I’m always amazed at how familiarity leads us to take things for granted. Take, for example, the conveniences of modern life. It’s one of the reasons I enjoy backpacking. When I return to a hot shower and ice cream I appreciate them in a way that I didn’t before the hike.
The same is true of some truly remarkable facts about our world. Let me take Zeno’s paradoxes as an example, since I find they’re so familiar that many people simply roll their eyes when you bring them up.
I remember with clarity the day my father introduced me to a version of one. We were driving home from an A&W drive-through with a quart of root beer back when you couldn’t get A&W root beer in the store. He pointed out that in order to get home, we’d need to go half way, then half of the remaining distance, then half of the remaining distance, and so on. “Therefore,” he concluded for me, “we’ll never get home.”
As wonderfully surprising as his argument was, by the end of the day I was no longer puzzling over it. As I ran into it again and again over the years, it ceased to evoke any wonder. And when I was introduced to limits in high school I thought I had the explanation I needed (see my blog of 19 October 2017, Does 1 = .99999… for a discussion of limits).
It was only decades later that I again came to appreciate Zeno’s paradoxes as I realized that some things are likely beyond comprehension.
I can’t recreate the wonder I once felt – that’s one of the consequences of familiarity. But I can appreciate that something’s askew. In traveling home with my father, not only did we have to cover an infinite number of distances, but individually each one had finite length. When would we actually cross the threshold and arrive at our destination?
Hopefully many of the examples in my book are new to the reader and elicit a sense of wonder. Others, like Zeno’s paradoxes, may not. But that doesn’t mean we shouldn’t stop and consider them one more time. The world’s filled with surprises. We’ve often just become too familiar with them to appreciate what’s right in front of us.
The same is true of some truly remarkable facts about our world. Let me take Zeno’s paradoxes as an example, since I find they’re so familiar that many people simply roll their eyes when you bring them up.
I remember with clarity the day my father introduced me to a version of one. We were driving home from an A&W drive-through with a quart of root beer back when you couldn’t get A&W root beer in the store. He pointed out that in order to get home, we’d need to go half way, then half of the remaining distance, then half of the remaining distance, and so on. “Therefore,” he concluded for me, “we’ll never get home.”
As wonderfully surprising as his argument was, by the end of the day I was no longer puzzling over it. As I ran into it again and again over the years, it ceased to evoke any wonder. And when I was introduced to limits in high school I thought I had the explanation I needed (see my blog of 19 October 2017, Does 1 = .99999… for a discussion of limits).
It was only decades later that I again came to appreciate Zeno’s paradoxes as I realized that some things are likely beyond comprehension.
I can’t recreate the wonder I once felt – that’s one of the consequences of familiarity. But I can appreciate that something’s askew. In traveling home with my father, not only did we have to cover an infinite number of distances, but individually each one had finite length. When would we actually cross the threshold and arrive at our destination?
Hopefully many of the examples in my book are new to the reader and elicit a sense of wonder. Others, like Zeno’s paradoxes, may not. But that doesn’t mean we shouldn’t stop and consider them one more time. The world’s filled with surprises. We’ve often just become too familiar with them to appreciate what’s right in front of us.
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