Exponentialists vs Intuitionists

Our brains find it hard to cope with exponential processes; and people who don't understand them can be distrustful of those who do

"Fragrant Water Lily Pair At Rieve's Pond" by matthewbeziat is licensed under CC BY-NC 2.0.

Please get a piece of paper and a pen. I’m going to begin this week’s column with two puzzles. I’ll give you the answers to both questions at the end of today’s post, but I need you to commit to your answers first. Ready?

Imagine a pond. One day an invasive species of lilies appears in one corner. It starts to grow exponentially and doubles in size every day. By day 20, lilies cover the entire pond. On what day did the lilies cover half the pool? Please commit to your answer by writing it down.

Next, imagine I offer you a choice of one million euros cash or one cent of a euro on day one, two cents on day two, four cents on day three and so on for thirty days. Which do you choose? Again, please commit to your answer by writing it down.

Unfortunately, our brains evolved in circumstances where understanding exponential processes didn’t offer much of an advantage to our ancestors. Grasping the sophisticated maths behind exponential growth is hard for all of us. It can be done, but it takes education, concentration and practice.

Imagine a graph showing how good people are at understanding exponential processes. You will probably find a number of people at one end, who have put in hours of hard study. We can call this cluster exponentialists. At the other end, we will have a group of people who much prefer trusting their instinctive answers to questions like the puzzles above and who didn’t pay much attention in maths class at school. We can call them intuitionists. Most people will probably fall somewhere between these two clusters.

When COVID-19 first started spreading like wildfire in early 2020, exponentialists got very scared indeed. The disease’s exponential growth meant that it would spread throughout the whole world much faster than intuitionists realized with no antibodies to provide friction. Its cumulative hospitalization rate by the end of March 2020 was 4..6 per 100,000. There were three serious risks. First of all, it would kill many. Secondly, it could crash hospital capacity, leading to many deaths from other causes. Thirdly, it could mutate into deadlier versions.

Exponentialists realized that if we didn’t flatten the curve and develop vaccines, the crisis could potentially be as serious as World War II, which killed around 3% of the population of the planet. We tended to respect the advice to stay at home, keep our hands clean and (later) wear masks, even if those of us of a liberal bent grumbled about some of the more excessive rules, like 40 days without being able to go for a walk for people in Spain. When the vaccines arrived, many exponentialists queued up to get them as soon as we possibly could.

On the other hand, intuitionists often failed to grasp the seriousness of the risks. They often compared the new virus to seasonal diseases, like the flu, which don’t tend to grow exponentially at all. They were often conspiratorial about official advice, as well as being reluctant to get vaccinated, not to mention being dogmatically contrarian.

If you want to meet more exponentialists, you will tend to find us over-represented in startups and tech companies. The reason is simple: exponentialists know that creating value for other people in new ways can generate enormous wealth if you can capture an exponential wave. Even those exponentialists who work in slower-moving fields will often be interested in investing in the shares of disruptive companies. Exponentialists also know that compound growth over extremely long time-spans can become exponential.

Many (but not all) exponentialists will be broadly sympathetic to institutionalism. The most thoughtful exponentialists realize that power corrupts. A system that provides checks and balances on executive power and encourages the peaceful transition of power will open up a space for innovators to create value in new ways. By contrast, removing the peaceful transition to power will quickly lead to a system of crony capitalism, which can extract great wealth from societies without creating value for anyone other than politicians and their buddies.

If, on the other hand, you want to meet more intuitionists, it would be a good bet to look for people interested in alternative health practices that don’t have strong scientific backing. These people will often deploy conspiracy theories as the bodyguards to failing ideas rather than installing the updates to their worldview - something that is hard for all of us.

Many intuitionists will be drawn to worldviews that seem odd to exponentialists, such as Flat Earth conspiracy theories. Of course, our intuition shows the world to be flat for most everyday purposes. Getting into the habit of trusting your instincts, distrusting experts and consuming content generated by algorithms can be a slippery slope with lots of strangeness at the bottom.

The crypto world is an odd case. Although many of the first movers were exponentialists, the movement was quickly colonized by intuitionists, who were often jealous of the wealth being created by startups. Unfortunately, many of them missed the memo about creating value for others. Too many of the projects are pyramid schemes and scams. Many bitcoin maximalists try to gain new converts with scare stories about the imminent collapse of mainstream currencies - a very low-probability scenario.

Exponentialists tend to have healthy concerns about fast-growing risks. Many are concerned about generative artificial intelligence (AI), for example. It is improving so fast that we have no idea what a super-advanced AI will look like or how it will think. Moderate and evolving regulations seem sensible, as well as keeping the nuclear codes away from AI.

Climate change is also seen as a big issue by exponentialists, who realize that the risks are growing in a non-linear way as the planet warms. You will find many exponentialists supporting moves to electrify our world. Intutionists, who worry about whether perpetual growth is possible, can be found on the other side of the great divide within the environmentalist movement, as well as among denialists about climate change and among conspiracy theorists concerned about environmental hacking.

In general, intuitionists tend to be very scared of exponentialists and deeply dislike our negativity. It should come as no surprise that intuitionist conspiracy theorists invent wild narratives about Bill Gates. An exponentialist, he made arguably the greatest deal in business history in 1980 when he cut a deal to get Microsoft software installed as a standard on personal computers. He knew that computing would grow exponentially. Making a little money on the majority of the computers that were going to be sold would make him very rich indeed.

Gates later used his knowledge of exponential growth to make prescient warnings about the spread of new diseases through globalized supply chains. Both the wealth generation and the warnings about emergent diseases must seem very disquieting to people who stared out of the window during high school maths classes.

Anthony Fauci, the former chief medical advisor to the President of the US, is another example. His experience as an expert in diseases gave him a very sophisticated understanding of exponential processes. Without understanding the basics of his worldview, intuitionists found him a sinister figure. The same is true of Klaus Schwab, founder and executive chairman of World Economic Forum, whose book on resetting the economy after the pandemic has been wildly misrepresented by intuitionist conspiracy theorists.

An earlier post in Sharpen Your Axe describes two games of politics: governing and winning elections. It should be clear that exponentialists tend to be much better at governing than intuitionists. Creating the conditions for innovation to flourish and grow exponentially can be good for society; while managing pandemics and other non-linear risks is difficult.

There are exceptions, most notably former UK Prime Minister Liz Truss, a hedgehog, who tried to apply a growth strategy at the time that the country’s central bank was trying to cool the economy to fight inflation. And, of course, if the Conservatives were serious about growth, they never would have left the European Union (EU) in the first place!

Meanwhile, intuitionists can have an edge in tight elections when the economy is in a bad phase of the cycle. Emotionally appealing narratives can gain traction with voters, even if the stories don’t have much of a basis in reality. Narcissists and populists will be particularly attracted to these stories, since they know that the combination of certainty with our intuititive insights can pack an emotional punch that many find difficult to resist. Telling people that maths should over-ride their emotions is a much harder position to sell.

The conflict between good governance and election-winning narratives can provide a dilemma for political parties. The Republican Party in the US is a case in point. In 2012, it presented Mitt Romney as its presidential candidate. A veteran of Bain & Co and Bain Capital, he was a true exponentialist, who had thought long and hard about growing businesses. Whether or not you agree with his politics, it is difficult to imagine his governance being particularly incompetent if he had won in 2012.

By 2016, Donald Trump had become candidate for the same party. As someone who inherited vast wealth, specialized in real-estate deals and played a successful businessman on TV, as well as fleecing suckers through various grifts, he is a great example of a conspiratorial narcissist. He showed that the party could develop an intuitionist and populist base, although he fell short of a true majority both in 2016 (when he won a majority of the electoral college) and in 2020 (when he lost). His management of the pandemic was a failure and he later tried to destroy liberal democracy. If he had succeeded, crony capitalism would no doubt have followed soon afterwards.

The exponentialist wing of the Republican Party faces an uphill battle if it wants to regain control of the party ahead of the 2024 election given the strength of its intuitionist base. Meanwhile, anti-vaxxer Robert F. Kennedy Jr. wants to take the Democratic Party in an intuitionist direction. While President Joe Biden might not be as much of an exponentialist as Romney, he surrounds himself with people who understand maths; and has been unafraid of quick actions in a crisis that benefit startups. Exponentialists will be backing Biden over Kennedy and later against Trump if he gets the nomination, despite the President’s advanced age.

Do you remember the puzzles at the beginning of the column? The answer to the first one is that the lilies will cover half the pond on day 19. This seems strange to us, but if you pause to think about it, it makes sense. The number of lilies doubles every day. Half times two is one, which means that the lilies will cover half the pond on the penultimate day.

By now you will probably have guessed that you should take exponential growth in cents, even if that isn’t the answer that you down on a piece of paper. If you did, you would receive nearly 5.4 million euros, or 5.4x more than accepting one million euros in cash.

If you want to geek out a little, the three books below will help you get to grips with why maths can be so hard for our brains to grasp. The comments are open. Finally, if you enjoyed this content, please share it! Many of my followers found out about this blog on Twitter. Elon Musk has changed the algorithms to make it much harder to find this kind of content, so your support in spreading the word is appreciated. See you next week!

Further Reading

The Number Sense by Stanislas Dehaene

Innumeracy by John Allen Paulos

Thinking, Fast and Slow by Daniel Kahneman

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