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🧵 )

https://www.nature.com/articles/s41598-024-52711-2

@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.

@freemo That being said, you're right that arithmetic growth can show more growth than geometric growth over the first increments (and I should've said that in my first response.) But in this case, with risks rising exponentially, I think the distances we're talking about our small and the larger finding is accurate--we underestimate how rapidly risks rise or fall with short distances.

@augieray You have no basis for asserting the distance is small... what are you basing that off of?

Depending ont he exact value of the variables linear growth can exceed exponential growth at any arbitrary point. It is just as possible exponential curve doesnt win out until the last 1 mm of distance.

The point is you can not say it overestimates or underestimates... All you can say is it incorrectly estimates., far away in overestimates the risk, but at some point arbitrarily close it will begin to underestimate the risk.

@freemo From the study. Did you read it? (I feel like you're now arguing to argue. Your point was theoretical, not practical and related to the study.)

If you want to argue with the study authors, please do so. I am not going to engage in a rather silly discussion of whether inches or feet matter when the study is accurate in ways that matter (which isn't whether someone moving six inches changes risk but that people underestimate the importance of distance from infected persons.)

@augieray I read it before you even posted it. I am a profession Research Scientist who worked on COVID and had some pretty big breakthroughs in my career... yes ive read it. No my point is not purely theoretical.

I am not arguing with the study authors, I am agreeing with, as I explicitly stated. I am disagreeing only with your interpritation, nothing more.