Very interesting STUDY of people's perceived risks of contracting #COVID19 when around those infected.
Models show that risks increase/decrease exponentially with distance, but many think it changes arithmetically. In other words, we “underestimate the increase of risk in an approach to an infected person” and “are not aware of how fast risk decreases in a movement away from an infected person.” (1/4🧵 )
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@augieray The interpritation here isnt a great one.
The wording is proper to say that we expect arithmetic growth but get exponential. But it is incorrect when the section starts with "in other words"... We do not **underestimate** the risk in approach, we misunderstand the growthrate of approach. This isnt the same because a linear growth can exceed an exponential growth during the relevant range of the function.
I attached an image as an example. Here I picked an agressive exponent to show the effect more clearly, the plot is of x vs x^5. Notice how during most of the graph the linear one actually significantly exceeds the exponential. This is my point, seeing linear growth will actually "overestimate" the danger of covid as you close distance not underestimate it, at least at first.
@freemo I don't know what tool you're using, but I think it's wrong. The blue bar shows ZERO growth until 0.5, which is not correct for something with exponential growth. Growth means growth--both arithmetic and exponential growth patterns will show growth at every increment. There is no ZERO growth increment for something with exponential growth.
> I don't know what tool you're using, but I think it's wrong.
No its correct, feel free to check.
> The blue bar shows ZERO growth until 0.5, which is not correct for something with exponential growth
No it doesnt. Just looks that way because of the resolution of the graph. The expopnential growth is monotonically increasing, that is to say, it is increasing at every point.
What is true is exponential growth is **very**slow at first, slower than linear, and only accelerates later. What you see here is the exact correct behavior of those plots.
> Growth means growth--both arithmetic and exponential growth patterns will show growth at every increment. There is no ZERO growth increment for something with exponential growth.
Yes and that is exactly whats happening in this graph, nowhere is there zero growth. You are confusing very slow growth with zero growth, not the same. Again plot it yourself youll get the same result.
@freemo Thanks. I understand. However, that doesn't change the findings and recommendations from the research. It might be that the first foot toward or away and infected individual doesn't change risks much, but we're only talking short distances here, ranging from 0.5 meter to 3 meters or so. The risks risk rise and fall very quickly with short distances toward and away from the infected.
@augieray
And yes the risks absolutely would "rise sharply" with distance, that is the nature of an exponent. Those ideas arent in question.
What is in question is that we underestimate this risk, or that it exceeds a linear estimation, which are not proper descriptions.