What if instead of about the same amount of change happening each year, change got faster and faster? This is the premise of exponential thinking, which posits that the changes caused by technology will grow more radical every year. As you’ll soon see, thinking about change exponentially makes a big impact on what we predict for the future.

For most of human history, change has happened in a linear fashion – which is to say there was about the same amount of change every year. If you plotted out how much things had changed from the very first days of civilization, you’d get a a nice straight line like this:

You can see the year 8 is less like the beginning than year 2, but the rate is the same. However, some futurists think that recent years haven’t fit that trend. They think the evidence suggests that the change caused by technology happens in an exponential fashion. The beginning of exponential change looks a whole lot like linear change, as you can see in the this graph:

It looks like a pretty straight line, right?

The trick is that the second graph is zoomed way, way in on the very beginning. If you zoom out a little bit, it looks like this:

Whoa! That’s a big difference! Now it’s obvious we’re on a curve. And if you zoom out even further, you get this:

All of a sudden it’s clear that the flat part we saw at the beginning was *really really tiny*. We had good reasons to think the graph would stay a nice straight line when we could only see a tiny bit of it, but even so the predictions we made with that straight line would have been totally wrong. The difference is getting to a height of 2 in eight years or in less than one!

So you can see why it’s very important to know if change will be exponential or not, but it’s hard to really know for sure, based on the data. And that’s even before we get into other, more complicated types of graphs like a sigmoid which me might be on. A sigmoid looks almost exactly like an exponential curve, except that when it gets tall enough it starts flattening out again, like this:

Thinking we’re in an exponential function when we’re really in a sigmoid function would make our predictions almost as wrong as when we thought we were in a linear function but we were really in an exponential function!

Ultimately, we don’t know what type of graph we’re on. Futurists disagree about it, and we don’t have the data to resolve those disagreements. The closest we can come to a definitive answer is that it seems like we’re probably not on a linear graph. That means that expecting the rate of change the stay the same will probably give you the wrong answers, but we just don’t know what the *right* answers are. Nevertheless, most people think about the future as if we were on a linear graph, so thinking about other ways things could happen is at least somewhat useful.