Why I Don’t Believe in the Butterfly Effect, Part 5
Part 5 of 12: Responding to Arguments in Favor of the Butterfly Effect
When I watch movies and YouTube videos that promote the idea of the butterfly effect, there are several arguments that show up over and over again. In this essay, I will identify three common arguments in favor of the butterfly effect, and I will rebut them. And through my rebuttals, I will show that the trick to disproving butterfly effect arguments is to stop asking “what if” and start asking “How did the probability change?”
1. Luck plays an important role in our lives. Therefore, if one little thing had happened differently, your whole life would’ve ended up completely different.
There can be no doubt that luck plays an important role in our lives and in world history. But that doesn’t mean that the butterfly effect is true. Luck just means that things have unintended consequences. It means that the probability of some event happening (or the expected value of some variable) is affected by unintended consequences of people’s actions. But it does not mean that if you changed one little thing, we would end up in a totally different world. I already showed that that’s not true (see Part 4).
(Please note: for the remainder of this series of essays, I will assume that the universe is non-deterministic, because 1. That’s what most people, including me, believe, and 2. If the universe is deterministic, then everything is pre-determined, and that’s not very interesting (see Part 4).)
2. There are so many possible ways things could have turned out, and no one branch looks like any other branch. That means that every time you make a choice, you leave behind whole worlds full of different histories that could have been.
It is true that there are many millions of branches. And it’s true that no two branches are the same. And it’s true that every time you make a choice, you leave behind and endless set of might-have-been histories. This leads people to think that even the most insignificant decision, like whether I eat oatmeal or waffles for breakfast, is actually extremely significant because of all the different might-have-been histories that it leaves behind and all the different might-be histories that are still ahead of us.
But that line of reasoning turns out to be fallacious. The best way to see this is to shift your attention away from the branching tree and towards a graph of probability over time. Let’s pick an event E in the future that people all over the world care about. Let’s say E is “Joe Biden wins the 2020 U. S. Presidential Election”, since that will be on everyone’s minds this year. Now let’s plot the probability of E over time. Every time anyone in the world makes a decision (that is, at every node along our path), the probability of E either slightly increases or slightly decreases.
But at most nodes, the probability of E only changes by a very small amount, regardless of whether it’s going up or down. It’s not possible for the probability of E to change drastically at every single node, because if it did, the probability would very quickly either hit 1 (E will certainly happen) or hit 0 (E cannot possibly happen), and that’s obviously not what happens. Thus, at the node in which I decided to choose oatmeal over waffles, the probability of E only changed by an extremely small amount.
(And that graph wasn’t even drawn to scale: if it were, then there would be billions of those little bumps, and the change in the probability at each bump would be extremely small. Keep in mind that each node is supposed to represent someone’s choice. If we assume that a person makes a choice every three seconds and that there are seven billion people in the world, that would mean we pass through another node every 0.4 nanoseconds. And at most of those nodes, the probability would only change by an infinitesimally small amount. At most moments in time, things don’t change very much.)
My decision to choose oatmeal over waffles did not affect the probability of any event that matters for the world or for anyone else’s life. The only events whose probabilities would be significantly affected by such a decision would be very local and personal events, such as the event that I get a “sugar high” an hour after breakfast. But it doesn’t affect the probability of any large-scale event or any far-away event, and therefore, it really is an insignificant decision. Seemingly insignificant decisions really are insignificant. Common sense is true after all. The butterfly effect is not real. And that’s a good thing.
What you can see here is that the trick to disproving these butterfly effect arguments is to ask the question, “How did the probability change?” We often observe that something relatively small (call it A) can lead to a cascade of causes and effects, and so it’s tempting to think that if we changed A, then the whole cascade wouldn’t have happened, and therefore, everything would be different. But if you pick some relevant event E (a generalized version of whatever happened at the end of the cascade) and you ask, “How did the probability change?” then you see that A only slightly changed the probability of E, because similar results could have occurred through different means, on different branches. And that goes to show that, again, seemingly insignificant decisions really are insignificant.
In fact, the neat thing about the probability tree is that even though no two branches are alike, at most nodes, the probability of most future events is almost identical on each of the options. For example, let’s say you’re at the circled node in the diagram above. Let’s say this node represents your choice about what to eat for breakfast. Again, let E be the event that Joe Biden wins the election. Let p be the probability of E if you choose the top branch (oatmeal), and let q be the probability of E if you choose the bottom branch (waffles). p and q are almost identically the same number. The difference between p and q is probably on the order of 10–100. The fact that there are so many branches of the tree makes it look like every little thing you do changes the world forever, but looks can be deceiving. In reality, the probability of E is almost exactly the same regardless of what you do. And that’s why the butterfly effect is not real.
3. Everything is connected. Therefore, if you change one little thing, it ends up changing everything.
It is true that everything is connected, and it is true that things affect other things. But that does not imply that if you change one thing, you change everything. The way to debunk this argument is exactly the same as the way to debunk the previous argument: just ask the question, “How did the probability change?”
If you have a chain reaction in which A caused B and B caused C and C caused D ……… and Y caused Z, then it’s tempting to think that A caused Z, that A led to Z, that A was necessary for Z to happen.
But it’s really not. The effects on probability diminish over time. If A hadn’t happened, that might have made C much less likely to happen, but it probably had no significant effect on the probability that Z would happen. There are way too many steps in between.
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As one final note, I should mention that these graphs of probability over time are what Nate Silver has become known for. Nate Silver is a statistician who has become quite famous in recent years. He uses his models to estimate the probability of victory for sports games and presidential elections. He updates his estimates very frequently, as new information and new polls become available. He then makes graphs of how his estimated probability has changed over time, and he puts these graphs on his website, FiveThirtyEight.
For reasons that are over my head, Silver seems to have a better ability to estimate these things than anyone else, and he seems to have a knack for getting things right when everyone else gets them wrong. For example, two days before the 2016 Presidential Election, he posted on Facebook, “A lot of people I know are slightly in denial about the fact that the race has tightened and that Trump has a real shot.” Yeah, we should’ve listened to him.
I don’t know whether or not Nate Silver believes in the butterfly effect. I don’t think he’s ever discussed that.
That concludes Part 5. In Part 6, I will examine some of the rare exceptions: a few instances in history where something that seemed minor was actually very important. But I will also argue that these rare exceptions do not imply that the butterfly effect is true.
Other parts of this series:
Part 2: The Butterfly Effect in Pop Culture
Part 3: The Wrong Way to Disprove It
Part 6: Exceptions (And Why They Aren’t Really Exceptions)
Part 7: Three Wrong Ways to Discuss Alternative History
Part 8: The Right Way to Discuss Alternative History
Part 9: How I Would Interpret Lorenz’s Observations
Part 10: The Butterfly Effect and the Slippery Slope