Zeroing in on Emptiness: Understanding Emptiness Through the Lens of Number Zero

How did zero invite the number one to hang out? “Hey, let’s kick it! I promise it’ll be a zero-pressure situation!” Now, I must admit this does NOT feel like a zero-pressure situation. As keen as I was to serve up this Sangha Share, I’ve got to confess, blending Buddhist emptiness with mathematical zero is like juggling tofu and bowling balls – not your everyday combo! So, if you catch yourself nodding off during my brainy banter, no worries! You can blame Ginger, our Zen master, for letting an over-ambitious chemical engineer like me take the stage!

In Buddhism, the concept of “emptiness” is a fundamental philosophical idea that plays a central role in understanding the nature of reality and the path to enlightenment. On its essence, emptiness refers to the idea that all phenomena lack inherent, independent existence. Instead, they are dependently originated, meaning they arise in dependence on causes and conditions, and are interrelated with everything else in the universe. The idea of emptiness can be challenging to understand, as it runs counter to our ordinary way of perceiving and understanding the world. However, it is a key concept in Buddhist philosophy, particularly in Mahayana Buddhism. Nagarjuna, the third century Buddhist philosopher monk of the Madhyamika school said, “When emptiness is possible, everything is possible. Were emptiness impossible, nothing would be possible.”

So, the question then arises what is the world empty of? The Buddha was asked by his cousin and longtime attendant, Ananda, “Venerable sir, it is said, ‘Empty is the world, empty is the world.’ In what ways it is said, ‘empty is the world’?”  The Buddha replied, “It is, Ananda, because it is empty of self and of what belongs to self that it is said, ‘Empty is the world.’” Buddha said, in our obsession with self, we are like a barking dog tied to a post, running endlessly and fruitlessly around a single point, yet we fundamentally misunderstand what it is. “In whatever way they conceive of self,” he said, “the fact is ever other than that.” Philosophically saying, the world is empty of self is a clear statement of absence. Later, we will see how this corresponds to the number Zero.

Buddhism views excessive self-centeredness as the primary source of suffering. This self-identification happens in several ways – “I” as the body (for example, I am thirty five years old), the owner of the body (my eyes are black), the emotions (‘I am happy’ – we equate “I” with happiness, an emotion), the owner of emotions (my joys and my sorrows), the observer (‘I am seeing’, ‘I am hearing’). If we investigate these identifications, the emptiness of the self becomes evident. If I say I am thirty-five years old, I don’t necessarily mean all of me is thirty-five. After all, are my thoughts thirty-five years old? What is the age of the mood I am feeling right now? Perhaps it came on today or a few minutes ago. Similarly, we cannot find the “owner of the body” as we are unable to pin down the exact location of the owner.  When we move from “I am happy” to “my joys and my sorrows”, we are moving from identifying with the emotion to being the owner of the emotions.  Am I the emotion or the owner of the emotion? Can I be both? J. Krishnamurthi, the Indian philosopher and sage of the last century was fond of saying, “The observer is observed.” In other words, “the observer does not exist apart from the observed.” When we are observing anger, we are in part, that anger. When we are observing love, we are that love. We do not stand apart from the experience. When we think that what we really are is separate from what we experience, we create an auxiliary entity that does not exist. We are reminded of the famous comment by Ludwig Wittgenstein that the self is only a shadow cast by grammar.

For two and half millennia, Buddhist practitioners have explored emptiness and found the highest levels of happiness and freedom. Yet, it must be said that emptiness is an unusual term for the central philosophy of a spiritual teaching. Therefore, we need to examine the word “emptiness” with much more precision. The quality of something being empty is the simplest meaning of emptiness. These two words, empty and emptiness, are in language terms, adjective and noun. The noun emptiness is derived from the adjective, empty. We need to remember that that when a noun is derived from an adjective, it doesn’t mean the noun refers to something that exists independently as an object on its own. This is the trickery of language. Therefore, let’s go to the source of the Buddhist teachings. The Sanskrit word for empty is Shunya. This word, Shunya, in my mother tongue, Bengali (which inherited words from Pali, Buddha’s spoken language), is literally the term for number zero. The word emptiness, in Pali, Sunyata, then means the “the quality of being zero.” Therefore, the Buddhist teachings of emptiness/sunyata and the symbolism of number zero seems inextricably linked.

Alright, folks, brace yourselves as we embark on a wild journey into the mystical land of mathematics! From counting cookies to deciphering the secrets of the universe, math takes us on a rollercoaster ride of numerical excitement. But fear not, I won’t subject you to the mind-bending madness of differential calculus… well, maybe just a little bit. So, buckle up as we unravel the enigma of the number zero in the wonderful world of math!

Zero, that cheeky little O without a figure, as Shakespeare so eloquently put it, struts around like it owns the place in the wacky world of mathematics! But seriously, why does this humble digit steal the spotlight and hog all the glory in any list of the most important numbers? And hold on to your hats because here comes the real kicker: some folks actually had the audacity to claim that because 0 times 0 equals 0, that somehow proves numbers are as real as it gets! Talk about seeing the world through math-colored glasses!

Now picture this: you’re staring at a bowl filled with five juicy apples, but here’s the twist – the number ‘five’ doesn’t belong to any single apple. Nope, not even to the sneaky last one you counted, because let’s face it, you could’ve shuffled them around and changed the whole game! And if you happen to devour one of those delicious apples (hey, hunger strikes!), suddenly the mystical number ‘five’ seems to vanish into thin air! Where did it go, you ask? Well, that’s the million-apple question!

So, what is it with the curious case of zero! While names happily attach themselves to objects, poor zero is left pondering the void, counting the absence of things. It counts the totality of what isn’t there. It’s neither team positive nor negative – talk about being stuck in the world’s smallest no-man’s land! But fear not, because zero is not just lounging around; it’s the ultimate referee, marking the boundary between the positive and negative realms like a pro! That’s why it’s the star player on many scales, boldly standing at the starting line like it’s the grand marshal of a number parade. And get this: zero is not just a pretty face; it’s the secret sauce behind explaining stuff that’s so abstract, it doesn’t even bother with physical forms!

When 0 is coupled with 1 we get the entire world of whole numbers. In fact, we can use the concept of zero to derive all the other numbers in the universe.

Let’s take a thought exercise first described by the mathematician John von Neumann. It’s deceptively simple.

Imagine a box with nothing in it. Mathematicians call this empty box “the empty set.” It’s a physical representation of zero. What’s inside the empty box? Nothing.

Now take another empty box and place it in the first one.

How many things are in the first box now?

There’s one object in it. Then, put another empty box inside the first two. How many objects does it contain now? Two. And that’s how we derive all the counting numbers from zero … from nothing. This is the basis of our number system. Zero is an abstraction and a reality at the same time. “It’s the nothing that is,” said the Harvard math professor Robert Kaplan.

Ah, poor zero, the loneliest digit in the numerical universe! It’s like the oddball at a party, always needing someone else to tag along for the ride. Left, right, center – zero’s always looking for a companion to tag along.  But let’s be real, without its numerical squad, zero’s just like a lone wolf howling at the moon – a bit lost and maybe a tad melodramatic! Ring any bells? Ah yes, the timeless teachings of emptiness! Just like how emptiness highlights the interconnectedness and impermanence of all things, zero relies on its numerical buddies to give its life some meaning. It’s a match made in mathematical nirvana!

Zero’s influence on our mathematics today is twofold. One: It’s an important placeholder digit in our number system. Two: It’s a useful number in its own right.

Let’s talk about everyone’s favorite number, 107! But hold up, what’s that zero doing there? It’s not just chilling – it’s the unsung hero of the tens column, keeping things in check like a boss. Without it, we’d be in a world of numerical chaos, mistaking our glorious 107 for a mere 17! So let’s give a big round of applause to zero, the ultimate placeholder, ensuring we never underestimate the power of proper place value!

Zero isn’t just a representation of nothingness; it also serves as a versatile part of speech. Whether it’s playing the role of a noun, verb, adverb, or adjective, like in “zero possibility” or “we zeroed in on the cause,” its meaning can vary. When used as a verb, such as “zeroing in on emptiness,” it implies narrowing down options until only one remains, essentially equating zero to one. However, when describing “The result was a big, fat, zero,” it takes on the noun form, signifying a total absence of results. In this context, zero embodies the notion of nonexistence.

Even though we just demonstrated the nothingness quality of zero, there are many practical applications of zero in our everyday life. All our calculators, computers, smartphones, and televisions – every piece of electronic equipment – operate on the basis of numbers rewritten in a binary code of 0 and 1, corresponding to off and on. The foundation of calculus rests on the idea of a limit, approaching a value infinitely close to zero. When we talk about the rate of change (like speed or acceleration of a car), we’re discussing values as they approach zero. In coordinate systems (like Cartesian coordinates), the point (0,0) is the central origin from which all other points are measured. In Finance and Accounting, zero represents balanced accounts, a point where assets match liabilities.

The concept and symbol of zero have a rich and complex history that spans multiple cultures and civilizations. The use of a placeholder to denote absence or nothingness in numerical systems likely dates back to ancient Babylonian and Sumerian civilizations around 3rd millennium BCE. However, these placeholders weren’t exactly zero; they served more as empty spaces to maintain positional notation. Around 1,500 years ago (or perhaps even earlier), in India, zero became its own number, signifying nothing. The ancient Mayans, in Central America, also independently developed zero in their number system around the dawn of the common era. The modern symbolic representation of zero as a circle or oval shape likely evolved from earlier Indian and Arabic scripts, where zero was represented as a dot or a small circle. This symbolic representation became standardized over time and is now universally recognized as the numerical symbol for zero.

Whether the Indians came up with the dot or circle for zero or not, what is much more significant is how they thought about this zero once they had it. Remarkably enough, the dot was used by them not only for zero but for the unknown, the way we use x.

In 630 AD, Brahmagupta coined the term “as much as,” ‘yavat tavat’, represented by the abbreviation “ya,” for his variable. When he required additional variables, he turned to color names like black, blue, yellow, white, and red, abbreviated as ca, ni, pi, pa, and lo, reminiscent of the convention of using x, y, z. However, Indian mathematicians later saw no issue in using the term “Shunya” to represent both nothing and something, and this usage became established. Shunya isn’t merely an absence, but rather a space of potential, akin to a hollow ready to be filled, originating from the root “svi,” meaning swelling. Its counterpart “Kha” derives from the verb “to dig,” suggesting a sense of emptiness to be filled. Additionally, two names for the concept of Brahman – “akasha” and “purna” – also appear as names for zero. “Akasha” first appears in Varahmihira by Brahmagupta, while “purna” emerges later in Bhaskara by Mahavira.

Alright, let’s fast forward through the epic saga of how zero went from India to the Islamic world and then crashed the medieval Europe party like a mathematical rockstar! Picture this: zero sets off on a wild adventure, hitching a ride through trade routes and scholarly chats, until it finally lands in the lap of medieval Europe during the Middle Ages. But oh boy, did it face some haters! Skepticism and resistance were its constant companions, like annoying sidekicks on a road trip. Yet, our plucky little zero didn’t give up – oh no! By the 13th century, it had charmed its way into the hearts of European mathematicians, becoming the belle of the mathematical ball. Now that’s what I call a zero to hero story!

The ancient Greek philosopher Parmenides presented young Socrates with a puzzling challenge: “Your thoughts are limited to ‘Being is.’ You can’t conceive of non-being, nothingness, or void.” He paradoxically used negation to tell us we cannot use negation. According to him, notions like motion, change, difference, past or future, here and there, and even you and me, all necessitate the notion of ‘not’. Thus, our cognition is confined to the declaration: ‘Being is.’ Fast forward two millennia, and mathematician Gottfried Leibniz, upon hearing Parmenides’ conundrum, found delight in the completeness of existence. To him, there were no gaps, no voids – even the tiniest entities held substance. “The world as empty (Shunya), the world as full (ashunya): take your pick,” proclaimed Nagarjuna, the Mahayana Buddhism master. He recognized that opposites, like something and nothing, are merely illusions created by language, equally devoid of true substance.

To sum up, Buddhist teachings cultivate a comprehension of emptiness, empowering individuals to recognize interconnectedness and coexist harmoniously. The symbolism of zero further enriches this understanding, embodying both absence and limitless possibilities. Their combined influence nurtures a deeper understanding of the impermanent and interconnected fabric of existence, promoting wisdom and freedom from suffering.

Wrapping up this talk, I’ll leave you with a quote from Robert Kaplan, a mathematics professor at Harvard University. In his book “The Nothing That Is: A Natural History of Zero,” he eloquently states, “Zero stands as the far horizon beckoning us on the way horizons do in paintings. It unifies the entire picture.  If you look at zero you see nothing; but look through it and you will see the world”.


The Nothing That is: A Natural History of Zero

Robert Kaplan

Emptiness: A Practical Guide for Meditators

Guy Armstrong