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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

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.

bryanrasmussen 7y ago
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.
- chongli 7y ago
  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."
  - thedance 7y ago
    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.
    - ChristianBundy 7y ago
      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.
    - chongli 7y ago
      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!
      - sjy 7y ago
        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.
        chongli 7y ago
        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.
  - bryanrasmussen 7y ago
    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
submaroon 7y ago
> 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/ https://www.scientificamerican.com/article/a-natural-log/
- nine_k 7y ago
  ...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.
  - mirimir 7y ago
    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.
    - StephanTLavavej 7y ago
      And that's only quadratic growth, not exponential.
    - MiroF 7y ago
      That's a terrible example, why would pick an explicitly sub-exponential relationship?
      - bonzini 7y ago
        Because exponential is even worse.
        mirimir 7y ago
        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.
psadri 7y ago
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.
- nine_k 7y ago
  Unfortunately, seeing oneselves as special is one of the most widely spread cognitive biases :(
  - hatenberg 7y ago
    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
hatenberg 7y ago
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.
- iagovar 7y ago
  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.
  - sjy 7y ago
    What “numbers” were you doing back in December? The virus had not spread outside of Wuhan, or been named or sequenced, by that point.
    - mraudiobook_com 7y ago
      Sounds like a Spanish Greg Maxwell.
    - iagovar 7y ago
      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.
ajmurmann 7y ago
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.
- edejong 7y ago
  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.
threatofrain 7y ago
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.

bryanrasmussen 7y ago

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.

chongli 7y ago
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."
- thedance 7y ago
  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.
  - ChristianBundy 7y ago
    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.
  - chongli 7y ago
    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!
    - sjy 7y ago
      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.
      - chongli 7y ago
        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.
- bryanrasmussen 7y ago
  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

submaroon 7y ago

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

nine_k 7y ago
...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.
- mirimir 7y ago
  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.
  - StephanTLavavej 7y ago
    And that's only quadratic growth, not exponential.
  - MiroF 7y ago
    That's a terrible example, why would pick an explicitly sub-exponential relationship?
    - bonzini 7y ago
      Because exponential is even worse.
      - mirimir 7y ago
        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.

psadri 7y ago

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.

nine_k 7y ago
Unfortunately, seeing oneselves as special is one of the most widely spread cognitive biases :(
- hatenberg 7y ago
  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

hatenberg 7y ago

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.

iagovar 7y ago
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.
- sjy 7y ago
  What “numbers” were you doing back in December? The virus had not spread outside of Wuhan, or been named or sequenced, by that point.
  - mraudiobook_com 7y ago
    Sounds like a Spanish Greg Maxwell.
  - iagovar 7y ago
    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.

ajmurmann 7y ago

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.

edejong 7y ago
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.

threatofrain 7y ago

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.