We most often get the future wrong because, to paraphrase economist Paul Romer, “Opportunities don’t add up, they multiply.” Stick with me for a few minutes because the math behind that isn’t as straight forward as it appears to be.

So much of the promise of technologies such as Artificial intelligence seems to be at the very outer edge of a very distant future. It’s not. If there is one sentiment shared equally with everyone I’ve interviewed for an upcoming book, Revealing The Invisible (June 2018), it’s that the future is coming at us much faster than we are able to comprehend.

You’ve likely heard about accelerated exponential change or the singularity. I wrote about both in my recent Inc.com article, According to Peter Diamandis and Ray Kurzweil, These Are the Most Dangerous and Disruptive Ideas.

Diamandis and Kurzweil regularly point out that understanding that rate of technology change may well be one of our biggest obstacles in adapting to it and building businesses that can take advantage of it.

Advances in artificial intelligence are not progressing in a linear fashion, and that represents a huge challenge for humans who are inherently linear thinkers. Trying to grasp non-linear change that is geometric or exponential is just not how we are wired. We think in linear terms because that is what we’ve observed in how the natural world operates. But that creates a huge disconnect between our intuition and the implications of the actual rate of change. And that disconnect only grows as we add accelerated exponential growth.

For instance, consider this following thought experiment.

## Take Me To The Moon

Imagine that I’ve just given you a super ball that has the ability to bounce to an unlimited height (we’ll suspend the laws of physics for this). I then ask you to start bouncing the ball, with the knowledge that each bounce will be twice as high as the previous one. If the first bounce is 10 feet off the ground how high will it go on the 10^{th} bounce? The answer is that it will have topped a small mountain of about 5000 feet.

That’s high but it doesn’t seem extraordinary, and your intuitive guess was probably pretty close. However, how high will it be after four more bounces? By the 14^{th} bounce it will have crested the Summit of Everest and be approaching the ceiling of commercial air traffic.

That’s a bit more impressive, but let’s not stop there. After all, I said that it can reach an unlimited height. So, how high would the ball have bounced after 21, 29, 37, and 45 bounces? The answers now start to stretch our ability to comprehend the distances involved.

“Technology advances no longer add up; they multiply–in the case of AI, by increasingly larger exponential multipliers.”

At 21 bounces our ball is approaching low earth orbit, after 29 we’ve passed by Earth’s moon, another eight bounces and we’re zipping by Mars, and then on the 45^{th} bounce NASA might pick up its faint signal as it whizzes past the first Voyager spacecraft nearly 17 billion miles into deep space. After 88 bounces you’ll never see the ball again since it would now be outside of the visible universe.

Still not impressed? I expected that you might not be, after all, we’ve become somewhat immune to large numbers when it comes to projecting the trajectory of technology. Congratulations you’re starting to think exponentially. But wait, I need to make a confession. I’m really not trying to impress you with how fast a doubling phenomenon can scale. That’s so 20th Century. My objective is something else altogether, how we perceive accelerated exponential growth.

## Objects In The Future Are Closer Than They May Appear

So, try just one more question.

If you had purchased a discount super ball that bounced only one inch, instead of 10 feet, (In other words less than one percent of the 10 foot bounce from our full-price super ball) but it bounced three times as high each time (instead of two times as high), at what height do you think it will have bounced past the earlier ball that started at 10 feet? Don’t do the math, just take a guess. Will it have caught up by Everest, low Earth orbit, the Moon, Mars, or Voyager? Incredibly our discount super ball, that starts of with only a minuscule one-inch bounce, will have caught up by the time it reaches Everest, after only 14 bounces!

In fact, if you’d started with a ball that bounced a full mile the first time (528 times as much as your original super ball and 6,336 times as much as our discount one-inch super ball) the discount one-inch-bounce super ball would catch up with the one-mile-bounce super ball just after passing the moon! This makes sense when you stop to do the math but it’s far from intuitive.

The reason I’m making this point is to show that linear growth (the actual increase in the initial bounce from 10 feet to one mile) and exponential growth (the doubling effect) both pale in comparison to the accelerated exponential growth of our discount super ball that starts off with just a one inch bounce. When anything progresses with accelerating exponential growth you very quickly get to a stage where the acceleration of change is so great that it just doesn’t matter where you start.

The same is true of how quickly technologies such as AI are evolving by learning at accelerated rates that have no precedent in the way humans learn. A simple artificial intelligence engine can learn overnight how to play the classic computer game of Space Invaders better than any human can.

Like our discount super ball, AI is accelerating in its exponential rate of evolution. We can argue how incipient or immature it is today but it will soon make no difference. The trajectory we are on will lead us to the future much faster than any of us think it will. Technology advances no longer add up; they multiply–in the case of AI, by increasingly larger exponential multipliers.

Given that trajectory, within just five to ten years I confidently expect that machines with human-level intelligence will be well entrenched within the mainstream of our lives and businesses.

Naive thinking? It’s only naive if you focus on adding up the challenges, rather than multiplying the opportunities.