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Comment by lsb | Hacker News Reader

Acceleration.

The rate of change of the rate of change of deaths.

The word exponential only occurs once in the paper, and the rate of change of an exponential is an exponential, so take as many derivatives as you want and it's still going up. Why they don't take the log of deaths over time isn't explained.

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I've seen very little coverage that really uses the term exponential in a way that suggests those reporting know the implications of that. I've seen one plot with a logarithmic y-axis, and that was in the Guardian some time ago. From it, it appeared a crude heuristic could be drawn that from the point that lockdown is implemented, the cumulative deaths appear to grow between two and three orders of magnitude.

I've been grabbing the data put out by Johns Hopkins [0] for the last few days to update some plots in a very hacky Jupyter notebook.

Crucially, the plots are normalized to (estimated) populations and the y-scale is logarithmic. I've put them on github in case anyone else is interested [1].

[0] https://github.com/CSSEGISandData/COVID-19

[1] https://github.com/dpwm/covid19-analysis/blob/master/Coronav...

edit: Clarified that though exponential growth is widely used, the implications of that are not followed up. It's past my bedtime!

Even fewer people understand logarithms than exponential growth. If you publish graphs with a log scale you will certainly confuse some people into thinking that the illness is tapering off.

Hmm...I see the term exponential everywhere, but based on comments I read on public Facebook posts, almost nobody in the general public has any clue what it means or implies. But this site is widely referenced. It has a log scale option: https://www.worldometers.info/coronavirus/country/us/

> I've seen one plot with a logarithmic y-axis, and that was in the Guardian some time ago.

You mean like the widely cited NYT Coronavirus death tracker[1]?

[1] https://www.nytimes.com/interactive/2020/03/21/upshot/corona...

It's not an exponential. It's a shifted sigmoid.

The logistic function specifically, which is a blend of an exponential growth and an exponential asymptote. So initially it behaves indistinguishably from an exponential function, until you get close to the inflection point.

No it's not the logistic function. Sigmoid is a general term of the shape, logistic specifically refers to an equation that's almost certainly not correct. It's probably close to stretched exponential, which is a reasonable approximation of the curve of an autocatalytic process that is controlled by stochastic collisions that can self-exhaust, but even that's not exactly correct.

yep. My first thought was why the hell they didn't they use the word acceleration for better readability.

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