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Comment by chongli | Hacker News Reader

Human beings do not intuitively understand exponential growth. It's just too fast for our primitive brains. In some sense, we are standing in the middle of the road, frozen like deer in the headlights.

Science is supposed to mitigate the shortcomings of our natural intuitions and cognitive biases. The problem is that most people are not scientists. When a non-scientist is asked to trust a scientist, he or she is subject to all of the usual suspects: arguments from authority, confirmation bias, Bulverism, appeal to emotion, etc. What this means in practice is that scientists are generally not trusted over the word of one's friends and family.

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> Human beings do not intuitively understand exponential growth.

This layman has read that we intuitively think of numbers logarithmically, which makes him wonder if we human beings do, in fact, intuitively understand exponential growth.

https://www.scientificamerican.com/article/a-natural-log/

...and see it as merely linear. That's the problem.

Exponential growth is like dynamite. It's absurdly fast, compared to anything people see in daily lives.

Dropping stuff and falling are good examples. If you're paying attention, anyway. I can still grab stuff that's fallen maybe 10-20 cm, but by 50-100 cm it's moving way too fast.

And that's only quadratic growth, not exponential.

That's a terrible example, why would pick an explicitly sub-exponential relationship?

Because exponential is even worse.

Right. Because it's not linear.

The only truly exponential example that comes to mind is milk souring. But that's too slow, unless you keep notes.

Population and GDP also grow exponentially, but we’ve been watching those numbers go up for decades. Most things that grow do so exponentially. Growth always comes to an end, but that often happens well before the rate of change becomes “absurdly fast.“

Interesting. I do think that few people understand what a billionaire actually is, i.e. what force you can mobilize if you are one.

Humans don’t understand exponential growth. But they could look at China and Italy and think - those guys are the same as us. We are not special. The same thing that is happening to them is going to happen unless we act now.

The real sad part of all this is that this is simply human nature. And we are next gonna go down the same path with climate change. And then not even lock downs will help.

Unfortunately, seeing oneselves as special is one of the most widely spread cognitive biases :(

The German press was explaining Italy all week... mostly trying to explain how it's all different.

Having seen the cutting of rural hospitals over the last two decades it will be a shitshow

That may explain but certainly not excuse. We submit our individual freedoms to governments we vote for to be able to act better than our ingrained short term reflexes. Best and brightest and all.

It's also not necessarily an indictment of democracy- Taiwan clearly has been on the ball here. But it is absolutely an indictment of our current state of affairs in many western countries.

Spanish lead epidemiologist was telling us a few weeks ago that nothing was going to happen here.

I did my numbers back in December. In January was already pretty worried, but I'm not an expert I thought. Maybe there's something I'm not taking in account.

So I kept reading about models and stats. Not that difficult. Ran my numbers again and again, yep it seemed pretty bad no matter what I cheated myself with parameters etc.

Then it came to Spain. I was pretty nervous by that time, kept it cool, tried to warn to people that this was no joke, everyone thought that I was a bit crazy and alarmist. Days passed, government went absolutely erratic and irreposible, lost all my trust in the lead epidemiologist and the ministry of Healthcare, not to mention the HUGE amount of healthcare workers that were insisting that it was just a flu and some of us were alarmists for two month and turned 360 in a few days.

Too late. Now I'm in it.

What “numbers” were you doing back in December? The virus had not spread outside of Wuhan, or been named or sequenced, by that point.

Maybe my memory is fuzzy, but the moment I've got the first reports about R0 incubation period etc.

I have to say that some time ago I had a course of applied statistics with epidemiology exercises so I was not really an alien to it, but not an expert either.

by intuitively I suppose you mean feel it, which I guess is true, but it does not take a genius to actually understand the concept, especially if it is explained as right now you will get this many people per day, in a week you will get this many, in a month this many. That is pretty easy, a politician should be able to follow it.

But as has been pointed out before most people think if you do something big and dramatic to fix an oncoming problem, and it does fix it, lots of people will stupidly assume that you did not need to do the big, dramatic thing because it wasn't really a problem. So any politician who reacted appropriately would run the risk of fixing the problem and losing power in doing so, I would prefer to fix a problem like this even if it meant I would not have the power to fix later problems as my calculation would be if I do not fix this problem now I probably won't have the power to fix later problems anyway.

One way to test this is to ask random people the question:

"The number of lily pads on a pond double every day. If it takes 20 days for the lily pads to completely cover the pond, how long does it take to cover half the pond?"

I think you will be surprised by how many people say "10 days."

This is because most people are unable to suppress their reflexive response to being asked what's half of 20, not because people don't understand exponentiation.

Yes, the point being that linear halving is much more intuitive for most people than exponential halving. Even when you're told the doubling rate, your brain reaches for the wrong answer every time.

My point was not about whether people are incapable of understanding exponentials, it was about whether they understand them intuitively. You used the term “reflexive response” but what we’re both describing is intuitive or automatic thinking.

Why is it relevant that people don’t correctly apply exponential reasoning automatically? Because when people encounter information in everyday life (outside of the specific job they’ve been trained to do) they tend to use intuitive thinking predominantly. This matters a hell of a lot when it comes to making political decisions of a technical nature, such as infectious disease planning and response. Lo and behold, this is the exact problem the Italians are trying to warn everyone about!

Show someone an animation of the lily pads doubling every day and ask the same question and you’ll realise that they understand exponential growth intuitively, they’re just not good at word problems.

Show someone an animation of the lily pads doubling every day and ask them when the pond is half-covered? You're not even asking them to solve a problem at that point, only to point at the animation when it looks half-covered.

Relating this to the spread of the virus, people aren't carrying around an animation of this in their minds. Perhaps science communicators should do a better job of communication and produce such an animation? But then you're still not getting people to understand the concept. You're telling them "this is what it looks like, sort of, now just trust us." The problem is that people don't trust scientists (and mathematicians) as it is.

I agreed that people did not understand exponential growth, but I pointed out that "but it does not take a genius to actually understand the concept, especially if it is explained as right now you will get this many people per day, in a week you will get this many, in a month this many."

So if you explain to the politician, once you start getting cases in your country and give them the actual growth rates, and what slowing down the growth rates will mean, with nifty charts and so forth.

Like maybe they should do in the movie Outbreak where they have display of the red spreading across the country on its way to the White House, with a timeline animated below it, then the politician will understand the situation without intuitively understanding exponential growth.

I suppose reasonably competent data visualizers who have ever had to explain complicated things to non-technical people in an important meeting would know how to represent the concept in their particular domain without much problems.

on edit: changed our to your

It's so unfortunate that Western society also seems to be losing trust in experts. As the world gets more complicated one would expect that trust in experts would be more important.

Policy makers are often incorrectly or selectively writing experts to push their agenda. Confidence intervals become averages. Multi variate predictions become univariate. 30 year models become absolute truth. No wonder people lose trust.

You don't have to understand exponential growth to look at how seriously other nations have treated the issue. Many large respectable nations have entered some kind of lockdown mode.

And I don't believe you should have to understand exponential growth to listen to clear government messaging about the severity of a problem. This is a failure of messaging by the relevant authorities.

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