It's hard to see the world through the eyes of somebody who doesn't know what you know, especially when it comes to really fundamental knowledge about the way the world works. I managed to make it 30-something years into life without taking a chemistry class. When I finally did, as part of a quixotic premedical postbaccalaureate zig on the long and winding road of my life, take a bunch of chemistry classes, the new knowledge irreversibly changed the world for me. I see the chemistry of things everywhere now, all the time: the reactions in soft drinks, the ideal gas law at work, the molecular structures of things like caffeine and perfluorooctanoic acid. Having gone decades without this understanding, though, I can sometimes, with a little effort, turn my knowledge off and get access to a mindset that sees more inscrutable mystery in the makeup of things.
I cannot do that with probability. Is it the fact that I took AP Statistics at the formative age of 16? Or just a lifetime of playing with dice?
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Anybody who's spent 15 minutes talking history with me (or letting me talk history at them) has probably heard me gripe about what a hard time people have seeing the past as having been anything other than inevitable. Some people do believe this literally, of course—that everything was foreordained by God—but many others start with at least a fuzzy understanding of contingency. You look at the present moment, you see the possibilities arrayed before us, and you understand that people living in the past also faced uncertainty and choices that had to be made with incomplete information. Oddly, though, many people then begin constructing an edifice of historical argument that denies or downplays that quality of contingency. Whatever did happen, even if it wasn't preordained and literally inevitable, must have been likely to happen, right? Very likely, in fact, given that it happened and the alternatives didn't. People look for factors that explain why what did happen was likely; they do not look for factors that support a contrary argument—that something that didn't happen actually was likely, or that what did happen was, before its realization, improbable.
We get a lot of post facto justifications for things that were extremely improbable. Ask the average reasonably well educated person why the German invasions of Poland and France were so successful, and you'll probably get some species of Nazi mythmaking. It was the genius of the German Blitzkrieg strategy. It was their highly advanced weapons. (Or, in a specious latter-day variant, it was that they were all hopped up on meth.) It was their iron will to power, whereas the Poles and French were unmotivated and demoralized.
These things aren't all false—German doctrine was better suited to modern combined-arms warfare than Franco-Polish doctrine was, and that made a big difference—but several of them aren't as true, or as significant, as people assume. German armor was inferior to the best French and Polish designs. Many of their aircraft were obsolete. They had few halftracks and trucks; the vast majority of the Wehrmacht infantry and artillery moved on foot or was dragged by pack animals (this remained the case throughout the war). They had neither a major technological advantage nor an overwhelming numerical advantage over Poland, to say nothing of France; the decisive factors in the invasion of Poland were the fact that the French did not attack the weakly defended German west and that the Soviet Union did, after some delay (waiting to see what France would do), invade Poland from the east. The decisive factor in the subsequent invasion of France was either German boldness or luck, depending on how you want to look at it—they gambled on a high-risk, high-reward strategy and happened to line it up very well with Allied weakness.
The German planners, in 1939, were pessimistic. (Consider the series of false-flag attacks that German agents and German soldiers in Polish uniform carried out in the run-up to the invasion of Poland. People today often sneer at these efforts—who in the international community was going to be convinced by these brazen fabrications? But the audience wasn't France or Britain or the Soviet Union. It was the German public, who were extremely unenthusiastic about the prospect of war.) The world, in 1940, was astounded that France fell so quickly. Today, everybody just assumes it was inevitable. Nazi super science and übermenschlich tenacity carried the day!
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I've realized lately that this blindness to the possibility that low-probability events can (and, in the big scheme of things, often do) defy the odds runs forward as well as backward. People don't just look at the past and assume that whatever did happen must have been most likely; they look at the future and assume that whatever they're told is the most likely outcome will happen. Models that said that Hillary Clinton had a 90% chance to win the 2016 election must have been wrong, because if she had actually had a 90% chance, she would have won: 90% is a very large percentage.
And it doesn't just have to be that large; 70% seems to be enough now to make people think something is essentially inevitable in political polling. Watching people respond to shifting recession forecasts in recent months has been bewildering; people (media outlets, even) keep reading a move from “45% chance of recession” to “55% chance of recession” as “recession now likely," as though 50% is some magical threshold. It's like a weird mutation of the old joke that everything has 50/50 odds—either it happens or it doesn't. Now everything is either certain to happen or certain not to.
My girlfriend works in public health, and was involved not long ago in a conversation about risk that baffled her. The doctors and public health experts in the room were arguing that a 0.1% chance of infecting each patient with a potentially deadly disease was unacceptable. Given a few years, this team will see hundreds, maybe more than a thousand patients, and one or two of those people will probably contract this infection, something they can't have on their conscience. But to others in the room, this seemed absurdly overcautious. A 99.9% chance of being safe? That's basically a guarantee. And if each individual patient is perfectly safe, what could possibly go wrong even in a large population, across a long stretch of time?
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All of which is to say…I don't know, that maybe people ought to play with dice more? There's something about the physicality of them (even digital simulacra of them) that breathes life and menace (or hope) into low-probability outcomes. When percentages show up in videogames, they always seem to lead to frustration. I had a 95% chance of making that shot in XCOM—how could my dude have missed? It was supposed to be a guaranteed hit! But nobody rolling an actual d20 is ever blindsided when a natural 1 turns up. You're always holding your breath, watching it skitter across the tabletop, bracing for the worst or hoping for the best. Nothing is inevitable.
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