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.

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Categories: Epistemology, Logic

96 replies

  1. Dbholmes,
    even if I found your linked articles less than fully persuasive (here is for example a little diffener view: http://tinyurl.com/h2szxtt). I can accept your argument.

    But that is still far away from assertion that very high number of vaccinations in USA is in any way advantegous.

    So my other argument still stands.

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  2. Darko, that there are problems with US healthcare (or financial inequality) leading to higher mortality than other countries I can certainly believe.

    That we may not need all the items being vaccinated for (superfluous vaxx’s) I could also believe, but I would like to see data (though I would point out that doesn’t mean unnecessary is harmful).

    The question is on your claim, that specifically relating vaccination and mortality.

    I am unsure why you did not find the article I linked to persuasive, when your own starts with this:

    “The first nuance is one of definition. Infant mortality is defined as the death of babies under the age of one year, but some of the differences between countries can be explained by a difference in how we count. Is a baby born weighing less than a pound and after only 21 weeks’ gestation actually “born?” In some countries, the answer is no, and those births would be counted as stillbirths. In the United States, on the other hand, despite these premature babies’ relatively low odds of survival, they would be considered born — thus counting toward the country’s infant mortality rates.

    These premature births are the biggest factor in explaining the United States’ high infant mortality rate.”

    That is one of the major points made by the article I linked to. And the other issues they raised seem just as important (from a stats POV).

    Liked by 2 people

  3. USA has very high IMR despite of maybe highest vaccination schedule

    But the infant mortality rate in the US is NOT higher than in comparable countries for relatively wealthy communities in West Coast or East Coast states which have good access to health care and which tend to follow vaccination advice.

    The US infant-mortality rate is indeed relatively high in relatively poor communities in places like Mississippi and Alabama and other Southern states which tend to have poor access to health care (the US is one of the few rich nations without universal health care!), which are less likely to follow vaccination advice, which have an above-average rate of births to very young, poor and less-educated mothers, which can often be very religious communities with an anti-science attitude (some favouring praying for sick children rather than giving them medical care), et cetera.

    Liked by 5 people

  4. And just to add that the hundreds of American kids killed each year in gun accidents — something that just doesn’t happen in countries with sane attitudes to guns — doesn’t improve the US infant-mortality statistics. (e.g. link)

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  5. Alan,

    Not just ignorance, but feedback. Money generates money.

    The ignorance is that it functions as a contract, in that every asset is the other side of an obligation, but we treat it as a commodity that can be mined or manufactured, from gold to bitcoin. We experience it as quantified hope and so there is great political impulse to create as much as possible, which requires significant debt to be incurred.
    It really wouldn’t be hard to control government spending, because they don’t actually budget, they just put together these enormous bills, add enough extras to get the votes and the president can only pass or veto it.
    The elder Bush floated the idea of a line item veto as a campaign slogan, but it would never work because it removed control over spending from the legislature. If they wanted the idea to work, they could break the bills into all their various items, have every legislator assign a percentage value to each one, put the bill back together in order of preference and have the president draw the line at what is to be funded. “The buck stops here.”
    That would be actual budgeting; To set priorities and spend according to them.
    Yet it would completely blow up capitalism as we know it, because the system wouldn’t be floating on this sea of government debt. Which will eventually blow up anyway, given there isn’t much return on investment in blowing up other countries.
    Rather than borrowing excess money out of the system and creating that illusion of enormous notational wealth, the government could threaten to tax it back out and then people would quickly find other ways to store wealth, such as in stronger communities and healthier environments. Given most people save for the same basic reasons, from children to retirement. These could go back to being more organic reciprocal functions, than having our bank accounts as economic umbilical cord.
    In the body, blood is the medium and fat is the store. We can’t store much excess blood and neither can the system really store a lot of excess money. If we start to think of it as the public utility it is, like roads are a medium, we might better grasp how it functions and overcome our ignorance.
    Don’t hold your breath.

    Liked by 1 person

  6. Astro,

    We can complain about the mainstream media all you want, and I have much to sympathize about it. The question is: what are the better alternatives? So far as I can see, very little stacks up to the New York Times, The Guardian, the BBC, NPR, the Atlantic, and a few other of the outlets I check routinely.

    Bayesianism is about updating beliefs, not truth. But the idea is that if the updating is done properly the belief will converge toward the truth, as understood to the best of our abilities.

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