Ever since Thomas Malthus used simple mathematics to model the evolution of food production vs the increasing human population of planet Earth and declared that we would very soon eat ourselves out of house and home, politicians have been falling hook, line and sinker for mathematical models. This paper examines how and why the mathematical modelling of complex systems has proved unreasonably effective in convincing mathematically illiterate politicians to take practical measures that have turned out to be disastrous. It then suggests that mathematical modelling of the human brain is not a good strategy to pursue.
Introduction
As a teenager, I admit to having regarded the subject of mathematics with suspicion and distaste. My problem was basically that I could not work out whether mathematics was a science, or an art — and neither could I make any of my teachers even understand the question. Was mathematics something that existed independently of humans and was out there waiting to be discovered (which in my view would have made its study a form of science)? Or was mathematics simply a human invention (which would have made it an art)? When I got to university, the fact that mathematics departments generally inhabited both science and arts faculties at the same time suggested that my confusion was widely shared. I continued to avoid the subject.
Sixty years later, when I finally got around to reading Eugene Wigner's famous paper "The unreasonable effectiveness of mathematics in the natural sciences" (Wigner, 1960), his conclusion seemed to settle the matter. As Wigner put it: "mathematics is the science of skillful operations with concepts and rules invented just for this purpose. The principal emphasis is on the invention of concepts". So, clearly Wigner was using the word 'science' here in the sense of 'body of knowledge about how to do' — as in 'the science of skillful oil painting.' Indeed, Wigner's further comment, that "Most more advanced mathematical concepts, such as complex numbers, algebras, linear operators, Borel sets ... were so devised that they are apt subjects on which the mathematician can demonstrate his ingenuity and sense of formal beauty. In fact, the definition of these concepts, with a realization that interesting and ingenious considerations could be applied to them, is the first demonstration of the ingeniousness of the mathematician who defines them" suggested that serious mathematicians are less interested in understanding the outside world than in demonstrating their own brilliance. I felt relief that, as someone who wanted to understand biology, I had not wasted too much time on maths.
But then, of course, Wigner went on to point out that mathematics is "unreasonably effective in the natural sciences" (by which he meant physics). However, physics is concerned mainly with simplified interactions between inanimate objects. And indeed, even then the mathematical modelling of such simplified interactions can be slippery, to the extent that a certain amount of "randomness" has to be invoked to drag the observed quantum mechanical relations between postulated quantum-sized objects into line with mathematical descriptions of them. And systems involving biological elements — epidemiology, climatology, economics — are much, much worse. Such systems are so many orders of magnitude more complex than the systems treated by physics that it is extraordinarily difficult to use mathematics to model them at all, let alone to do so with any degree of predictive accuracy.
The main problem to be solved in this regard is that when complex systems are considered, a fairly large number of assumptions have to be made, in order to simplify the system enough for any mathematical model at all to be constructed. And since very few people even realize that such assumptions have been made — let alone ask to see them — it is all too easy to hide the fact that the assumptions underlying any such model are almost always either completely untested, or (worse) obviously at odds with reality. Combine this with the fact that many if not most people (including virtually all politicians, who are generally lawyers by trade) are functionally illiterate in both science and mathematics — and will thus happily accept as "the science" anything a mathematical modeller tells them — and mathematical modelling becomes a priceless political tool.
The steps necessary to use this tool are simple:
- Assume the truth of whatever you want the public to believe.
- State this assumption in suitably mathematical terms.
- Build a mathematical model around it.
- Run the model.
- Assert that the output of the model (a.k.a. "the science") proves your original assumption. (Yes, of course this is absolutely classic circular reasoning. But since nobody knows about steps 1 to 3, nobody will notice that).
- Sit back and watch everyone believe your original assumption, because it has now been proven mathematically and therefore must be right.
- Act on whatever you have programmed "the science" to show.
- And with a bit of luck, by the time the political actions based on this particular manifestation of "the science" have been shown to be catastrophically counterproductive, everyone will have forgotten that it was your model which caused those political actions in the first place.
The first three steps in this series must be done very quietly. Steps 4 — 8 can be trumpeted loudly (except that the word "assumption" must never be uttered). And yes, gentle reader, that's how it's done.
The rest of the present paper first lists three different situations in which this political tool has been — and still is being — used to great effect. It then suggests some places where mathematical modelling should probably NOT be tried in the future.
1. The Imperial College Epidemiological Model
Professor Neil Ferguson of Imperial College London has a splendid track record in this regard. The unreasonably astonishing thing about his situation is how British and other politicians have continued to believe his prognostications, despite a litany of erroneous earlier predictions. Dowd (2022) lists some of these, on his page 96:
2001: Predicted 150,000 people would die from foot and mouth disease. Actual number of deaths 200.
2002: predicted up to 156,000 deaths in the UK from Mad Cow Disease. Actual number of deaths 177.
2005: Predicted up to 200 million would die from bird flu. Actual number of deaths 282 over 6 years.
2009: Predicted 65,000 deaths from swine flu in UK. Actual number of deaths 45.
2020: Predicted up to 179,000 COVID deaths in Taiwan in first full year of covid pandemic. Actual number of deaths 10.
As Dowd puts it "Despite decades of dramatic and persistent failures, Neil Ferguson's prediction that as many as two million Americans would die from COVID in 2020 was used to justify lockdowns, school closures, social distancing and all that followed."
So clearly this particular mathematical model does not and never has produced results consistent with reality. But then, of course, the counter measures taken on the basis of the model's over-the-top predictions have been given the credit for the reduced number of deaths.
That being said, this instance is not necessarily an example of the 8-step political scenario outlined above. Software engineer Denim (2020a, b) investigates Ferguson's computer code and says "Due to bugs, the code can produce very different results given identical inputs. They routinely act as if this is unimportant. This problem makes the code unusable for scientific purposes, given that a key part of the scientific method is the ability to replicate results. Without replication, the findings might not be real at all."
So strictly speaking, this case illustrates that no political intent need be inferred in order to distrust the results of mathematical/computer modelling. Of the two major theories of history, the cock-up theory can operate independently of (as well as in concert with) the conspiracy theory. However, some level of conspiracy is suggested here both by the continued refusal of Imperial College to admit error and either withdraw or adequately fix the code — and by the point-blank refusal of governments around the world to consider the Imperial College group's dismal past performance when deciding whether or not to believe and act on their COVID predictions.
Following on from this, the (previously) most respected medical journal in the world, The Lancet, has published yet another mathematical model — this time written by a different set of Imperial College dwellers (Watson et al., 2022) and quite openly funded by a long series of dedicatedly globalist organisations, some with rather obvious financial conflicts of interest — claiming that "COVID-19 vaccination has substantially altered the course of the pandemic, saving tens of millions of lives globally." This quite astonishingly flawed paper once again fits earlier COVID-19 transmission models (constructed by the same Imperial College group) to both reported COVID deaths and excess mortality at various unspecified times during the WHO-declared pandemic — to purportedly calculate the number of deaths that COVID would have caused had no "vaccine" been developed at warp speed and administered by coercion. In doing so, it completely ignores the facts that:
- the transmission models have never been validated
- the numbers of 'official reported COVID deaths' used in this paper are embarrassingly unreliable, thanks to the combination of (a) the WHO's decision that no actual symptoms of COVID were required to declare someone a 'confirmed case' of the disease — just a cycle threshold of less than 40 on a PCR test that was never remotely fit for purpose and thus scored as 'confirmed cases' an unknown percentage of asymptomatic people who likely never harbored any coronavirus at all, let alone any virus capable of infecting others: and (b) the fact that virtually all 'COVID deaths' in the pre-vaccine era were suffered by elderly people who had been admitted to hospital on the verge of death from multiple unrelated comorbidities anyway, but who tested positive on admission (using the unsound PCR test) and whose subsequent demise was thus scored as a COVID death.
Dowd (2022) for example, documents an epidemic of completely unexpected sudden deaths in previously healthy young people, immediately following injection of COVID "vaccines" (which, it should be noted, are not classical vaccines at all, but experimental gene-therapy shots fraudulently represented to the public as "safe and effective" vaccines).
However, since the magic words "Mathematical Modelling" appear in the title of the aforementioned Lancet paper — and because the editor-in-chief of this erstwhile globally respected medical journal permitted its publication — the paper was widely taken as proving that the experimental gene-therapy concoctions fraudulently shot into arms all over the world have not, in fact, killed or maimed an unacceptable number of their recipients, but on the contrary have saved millions of lives — and that more such shots would be even better.
At the time of writing it is too early to tell the ultimate outcome of this travesty of science and medical ethics, but I predict that it will not be pretty. And it was all justified using Professor Ferguson's appallingly unreliable mathematical model.
2. Mathematical Modelling of Climate Change
Exactly the same strategy has been used for many years now to convince people that the current warming trend in Earth's climate is (1) unprecedented (2) likely to fry us all within a few years and (3) caused by human production of "greenhouse gases".
Here there is no doubt that this is a case of deliberate fraud. In 1991, Alexander King and Bernard Schneider published a book called "The First Global Revolution: A Report by the Council of the Club of Rome" (now scrubbed from the internet) in which they say on p. 75 "In searching for a new enemy to unite us, we came up with the idea that pollution, the threat of global warming, water shortages, famine and the like would fit the bill." [emphases added]. In the 1993 edition, they added "In their totality and their interactions, these phenomena do constitute a common threat which must be confronted by everyone together. But in designating these dangers as the enemy, we fall into the trap which we have already warned readers about, namely mistaking symptoms for causes. All these dangers are caused by human intervention in natural processes, and it is only through changed attitudes and behaviour that they can be overcome. The real enemy, then, is humanity itself." [emphasis added]. In other words, doom is upon us, it's all your fault and the only way to save the planet is for everyone to do as we tell them. (And oh, by the way, this means we really need a Global Government, run by us).
And then, the unreasonable political effectiveness of mathematics came into play. In order to convince people to "unite against" this "new enemy", it became necessary to show that human intervention in natural processes does indeed cause global warming. And therefore, since the only mechanism anyone could come up with by which humanity MIGHT be able to cause global warming was to spew lots of polluting gases into the air, it became necessary to show that global temperatures had increased dramatically after the First Industrial Revolution.
Well, this posed a bit of a problem. The trouble was that the First Assessment Report put out by the United Nations IPCC (Intergovernmental Panel on Climate Change) in 1990 had accepted unequivocally that global temperatures during the Medieval Period (from approx. AD 1000 to AD 1300) were significantly warmer than they are today. Grapes grew in London then. Greenland was ... green. So Figure 7.1(c) on page 202 of that first IPCC report showed this:
And the problem? This graph made it all too clear that (1) temperatures today are nothing out of the ordinary in historical terms — and (2) today's temperature is probably NOT significantly affected by the industrial release of CO2. Why? Because there was no industrial release of CO2 during the medieval period, yet the climate then was roughly 3°C warmer than it is now.
They couldn't just scrub this graph from the internet (the current go-to method of getting rid of inconvenient data) because there were too many hard copies out there. So then began the perversion of science that has characterised the "climate crisis" narrative ever since. The deliberate nature of the fraud is revealed by Deming's report a decade later (Deming, 2005) that after he had published a short 1995 article in the prestigious journal Science, he "... gained significant credibility in the community of scientists working on climate change. They thought I was one of them, someone who would pervert science in the service of social and political causes. So, one of them let his guard down. A major person working in the area of climate change and global warming sent me an astonishing email that said "We have to get rid of the Medieval Warm Period."
Well, all right then! So "get rid of the Medieval Warm Period" is exactly what a new cabal of well-paid 'climate scientists', peer reviewers and journal editors obediently did. In 1998, Michael Mann and colleagues published a paper in Nature saying that temperatures in the late 20th century were warmer than at any time since 1400 (Mann et al., 1998). OK, not controversial. But then, a year later, the same authors extended their analysis back to the year 1000 (Mann et al., 1999) — and poof — the Medieval Warm Period was gone. A well-known summary of the graph published in the 1999 paper is:
Medieval Warm Period? What Medieval Warm Period? The above graph was front and centre in the 2001 Third Assessment Report of the IPCC — and was subsequently sent by the Canadian government to all schools in Canada, with the catchy sobriquet "hockey stick." It was necessary to terrify the children.
But how was this miraculous disappearance of the Medieval Warm Period engineered? Well, by the judicious manipulation of mathematical modelling — or in other words, by the use of "lies, damned lies and statistics". Mann's refusal to make public either his data or the detail of his methodology became legendary (Ball 2014) and the issue soon blew up into an affair known as 'Climategate'. Eventually Mann was forced to release his data; but he has continued to refuse point-blank to share the computer code he used to analyse them. Finally, it became clear that he had manipulated the underlying statistics to the extent that when random numbers were input into the methodology he had published, a hockey-stick shape was produced 99% of the time (McIntyre & McKitrick 2005 a,b). In summary, it can reasonably be said that this episode helped to (a) reduce public faith in the scientific objectivity of the IPCC (for further evidence on how the IPCC routinely first publishes an alarmist Summary for Policy Makers, then edits their Scientific Report to fit) and (b) convince anyone who was paying attention that there is no "climate emergency" — and that Earth's climate, though constantly changing, is not significantly affected by anthropogenic CO2. For a Declaration to this effect signed by 1,200 global climate scientists.
But of course, politicians bother about science only when "the science" supports their political agenda — and children believe whatever they're told by their teachers. So, for reasons the politicians choose not to disclose, they continue (while they are allowed by their adult public to do so) to impose draconian taxes and policies advantageous to only a few, all justified by firm statements that anthropogenic CO2 is causing catastrophic global warming, which will fry us all unless we do what they tell us immediately. This narrative is greatly assisted by compliant school-teachers and by a news media interested only in horror stories (partly because the politicians reward such behaviour financially and partly because the boring old truth is just not click-bait). More to the point in the context of the present paper it is further supported by a raft of "climate models" all engineered (to the significant financial benefit of their makers) by way of the eight-step protocol detailed in the Introduction to the present paper.
Those interested in the actual mathematics involved in the hundreds of climate models that confidently predict how warm Earth will be in a hundred years (despite the fact that weather forecasters are notoriously unable to predict the weather accurately three days hence) can find such details in Ball et al (2011).