The Power of Exponential Thinking in a Linear World

Humans are linear thinkers living in an exponential world.

Our brains haven’t had a significant upgrade in over two million years, whereas the technology we’re using is doubling in power every 18 to 24 months.

To succeed as an entrepreneur in our technologically accelerating world, it’s critical to internalize and use the power of exponentials to your advantage.

Let’s dive in…

Grokking Exponential Growth

The impact of exponential tech is a tricky thing for humans to fully grok since we intuit our world in a linear fashion.

Deeply engrained in the wiring of our brain are linear prediction circuits—take 10 linear steps, you end up across the room, 10 meters away. We are all incredibly good at accurately predicting where you’ll be in 20 or 30 linear steps.

Predicting exponential growth, however, is not intuitive, often surprising and disrupting us.

If instead of 30 linear steps, you take 30 “exponential steps,” where an exponential is a simple doubling pattern (1, 2, 4, 8, 16, 32...), after 30 doublings you don’t end up 30 meters away. Instead, you end up a billion meters away having circumnavigated the planet 26 times.

For starters, it’s worth memorizing a few basics:

• Doubling something 10 times, makes it approximately 1,000 times bigger.
• Doubling something 20 times, makes it approximately 1,000,000 times bigger.
• Doubling something 30 times, makes it approximately 1,000,000,000 times bigger.

To lock in the non-intuitive nature of exponential growth, allow me to share a couple of stories to help you “feel” how powerful this growth can be.

The Story of the Invention of Chess (A Fable)

Once upon a time, long, long ago, the King of India offered to reward the inventor of chess because of the beauty of the game.

The King asked the inventor, “What would you like as a reward? Name anything in my Kingdom and it will be yours!”

The inventor responded: “Dear King, all I ask is that you place one grain of rice in the first square, two grains on the second square, four on the third square and so forth, doubling the number of grains of rice on each subsequent square.”

The King, who did not understand the power of exponential growth, was surprised by what he considered such “a meager request.”

A chess board has 64 squares.

By the time the first row of 8 squares was counted, the King’s team had placed 128 grains of rice (a handful) on the 8^th square. (This is the deceptive phase of exponential growth.)

Halfway through the board (32 squares) the number of grains of rice had become frightening at 2.1 billion grains of rice (equal to 10,000 kilograms).

By the 64th doubling, the amount of rice had become unfathomable, reaching 461 billion tons of rice, a mound the size of Mount Everest.

That is the power of exponential growth. It goes without saying that the King was not happy to find this out.

Failure to understand this power can have dire consequences.

An Experiment for Your Kids

If you have younger kids or cousins around, give them a choice of the following two options, and ask them which they would rather have…

Option #1: I will give you $1 per day for the next 30 days. 

Or, would you rather... 

Option #2: I will give you a penny on the first day, two cents on the second day, four cents on the third day, eight cents on the fourth day, and keep doubling every day for a total of 30 days. 

Now, choose. 

Option #1 will net you $30. It’s predictable—the definition of linear. 

But with option #2, the exponential growth goes from deceptive to disruptive. 

The first five days (1, 2, 4, 8, 16 cents) net you just 31 cents. It’s deceptively dismal. 

But after 30 doublings, the situation gets disruptive. We’ve increased the payout one-billion-fold.

By day 30, your payout is now $10,737,418.24. 

That’s the promise and power of exponential growth!

Why This Matters 

One of our biggest challenges as entrepreneurs and leaders is to train our brains to think exponentially, which can be a very difficult thing to intuit.

Our brains evolved in a local and linear environment where nothing changed over time. Back 100,000 years ago, the life of your great-great-great-grandfather was effectively the same as the life of his great-great-grandson. Nothing changed over centuries or millennia.

But today’s world is global and exponential. Global because if something happens on the other side of the world, we hear about it microseconds later.

And exponential because the rate of computational change (and all exponential technologies) doubles in price performance every 18 to 24 months.

Forget about the potential difference between generations—today, mere months can bring a revolution. 

Understanding exponentials can mean the difference between success and failure, between leading disruptive change or being the victim of it.

In our next blog in this Scaling Abundance series, we’ll explore what happens when companies and their leaders ignore exponential change.