I am no mathematician or scientist. I hear the term "exponential growth" and I fade into a painful reverie that includes all of the math and science teachers who ever looked over their glasses at me, exasperation brimming in their throats, as I brought a paper up to their desk with yet another question. The definition - Exponential growth occurs when the growth rate of a mathematical function is proportional to the function's current value - clears nothing up for me.
This week, I watched Earth Days on PBS, a documentary about the development of the environmental movement. Dennis Meadows, the author of The Limits to Growth, the 1972 book decrying the consequences of a rapidly growing world population and finite resource supplies, began to discuss the concept of exponential growth using a tablecloth as an example;
Most of us don’t have an experience of growth the way it’s impacting the planet because you get up every morning and look around and it seems to be pretty much as it was yesterday. Our species just naturally tends to assume that change happens more or less linearly: one, two, three, four, five, six. Like that. But in fact, the problems that are causing environmental deterioration arise out of exponential growth, which is where instead of going up by a constant amount over some time period; it goes up by a percentage over some time period.
I’ve tried to illustrate what this means with a very simple example, I bring out a tablecloth, is show it to everybody. I fold it four times. So I am doubling the thickness of the tablecloth four times. And I let everybody see it, and I say suppose that is half an inch thick, not much. If I were to fold it another 15, 16 times, how thick would it be? Now I can’t actually, but suppose I could do that. When you keep doubling the tablecloth, of course it is growing exponentially, and after 21 folds it’ll be about a mile thick. If I double it another five or six times, it extends out past the edge of space. Continuing that process, rather quickly it gets you amazingly big numbers. With just 39 folds, it is already shooting past the moon. That is how quickly you get to very large numbers when a process grows exponentially.
This video is another visual example of exponential growth; the chain reaction set off by the action of one item involving itself with another. Which involves itself with another. And so on.
Most of us don’t have an experience of growth the way it’s impacting the planet because you get up every morning and look around and it seems to be pretty much as it was yesterday. Our species just naturally tends to assume that change happens more or less linearly: one, two, three, four, five, six. Like that. But in fact, the problems that are causing environmental deterioration arise out of exponential growth, which is where instead of going up by a constant amount over some time period; it goes up by a percentage over some time period.
I’ve tried to illustrate what this means with a very simple example, I bring out a tablecloth, is show it to everybody. I fold it four times. So I am doubling the thickness of the tablecloth four times. And I let everybody see it, and I say suppose that is half an inch thick, not much. If I were to fold it another 15, 16 times, how thick would it be? Now I can’t actually, but suppose I could do that. When you keep doubling the tablecloth, of course it is growing exponentially, and after 21 folds it’ll be about a mile thick. If I double it another five or six times, it extends out past the edge of space. Continuing that process, rather quickly it gets you amazingly big numbers. With just 39 folds, it is already shooting past the moon. That is how quickly you get to very large numbers when a process grows exponentially.
This video is another visual example of exponential growth; the chain reaction set off by the action of one item involving itself with another. Which involves itself with another. And so on.
This morning, I woke up and thought about Earth Day. I've thought about all the changes I've made to the way I live my life with regards to my health and the health of the world in which I live. I thought about how some of those changes are second-nature now and some are still a struggle.
Then I thought about reusable bags.
Only a couple of years ago, checkers at various stores looked at me cross-eyed when I held out my reusable bag and, trying to inject levity in what was an uncomfortable situation because of their judgmental raised eyebrows, said, "Trick or Treat!" I still say "Trick or Treat" but now the person behind me has their own bags, too. And the person in front of me apologizes for having forgotten theirs in the car.
Then I thought about reusable bags.
Only a couple of years ago, checkers at various stores looked at me cross-eyed when I held out my reusable bag and, trying to inject levity in what was an uncomfortable situation because of their judgmental raised eyebrows, said, "Trick or Treat!" I still say "Trick or Treat" but now the person behind me has their own bags, too. And the person in front of me apologizes for having forgotten theirs in the car.
Exponential growth. In a fit of hubris, I can see that someone like me, having the guts to go into Target with my reusable bag, caused someone else to have the guts to do the same. And then that someone else inspired someone else. And so on.
These are not heroic actions; it used to be uncomfortable and rather embarrassing to walk into a huge chain store with a reusable bag. But it was never brave. Strangers laughed or rolled their eyes. Some of the more crotchety and cheeky folks had the gall to lecture me; "One person cannot make a difference. And you're holding up the line." I would smile and say, "Maybe not. But it doesn't hurt to try. Sorry to inconvenience you."
But it isn't uncomfortable anymore. Bringing your own bags is now the acceptable norm. Even the crotchety, cheeky people are doing it.
How did that happen? Exponential growth.
We often hear the term applied to unfathomable concepts. Or used by preachers of doom to scare us into a sense of paralyzing fear. But why can't we rehabilitate it and use it to help us make our small changes meaningful?
Think of one of your small gestures to improve the world around you. Now think of one person you may have inspired to do the same. Now think of the people that person may have inspired. And so on.
Exponential growth.
Some days - most days - all days - the problems of the world seem too insurmountable to fix. So we stop doing even the small things. Because the small things are useless. The small things are futile. The small things cannot possibly make a difference.
But they can. The potential for exponential growth makes our small gestures mammoth forces. Agents of change. A recipe for a better world.
What did you do today that has the potential for positive exponential growth?
so exciting to see you using math terms!!
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