Note the log in the first sentence, the range is not from 3 to 10 — about a factor of 3 — it is from 103 to 1010 viruses per millilitre — a range where the top end is 10 million times the bottom end. In other words, some people at some times during their COVID-19 infection have ten million times as much virus as others do. On a log scale, the average is 106.5 ~ 3 million viruses per millilitre but some infected people have thousands of times more, while others have thousands of times less.
Transmission of the corona virus (aka SARS-CoV-2) is very complex, which is basically why it is so poorly understood. But in true theoretical-physicist style, a minimal model has been developed, by a guy called Roland Netz (who is a theoretical physicist in Berlin). It makes a lot of assumptions, and it is clear that there is lot of variability, between one infected individual and another and between one situation and another, so its predictions should be taken with a large pinch of salt. But in this post I will outline this minimal model.
Today I am reading both Calling Bullshit by Jevin West and Carl Bergstrom, and of a “growing crisis” over Scottish Higher results — presumably a similar crisis will happen for A levels when the results are released in a few days. I have got to the bit in Calling Bullshit where West and Bergstrom talk about bullshitting via statements that superficially look rigorous, but in reality are pretty flaky. In this blog post I want to suggest, possibly controversially, that the distinctions at the root of the growing crisis in Scotland, between a grade A and B in a Scottish Higher*, or a B and C, etc, have a slight whiff of bullshit about them.
Colleagues at the University of Bristol and I are working on trying to understand how masks work. One fundamental aspect of this is that a mask, like any filter, fundamentally involves a trade off. A mask must as permeable as possible to air, but as impermeable as possible to virus-containing droplets. Air must flow through a mask as freely as possible, but droplets should find the mask as close to impenetrable as possible. The problems is that these two design constraints directly contradict each other, and so any mask, any filter in fact, is a compromise.
Last year I changed my second-year computing teaching to Jupyter Python notebooks. I think Jupyter notebooks worked well at teaching how to do useful stuff like analyse data. The notebooks were hosted on the Micrsoft service Azure which wasn’t great but basically worked. However, not only is Azure far from perfect, it is also being binned around about week 2 of semester.
The beautiful behaviour of this flock of starlings is an example of a class of phenomena variously known as emergent, collective or more-is-different behaviour. The point is that a single starling, or two starlings cannot show this striking phenomenon, you need hundreds or thousands of starlings, to see it. A liquid is a less obviously exciting example of an emergent phenomenon. One or two water molecules aren’t a liquid, you need at least about a hundred to make even a tiny water droplet.
Chemical engineers, chemists, physicists and food scientists have been studying coexisting liquids like the (black) balsamic vinegar and (yellow) olive oil above, for over a hundred years. Cell biologists have been busy with other things over this time. But over the last few years at least some cell biologists seem to not only be studying coexisting liquids but arguing over them.
The people at Brilliant have done a lovely short (few minutes, last minute is an ad for Brilliant) video explainer on the physics of how masks work. It does a good job of saying why droplets a fraction of a micrometre across are the tough ones to catch, and why you can’t think of a face mask as a simple sieve. It compares a mask to a spider’s web, a comparison I like very much. But one thing it skips over is the physics of why when a droplet hits one of the fibres inside a face mask, we expect the droplet to stick.
The picture above shows three trajectories — red, green and orange curves — of particles through a model of a face mask. Face masks are meshes of long thin fibres and the brown discs are cross-sections through these fibres — in a simple model. The blue lines are what are called streamlines, they show the the paths taken by air flowing through the mask, due to the wearer breathing. The trajectories show (at least part of) why masks filter out the bigger droplets from a person’s breath, and it is not because the droplets are too big to fit through holes in the mask.