Determined, page 19
At Last, Some Conclusions
Thus, in my view, emergent complexity, while being immeasurably cool, is nonetheless not where free will exists, for three reasons:
Because of the lessons of chaoticism—you can’t just follow convention and say that two things are the same, when they are different, and in a way that matters, regardless of how seemingly minuscule that difference; unpredictable doesn’t mean undetermined.
Even if a system is emergent, that doesn’t mean it can choose to do whatever it wants; it is still made up of and constrained by its constituent parts, with all their mortal limits and foibles.
Emergent systems can’t make the bricks that built them stop being brick-ish.[*],[11]
These properties are all intrinsic to a deterministic world, whether chaotic, emergent, predictable, or unpredictable. But what if the world isn’t really deterministic after all? On to the next two chapters.
9
A Primer on Quantum Indeterminacy
I really do not want to write this chapter, or the next one. I’ve been dreading it, in fact. When friends ask me how the book writing is going, I grimace and say, “Well, okay, but I’m still postponing doing the chapters on indeterminacy.” Why the dread? To start, (a) the chapters’ subject rests on profoundly bizarre and counterintuitive science (b) that I barely understand and (c) that even the people who you’d think understand it admit that they don’t, but with a profound noncomprehension, compared with my piddly cluelessness, and (d) the topic exerts a gravitational pull upon crackpot ideas as surely as does a statue upon defecating pigeons, a pull that constitutes a “What are they talking about?” strange attractor. Nonetheless, here goes.
This chapter examines some foundational domains of the universe in which extremely tiny stuff operates in ways that are not deterministic. Where unpredictability does not reflect the limitations of humans tackling math, or the wait for an even more powerful magnifying glass, but instead reflects ways in which the physical state of the universe does not determine it. And the next chapter is about reining in the free-willers in this playground of indeterminacy.
Were I to chicken out and end this pair of chapters right here, the conclusions would be that, yes, Laplacian determinism really does appear to fall apart down at the subatomic level; however, such eensy-weensy indeterminism is vastly unlikely to influence anything about behavior; even if it did, it’s even more unlikely that it would produce something resembling free will; scholarly attempts to find free will in this realm frequently strain credulity.
Undetermined Randomness
What exactly do we mean by “randomness”? Suppose we have a particle that moves “randomly.” To qualify, it would show these properties:
—If at time 0 a particle is in spot X, the most likely place you’d expect to find that randomly moving particle for the rest of time is back at spot X. And if at some point after time 0, the particle happens to be in spot Z, now for the rest of time, spot Z is where it’s most likely to be. The best predictor of where a randomly moving particle is likely to be is wherever it is right now.
—Take any unit of time—say, one second. The amount of variability in the particle’s movement in the next second will be as much as during one second a million years from now.
—The pattern of movement at time 0 has zero correlation with time 1 or −1.
—If it looks as if the particle has moved in a straight line, get that magnifying glass and look closer and you’ll see that it isn’t really a straight line. Instead, the particle zigzags, regardless of the scale of magnification.
—Because of that zigzagging, when magnified infinitely, a particle will have moved an infinitely long distance between any two points.
These are stringent features for a particle to qualify as undetermined.[*] These requirements, especially that spacey Menger-sponge business about something infinitely long fitting into a finite space, show how capital-R Randomness differs from random channel surfing.
So what does a particle being random have to do with your being the agentive captain of your fate?
Low-Rent Randomness: Brownian Motion
We start with the Jane and Joe Lunchbucket version of indeterminism, one that is rarely contemplated at meditation retreats.
Sit in an otherwise dark room that has a shaft of light coming in from a window, and look at what is being illuminated along the way by the shaft (i.e., not the spot on the wall being lit up but the air illuminated between the window and the lit wall). You’ll see minuscule dust particles that are in constant motion, vibrating, jerking this way or that. Behaving randomly.
People (e.g., Robert Brown, in 1827) had long noted the phenomenon, but it wasn’t until the last century that random (aka “stochastic”) movement was identified to occur among particles suspended in a fluid or gas. Tiny particles oscillate and vibrate as a result of being hit randomly by photons of light, which transfer energy to the particle, producing the vibratory phenomenon of kinetic energy. Which causes particles to bump into each other randomly. Which causes them to bump into other particles. Everything moving randomly, the unpredictability of the three-body problem on steroids.
Mind you, this isn’t the unpredictability of cellular automata, where every step is deterministic but not determinable. Instead, the state of a particle in any given instant is not dependent on its state an instant before. Laplace is vibrating disconsolately in his grave. The features of such stochasticity were formalized by Einstein in 1905, his annus mirabilis when he announced to the world that he was not going to be a patent clerk forever. Einstein explored the factors that influence the extent of Brownian motion of suspended particles (note the plural on particles—any given particle is random, and predictability is probabilistic only on the aggregate level of lots of particles). One thing that increases Brownian motion is heat, which increases kinetic energy in particles. In contrast, it’s decreased when the surrounding fluid or gas environment is sticky or viscous or when the particle is bigger. Think of this last one this way: The bigger a particle, the bigger the bull’s-eye, the more likely it is to be bumped into by lots of other particles, on all its sides. Which increases the odds of all those bumps canceling each other out and the big particle staying put. Thus, the smaller the particle, the more exciting the Brownian motion that it shows—while the Great Pyramid of Giza may be vibrating, it isn’t doing it much.[*]
So that’s Brownian motion, particles bumping into each other randomly. How does that relate to biology (a first step toward seeing its relevance to behavior)? Lots, as it turns out. One paper explores how a type of Brownian motion explains the distribution of populations of axon terminals. Another concerns how copies of the receptor for the neurotransmitter acetylcholine randomly aggregate into clusters, something important to their function. Another example concerns abnormality in the brain—some mostly mysterious factors increase the production of a weirdly folded fragment called the beta-amyloid peptide. If one copy of this fragment randomly bumps into another one, they stick together, and this clump of aggregated protein crud grows bigger. These soluble amyloid aggregates are the most likely killers of your neurons in Alzheimer’s disease. And Brownian motion helps explain probabilities of fragments bumping into each other.[1]
I like teaching one example of Brownian motion, because it undermines myths of how genes determine everything interesting in living systems. Take a fertilized egg. When it divides in two, there is random Brownian splitting of the stuff floating around inside, such as thousands of those powerhouses-of-the-cell mitochondria—it’s never an exact 50:50 split, let alone the same split each time. Meaning those two cells already differ in their power-generating capacity. Same for vast numbers of copies of proteins called transcription factors, which turn genes on or off; the uneven split of transcription factors when the cell divides means the two cells will differ in their gene regulation. And with each subsequent cell division, randomness plays that role in the production of all those cells that eventually constitute you.[*],[2]
Now, time to scale up and see where Brownian-esque randomness plays into behavior. Consider some organism—say, a fish—looking for food. How does it find food most efficiently? If food is plentiful, the fish forages in little forays anchored around this place of easy eating.[*] But if food is diffuse and sparse, the most efficient way to bump into some is to switch to a random, Brownian foraging pattern called a “Levy walk.” So if you’re the only thing worth eating in the middle of the ocean, the predator that grabs you will probably have gotten there by a Levy walk. And logically, many prey species move randomly and unpredictably in evading predators. The same math describes another type of predator hunting for prey—a white blood cell searching for pathogens to engulf. If the cell is in the middle of a cluster of pathogens, it does the same sort of home-based forays as a killer whale feasting in the middle of a bunch of seals. But when the pathogens are sparse, white blood cells switch to a random Levy-walk hunting strategy, just like a killer whale. Biology is the best.[3]
To summarize, the world is filled with instances of indeterministic Brownian motion, with various biological phenomena having evolved to optimally exploit versions of this randomness. Are we talking free will here?[*] Before addressing this question, time to face the inevitable and tackle the mother of all theories.[4]
Quantum Indeterminacy
Here goes. The classical physical picture of how the universe works, invariably attributed to Newton, tanked in the early twentieth century with the revolution of quantum indeterminacy, and nothing has been the same since. The subatomic world turns out to be deeply weird and still can’t be fully explained. I’ll summarize here the findings that are most pertinent to free-will believers.
Wave/Particle Duality
The start of the most foundational weirdness was the immeasurably cool, landmark double-slit experiment first carried out by Thomas Young in 1801 (another one of those polymaths who, when he wasn’t busy with physics, or outlining the biology of how color vision works, helped translate the Rosetta stone). Shoot a beam of light at a barrier that has two vertical slits in it. Behind it is a wall that can detect where the light is hitting it. This shows that the light travels through the two slits as waves. How is this detected? If there was a wave emanating from each slit, the two waves would wind up overlapping. And there’s a characteristic signature when a pair of waves does this—when the peaks of two waves converge, you get an immensely strong signal; when the troughs of the two converge, the opposite; when a peak and a trough meet, they cancel each other out. Surfers understand this.
So light travels as a wave—classical knowledge. Shoot a stream of electrons at the double-slit barrier, and there’s the same punch line—a wave function. Now, shoot one electron at a time, recording where it hits the detector wall, and the individual electron, the individual particle, passes through as a wave. Yup, the single electron passes through both slits simultaneously. It’s in two places at once.
Turns out that it’s more than just two places. The exact location of the electron is indeterministic, distributed probabilistically across a cloud of locations at once, something termed superposition.
Accounts of this now usually say something to the effect of “Now things get weird”—as if a single particle being in multiple places at once weren’t weird. Now things get weirder. Build a recording device into the double-slit wall, to document the passage of each electron. You already know what will happen—each individual electron passes through both slits at once, as a wave. But no; each electron now passes through one slit or the other, randomly. The mere process of measuring, documenting what happens at the double-slit wall causes the electrons (and, as it turns out, streams of light, made up of photons) to stop acting as waves. The wave function “collapses,” and each electron passes through the double-slit wall as a singular particle.
Thus, electrons and photons show particle/wave duality, with the process of measurement turning waves into particles. Now measure the properties of the electron after it passes through the slits but before it hits the detector wall, and as a result, each electron passes through one of the slits as a single particle. It “knows” that it is going to be measured in a bit, which collapses its wave function. Why the process of measuring collapses wave functions—the “measurement problem”—remains mysterious.[5]
(To jump ahead for a moment, you can guess that things are going to get very New Agey if you assume that the macroscopic world—big things like, say, you—also works this way. You can be in multiple places at once; you are nothing but potential. Merely observing something can change it;[*] your mind can alter the reality around it. Your mind can determine your future. Heck, your mind can change your past. More jabberwocky to come.)
Particle/wave duality generates a key implication. When an electron is moving past a spot as a wave, you can know its momentum, but you obviously can’t know its exact location, since it’s indeterministically everywhere. And once the wave function collapses, you can measure where that particle now is, but you can’t know its momentum, since the process of measurement changes everything about it. Yup, it’s Heisenberg’s uncertainty principle.[*]
The inability to know both location and momentum, the fact of superposition and things being in multiple places at once, the impossibility of knowing which slit an electron will pass through once a wave has collapsed into a particle—all introduce a fundamental indeterminism into the universe. Einstein, despite upending the reductive, deterministic world of Newtonian physics, hated this type of indeterminism, famously declaring, “God does not play dice with the universe.” This began a cottage industry of physicists trying to slip some form of determinism in the back door. Einstein’s version is that the system actually is deterministic, thanks to some still-undiscovered factor(s), and things will go back to making sense once this “hidden variable” is identified. Another backdoor move is the very opaque “many-world” idea, which posits that waves don’t really collapse into a singularity; instead their wave-ness continues in an infinite number of universes, making for a completely deterministic world(s), and it just looks singular if you’re looking from only one universe at a time. I think. My sense is that the hidden-variable dodge is most doubters’ favorite. However, the majority of physicists accept the indeterministic picture of quantum mechanics—known as the Copenhagen interpretation, reflecting its being championed by the Copenhagen-based Niels Bohr. In his words, “Those who are not shocked when they first come across quantum theory cannot possibly have understood it.”[*],[6]
Entanglement and nonlocality
Next weirdness.[*] Two particles (say, two electrons in different shells of an atom) can become “entangled,” where their properties (such as their direction of spin) are linked and perfectly correlated. The correlation is always negative—if one electron spins in one direction, its coupled partner spins the opposite way. Fred Astaire steps forward with his left leg; Ginger Rogers steps back with her right.
But it’s stranger than that. For starters, the two electrons don’t have to be in the same atom. They can be a few atoms apart. Okay, sure. Or, it turns out, they can be even farther apart. The current record is particles nearly nine hundred miles apart, at two ground stations linked by a quantum satellite.[*] Moreover, if you alter the property of one particle, the other changes as well, implying a causality that isn’t local. There is no theoretical limit for how far apart entangled particles can be. An electron in the Crab Nebula in the constellation Taurus can be entangled with an electron in the piece of broccoli stuck between your incisors. And as the strangest feature, when the state of one particle is altered, the complementary change in the other occurs instantaneously[*]—meaning that the broccoli and the Crab Nebula are influencing each other faster than the speed of light.[7]
Einstein was not amused (and labeled the phenomenon with a sarcastic German equivalent of spooky).[*] In 1935, he and two collaborators published a paper that challenged the possibility of this instantaneous entanglement, again positing hidden variables that explained things without invoking faster-than-the-speed-of-light mojo. In the 1960s, the Irish physicist John Stewart Bell showed that there was something off in the math in that paper of Einstein’s. And in the decades since, extraordinarily difficult experiments (like the one with that satellite) have confirmed that Bell was right when he said that Einstein was wrong when he said that the interpretation of entanglement was wrong. In other words, the phenomenon is for real, although it still remains basically unexplained, nonetheless generating highly accurate predictions.[8]
