Let me start by telling you three stories. The first is one you very likely know. A fraudulent tailor with no money to buy cloth nevertheless persuades a wealthy emperor that he will make him the finest suit of clothes imaginable. The emperor, deceived by the flattery of the tailor, believes that he is wearing a beautiful new outfit (made of very lightweight material). In fact, he goes out to greet his subjects stark naked. The rest of the crowd falls prey to the same mass delusion until a little boy points out the truth and then the spell is broken and the emperor becomes a laughing stock.<\/p>\n
Now let\u2019s also consider the story of the fraudulent Hitler diaries. Unlike the fable of the emperor\u2019s new clothes, this is a true story (although I don\u2019t swear that every detail here has been forensically researched). A fairly incompetent forger named Konrad Kujau wrote them himself during the early 1980s, staining the pages with tea to make them look old, before he sold them to the German news magazine Stern for several million pounds. Stern relied on the analysis of English historian Hugh Trevor-Roper who pronounced them genuine. Only after the fraud was uncovered did Trevor-Roper reflect on his thought process which included factoring in that Stern was paying a vast sum for the publication rights. Since fraudulent Hitler diaries had no value, he reasoned, these must therefore be authentic.<\/p>\n
Finally, let us consider Edmund Landau and Fermat\u2019s Last Theorem. As many people know, the brilliant 17th century mathematician Pierre de Fermat once scribbled in the margin of a book the equation xn<\/sup> + yn<\/sup> = zn<\/sup> and asserted that he had discovered a truly marvellous proof that there were no whole number solutions where n > 2. (If n = 2, this is Pythogoras\u2019s theorem.) He did not alas provide the proof, claiming that the margin was too small to contain it. The theorem was finally proved in 1995 by English mathematician Andrew Wiles, whose proof ran to many dozens of pages and build on the work of Gerhard Frey and Ken Ribet and required a deep understanding of semistable elliptical curves. Evidently, this was not the proof which Fermat had (or thought he had).<\/p>\n Fermat\u2019s Last Theorem was for three hundred years the outstanding unsolved problem in mathematics. Not because it was particularly important (although Wiles\u2019 work did open up new avenues of exploration) but because it had remained unsolved for so long and yet it could be stated in terms which anyone with a passing knowledge of algebra could understand. This meant that it attracted the attentions of a great number of enthusiastic amateurs, all of whom imagined that they would be the ones to solve the unsolvable.<\/p>\n The problem was compounded in 1908 when industrialist Paul Wolfskehl offered a large cash prize for a valid proof. Edmund Landau was the mathematician who was, for a while, responsible for assessing entries. Overwhelmed by the sheer number of submissions, many of which were little more than gibberish, he eventually had a stack of cards printed which read: \u201cDear [BLANK]. Thank you for your manuscript on the proof of Fermat\u2019s Last Theorem. The first mistake is on line [BLANK]. This invalidates the proof.\u201d He gave the job of filling in the blanks and returning the cards to his students.<\/p>\n What does all of this tell us about vaccines, conspiracy theories and the nature of evidence?<\/p>\n I had high hopes that the natural experiment currently being run in which tens of millions of healthy adults are being given a vaccine to help prevent them from contracting COVID-19 would silence the anti-vax brigade. If it were true that vaccines were toxic in any way at all, then we would see a huge wave of whateveritis sweeping the globe. No such wave has in fact materialised. The best (ugh) the anti-vaxxers could muster were a few cases of blood-clotting, which were at such a low incidence it was barely possible to connect them to the vaccine at all.<\/p>\n Although something of a side issue here, the case of blood clotting is instructive when it comes to vaccines in particular. Even though the incidence was so low that it was almost impossible to distinguish from the base level (some people will get blood clots anyway), it was determined that one brand of vaccine could increase the likelihood of developing a blood clot in some people. Okay then. We have identified a risk. Somebody fearful about developing a blood clot would be sensible to refuse the vaccine. Even if the risk is small \u2013 blood clots are nasty and can be fatal.<\/p>\n Except\u2026 that by not getting the vaccine, you are increasing your risk of contracting COVID-19. And one of the possible complications of COVID-19 is \u2013 blood clots. In fact, you are many, many times more likely to develop a blood clot as the result of contracting COVID-19 than you are from getting the vaccine.<\/p>\n Life is a game of risk vs benefit. The problem is that we tend to see risks where we take positive action (getting a shot) and ignore them where we are passive.<\/p>\n But that alone can\u2019t explain the demented anti-vax brigade rapidly pouring on to social media to tell me that vaccines are toxic, that they aren\u2019t properly tested, that diseases don\u2019t exist and that I should do my own research. There\u2019s an enormous appeal for some people in the conspiracy theory. It enables the conspiracy theorist to be the brave little boy in the story of the emperor\u2019s new clothes, whose plain common sense and straightforward approach cuts through all of the sophisticated bullshit to expose the obvious truth. Of all the characters in that story, the one we want to be is the little boy. We don\u2019t want to be the villainous tailor whose nefarious plans are ruined and we certainly don\u2019t want to be the foolish emperor, taken in by such a simple trick. The appeal is obvious.<\/p>\n The trouble is that fate is manifestly unlikely to present us with such a situation. Randall Munroe in one of his XKCD comics, imagines a riposte to a parent who asks \u201cIf all your friends decided to jump off a bridge \u2013 would you?\u201d as follows: \u201cWhich scenario is more likely: every single person I know, many of them level-headed and afraid of heights, abruptly went crazy at exactly the same time… or the bridge is on fire?\u201d<\/p>\n Thus, Edmund Landau\u2019s pre-printed cards. Landau didn\u2019t need to read these crazy would-be proofs, and nor did he fear missing the mathematical discovery of the century. Anyone who had done the necessary work to even begin to attack this prodigiously difficult problem would of necessity be someone in the mathematical community who was publishing on a regular basis, and that is where the proof would turn up (if it were ever found). Landau didn\u2019t live to see Wiles\u2019 proof which was published nearly a century after his death, but its form and the manner of its revelation would not have surprised him.<\/p>\n That brings us to the key question. How can I, with a 2:2 in mathematics, know that Wiles\u2019 proof is correct? I have read an outline of the proof intended for the curious lay reader, and I failed to keep the concepts clearly in my head. I do not have a mental model I can use for considering modular groups or elliptic curves or how they relate to each other. In fact, when Wiles\u2019 proof was first published, an error was found and it took Wiles and a colleague several further months of work to patch the problem. Probably there are less than 100 people living who can read and appreciate every line of the final version \u2013 such is the obscurity of modern mathematics, all of it resting on pre-existing understanding of already fairly abstruse and difficult material.<\/p>\n In practice, I cannot \u201cdo my own research\u201d. It is too late for me now to begin a decades-long career in number theory and I do not believe that the investment of time and energy would have a satisfactory payoff. So, how can I be sure that I am not poor foolish Hugh Trevor-Roper, who takes the fact that Stern believes in the Hitler Diaries as a reason to vouchsafe to that same organ that they are worth the sum proposed for their publication rights?<\/p>\n This is the charge that the conspiracy theorists level at those of us who subscribe to scientific scepticism. Some of the more obviously loopy ones will happily (and loudly) present themselves as the little boy pointing at the naked emperor. The idea that a minority opinion is likely a false one has never entered their head. They so enjoy the heady rush of being in the select group of the clear-thinkers and the far-seers that they never stop to question why no-one else can think those same clear thoughts and see those same far-off things.<\/p>\n But the charge of blind obedience or fatuous credulity is a harder one to dismiss. You\u2019re just believing what you\u2019re bring told. You\u2019re Hugh Trevor-Roper falling for the Hitler diaries because some authority figure tells you they\u2019re genuine. And look! They proclaim. Here is a paper which proves what I am saying is correct. Here is a doctor who doesn\u2019t believe in germs. Here is an engineer who doesn\u2019t believe the Twin Towers could have fallen without demolition charges. Here is an Air Force pilot who has seen flying saucers. Here is an astronaut who believes the Earth is flat. Here is a photo of Bigfoot. Here is a NASA scientist who can read minds. Et cetera and so forth.<\/p>\n Particularly with medicine, online debate-via-link-to-scholarly-journal is rife. Don\u2019t take my word for it, look at the conclusion reached by this research team. This exchange of technical papers which neither party can properly understand is the height of pointlessness. I was (unwisely) drawn into a debate about the events of 9\/11 on Facebook not long ago. A \u201cnew\u201d paper had been published (several years ago), paid for by a group whose only purpose is to find any contradiction at all in the \u201cofficial story\u201d. This piece of mathematical modelling purported to show that the collapse of Building 7 was inexplicable without some additional force acting (they coyly stop short of saying the word \u201cexplosives\u201d). Online it was easy to find people with far more expertise than me taking this paper apart, but the technical details were beyond me and so I saw no reason to comment on its contents.<\/p>\n What I found fascinating was the existence of another paper which had been published many years earlier which had modelled the collapse and found that the weakening of the structure due to the immense heat of the fires which burned for nearly an hour was entirely sufficient to explain what was observed on that horrific day. I was angrily told by defenders of the later paper that they had been researching the subject for years and were expert in this field (and by those same defenders that the online criticism which I provided links to was too technical). But the existence of this earlier paper seemed not to have registered.<\/p>\n Surely, if a second analysis has been performed which comes up with a different result, then the first question to ask would be: what was the difference in approach and what were the faulty assumptions made by the first team? Otherwise, what sense does it make to accept the conclusions of the second paper wholesale and completely dismiss all of the conclusions of the first? Without an understanding of what led to the difference, we\u2019re simply being asked which black box we prefer. How can we possibly learn any objective truths about the world by doing this?<\/p>\n So, are we doomed to just saying \u201cnobody knows\u201d or committing to decades of re-education to get to the truth? I don\u2019t believe so. In practice, we don\u2019t need to even ask these basic questions. We don\u2019t need to take the paper(s) apart. We don\u2019t need to begin a lengthy career of detailed study to be able to critique the work of both teams. We can just ask instead: who else believes this?<\/p>\n Science proceeds in general not because of individual mavericks whose ideas seem crazy at first. Instead, evidence gradually piles up in favour of one conclusion more than the others. It was well-known and agreed by almost all medical practitioners that stomach ulcers were caused by stress, until it was shown that they were caused by bacterial infection. Now, virtually every doctor prescribes antibiotics. Palaeontologists used to believe that dinosaurs were likely scaly and reptilian. Now the preponderance of evidence suggests instead that many of them were feathered. The evidence moved the consensus of opinion over time.<\/p>\n With COVID-19, we have seen this play out as we\u2019ve watched. Early guidance emphasised handwashing, because (for a variety of reasons) the importance of aerosolised viral particles was underappreciated. Now, both mask-wearing and crucially ventilation for indoor events is understood to be key. We didn\u2019t know that when the pandemic started. But the consensus of medical opinion moved as the evidence accumulated.<\/p>\n And this brings me to my last bugbear regarding Internet vaccine warriors. We have seen that \u201cdo your own research\u201d is ridiculous. We are simply not equipped to do anything of the sort. Instead, we need to appreciate that we are not likely to be the little boy pointing out that the emperor has no clothes \u2013 if everyone else sees clothes and we don\u2019t, it\u2019s far more likely that we are having a stroke. But the world is full of plausible sounding people who write articles and share videos (and post blogs!) and it\u2019s easy to get seduced by their rhetoric.<\/p>\n \u201cWatch this video, then you\u2019ll understand.\u201d \u201cThis doctor gets it, read what she writes.\u201d \u201cThis book really changed my mind about this topic.\u201d<\/p>\n So now we have an expert who is explaining complicated ideas in ways that we lay people can understand. We don\u2019t have to worry about whether we can master the technical details. If this expert can explain this in a way which makes sense to us \u2013 then we will understand it. Right?<\/p>\n Wrong.<\/p>\n This is in fact the very error made by Hugh Trevor-Roper, who took the opinion of Stern as the basis for his conclusion. You can\u2019t learn about scientific consensus by listening to one expert, no matter how slick, folksy, friendly or straightforward they seem.<\/p>\n Watching well-produced explainer videos on YouTube is a great way to learn about stuff and there are some great creators out there. But you don\u2019t discover objective truths about the world by opinion shopping. You can\u2019t sift through a few different takes on a complex subject and then decide \u201cI\u2019ve found my guy.\u201d That only works if your guy is just saying what everyone else is saying. But if your guy is an outlier, you need to ask why. If your guy\u2019s evidence \u2013 which might be highly convincing to you, a non-expert \u2013 has failed to convince the other experts, you need to ask why not.<\/p>\n So, if 99 doctors tell you that the vaccine is safe and it\u2019s in your best interests and society\u2019s best interests for you to take it as soon as you are offered it, the fact that you can find a 100th doctor who tells you something else is not relevant. At all. Because if that one doctor had real evidence that the other 99 were wrong, the other 99 would change their minds. How do we know? We have seen it happen in real time as the pandemic has played out, and we have seen it happen throughout the history of science. Your one paper \u201cproving\u201d that masks don\u2019t slow the spread of this, or any disease, does no such thing. It\u2019s an outlier. The consensus is that they do help. Your one paper is wrong. (Or it isn\u2019t widely applicable. Or you\u2019ve misunderstood it. Or it doesn\u2019t say what you claim it does.)<\/p>\n Salinsky\u2019s Second Law: You can prove anything with one<\/em> study.<\/p>\n This has become a very long post, for which apologies. My point really is a simple one.<\/p>\n We believe our dentist when we are told we need a filling. We believe the mechanic when we are told that our car needs a new fan belt even though we couldn\u2019t pick a fan belt out of a line-up. We trust experts all of the time and don\u2019t feel the need to \u201cdo our own research\u201d \u2013 unless and until a campaign grows around a particular topic and a small but insistent band desperately needs to believe that the emperor has no clothes on.<\/p>\n So, I don\u2019t really mind where you fall on the scale from \u201cI\u2019m not anti-vax, I just don\u2019t feel this has been tested enough,\u201d to \u201cYou\u2019ve been lied to! Disease isn\u2019t real!\u201d Both those positions are wrong because both of them misunderstand what science is and how it works. You can\u2019t possibly know what \u201ctested enough\u201d means. You don\u2019t (and I don\u2019t) have even a basic working knowledge of how vaccines are routinely developed or tested and what happened in this case. The first error is in word eight. This invalidates the argument.<\/p>\n So, by all means \u201cdo your own research\u201d. Research is fun. You can teach yourself a lot and you can end the day understanding more about virology, immunology, biomedical research and the spread of infectious diseases than you did at the beginning. But if you fail to take into account where the conclusion you are satisfied with sits in relation to the scientific consensus, you are not avoiding the error made by Hugh Trevor-Roper, you are committing it.<\/p>\n Don\u2019t be Hugh Trevor-Roper. The bridge may very well be on fire.<\/p>\n","protected":false},"excerpt":{"rendered":" Let me start by telling you three stories. The first is one you very likely know. A fraudulent tailor with no money to buy cloth nevertheless persuades a wealthy emperor that he will make him the finest suit of clothes imaginable. 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