Exponential thinking: From one to 281 trillion in 48 moves…

Take the smallest integer – one – and double it. Now take the result – two – and double that. Take the four and double that.  Keep going – but not for too long… Perform this doubling procedure just 48 times and you’ll soon have 281,474,976,710,656.

Believing it only takes 48 doublings to go from one to more than 281 trillion seems like madness… at least at first.

That is because in all parts of our life we are prone to thinking in a linear fashion. If something is growing quickly, we often conceive its progress goes something like 100 + 100 + 100 + 100. This is linear growth. Exponential growth, however, takes us from one to 281 trillion in 48 steps.

I believe we all habitually underestimate the power of exponential growth – simply because it is so difficult to conceptualise the speed at which it occurs. 

Filling up Wembley Stadium

To understand the difference between linear and exponential growth, consider this:

• If you were to place one drop of water in the middle of Wembley Stadium, wait for a minute and then place two drops, wait another minute and place four drops you would have filled the stadium with over 281 trillion water drops in the 48th minute

Not mind-blowing enough for you? Then consider this:

• As late as the 40th minute, despite the doubling of the drops being added every minute, none of the crowd would have noticed the water
• Even after 45 minutes – just as the half-time whistle blows – even the people sitting in the row of seats nearest the pitch would be dry and safe
• Yet just a few minutes later, panic would set in

Compare this to linear growth; if you placed one drop each minute it would take you 535 million years to fill Wembley. Even if you worked a little bit faster and placed a drop on the pitch every second it would take you nine million years. 

The limits of linear growth

Exponential growth is how natural disasters – and the explosion in cases during a pandemic – happen and why they take us by surprise. If our Wembley experiment were real, then the spectators sitting in the stadium would surely be in danger of being killed simply by failing to grasp the power of exponential growth.

Exponential growth and the dangers of complacency

It is exactly the same in the business world.

A disruptor may be growing quickly but no one takes any notice, let alone the companies that find themselves being disrupted. If they do notice, then they are likely having a little chuckle to themselves. As if anyone would want to rent movies by post, to buy books online or to drive a car powered by a battery...

Then one day (probably equivalent to the 44th minute in our rapidly submerging Wembley) the world suddenly takes notice of the disruptor. At this point, it is often too late for the incumbent to react. Denial, fear and maybe even anger set in. How did this happen? All our clients said they needed extra disk drive space. Everyone told us they would only ever use a mobile phone for calls and text messages. Nobody told us the price of solar power would fall so far…

The surprising growth of Company X

Although exponential growth in the business world is usually less dramatic than in our stadium story, it is still often underestimated, underappreciated and – most importantly for investors – under-priced. One of the reasons for this is we often talk about growth in terms of percentage change. If a company grows by 20% a year for five years that sounds linear in nature; its rate of growth sounds constant. In reality, it is actually experiencing exponential growth…

Take the following hypothetical example:

• Company X has £10m in sales
• It then grows by 20% in year one. It now has sales of £12m
• So if it increases its sales by 20% again in year two it will have sales of £14.4m not £14m as many would expect
• By year five, its sales are £29.86m; the dominance of linear thinking means that many might guess this figure to be £20m or close to it

But if the growth was linear it would remain at £2m a year and the initial 20% growth rate would have slowed each year. In reality, Company X’s sales have reached £75m by year 10.

This is exponential growth at work. 

Underestimation of exponential growth provides us with an opportunity…

My colleagues and I in Artemis’ impact equities team spend our time looking for companies making a transformational positive impact on the world.

We also want to find companies that are, like Company X, growing exponentially – by 20% or more for each of the next five or 10 years (the bigger winners maintain their growth for even longer).

We believe that other market participants consistently underestimate this growth, either because they have a shorter-term outlook than we do or because they underestimate the power of disruptive, exponential growth. This provides us with an opportunity.

Yes, disruption is hard. And yes, it is often doomed to failure: around 90% of pre-revenue companies don’t make it. This is one of the reasons we avoid them, despite the temptation they offer.

But those disruptive businesses who can deliver exponential growth usually go on to be the big winners of the future.

Neil Goddin is a member of Artemis’ impact equities team. Here you can learn more about the team’s approach.