Why I Don’t Believe in the Butterfly Effect, Part 8
Part 8 of 12: The Right Way to Discuss Alternative History
People often wonder about what might have happened if something had happened differently in the past. Examples include, “What if Kennedy hadn’t been killed?” “What if I had gone to a different college?” “What if Odell Beckham Jr. hadn’t caught that pass?” “What if I had dated women earlier in life?” “What if the 49ers had drafted Aaron Rodgers, instead of the Packers?”
Human beings (myself included) tend to be remarkably bad at answering these alternative history questions. In my last essay, Part 7, I discussed three common wrong answers: 1. Everything would be different (i. e. the butterfly effect). 2. Everything would be the same, except for the one thing that was changed. 3. We’ll never know, because it didn’t happen.
But there is also a correct answer, and it involves the concepts of probability and expected value. The correct way to answer an alternative history question is as follows: if something had happened differently in the past, then………
1. There would have been many possible branches of history open, just as there were still many branches open given that things happened as they did.
2. The probabilities of certain future events would have been different.
3. The expected values of certain quantities would have been different.
To make that a little clearer, I’ll provide an example: I’ll attempt to answer the famous question, “What if Kennedy hadn’t been killed?”
But before I do that, I would like to mention, as an aside, that it’s a little bit silly that “What if Kennedy hadn’t been killed?” has become the quintessential alternative history question. In reality, Kennedy’s death was not an extremely important historical event. It was certainly important, but it wasn’t as important as something like the Cuban Missile Crisis, which happened a year earlier. On the day of the Kennedy assassination, the fate of one person was at stake; during the Cuban Missile Crisis, the fate of the whole world was at stake. Clearly, the Cuban Missile Crisis was more important. I also think that the assassination of Abraham Lincoln was much more consequential than the assassination of John Kennedy, because Lincoln was succeeded by someone who disagreed with him (Andrew Johnson), whereas Kennedy was succeeded by someone who had the same platform that he did (Lyndon Johnson).
But it’s okay. Since that seems to be everyone’s favorite alternative history question, that’s the one that I will answer. Here is my answer to the famous question, “What if Kennedy hadn’t been killed?”
If John F. Kennedy hadn’t been killed on November 22, 1963, then there would have been many possible branches of history open, just as there were many branches open given that he was killed. But if he hadn’t been killed, then the probability of the Democrats winning the presidency in 1968 would have been higher, because Kennedy was more likeable than Johnson. However, the expected value of the number of progressive bills passed over the next five years would have been lower, because Johnson was better at manipulating Congress than Kennedy was.
And that’s the correct way to answer alternative history questions. You can find countless books, magazines, YouTube videos, etc. that will tell you that if Kennedy hadn’t been killed, then such-and-such would have happened. But they are forgetting that there would have been many possible branches of history still open, and they fail to realize that it makes more sense to talk about how probability changed than it does to identify a single alternate timeline.
However, you can also see that it is still possible to answer the question. The third wrong answer (see Part 7) asserted that there is no way to answer a question about alternative history. But there actually is. There’s nothing wrong with talking about alternative history; you just have to make sure you’re talking about probability and expected value, rather than falling for the fallacy of assuming that there was just one alternate timeline.
Probability and expected value are magical concepts, because they allow you to take a plethora of possibilities — all those branches of that big probability tree — and condense them into a single number. We can’t say that if Kennedy hadn’t been killed, then X, Y, and Z would have happened, because there were so many branches either way. But we can say that if Kennedy hadn’t been killed, then the probability of such-and-such would have been higher, or the expected value of such-and-such would have been lower. That is the secret to answering alternative history questions.
To better illustrate my points, I will provide a few more examples:
1. Instead of saying, “If George Bailey hadn’t been born, then his brother Harry would’ve died as a child, and then all of Harry’s comrades would’ve died in the war, and the whole town of Bedford Falls would be a sleazy dump owned by the evil Henry Potter,” it makes more sense to say, “George Bailey’s birth increased the expected value of the total amount of happiness in Bedford Falls.”
2. Instead of saying, “If he hadn’t fumbled in the first quarter, we would’ve won,” it makes more sense to say, “His fumble in the first quarter reduced the probability that we would win.” Or, you could put it in terms of alternative history: “If he hadn’t fumbled in the first quarter, the probability that we would win would have been higher.”
3. Instead of saying, “If Bill Clinton hadn’t had that affair with Monica Lewinsky, Al Gore would’ve won in 2000,” it makes more sense to say, “Bill Clinton’s decision to have that affair with Monica Lewinsky reduced the probability that the Democratic candidate would win in 2000.”
4. Instead of saying, “I would’ve been a success in life if I had gone to grad school,” it makes more sense to say, “If I had gone to grad school, the expected value of the amount of success I would have in life would have been higher.”
5. Instead of saying, “If David Tyree hadn’t caught that amazing catch at the end of Super Bowl XLII, then Tom Brady would have ended up with seven Super Bowl wins instead of six,” it makes more sense to say, “David Tyree’s amazing catch decreased the expected value of the number of Super Bowl wins Tom Brady would accrue over the course of his career.”
6. Instead of saying, “If Trump had acted a month earlier on Covid-19, we would’ve ended up with half as many deaths,” it makes more sense to say, “If Trump had acted a month earlier on Covid-19, the expected value of the final number of deaths in the U. S. from Covid-19 would have been 50% lower.”
7. Instead of saying, “All the wars that the U. S. has fought since 2001 have been a consequence of 9/11,” it makes more sense to say, “9/11 increased the expected value of the total amount of war that the U. S. would fight over the course of the next two decades.” And personally, I would phrase it in terms of alternative history: “If the 9/11 plot had been foiled before it came to fruition, such that the attacks did not happen, then the expected value of the total amount of war that the U. S. would fight between 2001 and 2020 would have been lower.”
8. Instead of saying, “We’ll never know what might’ve happened if Kennedy hadn’t been killed,” it makes more sense to say, “If Kennedy hadn’t been killed, then the probability of [such-and-such] would have been higher, while the expected value of [such-and-such] would have been lower.”
In fact, you could define the influence of an event as the extent to which it changes the probability of something else (or the expected value of something else).
Of course, you don’t have to actually give these answers in real life. Some of these answers are very wordy. But even if they’re wordy, they are the most correct answer, because they make use of the magical concepts of probability and expected value.
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As a footnote to this essay, I would like to clarify exactly what I mean when I speak of probability and expected value.
There are three interpretations of what “probability” really means: the frequentist school, the Bayesian school, and the propensity theory. I subscribe to the propensity theory of probability, which means that I think of probability as being an inherent property of the universe that tells you how likely it is that some future event might occur. I explored the three interpretations of probability in another blog post.
Meanwhile, expected value is a concept in probability and statistics that gives you the “center of gravity” of a probability distribution. For example, if you have a normal distribution, the expected value is μ, the mean. I explained the concept of expected value in more detail in another blog post.
Other parts of this series:
Part 2: The Butterfly Effect in Pop Culture
Part 3: The Wrong Way to Disprove It
Part 5: Responding to Arguments in Favor of the Butterfly Effect
Part 6: Exceptions (And Why They Aren’t Really Exceptions)
Part 7: Three Wrong Ways to Discuss Alternative History
Part 9: How I Would Interpret Lorenz’s Observations
Part 10: The Butterfly Effect and the Slippery Slope