Trespassing on Einstein's Lawn (18 page)

I had already discovered that instrumentalism was a common position among physicists, who always seemed to squirm at any mention of the
R
-word.
It's the philosophers' job to worry about reality
, they'd say.
We just calculate and predict and test.

No matter how many times I heard that, it always struck me as total bullshit. Okay, maybe if you were an electrical engineer or a surgeon or a meteorologist you'd just be concerned with predictions and the outcomes of experiments, but the people I was hearing this from were physicists.
Theoretical
physicists. People who were dealing with black holes and multiple universes and glitches in the simulation. Maybe when you work in theoretical physics, you feel the need to overcompensate by pretending to be as no-nonsense as a refrigerator repairman, but at the end of the day, who are you kidding? You stay awake nights worrying about how matter behaves at length scales a millionth of a billionth of a billionth of a billionth of a centimeter in six extra dimensions undetectable by any foreseeable experiment, but you don't care at all what reality is? Please.

Given my propensity for worrying about simulations and shadows and butterfly dreams, I wouldn't have guessed that I would find myself advocating a strict realist view. Then again, I was a self-proclaimed reality hunter, so entertaining any antirealist ideas would be like shooting myself in the foot. Besides, at times the arguments for antirealism struck me as utterly absurd. The pinnacle of absurdity came one afternoon when a girl in my class argued her antirealist position from a feminist standpoint.

“Wait, did she just say ‘feminist'?” I asked the guy next to me. “Feminist physics?” I couldn't imagine where this was headed.

“Not only is science a socially constructed enterprise, it is also explicitly male-centric,” she explained to the class. “Think about the terminology.
Particles are represented as
balls
, and they interact with each other through
forces.
”

Seriously? Balls? I coughed to cover my snickering. Judging by her expression, this was a very serious matter.

“So if physics is socially constructed,” one guy began, “regardless of whether it's constructed by men or women, you don't think it corresponds to reality at all?”

“No, I don't,” she replied.

I couldn't stop myself from joining in. “So how exactly do, say, airplanes fly?”

“Because we all agree that they do,” she responded.

I blinked. “Are you serious?”

Somehow, seemingly instantaneously, the classroom had divided itself into teams—realists versus antirealists. We even shuffled our desks around to make it known exactly which side of this fight we were on.

Antirealism had seemed a rather insane position until I felt the sting of its best right hook: every previous scientific theory ever devised in the history of science has, until now, turned out to be wrong. So what kind of morons would we have to be to believe that our current theories are the exception, the one time mankind—or womankind—has ever gotten it right? And if theories are always turning out to be wrong, how can they possibly be telling us anything about the true nature of reality? I learned that this rather fatal blow is known in philosopher-speak as the “pessimistic meta-induction,” which just means that with some solid inductive reasoning it becomes obvious that science is a hopeless enterprise.

It was a depressing thought, but luckily realism had its own uppercut ready, the argument that I had unknowingly made against the girl who was mad about balls: if scientific theories don't describe at least part of the true reality out there, then the success of technology—not to mention the success of a theory's bold, novel predictions that go way beyond whatever observations were fed into it in the first place—has to be chalked up to a miracle.

Okay, so all theories turn out to be wrong, but the technologies we build based on those theories miraculously work. The pessimistic
meta-induction and the no-miracles argument formed a kind of stalemate, and philosophers had been bickering about it ever since. One philosopher, however, had found a middle ground. He happened to be sitting in an office down the hall.

I had barely unpacked my things when I started hearing the noises. Scurrying noises. A rustling. On a few occasions I swore I saw a blur of motion out of the corner of my eye. Then one night, lying in the loft, half asleep, I heard a guttural sound, the kind of sound a cat makes before it jumps, a sort of revving of the motor. It startled me and I sat up without thinking, bashing my head into the ceiling. By the time I managed to turn on the light, whatever had made the sound was gone.

It wasn't hard to guess what was happening. This was London, after all. I had read somewhere that wherever you stand in the entire city, you're never more than twenty yards from a rat. There were 50 million of them. That was like seven rats per human. Could seven rats even fit in my flat? Not if this one was big enough to make guttural sounds, I thought. I tried to go back to sleep, assuring myself, unconvincingly, that rats can't climb ladders.

In the morning I went to the hardware store, where I found a disconcertingly large selection of rodent control devices, a whole wall of them. I was gazing at it in awe and confusion when the sales guy asked if he could help.

“I don't want to be cruel,” I said. “I mean, I want them out. If I could reason with them, I would. I just want something that doesn't make me a terrible person.”

He nodded. “Then I'd avoid the glue traps.”

He showed me a trap that consisted of a box that you rig with bait and when the rat goes in to get it, it triggers this sort of garage door that falls shut, locking the rat inside, where it waits for you to take it outside and set it free. Not into the wild per se, but at least headed for someone else's flat. I bought two.

I heard them rustling around down there as I drifted off to sleep that night.
Esse est percipi. Esse est percipi.
I chanted the phrase like a
spell, hoping it might transform any ontologically valid rats into vaporous thoughts I could sleep off by morning. Perhaps the real estate agent had meant to say that this flat was modern
and
mind-dependent. Reassuringly, I had yet to actually perceive any living creatures; their existence was nothing more than a pessimistic induction.
Cogito ergo rats.
Maybe the programmers were messing with me. Maybe the strange sounds were just glitches in the simulation. Or maybe my dad had been right and this place was subject to quantum fluctuations, the sudden but fleeting appearance of rodents from an ever-churning vacuum. Maybe as long as I didn't observe them, they'd be stuck suspended in a kind of quantum mousetrap, half real, half illusion. Schrödinger's rats.

But in the morning, when I observed them, the traps were empty.

John Worrall had a sweet look about him, like the kind of guy who could broker peace among feuding academics, or the kind who would one day become the leader of a philosopher-of-science-made rock band called Critique of Pure Rhythm. He had started out in statistics but been lured to philosophy by Karl Popper, who had founded the philosophy of science department here.
In 1989 Worrall published an article in the journal
Dialectica
arguing for a middle ground between realism and antirealism. He called his view structural realism, and claimed that it held the best of both worlds: it could explain science's success without invoking miracles and account for its pessimistic progression from one wrong theory to the next.

The problem, Worrall explained, was that realists were being realists about the wrong things. In fact, “things” were precisely the problem. Realists talked about a real mind-independent world, out there, composed of real things such as atoms and tables and rats. But when you look closely, scientific theories aren't about “things” at all. They're about mathematical structure.

A mathematical structure is a set of isomorphic elements, each of which can be perfectly mapped onto the next. The notations 25, 5
²
, and (27 – 2) all share the same mathematical structure. The structure isn't any particular number—it's the whole set of equivalent representations
of a number, the steady, singular truth behind a multitude of mere appearances. Sets are more fundamental than the numbers themselves.

All of mathematics—all of structure—comes down to sets?
I wrote in my notebook. I remembered reading somewhere that the entire number line could be built from the empty set: the set containing nothing. Inside the empty set is nothing. Zero. But the set that contains the empty set is not empty. It contains one element: the empty set. It's the number 1. Not merely equal to 1, but the very definition of the number 1. The set that contains both the empty set and the set that contains the empty set is 2. Ad infinitum. Or ad nothing.

The number line was nothing more than a series of nested sets, and in its hidden center was nothing. Worrall said that physics was about mathematical structure. Set theory said that mathematical structure was about nothing.

The idea that you could build the number line from the empty set—was it a clever trick or was it telling us something profound about the universe? Was it telling us how to turn nothing into something?
Put brackets around it. A boundary.
Somethingness emerges from a change in point of view. Inside to outside.

I wasn't sure how you'd apply that lesson to something like a universe, something that doesn't have an outside.
One-sided coin, the side of things.
How do you make something out of that? Even if you could, you'd still be stuck with Russell's paradox. The barber shaves every man who doesn't shave himself—so who shaves the barber? If he shaves himself, he doesn't shave himself, and if he doesn't, he does. The issue wasn't about facial hair. It was about the paradoxes that arise if sets can contain themselves. When you take the view from outside the brackets and try to shove it back inside.

Worrall attributed structural realism to Henri Poincaré, who in 1905 wrote,
“Equations express relations, and if the equations remain true, it is because the relations preserve their reality.… The true relations between these real objects are the only reality we can attain.” Theories are just sets of mathematical relations—equations related by isomorphisms. By equals signs. Quantum field theory doesn't talk about hard little (
cough
) balls called particles; it talks about “irreducible
representations of the Poincaré symmetry group.” If it makes it easier to picture those irreducible representations as little spheres, that's your right. But if that picture doesn't hold up in light of new evidence, don't get mad at the theory. Quantum field theory is a group of mathematical structures. Electrons are little stories we tell ourselves.

Of course, we need stories. There's a reason “42” is not a satisfying answer to life, the universe, and everything. Structure alone doesn't quench our existential thirst. We want meaning. And for our brains, meaning comes in the form of stories.

Still, it's important to separate what theories mean to us from what they actually say. That was Worrall's point. Theories never talk about objects—only our
interpretations
of theories do. Theories themselves only talk about mathematical structure. And if we're realists about structure, the pessimistic meta-induction no longer applies.

When theories turn out to be wrong, Worrall said, it's usually our interpretative story that's wrong—not the structure. Take gravity. According to Newton, gravity is a force that masses exert on one another from a distance. According to Einstein, it's the local curvature of spacetime. The two ideas are contradictory. Both couldn't be right, so clearly, the antirealists said, Newton's theory wasn't describing reality at all, a fact that made it pretty hard to explain how he was able to predict the motions of the planets. Worrall disagreed. If you take away the interpretations and just look at the math, it's a whole different game. When gravity is weak and velocities are low, Einstein's equations give way to Newton's. Newtonian gravity is the low-energy limit of general relativity. Newton had the wrong story but the right structure—only it turned out to be a tiny corner of something much, much bigger. We don't need miracles to understand why Newtonian gravity worked; it was successful because it had homed in on a small piece of reality's structure. Einstein discovered a bigger piece, and there's still more to be found.

The same went for quantum mechanics. Although its
description
of the world is drastically different from that of classical mechanics—where particles have simultaneously defined positions and momenta, cat obituaries are far more straightforward, and demons can predict the future to infinite accuracy—its mathematical structure reduces to
that of classical mechanics when physical systems are large compared to the size of Planck's constant. As one theory surrenders to the next, physical interpretations are left behind in ruin, but mathematical structure persists. Scientific progress isn't a parade of miraculously wrong theories—it's an optimistic snowball, gathering the structure of reality as it rolls.

Several more rustling nights were followed by several more ratless mornings.

I hunted around the flat, looking for any rat-sized entryways. I taped up the tiniest cracks in the walls and stuffed the openings around pipes with steel wool. To be extra-cautious, I stacked books all along the perimeter. Just in case they could jump the books, I created various obstacles for them to encounter on the other side. The whole setup got quite elaborate, with makeshift forts and moats and the garage-door traps in the center. The rats might be clever and resilient, I thought, but I had physics books and duct tape and opposable thumbs.

Still, the rustling continued, and one night I was awoken by the thump of a book falling from its fortress. In the morning I saw that it was Julian Barbour's
The End of Time.
I wondered if the rats were trying to tell me something.