Anatomy of a frustrating conversation

Bates equationAs readers of this blog, of my books, and of pretty much everything else I’ve written so far know, I value rational discourse and (still) believe it to be the only way forward open to humanity. But boy it can get frustrating, sometimes! One such example occurred recently, during an increasingly surreal discussion I had with one of my relatives — about politics, pseudoscience (specifically, the non-existent connection between vaccines and autism), conspiracy theories (9/11), and much, much more.

Of course, I should have known better than to start such discussion, especially with a relative who I knew subscribed to all those notions. Blame it on the nice bottle of Aglianico wine we had been sharing during the evening.

Anyway, the pattern was the expected one on such occasions: denial of relevant expertise (you know, they thought Galileo was crazy too!), while at the same time vigorously — and apparently entirely obliviously to the patent contradiction — calling on someone else’s doubtful expertise (the guy is an engineer! No, he isn’t…). There was also continuous side-tracking by bringing up irrelevant or unconnected points (in informal logic that’s red herring), as well as pleads to go “beyond logic,” whatever that means. You know, the usual fun.

And then another one of my relatives, present at the discussion and very much amused by it, hit the damn nail right on the head. He explained that my interlocutor was simply confusing probability with possibility. I stopped dead in my tracks, considered the suggestion, and had a Eureka! moment.

Yes, that was indeed exactly what was happening. Pretty much all of her arguments were along the lines of “well, it is possible that…” or “but you can’t exclude the possibility that…” And of course she was right. I explained, however, that this was a Pyrrhic victory. Yes, it is true that for most things (in fact, for any statement that is not mathematical or purely logical) there is always the possibility that one is wrong. But usually we don’t make decisions based on possibilities, we use the much more refined tool of probabilities (estimated to the best of our abilities).

I tried to make the point by drawing two diagrams, like this:

probability distributions

The graphs illustrate two hypothetical probability distributions for a set of events, with the probability estimate on the vertical axis and the type of event on the horizontal one. The top diagram represents my relative’s view of the world: she is acting as if all events had equal probability. Not literally, because she does understand that some outcomes are more likely than others; but in practice, since she considers mere logical possibilities, however remote they may be in reality, to be worthy of the same amount of attention as outcomes that are much more likely to occur. The lower diagram shows how the real world actually behaves. Some ranges of outcomes have much higher probabilities than others, and the resulting distribution (which doesn’t have to take the shape I drew, obviously) is far from flat.

If you smell Bayesianism coming, you are right. I resumed our discussion with David Hume’s famous statement in Of Miracles (part of the Enquiry Into Human Understanding), to the effect that a reasonable person proportions her beliefs to the evidence, a statement later made famous by Carl Sagan within the context of discussions of pseudoscience: extraordinary claims require extraordinary evidence.

Then I moved to the basics of Bayes’ theorem, explaining the famous equation (see top image). It says that the probability of a theory A, given the available evidence B, is proportional to two factors (standardized by the denominator in the equation, so to come out as a number between 0 and 1): the probability of observing evidence B IF hypothesis A were true, multiplied by the probability that A is true based on initial considerations (the so called “priors”).

The beauty of Bayes’ theorem is that it keeps updating itself in a recursive fashion, as new evidence becomes available. The left-side of the equation is called the posterior probability, and it is obtained — conceptually speaking — by updating the priors in proportion to the newly available evidence. While there is much discussion about subjective vs objective Bayesianism (with reference to whether one should use only objective priors or whether subjective ones are acceptable), the nice thing is that one can show that no matter what the initial priors are, after a sufficient number of iterations the posteriors converge toward the true value.

This makes Bayes’ theorem a formidable tool in decision making procedures, and more generally a good guide toward rational assessment of pretty much everything. It is true that some people have gone so far as to make Bayesianism into an all-encompassing and rather strict ideology, almost worshiping the damn thing (I’m looking at you, Less Wrong), but that’s going too far. It is simply a very convenient tool in a lot of practical situations (especially when we have access to objective priors) as well as a good metaphor for how to go about assessing beliefs (as Hume advises, in proportion to the — ever changing — evidence).

I concluded my explanation to my relative by suggesting that when we make an assessment of any given notion we are basically placing a bet. Given the best understanding I have of the vaccine-autism controversy, for instance, I bet (heavily) that vaccines do not, actually, cause autism. Do I know this for certain? No, because it isn’t an a priori truth of mathematics or logic. Is it possible that vaccines do cause autism? Yes, that scenario does not involve a logical contradiction, so it is possible. But those are the wrong questions. The right question is: is it likely, on the basis of the available evidence? If you had to bet (with money, or with the health of your kids), which way should you bet? But by that time we had ran out of Aglianico, and the evening was coming to a close.

96 thoughts on “Anatomy of a frustrating conversation

  1. Michael Fugate

    your first argument is ‘red herring’ and your second argument is ‘ad hominem’.

    And correlation is not causation. Tell us the causal link between vaccines and infant mortality or autism. We know that autism incidence has gone up and so have vaccines prescribed to children. Did you know gas mileage of cars has gone up too?

    Liked by 2 people

  2. Massimo Post author


    I’m going to answer for Coel here because I have gotten into this kind of discussion for years now. The reason it is useless to provide you with links to support his point is because you will then counter-link with something on your side, to which he will counter-counter-link, and so forth ad nauseam. When it comes to things like vaccines, global warming, 9/11, etc. it is extremely easy to get information from reliable (which does not mean infallible!) sources, and there is no point in Coel, or me, doing it for you. You can type into Google or, better, go to a public library, just as well as we can.

    I have decided that I’m going to engage in the specifics of a given topic only when the topic falls directly under my expertise, either as a biologist or as a philosopher. Because there I have first-hand understanding of the subject matter. For everything else, again, there’s Google. But one needs to use it intelligently (I suggest Google Scholar, for instance, instead of a regular search).

    Liked by 3 people

  3. SocraticGadfly

    Massimo, I was just thinking the same thing. It’s the same game creationists play with fossils.

    “Here, I found your so-called missing link.”

    “Thanks, but now you have two new missing links.”


    Michael, all: Re autism, I’ve seen more reliable studies that indicate BOTH parents’ birth ages can be a contributory factor. As child-bearing gets ever more delayed across the modern western world, this should be of no surprise.


  4. Darko Mulej

    I think I know correlation is not causation. Let me try to put it more clearly.

    If one agrees with US vaccination policy then he or she should, first, provide data, that US has now better children morbidity and mortality situation than cca 40 years ago, and second, explain, why some countries with less vaccination load has better situation.
    I am not implying causation here (but it’s not out of question either), but definitely this should could be opportunity for some reflection.
    Now I suspect this two explanations would be a toll order for majority to provide but then at the very least this people should respectfully accept that some other people would make different conclusion: that US vaccination policy is wanting.

    In this discussion (comments thread) I was trying to show that position of vaccination sceptics and 9/11 ‘conspirators’ is quite reasonable and defensible. Now it was a bit unfortunate that we started with two ‘hot button’ topics, 9/11 and vaccination – autism link, it would be more productive to discuss for example JFK and US vaccination policy. For example, according to Gallup survey in 2013

    Three-quarters of Americans recently told Gallup that they think more than one man was involved in Kennedy’s assassination.

    Now if one does accept this majority opinion then more or less the same line of reasoning applies to 9/11, although definitely not with probabilty 75%, but either not with negligible probability.
    But if not, then he is in minority, so some explanation would be in order:)

    Apropos vaccination: if one accepts that there are some open questions and if one knows that ‘concoting’ new vaccine is a tricky business (where success is not guaranteed), many times includes try and error method (think HIV vaccine, or Ebola, or Zika, or malaria, not to mention cancer vaccine) then I see now contradiction or sloppy reasoning if one has healthy sceptic position on this things.


  5. Markk

    Since we’re talking conspiracy theories, has anyone here heard of Jim Fetzer?

    I found a leaflet in my letterbox about his YouTube videos. He is a philosopher of science and conspiracy theorist. What a combination. Imagine talking to him at a party – one moment he’d be talking about AI and consciousness, the next about how Mossad did 9/11. He even has a conspiracy theory about The Beatles. Paul McCartney died and was replaced by a body double, or something. I don’t know why the conspirators would bother.


  6. brodix


    Yes, the picture of Carter is more complex, but, like this discussion, it is difficult to distill a concise point from such complex circumstances.

    Since I seem to be put in the conspiracy group, I’ll offer up one of my own;

    Volcker is credited with bringing inflation under control by raising interest rates. This didn’t really start to work until 82, by which time the deficit topped 200 billion, under Reaganomics. One of the ways the Fed tightens is to sell some of the bonds it bought to issue money in the first place and essentially cancel the money it collects.
    So what is the difference between the Fed selling debt it is holding and Treasury issuing new debt?
    Consider initially higher interest rates slowed economic activity, thus reducing the need for money and only causing more stagflation. Yet when the government borrows it, it gets spent in ways which support the private sector, without actually competing with it. Such as building up a military, which is not a particularly productive investment, but it does make all the suppliers and contractors quite happy.
    So my (conspiracy) theory is inflation was mostly cured by the government borrowing excess wealth out of the system and spending it willy nilly, much on the military. The eventual problem being is that it became habit forming and now with the deficit topping 20 trillion, no one is quite sure what to do next. Go fight the Russians?

    Of course, this is all just conspiracy theory, but I find it interesting to consider.


  7. dbholmes

    Darko, in addition to the links presented by others I specifically linked to an article explaining why there can be differences seen between the US and other countries on mortality. After acting like no one has presented anything (as if they couldn’t) it would be good if you could take the information you have been presented and explain how your position is still viable.

    I also challenged you regarding 9/11 in that you seem to want to cite Chomsky when he has criticized 9/11 conspiracy theories.

    And finally, I have asked how do you distinguish between conspiracy and miracle?

    Liked by 1 person

  8. marc levesque

    Addendum to my previous comment.

    In my first comment responding to Darko for some odd reason I misread him and thought he was challenging Coel to produce a link to mortality rates in general.


  9. Darko Mulej

    Marc, thanks for link for
    “that clearly shows better picture in child mortality and morbidity, comparing years 1975 and 2015 (or something similar)”

    That was a little bit reckless of me.

    Of course, the other argument still stands – USA has very high IMR despite of maybe highest vaccination schedule.


  10. wtc48

    Coel: “These conspiracy theories are not about evidence, they are a quirk of human psychology to do with people liking to think they have superior insight and that they see through “the establishment”. People believe them because it boosts their self image to believe them.”

    The traditional definition of conspiracy refers to two or more individuals plotting secretly against a government (e.g., Guy Fawkes and the Gunpowder Plot). Tradition stands on its head when the conspiracy proceeds from the government itself: e.g. the US-backed coup in Guatemala in 1954. I mention this in particular because I remember discussing it at the time with a friend, two college freshmen somewhat non-plussed by the information that our Marines had landed on a foreign country and no one seemed to care. This type of real conspiracy provides a fertile field for the appearance of a thousand fake conspiracies, all of which are at least plausible against this background. Plausibility thus becomes an ugly alternative between possibility and probability.

    Liked by 1 person

  11. SocraticGadfly

    Massimo changes page design again. Must practice Stoic discipline.

    For me, blogging is often, and Twitter even more so, a set of Neo-Cynic exercises. And, will become only more of that as I get even older. And, speaking of …

    DB: A conspiracy, unlike a miracle, involves black helicopters, the UN, golf courses, and stuff like that. That was easy!

    Liked by 2 people

  12. brodix


    After weeks of flashing notices, I allowed my phone to upgrade overnight and all the normal stuff changed. Then this site does the same. It is definitely a conspiracy.


  13. SocraticGadfly

    DB: Here’s how a miracle becomes a conspiracy theory, though.

    Jesus approached the tomb, and said, “Lazarus, come forth!” And Lazarus came out, alive. He went home, and bathed, and dressed, and went to the UN General Assembly, and he then played golf 21, mark that, 21 times.

    A bitter disciple of Jesus, Cruzus Texcariate, saw Lazarus play golf those 21 times, and recognized that this was part of a secret UN plan to take over golf courses, block proposed stringent state laws requiring burning of aborted burial shrouds, and national miracle-care coverage, so that Jesus would raise poor Palestinians from the dead, too.

    Clear enough?

    Liked by 1 person

  14. brodix

    I’m having fun with this, so;

    One of my nephews stopped by work today and conversation got around to a horse my wife had many years ago, named Tartan’s Five. It so happened that they entered her in a race up at Penn National Race Course.
    It was the 5th of May, 1985. They put the race up as the 5th and she drew in the 5th post position, so they decided to bet it big. Unfortunately the horse ran 5th.

    Liked by 1 person

  15. Michael Fugate

    Darko, if individuals don’t vaccinate their children, then the schedule doesn’t matter. What you want is data on deaths in vaccinated children, not all children.


  16. astrodreamer

    I must say I’m still not clear (nor is your relative, I expect) on why Bayes theorem is “a good guide toward rational assessment of pretty much everything.” That is, beyond the Humean given of “assessing beliefs (as Hume advises, in proportion to the — ever changing — evidence).” It’s common knowledge that reaching a judgment requires analysis of incoming information in successive summation. Bayes mathematization of this process is useful on data sets for mathematical statistics. Pieces of evidence in the investigation of conspiracy theory cannot be treated as mathematical data.

    “The beauty of Bayes’ theorem is that it keeps updating itself in a recursive fashion, as new evidence becomes available.” But that’s is how we all think! The beauty is that Bayes introduces that process into mathematics. So, bringing up Bayes is a snow job.

    Moreover, recourse to Bayes ought to requires openness to the flow of new evidence, not adamant insistence on the official tale. That means exploring numerous sources outside the controlled media, and actually assimilating and analyzing it (or just intuitively weighing it) rather than passively accepting the predigested versions presented to the public by power.

    Your last paragraph floors me. There are so many different kinds of bets, horserace, athletic contests, roulette, Russian roulette, lottery, poker, each with its own parameters and strategies. I suppose that heated discussions of conspiracy theories may lead to the outcome of some wild placing of bets, but on the arrival of what sort of proof? It makes no sense, by discussing the pros and cons of a conspiracy theory you are precisely not making a bet, not putting anything at risk, not gambling, unless the question becomes subject of a pool. Be that as it may, surely anyone’s betting strategy will differ if the sum involved is $50, or “the health of one’s kids”.


  17. Massimo Post author


    Very few people actually work in a Bayesian way. Bayes theorem makes Hume’s dictum rigorous and provable. That’s not a small accomplishment.

    If you want to know more:

    I would like to see your evidence for the existence of such things as “the controlled media,” a generic label that could mean anything, or nothing at all.

    The best thing is an analogy. The idea – well supported in social science – is that people may say they believe X, but a good way to find out is to see how much they would be willing to bet, in money, on the truth of X.

    Liked by 1 person

  18. Alan White

    Pretty interesting this thread has replicated the very confusion of possibility and probability that the OP warns against.

    One thing I have told my students across my career–the truth just might be so audacious as to appear to be just as revealed in your everyday lives–where intentionally covert conspiracies beyond one person never remain concealed for long. The real conspiracies are those in plain sight–the fact that, for example, 8 men hold as much wealth as 3+ billion people on this planet. Such conspiracies require ignorance for their survival, and apparently, that is in great supply.

    Liked by 6 people

  19. astrodreamer


    Rather than call it ‘controlled’ media, might I say simply ‘mainstream’ media, or even ‘readily accessible, spoonfed’ media, or just ‘commercial’ media, media that mainly slickly packages and passes on press releases of the authorities, and is more likely to pursue ratings than truth. Surely you don’t need me to provide evidence of that sort of media.

    As for the betting analogy, the amount one is willing to wager might tell us something about how much a person ‘really’ believes something but what has it got to do with ascertaining the truth of a proposition? And does a man with money to burn who places $1000 bet on a proposition believe it more than someone who hasn’t got a dime? I don’t understand.


  20. dbholmes


    “Of course, the other argument still stands – USA has very high IMR despite of maybe highest vaccination schedule.”

    How can it still stand when I provided a link and gave a short explanation that rejects this talking point by anti-vaxxers? Here is the link once again…

    Here is the explanation once again… In addition to errant methods of selection and grouping of nations, and numbering how many vaccinations are given… the US registers live births different than other nations in a way that skews mortality rates higher than other nations. This makes direct head to head comparisons difficult.

    So that explanation stands (as the most likely explanation).

    Liked by 1 person

  21. dbholmes

    In a related news item (this is true), the CIA has finally released its secret documents on things like UFO sightings and psychics… proving how they were part of a conspiracy to keep the truth from the world!

    Interestingly (and not joking) they had this to say on psychic tests of Uri Geller: “”demonstrated his paranormal perceptual ability in a convincing and unambiguous manner”.”

    One wonders if, while enlisting Uri Geller, they bothered to enlist debunkers like James Randi.


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