Ever since I first encountered this quote (in Professor Bartlett’s seminal lecture ‘Arithmetic, population and energy‘) I’ve been trying to think of ways of highlighting the problem, hoping that, in some small way, I might contribute to finding a solution. Examples of my humble offerings include ‘Bacteria in Bottles‘ (from that lecture), various attempts to publicise the ‘Impossible Hamster‘ video, and a kind of imagination exercise. I’m revisiting that last here, as I think I can do better.
This is the white gate I referred to in my post four years ago (‘Understanding the exponential function‘), and, for completeness, here’s what I said in that:
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 to 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.