Sunday 1 November 2020

k, R and the Scandal Reproduction Number

Readers with a background in physics may recall that there was a quantity from the late 1930's research into nuclear physics referred to as k, or the k-number. It refers to the way in which neutrons produced by one nuclear fission in a reactor can then go on to cause further fission in other nuclei of the reactor, leading to a successive chain of reactions. The account in Alwyn McKay's The Making of the Atomic Age, reads as follows:

This is called the neutron multiplication factor, and is usually denoted by k. If, for instance, the number doubles from one generation [reaction] to the next, k=2, and if it increases by  five per cent, k= 1.05. Any increase, be it noted, is at compound interest, and if unchecked, may lead to an explosion, whereas a decrease, with k less than one, implies that the chains will peter out.

In the days of coronavirus, we have become very familiar with the R-number, the virus reproduction number.  This is the average number of people to whom one infected person will pass the virus. Where the physicists of the 1930s were trying to achieve a k-number equal to or just above one so that a sustained chain reaction would be possible, public health officials of 2020 want to achieve a value of R that is less than one so that the transmission of the coronavirus will gradually die out. 

Now, I am not one of those who think that Pope Francis is a Pope who gives rise to scandal among the faithful. But, just for a moment, just suppose I was one such.... would I want to contribute to the scandal reproduction number by posting about it on the internet? In particular, would I want to do that by re-tweeting. embedding or re-posting someone else's observations about how scandalous Francis is? 

Just as with the k-number of the physicist and the R-number of the epidemiologist, there comes a point where a value greater than one for the scandal reproduction number gives rise to a permanent prevalence of scandal, even though the scandal at that stage may bear little or no relation to the original event that is claimed to have given rise to it. When this happens, the responsibility for the scandal lies with those who have been happy, in the first instant, to call it scandal; and, in the second instance and perhaps more significantly, with those who have been willing to repeat the message of scandal after them.


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