Sunday, November 01, 2020

One "potential infection" shortens the (total) remaining life expectancy of mankind by minutes

The potential infection may be worth 12-48 cents

I still can't understand how – despite those 8 months we have had to sort these questions in our minds – someone who could have been hired as a CERN scientist is "capable" of writing something as incredibly wrong as Tommaso Dorigo's text that has "calculated" that (when it comes to the harm done to the society) Joe's going to a party in 2020 is approximately equivalent to shooting several people by a Kalashnikov. His "calculation" contains pretty much all conceivable childish errors you can think of: the exponential growth is neverending; the whole tree of infections should be blamed on one particular member of a branch (instead of all the people inside the infection chain); the Covid-19 CFR is huge, and so on.

The Czechoslovak "vz 58" (vzor 58 meaning Model 1958) is a totally non-equivalent counterpart of the Kalashnikov and the Czechoslovak weapon is arguably superior. BREN successors of it are produced today.

OK, how much harm (quantified as the total shortening of the other people's lives) do you actually cause if you are an average person, with an average probability of being Covid-positive for your country, and you get close enough to another person so that the other person gets positive in the case that you are positive as well? According to Dorigo, it's "dozens of years" if not "centuries" because you have basically murdered several people by a Kalashnikov. In reality, it's just several minutes.

If you organize the calculation cleverly, as I will, it is straightforward to see it. Check the Czech Covid statistical page. Czechia has 10.7M (million) people. 2.3M tests have been done, 335k (thousands) people have been proven positive, 188k out of them are active cases as of now, 3251 have died with Covid. Hospitalizations, serious cases are a bit over 7k and 1k, respectively.

Now, the actual accumulated number of cases is about 20%, preliminary results of new antibody tests say, or 2M Czechs. The currently infected ones are 5-10% i.e. 500k-1M people. And about 1k people died "due to Covid" when the death is properly attributed to the causes. These days, about 10k-16k "new" people are tested positive every day. The actual number of infections per day is higher by a factor of 5+ or so (because tests only reach 0.4% of the population every day and the disease is clearly sufficiently out of control of the testers given the fact that 30-35% of the tests are positive). Let us round that number to 86,400 new infections a day (including the overlooked ones).

OK, so in Czechia, a nation of 10M people, a new person is infected each second (there are 86,400 seconds a day). Now, how can Joe (his proper Czech name is Pepíček but I don't want to overwhelm you with difficult technicalities) change the dynamics by going or not going to a party where he infects another person? It's simple. You must realize that Joe's party decision can't change his whole nation from a free-minded nation to a nation of China-style obedient robots (where very different collective behavioral patterns may be achieved). His effect is only a tiny fraction of that which reflects his being a small fraction of his nation. If described by the aggregate figures, the epidemic ultimately evolves in qualitatively the same way in the future. But if Joe infects another person, it means that all the future events are "shifted in time". How much? Exactly by one second, by my assumptions. Without Joe's party contact, the "next infection" would take place in one second but with his party contact, it already occurs now. (You must read the previous sentence in much less than one second for the sentence to be correct LOL.) The disease is ultimately tamed when and because it hits some limits, the number of the vulnerable people becomes low enough so that the Covid activity is bound to decrease.

Again, an extra infection caused by a contagious Joe accelerates (shifts) the whole Czech future Covid evolution by one second.

This simple effect of "shifting the curve in time by one second" is possible statistically. Like the butterfly wings, Joe may have changed the history and it may be different people who will be infected – and different people who will be saved (because their "risk of infection" will already occur at times when the disease is tamed, due to the immunity) – in the case of attending/avoiding the party.

Now, 3251 have died with Covid-19 so far. Some extra 3k-7k will die in the future because we're close to the middle but the decrease may be a bit slower. The people who have already died are unaffected by Joe's behavior. Only those who will die, between 3k and 7k "deaths with Covid", will be affected by Joe's decision. Their lives will be statistically shortened by another second. It means that in total, by infecting one additional person, (the assumed Covid-positive) Joe will reduce the total remaining life expectancy of all Czechs by 3k-7k seconds i.e. by 1-2 hours.

However, that result is only valid if we know that Joe is Covid-positive. If we deal with a truly average Joe (pun intended), his probability of being contagious right now is some 5-10 percent (that's the percentage of Czechs who are currently contagious). We must therefore reduce those 1-2 hours by a factor of 10-20 and we get 3-12 minutes. Even if deaths with Covid are fully counted as "deaths caused by Joe's possible infection", the potential infection only shortens the lives of all the other people in the world combined by 3-12 minutes. If you count "deaths with Covid", you should reduce the result by another factor of 3 or so:

Realistically, the average (just hypothetically contagious) Joe's potential infection of another person shortens the total remaining lifetime of all other people by 1-4 minutes.

Again, Tommaso Dorigo got "tens of years" or "centuries" while I got 1-4 minutes. At least one of us must be terribly wrong, right? Be sure it is not me. Mine is a valid strategy to organize the relevant calculation; his is just a pile of physically impossible assumptions, childish mistakes, religious references to the mysterious infinity, and irrational fearmongering.

Because the statistical effect is so tiny, it is more meaningful to convert it to dollars. The U.S. minimum wage is $7.25 an hour, it's about the price of one hour of someone's life, too. (If you work for $7.25 an hour, for 8 hours a day, for 200 days a year, for 50 years, you will earn $560k.) So the infection that might be caused by Joe (who has the average odds of being contagious) is about 12-48 U.S. cents. This is the approximate degree of guilt you should feel. If you feel guilty to have spoken to someone, without a face mask, and you had no intent to kill him (that's important) and no knowledge about your being positive, then pay 12-48 cents to that person or a charity and your guilt is eliminated.

Note that my result was derived from the Czech numbers and Czechia has a higher percentage of "currently infected people" than any country has ever had (with a possible exception of microstates) even though Belgium is getting closer again. If you consider a country where 0.1% of the people are infected right now, the total cost of the "potential infection" caused by a Joe (whose Covid status is unknown) will be lower by a factor of 100 (you will get to one second or so!). You may also try to consider some average global figures. Every day, some half a million new infections are proven. It means (because the tests overlook 80%) that about 2.5 million new people are infected every day. One infection per 0.03 seconds. Multiply it by another ~1 million of deaths with Covid-19 (or 300,000 due to Covid-19) that we expect and you get 7 hours (2 hours) when you know that Joe is infected. The percentage of the currently contagious people is 12 million (currently active) times about 5 over 8 billion which is about 0.75%. If you multiply 7 hours (2 hours) by 0.75%, you get about 3 minutes (1 minute), too.

If someone is capable of infecting 10 people a day, the expectation value of the damages caused to other people's longevity is about $1.20-$4.80. If the germophobic institutions cause a greater economic harm to such a person, that harm is demonstrably unjustifiable by the health considerations.

Localizing his mistake is hard

What is the "precise mistake" that Dorigo has made? It is hard to say because his argumentation is not very clear, to put it mildly. It might be some assumption about a neverending growth of the epidemic in the future. But I think that a much more important mistake is that Dorigo totally overlooks the positive consequences of the single infection by Joe. If many Joes infect others during the November 1st party tonight, the epidemic will be accelerated now and "almost completely over" by December, instead of January which would be the case otherwise, and that's why Joe's November 1st party activity will protect almost all the participants of the January parties from being infected! By thinking in some sloppy way, Dorigo has completely erased the terms with the opposite sign that he doesn't want, and that's why his "harm done to the society" ended up being 1 million times higher than it actually is! So this mistake may be considered a great example of the general insight that "leftists don't understand negative numbers so they omit them".

Alternatively, one might argue that he got the extra factor of one million by replacing the actual "expectation value" by some potential "worst case scenario" at many points. This (currently omnipresent) fundamental fallacy is known as the precautionary "principle". One must mention that some people do infect others who die (or their further contacts die and it's possible to trace the death to yourself). However, in that case, it's beneficial for the individuals and for the society as a whole to "insure" everyone and distribute the responsibility to everyone. When your contact dies of Covid, he is unlucky and so are you; the bad luck consists of the infector's being contagious at the moment (most people aren't) and the infectee's being vulnerable (most people aren't). None of you could really affect that you were among the unlucky infection pairs. That's why the society (and even your conscience) should treat you (the infector) as innocent. Any other societal arrangement may indeed lead to Dorigo's twisted logic (a party with sqrt(3000) participants is on par with 9/11) which leads to the permanent confinement of everyone (even because of the flu risks which are the same or just slightly lower).

(Note that I assumed that the epidemic goes through the normal epidemic peak. If you live in a country that wants to believe that it will avoid a substantial propagation of the virus forever or for years, one person who spreads the disease may have a bigger impact on the national project; but he is correspondingly less likely to be infected right now and one infection still doesn't guarantee that the events get out of control. The expectation values don't end up being too different, I leave the discussion as a homework exercise.)

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