Professor Albert Bartlett famously said:
The greatest shortcoming of the human race is our inability to understand the exponential function.
One of the reasons that this is a ‘shortcoming’ is simply that the term ‘exponential function‘ is obscure to many. I’ve been thinking about that for some time now, and I think I have a way to describe this term in a way that (I hope) is not too difficult to grasp.
Imagine you’re walking along a path through a field. Ahead of you, in the distance, is a white gate.
Now, pause, hold up one hand, and frame the gate between your fingers.
It’s tiny, right?
Far too small too get through! 🙂
As you continue to walk through the field towards the gate, at a steady pace, the gate appears to get larger and larger. But, more than this, the rate at which it gets larger accelerates, even though you’re not moving any faster. As you walk towards it, the gate gets bigger and bigger until, when you’re about ten paces from it, it suddenly begins to zoom in your field of view until… it’s plenty large enough to get through.
That, in a nutshell, is the exponential function in action.
I hope that makes sense (if not: please leave a comment!)
Now, armed with this new knowledge, you can watch Professor Bartlett’s lecture ‘Arithmetic, population and energy‘ without fear of being befuddled 🙂