Part one: Immensity
One of the most endlessly fascinating human concepts is the idea of infinity. It’s a concept that is referenced often, but seldom do we get the occasion to sit and deeply contemplate the idea. There are so many ways in which infinity is a breathtaking thought. Let’s delve into it!
The marvel which immediately comes to mind is the size of it. I think of a hundred as a big number. If I have 100 blueberry muffins, I’ve got more breakfast food than I could possibly eat. The refrigerator is going to be full, and even then, some of these things are probably winding up in the garbage. As much as I hate to see anything go to waste, and as much as I love eating a fluffy blueberry muffin, I simply cannot eat 100 of them. So 100 is a lot.
Stepping up one order of magnitude, if I had 1000 muffins, now I would have to start giving them away. There would be boxes everywhere. Definitely not enough space in the fridge and freezer combined, and now I think I never want to eat another muffin again. Even the ones with the sweet crunchy tops. Iew. If I had 10,000, now we’re dealing with a disaster. The landlord is incensed with the gargantuan piles spilling out all the doors, and there’s probably not much room to walk through the house. At 100,000 muffins, I would probably get killed. Squeezed to death by the immense force needed to cram so many into one house. Even when you compress all the air out of that fluffy goodness, we’re looking at some dangerous volumes.
But to a lot of people 100,000 is still not that big of a number. What about a million? That number gets tossed around like nothing. A million bucks for a mansion. A million oranges in a large plantation. 310 million people living in the United States. It’s a big country. But there’s almost 7 BILLION people living on planet Earth. 310 million US residents is not a lot of people compared to the 7 billion world population. We’re only 1/22nd of the total amount.
A billion, now that’s a really big number. The sun and the earth both formed about 4.5 billion years ago. The universe itself is estimated to be 13.75 billion years old, with a visible size of 46 billion light years. So big, you can no longer grasp how large that is. There’s easily over 100 billion galaxies in the observable universe. That’s more galaxies than even the widest, boldest mind can imagine. But there are bigger numbers still. And yet, the sizes of all these things are insignificant next to the size of infinity. A hundred billion is exactly the same distance from infinity as the number one. That’s the wonder of infinity!
Just for fun, let’s keep going. The number of bits available for storage on my 1.5TB hard drive, 12 trillion. The US national debt is currently 13.75 trillion. A hundred dollars for every year in the age of the universe! The number of neural connections in the human brain is over 10^14. There’s over 70 sextillion stars in the observable universe. That’s 70×10^21. 10^80 elemental particles present in the observable universe. Google, now a household word, is an alternate spelling of googol, which is the number 10^100. Written out, that’s:
Ten followed by a hundred zeros. But there’s even bigger numbers still! A googolplex is 10^10^100. In a scene from Cosmos, Carl Sagan humorously shows how it’s not possible to write out a googolplex because it’s simply too big–it wouldn’t fit inside our universe! Those 10^80 particles are simply insufficient for the task, even if one particle was used to represent one zero. And still, there are even larger numbers than the googolplex. Even dramatically larger numbers. But still, the idea persists that even the largest number conceivable is precisely the same distance from infinity as the number one.
Pt.2: Park it wherever you like
I’d like to talk a little bit about another fascinating property of infinity that gives me a lot of optimism and joy. When we think about infinity, my mind at least goes straight to the large: the vastness of the cosmos and the unending progression of time. But for all the giant spaces infinity implies, there are implicit minuscule ones as well. When we count from 1 to 2, we think of that as a finite interval. It’s easy to see, if I have one apple and you give me a second one, now I have two, a finite number of apples. I definitely don’t have infinite apples. (Although I wish I did.)
But for every number you can name between one and two, I can give you a number that’s halfway between your number and one. You say 1.5, I say 1.25. You say 1.1, I say 1.05. You say okay wiseguy, how about 1.000001? I reply 1.0000005. We can start using scientific notation and continue this volley–until forever. And just like that, we’ve slid down the chasm into infinity, INSIDE the space between one and two. Infinity can exist inside of finite boundaries, because of the idea that in addition to being endlessly large, infinity is also endlessly small.
This idea has tremendous philosophical ramifications. When we lay outside under the stars at night and gaze out upon the universe, the sheer scale of ourselves, compared to it, can really seem bewildering. Stupefying. Daunting. Maybe even a bit disheartening. We realize how utterly tiny we are. And how the vast spaces beyond our planet will never know our names, our histories, or the fruits of our lives work. The collective plight of our entire species will likely be a fraction of a fraction of a fraction of a blink in the scale of our own galaxy alone, nevermind the cosmos. We glimpse the scope of the large infinity and all the treasure we hold special suddenly seems not just petty, but outright laughable. When our train of thought goes so far down that track, infinity seems to be a source of despair, pointlessness.
It is in this moment we need to remind ourselves that the grandiose richness of detail, subtlety, and surprise that large infinities encompass is also fully present within the infinities of the small. And these infinities of the small reside within our familiar finite spaces. Holding two apples, one in each hand, you can hold the entire cosmos between your fingertips. That same infinity up in the sky at night is right here, literally in our hands, available to be reshaped, to be studied, played with, laughed about, and to reshape us with its own, bottomless insight. This idea of infinity, so breathtaking in immensity, is right here with us, a trove of eternal possibilities for inquisition.
It’s a mathematical proof for the idea of interconnectedness. Thich Nhat Hanh, the famous Buddhist, eloquently muses upon the idea of oneness using a single tree within the larger world:
A tree is very beautiful. A tree to me is as beautiful as a cathedral. Even more beautiful.
I look into the tree and I saw the whole cosmos in it.
I saw the sunshine in the tree. Can you see the sunshine in the tree?
Yeah, because without the sunshine, no tree can grow.
I see a cloud in the tree. Can you see? Without a cloud there can be no rain, no tree.
I see the Earth in the tree–I see everything in the tree.
So the tree is where everything in the cosmos… come into.
And the cosmos reveals itself to me through a tree.
Therefore a tree, to me, is a cathedral.
It inspires me so very deeply to think that infinity can be bounded within a finite space. It inspires me to think that the potential for limitlessness is anywhere you look. The comprehensive vast ‘everything’ is right here. All around us, within our hands, and inside of us. Exactly like Thich Nhat’s tree, we can look into ourselves, we can look between our hands, we can look…wherever we want, and see the whole cosmos.