From Ants to Galaxies: Visualizing Infinity on Pi Day
🥧 Happy 𝝅 Day, friends! Today, we celebrate this mathematical wonder – 𝝅 also known as 'pi'! 𝝅 is the number 3.1415926535897932... & on & on… for infinity.
𝝅 has fascinated mathematicians for centuries. As I was pondering what to share on this special day, my mind kept coming back to a very specific piece of pi: the never-ending digits that stretch on and on and on... into infinity. What does it really mean? 🤔 How can we even imagine something that goes on forever?
When I imagine infinity, I think of the vast expanse of the universe, with its billions of galaxies & countless stars 🌌. It's a humbling feeling to know that the universe goes on & on, seemingly without an end. But there are many other ways to think about infinity. 💭 Have you ever tried to count to infinity? It's impossible! You could spend your whole life counting, & you'd never get there. Infinity is a concept that challenges our minds & forces us to think beyond the limits of our everyday experiences.
So, how can we even begin to visualize something so mind-boggling 🤯? One way to visualize infinity is to consider what it means for something to be unbounded. Try to imagine a line that goes on forever in both directions, with no end in sight, & with every number imaginable on it. To be unbounded, means that this line has no ends – if you were walking along an unbounded line, you would never reach the end regardless of how long you walked for!
This visualization actually lends itself well to one of my favorite ways of contemplating infinity: imagining the perspective of an ant on a long, straight highway in the American Midwest 🐜. From the ant’s perspective, this road clearly goes on to infinity. The idea that this road ever ends or could ever be traveled fully is unbelievable from the perspective of the ant. But from our perspective as a human, we know that the road is not infinite, & we know the highway could be walked with the right amount of water, food, patience, exercise, & time. I like this particular contemplation for its ability to challenge us to understand how things like perspective & size can influence our definitions & contemplations of infinity.
On this 𝝅 Day, thanks for taking a moment to contemplate a slice of pi with me: the concept of infinity. I hope you’ve enjoyed challenging your thinking & are inspired to explore! With that, I leave you with one last series of questions – is there just one infinity, some number of infinites, or infinitely many infinites? How do you visualize this contemplation? Is there an answer? Share your thoughts & ideas in the comments below! Don't forget to like & share this post & follow my blog to stay tuned for more mathematical discussions. 🤓
