In a recent NOVA documentary, “Zero to Infinity,” host Talithia Williams explains the origins of zero and how zero has affected our approach to the mathematical concept of infinity. Prior to its introduction, people around the world contented themselves with just counting the things they had. Why, it was thought, would people bother to count the countless things they did not have. That would be a waste of time and energy.
Asian Indians fully developed the concept of zero around 500 A.D., centuries after zero was first introduced to the world. One theory is that it came from a need to mark a silent beat in Indian percussive music. The notation they used was a •; eventually this became an open circle, much like our modern-day 0.
On the surface, zero and infinity seem like opposites. Yet because of zero, cultures could now conceive of numbers going into infinity in each direction – negative and positive – from a 0-starting point (etc., -3, -2-, -1, 0, +1, +2, +3, etc.). Further, zero changed calculations forever: multiply any number by zero, the result is zero; conversely, divide any number by zero, the result is infinity.Cultures around the world accept these formulae, which show that zero and infinity contain all numbers.
Zero and infinity can be viewed from a Zen perspective.
Buddhism, which also began in India (before zero’s development), included teachings of the earliest sutras containing the idea of Sunyata, or Emptiness. These writings later evolved to become the Diamond Sutra and the Heart Sutra, both of which focus on Form and Emptiness as two sides of the same coin. You cannot have one without the other.
Many people feel there is something or someone that ties all things together, but what is it? There may be different names for that intangible “something” depending on their personal inclination: subatomic particles, God, spiritual intuition. Whatever we call it, though, it manifests itself in our daily lives as a myriad of forms or things, both material and non-material: computer, dog, idea, numbers. The intangible becomes the tangible with which we interface every moment, and yet the intangible retains its original nature throughout.
The Zen symbol “Enso” is a circle that represents Emptiness; at the same time the enso contains all things in the Universe before they are differentiated. From this perspective, we see that out of Emptiness comes all things, just as out of zero comes infinity. Here, mathematics and Zen come together.
Zero and infinity at the same time. Emptiness and Form at the same time.