Determined, page 13
Here’s my favorite finding pertinent to this chapter. There’s a task that can be done in two different ways: in version one, do some amount of work and you get some amount of reward, but if you do twice as much work you get three times as much of a reward. Version two: do some amount of work and you get some amount of reward, but if you do three times as much work, you get a hundred zillion times as much reward. Which version should you do? If you think you can freely choose to exercise self-discipline, choose version two—you’re going to choose to do a little bit more work and get a huge boost in reward as a result. People usually prefer version two, independent of the sizes of the rewards. A recent study shows that activity in the vmPFC[*] tracks the degree of preference for version two. What does that mean? In this setting, the vmPFC is coding for how much we prefer circumstances that reward self-discipline. Thus, this is the part of the brain that codes for how wisely we think we’ll be exercising free will. In other words, this is the nuts-and-bolts biological machinery coding for a belief that there are no nuts or bolts.[59]
Sam Harris argues convincingly that it’s impossible to successfully think of what you’re going to think next. The takeaway from chapters 2 and 3 is that it’s impossible to successfully wish what you’re going to wish for. This chapter’s punchline is that it’s impossible to successfully will yourself to have more willpower. And that it isn’t a great idea to run the world on the belief that people can and should.
5
A Primer on Chaos
Suppose that just before you started reading this sentence, you reached to scratch an itch on your shoulder, noted that it’s becoming harder to reach that spot, thought of your joints calcifying with age, which made you vow to exercise more, and then you got a snack. Well, science has officially weighed in—each of those actions or thoughts, conscious or otherwise, and every bit of neurobiology underpinning it, was determined. Nothing just got it into its head to be a causeless cause.
No matter how thinly you slice it, each unique biological state was caused by a unique state that preceded it. And if you want to truly understand things, you need to break these two states down to their component parts, and figure out how each component comprising Just-Before-Now gave rise to each piece of Now. This is how the universe works.
But what if that isn’t? What if some moments aren’t caused by anything preceding them? What if some unique Nows can be caused by multiple, unique Just-Before-Nows? What if the strategy of learning how something works by breaking it down to its component parts is often useless? As it turns out, all of these are the case. Throughout the past century, the previous paragraph’s picture of the universe was overturned, giving birth to the sciences of chaos theory, emergent complexity, and quantum indeterminacy.
To label these as revolutions is not hyperbolic. When I was a kid, I read a novel called The Twenty-One Balloons,[*] about a utopian society on the island of Krakatoa built on balloon technology, destined to be destroyed by the famed 1883 eruption of the volcano there. It was fantastic, and the second I got to the end, I immediately flipped to the front to reread it. And it was then almost a quarter century before I immediately flipped to the front to reread a different book,[*] an introduction to one of these scientific revolutions.
Staggeringly interesting stuff. This chapter, and the five after it, reviews these three revolutions, and how numerous thinkers believe that you can find free will in their crevices. I will admit that the previous three chapters have an emotional intensity for me. I am put into a detached, professorial, eggheady sort of rage by the idea that you can assess someone’s behavior outside the context of what brought them to that moment of intent, that their history doesn’t matter. Or that even if a behavior seems determined, free will lurks wherever you’re not looking. And by the conclusion that righteous judgment of others is okay because while life is tough and we’re unfairly gifted or cursed with our attributes, what we freely choose to do with them is the measure of our worth. These stances have fueled profound amounts of undeserved pain and unearned entitlement.
The revolutions in the next five chapters don’t have that same visceral edge. As we’ll see, there aren’t a whole lot of thinkers out there citing, say, subatomic quantum indeterminacy when smugly proclaiming that free will exists and they earned their life in the top 1 percent. These topics don’t make me want to set up barricades in Paris, singing revolutionary anthems from Les Mis. Instead, these topics excite me immensely because they reveal completely unexpected structure and pattern; this enhances rather than quenches the sense that life is more interesting than can be imagined. These are subjects that fundamentally upend how we think about how complex things work. But nonetheless, they are not where free will dwells.
This and the next chapter focus on chaos theory, the field that can make studying the component parts of complex things useless. After a primer about the topic in this chapter, the next will cover two ways people mistakenly believe they’ve found free will in chaotic systems. First is the idea that if you start with something simple in biology and, unpredictably, out of that comes hugely complex behavior, free will just happened. Second is the belief that if you have a complex behavior that could have arisen from either of two different preceding biological states and there’s no way to ever tell which one caused it, then you can get away with claiming that it wasn’t caused by anything, that the event was free of determinism.
Back When Things Made Sense
Suppose that
X = Y + 1
If that is the case, then
X + 1 = ?
—and you were readily able to calculate that the answer is
(Y + 1) + 1.
Do X + 3 and you’ve instantly got (Y + 1) + 3. And here’s the crucial point—after solving X + 1, you were able to then solve X + 3 without first having to figure out X + 2. You were able to extrapolate into the future without examining each intervening step. Same thing for X + a gazillion, or X + sorta a gazillion, or X + a star-nosed mole.
A world like this has a number of properties:
As we just saw, knowing the starting state of a system (for example, X = Y + 1) lets you accurately predict what X + whatever will equal, without the intervening steps. This property runs in both directions. If you’re given (Y + 1) + whatever, you know then that your starting point was X + whatever.
Implicit in that, there is a unique pathway connecting the starting and ending states; it is also inevitable that X + 1 cannot equal (Y + 1) + 1 only some of the time.
As shown dealing with something like “sorta a gazillion,” the magnitude of uncertainty and approximation in the starting state is directly proportional to the magnitude at the other end. You can know what you don’t know, can predict the degree of unpredictability.[1]
This relationship between starting states and mature states helped give rise to what has been the central concept of science for centuries. This is reductionism, the idea that to understand something complicated, break it down into its component parts, study them, add your insights about each component part together, and you will understand the complicated whole. And if one of those component parts is itself too complicated to understand, study its eensy subcomponent parts and understand them.
Reductionism like this is vital. If your watch, running on the ancient technology of gears, stops working, you apply a reductive approach to solving the problem. You take the watch apart, identify the one tiny gear that has a broken tooth, replace it, and put the pieces back together, and the watch runs. This approach is also how you do detective work—you arrive at a crime scene and interview the witnesses. The first witness observed only parts 1, 2, and 3 of the event. The second saw only 2, 3, and 4. The third, only 3, 4, and 5. Bummer, no one saw everything that happened. But thanks to a reductive mindset, you can solve the problem by taking the fragmentary component parts—each of the three witnesses’ overlapping observations, and combine them to understand the complete sequence.[*] Or as another example, in the first season of the pandemic, the world waited for answers to reductive questions like what receptor on the surface of a lung cell binds the spike protein of SARS-CoV-2, allowing it to enter and sicken that cell.
Mind you, a reductive approach doesn’t apply to everything. If there’s a drought, the sky dotted with puffy clouds that haven’t rained in a year, you don’t first isolate a cloud, study its left half and then its right half and then half of each half, and so on, until you find the itty-bitty gear in the center that has a broken tooth. Nonetheless, a reductive approach has long been the gold standard for scientifically exploring a complex topic.
And then, starting in the early 1960s, a scientific revolution emerged that came to be called chaoticism, or chaos theory. And its central idea is that really interesting, complicated things are often not best understood, cannot be understood, on a reductive level. To understand, say, a human whose behavior is abnormal, approach the problem as if this were a cloud that does not rain, rather than as a watch that does not tick. And naturally, humans-as-clouds generate all sorts of nearly irresistible urges for concluding that you are observing free will in action.
Chaotic Unpredictability
Chaos theory has its creation story. When I was a kid in the 1960s, inaccurate weather prediction was mocked with trenchant witticisms like “The weatherman on the radio [invariably, indeed, a man] said it’s going to be sunny today, so better bring an umbrella.” MIT meteorologist Edward Lorenz began using some antediluvian computer to model weather patterns in an attempt to increase prediction accuracy. Stick variables like temperature and humidity into the model and see how accurate the predictions became. See if additional variables, other variables, different weightings of variables,[*] improved predictability.
So Lorenz was studying a model on his computer using twelve variables. Time for lunch; halt the program in the middle of its cranking out a time course of predictions. Come back postlunch and, to save time, restart the program at a point before you stopped it, rather than starting all over. Punch in the values of those twelve variables at that time point, and let the model resume its predicting. That’s what Lorenz did, which is when our understanding of the universe changed.
One variable at that time point had a value of 0.506127. Except that on the printout, the computer had rounded it down to 0.506; maybe the computer hadn’t wanted to overwhelm this Human 1.0. In any case, 0.506127 became 0.506, and Lorenz, not knowing about this slight inaccuracy, ran the program with the variable at 0.506, thinking that it was actually 0.506127.
Thus, he was now dealing with a value that was a smidgen different from the real one. And we know just what should have happened now, in our supposedly purely linear, reductive world: the degree to which the starting state was off from what he thought it was (i.e., 0.506 rather than 0.506127) predicted how inaccurate his ending state would be—the program would generate a point that was only a smidgen different from that same point before lunch—if you superimposed the before- and after-lunch tracings, you’d barely see a difference.
Lorenz let the program, still depending on 0.506 instead of 0.506127, continue to run, and out came a result that was even more discrepant than he had expected from the prelunch run. Weird. And with each successive point, things got weirder—sometimes things seemed to have returned to the prelunch pattern but would then diverge again, with the divergences increasingly different, unpredictably, crazily so. And eventually rather than the program generating something even remotely close to what he saw the first time, the discrepancy in the two tracings was about as different as was possible.
This is what Lorenz saw—the pre- and postlunch tracings superimposed, a printout now with the status of a holy relic in the field (see figure on the next page).
Lorenz finally spotted that slight rounding error introduced after lunch and realized that this made the system unpredictable, nonlinear, and nonadditive.
By 1963, Lorenz announced this discovery in a dense technical paper, “Deterministic Non-periodic Flow,” in the highly specialized Journal of Atmospheric Sciences (and in the paper, Lorenz, while beginning to appreciate how these insights were overturning centuries of reductive thinking, still didn’t forget where he came from. Will it ever be possible to perfectly predict all of future weather? readers of the journal plaintively asked. Nope, Lorenz concluded; the chance of this is “non-existent”). And the paper has since been cited in other papers a staggering 26,000+ times.[2]
If Lorenz’s original program had contained only two weather variables, instead of the twelve he was using, the familiar reductiveness would have held—after a slightly wrong number was fed into the computer, the output would have been precisely as wrong at every step for the rest of time. Predictably so. Imagine a universe that consists of just two variables, the Earth and the Moon, exerting their gravitational forces on each other. In this linear, additive world, it is possible to infer precisely where they were at any point in the past and predict precisely where each will be at any point in the future;[*] if an approximation was accidentally introduced, the same magnitude of approximation would continue forever. But now add the Sun into the mix, and the nonlinearity happens. This is because the Earth influences the Moon, which means that the Earth influences how the Moon influences the Sun, which means that the Earth influences how the Moon influences the Sun’s influence on the Earth. . . . And don’t forget the other direction, Earth to Sun to Moon. The interactions among the three variables make linear predictability impossible. Once you’ve entered the realm of what is known as the “three-body problem,” with three or more variables interacting, things have inevitably become unpredictable.
When you have a nonlinear system, tiny differences in a starting state from one time to the next can cause them to diverge from each other enormously, even exponentially,[*] something since termed “sensitive dependence on initial conditions.” Lorenz noted that the unpredictability, rather than hurtling off forever into the exponential stratosphere, is sometimes bounded, constrained, and “dissipative.” In other words, the degree of unpredictability oscillates erratically around the predicted value, repeatedly a little more, a little less than predicted in the series of numbers you are generating, the degree of discrepancy always different, forever after. It’s like each data point you are getting is sort of attracted to what the data point is predicted to be, but not enough to actually reach the predicted value. Strange. And thus, Lorenz named these strange attractors.[*],[3]
So a tiny difference in a starting state can magnify unpredictably over time. Lorenz took to summarizing this idea with a metaphor about seagulls. A friend suggested something more picturesque, and by 1972 this was formalized into the title of a talk given by Lorenz. Here’s another holy relic of the field (see figure on the next page).
Thus was born the symbol of the chaos theory revolution, the butterfly effect.[*],[4]
Chaoticism You Can Do at Home
Time to see what chaoticism and sensitive dependence on initial conditions look like in practice. This makes use of a model system that is so cool and fun that I’ve even fleetingly wished that I could do computer coding, as it would make it easier to play with it.
Start off with a grid, like the one on a piece of graph paper, where the first row is your starting condition. Specifically, each of the boxes in the row can be in one of two states, either open or filled (or, in binary coding, either zero or one). There are 16,384 possible patterns for that row;[*] here’s our randomly chosen one:
Time now to generate the second row of boxes that are open or filled, that new pattern determined[*] by the pattern in row 1. We need a rule for how to do this. Here’s the most boring possible example: in row 2, a box that is underneath a filled box gets filled; a box underneath an open box remains open. Applying that rule over and over, using row 2 as the basis for row 3, 3 for 4, and so on, is just going to produce some boring columns. Or impose the opposite rule, such that if a box is filled, the one below it in the next row becomes open, while an open box spawns a filled one, and the outcome isn’t all that exciting, producing sort of a lopsided checkered pattern:
As the main point, starting with either of these rules, if you know the starting state (i.e., the pattern in row 1), you can accurately predict what a row anywhere in the future will look like. Our linear universe again.
Let’s go back to our row 1:
Now whether a particular row 2 box will be open or filled is determined by the state of three boxes—the row 1 box immediately above and the row 1 box’s neighbor on each side.
Here’s a random rule for how the state of a trio of adjacent row 1 boxes determines what happens in the row 2 box below: A row 2 box is filled if and only if one of the trio of boxes above it is filled in. Otherwise, the row 2 box will remain open.
