The most underestimated limit of the human mind: An intuitive grasp of the exponential curve

One of the greatest challenges for the human mind is to intuitively grasp the power of the exponential curve. This may sound like a dry subject, so let’s bring in chocolate 🙂

Imagine it’s 11:45 and you decide that for the next 15 minutes you’ll be eating an entire chocolate bar. But instead of eating equal amounts, you start with a tiny portion (0.003% of the chocolate bar) in the first minute and then every minute you double the portion you eat. So in the 2nd minute you eat 0.006%, in the 3rd minute 0.012% etc. When will you run out of chocolate? Let’s see …

It’s 11:45 and you have the entire chocolate bar. You take your first tiny bite …

During the first 6 minutes you almost get NO chocolate … I marked the tiny corner you ate on the left bottom … every little square represents 1 minute. It’s now 11:50 and a third of your time has gone by.

After most of the time is used up (13 minutes out of 15) you still have 3 quarters of the chocolate left over (75%). At 11:58 with so much chocolate left over, there is no way the chocolate could be almost used up, or can it?

At 11:59 with only 1 minute left you still have half of the chocolate. This is really deceiving. With half of the sweet bar in your hands who would think that it’s already a chocolate emergency?

Only 1 minute later it’s all gone. Each square represents the amount of chocolate eaten per minute.

Here is what your chocolate binge looks like as an exponential curve. From the left to the right, it shows the time, up and down it shows the amount of chocolate you ate …

If you would have thought about it, you may have seen the danger of the chocolate running out in only 2 minutes but your intuition would tell you that there is a lot of chocolate left.

Our brain is set up for linear thinking.

For most of our history, humans only had to think in linear terms. This is because we were dealing with things. As hunters and gatherers, as farmers and as workers in the industrial age factories, we made and used physical things. Only with the advent of computers and the proliferation of the internet, we started to create products with little to no weight. A kindle book download, a streamed song or movie, a word document. And in this brave new world, where products can have zero weight, they can be replicated at close to zero marginal cost. Therefore companies with such products can grow exponentially.

Chocolate consumption won’t be a problem but in other areas this limitation hurts us. Take CO2 pollution for example, is it getting out of hand? Here is your answer …

Our earth has finite resources, enough for everyone right? Well, think of it this way, same amount of drinking water and twice the number of people.  Look at our world population growth …

I calculated that based on current (2018-2019) population growth rates the world population will double in 63 years. That is during the lifetime of millennials. Same amount of resources with twice as many people.

Another exponential challenge is the difference between the growth of our economy vs. the extent to which workers  benefit from that growth. This will be increasingly caused and accelerated by automation. What may look like most of the “chocolate” is still there, is in reality going to change in a “New York minute”  …

Income inequality also follows the exponential trajectory. The inequality gap has risen to 1929 levels (year of Wall Street Crash and start of the Great Depression), the widest gap in a hundred years. Excessive inequality usually creates some kind of market correction. A Credit Suisse Global Wealth Report gave us an idea where this inequality trend is headed. By many measures economic disparity has already surpassed the 1790s when inequality sparked the French Revolution, a time when 17 thousand (upper-class) people lost their heads under the guillotine.

Last but not least computing and artificial intelligence are also on the way up the exponential roller coaster. As I wrote here, this has historic and unprecedented consequences. We are no longer replacing muscles with machines, we are now replacing brains. This means that in the past, one task say the telegraph was replaced with another task, say the telephone. Jobs were still around. Now the entire sequence of tasks is replaced and the remaining high end jobs to maintain the system will eventually also replaced by automated system maintenance AI’s. It’s time to start preparing for a predominantly automated economy. This could be a good thing. If productivity gains from automation can also benefit the broader population, you might soon have extended vacations courtesy of A.I. generated profit margins. 🙂


Just 2 minutes before midnight, at 11:58 the world can still look like it’s mostly ok. This false sense of security can harm us. The historic challenges we face are also a historic opportunity. A prerequisite to see these challenges/opportunities clearly is an intuitive grasp of the exponential curve.

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