6. Misusing mathematics: The reproduction number

The mystery deepens. On March 16th 2020, 13 days after the CDC paper[1] stating the inability to induce the particles, whatever they are, to harm humans, a prediction of large numbers of deaths was made by Neil Ferguson from Imperial College. If no harm can be induced, then logically contagiousness becomes an irrelevant concept. In fact, on the 5th of January 2020, sixteen days prior to its promotion of the Drosden test, the WHO affirmed there was “no evidence of significant human to human transmission and no health care worker infections report”.[2] The Lancet paper of 21 February honestly recognizes that “with the limited number of cases, it is difficult to assess host risk factors for disease severity and mortality”.[3] This prediction of large numbers of deaths used to justify the implementation of lockdowns was founded on mathematical applications. Such applications call for prudence. They are all too frequently misused, and have been by Ferguson in the past.[4]

Shortcomings of mathematical applications

To begin with, approximations cannot be avoided. A hypothesis has to be initially expressed in mundane language. The translation process into mathematical symbolism carries with it much loss of information. Those discounts most facets of phenomena as these are not quantifiable.

Even in the most appropriate mathematization, the equations obtained describe idealised interactions, not real ones. Among quantifiable features too, a choice has to be made. Mathematics can only deal with a very limited number of parameters, and only a very simplified version of their relations. This selection tends to be made for the sake of mathematical and computational convenience, not for any justified scientific reason.

Although equations do in theory have exact solutions, except in the simplest cases, contrived methods have to be used. These only give us approximate ones. This is usually the case for differential equations, namely equations indicating the evolution of a system over time or space and thus on which predictions are based. A whole series of approximations again occurs when retranslating our mathematical representation into mundane language, notably as they are likely to involve non-exact numbers such as √2 or π. In this retranslation, as in the context of quantum mechanics, another problem might arise, that of interpretation since the same set of mathematics can generate diverging scientific explanations.

In short, the perfect accuracy inherent in mathematical formalism allows us greater control on some quantifiable features, but, precisely because of this accuracy, it is a far cry from reality. “As far as the propositions of mathematics refer to reality they are”, to quote Albert Einstein, “uncertain; and as far as they are certain, they do not refer to reality,”[5] all the more so as they are inferred from knowledge which, as remarked by his fellow Nobel Laureate, the physicist Max Born, is necessarily both “limited and approximate”.[6]

Probability and statistics introduce a whole new set of issues, apart from the fact they enhance the reductionism of a mathematics that can only address identical objects, eliminating individual features, for it sets aside all that differentiates and only retains some common properties. Statistical methods consist in averaging out. Averages do not exist in reality. As decried by the father of physiology, Claude Bernard: “all the biological characteristics of the phenomenon disappear in the average”.[7] As for probability, it is bad enough in the context of events repeatable as many times as desired, but assigning probabilities to events that occur only a few times, like a pandemic, is evidently even more problematic. In this case a probability value is subjectively assigned by the investigator depending on his personal assessment of an event in the future. Until the event actually happens, there is no way of checking the quality of the assessment. After the event has happened, it has become fully certain, and this is no indication of the correctness of the probability assigned to it prior to its occurrence. Hence these assessments do not belong to the realm of science, but provide them with the veneer of scientific ‘respectability’ and apparent objectivity.[8]

The reproduction number

Keeping in mind the mathematical shortcomings, keeping in mind that cases and deaths alleged to be from covid-19 are nothing more than positive outcomes of tests, keeping in mind that according to pathologists “there is no one who has died from the coronavirus”,[9] at least in Europe and at least until 8 May 2020, let us proceed.

The March 16 predictions were founded on estimations of the reproduction number R0, which is supposed to indicate the potential of a disease to spread. This major tool in epidemiology cannot be evaluated through direct counting. It is a probabilistic and statistical abstract concept, whose estimation must perforce be based on mathematical models,“few of which agree with each other”.[10] This is little surprising since this number reflects all the issues described.

Based on multiple complex interdependent factors – “biological, sociobehavioral, and environmental”[11] –, it raises the spectre of unpredictability, likely a far greater issue in biology and sociology than in the physics of the inanimate world. It is also founded on innumerable unverified and unwarranted assumptions and thus is subjective. Regarding microbial diseases, not only are they assumed to be contagiousness, but that microbes can affect us all equally since it represents “the number of secondary cases which one case would produce in a completely susceptible population”.[12] It leaves aside the role of individual susceptibility and in the case at hand, local environmental and cultural factors on immunity. It fully standardizes. Besides, any empirical data it follows from is necessarily limited. Since a study based on non-reproducible observation runs the risk of not being scientific, to be convincing, the data would have to be accumulated over a period of several years, to notably be compared with data obtained over a sufficiently long period for other diseases.

Consequently, estimations can vary according to the methods applied as in the case of malaria, where, keeping all parameters constant, a slight change in one of them may alter the value of R0[13] – unsurprising since linearizing equations amounts to increasing unrealism, while non-linear expressions are greatly sensitive to input values.[14]

A mathematical model can be coherent, but only a strong empirical scientific foundation can save it from being totally unrealistic. Regarding our case, given this foundation is highly shaky at best, and more likely totally flawed, no wonder the estimation of R0 has widely varied, and in particular Ferguson’s model has proved to be wrong.[15] Yet unprecedented “[p]olicy decisions are being based upon the concept, with limited understanding of the complexity and errors that exist in the very structure of the concept”.[16]

    1. https://www.biorxiv.org/content/10.1101/2020.03.02.972935v1.full.pdf
    2. https://www.who.int/csr/don/05-january-2020-pneumonia-of-unkown-cause-china/en/
    3. https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(20)30183-5/fulltext
    4. https://www.spectator.co.uk/article/six-questions-that-neil-ferguson-should-be-asked
    5. Einstein, A. [1921] 1960. “Geometry and experience: Lecture before the Prussian Academy of Sciences on 27 January 1921”. Translated and revised by Sonja Bargmann. In Ideas and Opinions, 232–245. New York: Crown Publishers. p. 233
    6. Born, M. 1965. “In memory of Einstein”. In Born, M. 1970. Physics in my generation. London: The English Universities Press; Springer Verlag. p. 163.
    7. Bernard, C. (1865). An Introduction to the Study of Experimental Medicine.Translated by Henry Copley Greene. United States: Henry Schuman. 1949. p. 134.
    8. Ray, T. and U. Ray. 2020. On Science: Concepts, Cultures and Logic. London: Routledge.
    9. https://off-guardian.org/alexov-webinar-transcript/
    10. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3157160/
    11. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3157160/
    12. https://journals.sagepub.com/doi/abs/10.1177/096228029300200103
    13. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3157160/
    14. Ray, T. and Ray, U. 2020. On Science: Concepts, Cultures, and Limits. London: Routledge. 2020.
    15. https://www.aier.org/article/the-failure-of-imperial-college-modeling-is-far-worse-than-we-knew/
    16. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3157160/