3 ms·

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 comple

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

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