years. ZERO TO INFINITY premieres Wednesday, November 16, 2022 at 9pm ET/8C on PBS. The film, hosted by Harvey Mudd College Professor of Mathematics and Statistician Talithia Williams, will also be available for streaming at pbs.org/nova, NOVA on YouTube, and via the PBS Video app.
In science and mathematics, the most influential ideas are often the simplest. While zero and infinity appear simple, both concepts provoke our understanding of the universe, and force us to reckon with where we situate ourselves within time and space. Some infinities are larger than others as Georg Cantor, a 19th century German mathematician, has proven. But what does that actually mean in our modern world? In ZERO TO INFINITY, Dr. Talithia Williams explores some of our most fundamental mathematical concepts through several entertaining experiments and philosophical discussions.
Zero is a number that is often overlooked, but within its history is the story of our civilization. It is unlike any other number, signifying an absence rather than a countable quantity. While we might assume zero is intuitive, ancient civilizations such as the Sumerians, Babylonians, Egyptians, Ancient Greeks and Romans did not have a number zero. As far as we know, zero as a mathematical concept has arisen only twice. The Maya had a mathematical concept of zero depicted with the image of a sea shell. And the zero that we commonly use today originated in India about 1,700 years ago. By the seventh century, zero was in use in Indian mathematics systems as shown by the work of the influential astronomer and mathematician Brahmagupta who wrote rules for multiplication, addition, and subtraction of zero and investigated negative numbers. Today we see Brahmagupta’s lasting legacy when we place zero at the center of the number line between positive and negative numbers—a revolutionary idea that changed mathematics and made zero a legitimate number.
Before the Indian system became widely adopted, the main purpose of written numerals was for recording numbers, not calculating with them. Calculations were made with a variety of techniques and devices, such as abacuses or counting boards while numerals only served to store the results. But the Indian system uses the same numerals for storage and calculation—a fundamental breakthrough that is often taken for granted. This innovative system eventually became the most popular in the world, but not until after the ninth century when the work of Muhammad ibn Musa al-Khwarizmi, a Persian scholar in a variety of subjects, and other Islamic mathematicians helped spread the Indian Numeral system throughout and beyond the Islamic empire, a hub of industrial and intellectual trade at that period.
The film then shifts its historical lens to Europe, where the Indian-Arabic numeral system’s earliest users were Italian merchants who recognized its immediate advantages for business records and calculations. But it wasn’t made familiar to many until 1202, when the son of an Italian merchant, Leonardo of Pisa—better known today as Fibonacci—wrote a mathematics book called Liber Abbaci (The Book of Calculation) which showed people how to use the Indian-Arabic system for calculations. Ultimately, it would take hundreds of years for the new numerals to become the dominant mode of recording and calculating numbers. But by the 17th century the new system had been widely adopted in Europe, and it then spread around the world thanks to the printing press. Zero being a primarily modern phenomenon raises the question—who are we without zero?
Treating zero as a number transformed mathematics, because it is unlike any other number. Zero has unique properties, with some that make it a number and others that make it more of a concept. In subtraction and multiplication zero acts uniquely, but zero poses real problems for division—how do you divide a tangible thing by nothing? The film follows Talithia as she considers this paradox, named after the Greek philosopher Zeno of Elea, through an archery experiment with Paralympian and Physics and Engineering teacher Eric Bennett. Before zero came to be, Zeno invented a paradox that encapsulates its problem of division through the instantaneous speed of an arrow traveling to its target.
On the other end of the spectrum ZERO TO INFINITY also explores the philosophy of infinity, asking—what does it mean to be infinite? Infinity is one of the most powerful tools in math. Talithia meets Cornell University Mathematician Steve Strogatz at the National Museum of Mathematics (MoMath) in New York City where he poses a problem that confounded the ancients: how to find the area of a circle. He demonstrates the clever solution using—of all things—a pizza and in the exercise presents the power of infinity to provide a simple answer.
Later, along with Mathematician Eugenia Cheng, Talithia also visits the imaginary Hilbert’s Hotel, a thought experiment first proposed by Mathematician David Hilbert that further explores the mysterious and mind-bending properties of infinity. Hilbert asked a series of seemingly simple questions: If a hotel with an infinite number of rooms is full, is there room for one more guest? What room number would that person occupy? How about two more guests? How about an infinite number of new guests? Hilbert’s brilliant solutions are both surprising and down to earth in the way that they seemed to tame this untameable idea.
Next, with the help of mathematician Georg Cantor’s Real Numbers, Talithia and Eugenia discover that not all infinities are created equal. One of Cantor’s questions was: Can different infinities be larger than others? “His argument is so simple…so profound. It is one of the most ingenious, innovative ideas ever inserted into the study of numbers,” says Mathematician Manjul Bhargava of Princeton University. “Our understanding of infinity is forever changed because of Cantor’s incredible work.”
With a playful approach to some of our most abstract and philosophical concepts, ZERO TO INFINITYbrings together heavy hitters from the fields of math, science, and history to tell the story of our modern understanding of these numbers and notions. For humankind, the journey from zero to infinity has been extraordinary. The introduction of zero revolutionized mathematics and enabled a new means of calculation that helped to advance science, and harnessing the power of zero and infinity through calculus made many of our most vital technological breakthroughs possible. ZERO TO INFINITY explores the range of possibilities zero and infinity offer, and how the imaginative studies of these two concepts help us appreciate how we live in a universe of infinite possibilities.
“ZERO TO INFINITY tells the compelling story of two of the strangest beasts in all of mathematics,” saidProducer/Director Dan McCabe. “The film surprisingly reveals that in some ways, ‘nothing’ and ‘everything’ can be seen as two sides of the same coin.”
ZERO TO INFINITY premieres Wednesday, November 16, 2022 at 9pm ET/8C on PBS and will be available for streaming at pbs.org/nova, NOVA on YouTube, and via the PBS Video app, available on iOS, Android, Roku streaming devices, Apple TV, Android TV, Amazon Fire TV, Samsung Smart TV, Chromecast and VIZIO. PBS station members can view many series, documentaries and specials via PBS Passport. For more information about PBS Passport, visit the PBS Passport FAQ website.
ZERO TO INFINITY is a NOVA Production by Big House Productions, Inc. for GBH. Hosted by Talithia Williams. Produced by Kendra Gahagan and Daniel McCabe. Written by Daniel McCabe. Directed by Daniel McCabe and Jaroslav Savol. Executive Producers for NOVA are Julia Cort and Chris Schmidt. NOVA is a production of GBH. ZERO TO INFINITY is distributed internationally by PBS International.
ZERO TO INFINITY is made possible (in part) by the John Templeton Foundation.
Funding for NOVA is provided by Brilliant Worldwide, Inc. Consumer Cellular, the NOVA Science Trust, the Corporate for Public Broadcasting, and PBS viewers.