Other Voices #2

IS KNOWLEDGE PREDICTABLE?

 An Interview with David Deutsch

It's here," the taxi driver says and points to a crumbling wall Behind thrives vegetation that hasn't seen a gardener for a long time. I am not at all sure this is the right address, but I figure it won't be a long walk from here. I pay the driver and step into a sunny autumn day. It’s quiet street in the outskirts of Oxford, where I am looking for David Deutsch.

Closer Inspection of the house in front of me reveals it is the right address after all, and so I make my way to the door along a walkway infringed on by plants. The door is surrounded by cobwebs and could use new paint. I ring the bell. It doesn't take long for David to open the door.

Even for someone as nearly face-blind as I, David Deutsch is easy to recognize. His eyes seem too big for his sharp nose and lean face, and his hair, like that of most British men, is too long, He welcomes me with a big smile and asks me in. The inside of his house, I see, isn’t in any better condition than the outside, but as a mother of two children in primary still, I am practiced in carefully treading around stacks of toys, books, and unidentifiable craftworks. That skill comes in handy now.

David leads me to what I believe must be the living room. It contains couch opposite a huge flat screen on a desk, some folding chairs and bookshelves (from one of which I see Charles W. Misner, Kip S. Thorne, and John Wheeler's Gravitation greeting me), gardening tools, lots of boxes, cables, various computer accessories, a blue mini-trampoline, and a bright-red Japanese massage chair. The massage chair, David enthuses, is new, and he sets out to demonstrate its various functions. It takes all my willpower not to ask him for a mop and a vacuum cleaner. Instead, I accept a glass of water and look for my notepad.

David is best known for his seminal contributions to quantum computing for which, in 2017, he received the Dirac Medal of the International Centre for Theoretical Physics, adding it to a long list of awards and honors. But I am not here to talk about quantum computing. I am here because I have been most impressed by David's popular science books, The Fabric of Reality and The Beginning of Infinity. It isn’t only that David is exceedingly careful in laying out his rationale for thinking about what he is thinking about. It's also that he strikes me as a scientist who is way ahead of his time, interested not so much in the technologies of today as in the question how scientific know-edge grows, how it benefits our societies, and what knowledge is in the first place. David seems the right person to consult about the limits of reductionism.

I begin by asking him, too, whether he is religious. He answers with a straightforward no. He doesn't seem to have anything to add, so I move on to reductionism. "From a particle physics point of view, everything is made up of small particles, and in principle all the rest derives from it. Do you subscribe to this idea or do you think there are some things that cannot be reduced to their parts? “I don't subscribe to reductionism as a philosophy," David says. “That is, I don't subscribe to the idea that the only true explanations are reductive ones."

"Just to be clear, what type of reductionism do you mean?" I ask. Foremost purposes, the distinction doesn't matter, but there are two types of reductionism. One is theory reductionism-levels of theories whose higher levels can be derived from the deeper ones, as we discussed in the previous chapter. The other one is ontological reductionism, which means that we get better explanations by physically going to smaller and smaller scales. The distinction usually doesn't matter, though, be-cause they've historically gone hand in hand.

"I think both are false as philosophical principles," David answers. “But it so happens that some of the best theories of all time have been reductionist in both senses. For example, the periodic table. This was one of the explanatory triumphs of the nineteenth century, which linked all sorts of explanatory ideas, including the idea, resurrected from antiquity, that matter can't be infinitely subdivided. And like all solutions, this raised new problems. If the atoms can't be subdivided, how come they have different properties? And how come these prop-retires are regular? This suggests that there has to be an underlying structure. And that's also how I see modern particle physics. It's like chemistry was in the nineteenth century. Maybe unlike chemistry in the nineteenth century, it has a taint of this reductionist philosophy that only subdividing things into smaller things can ever be an explain-nation .... Ah, sorry, I've lost track. I got so excited about the peri-odic table, I have forgotten your question! “You were saying that some of the best theories that we have are reductionist in both ways."

"Ah, yes"-David picks up his lost thread-"but some of them are not. For example, the theory of universal computation, which says that all the laws of physics are, say, Turing computable. In terms of physics, that means that there's a possible physical object, like this computer, such that the set of all possible motions of this thing corresponds one-to-one, in some approximation, to the set of all possible motions of everything."

He gestures at his laptop and continues. "Now, that's a powerful statement about the universe, and most conceivable laws of physics would not satisfy it. We think that the actual laws do satisfy it. And yet this principle refers to a thing-the universal computer-that is highly composite and highly complex. So if this is a fundamental principle that all laws are Turing computable, then this law is not reductive, and reductionism is false right there. It's saying that a particular high-level object has fundamental properties. And I think there is scope for future laws of that kind. Of course we will accept them only if they are good explanations. But that they are not reductive is not a criticism in my view."

He adds, "Similarly, if a law is reductive, this is also not a criticism. Some people are the opposite: they are holists. They think that a re-educationist explanation can never be fundamental. I think that's false as well."

"You said you have this computer, so you have a higher-level object that has fundamental properties. But what exactly do you mean bifundamental here?"

"I mean that they are principles that we think are deep, universal truths about the world and not just accidentally true," David says. “Take, for example, the statement that there exists a solar system with eight planets, and the first three are rocky. We know that is true, because we live in one, but we don't think that's a fundamental statement. But the law of the conservation of energy, we think, is a deeper truth. And because it's deeper, it's a guide to future theories. When we are trying to write down new laws which fundamental particles may obey, we typically write down laws that obey energy conservation. We treat it as a principle that doesn't need to be ex-pained by anything else."

"So it's a fundamental principle, but it's not reductionist, because it applies to everything?"

"We don't derive energy conservation from other laws," David ex-plains. "We derive other laws from it. Well, of course, it may be false. But for it to be false, you need to have an explanation under which this could be false. For example, there are some understandings of general relativity in which energy is not conserved. And if that turned out to be correct, you would abandon that principle. It may happen, because general relativity is not totally satisfactory, as you know; we need a theory of quantum gravity."

I suggest, "Maybe the reason we don't have a theory of quantum gravity is that we're too tied to the idea that the more fundamental laws can be found on shorter distances. Is going to shorter distances maybe the wrong thing to do?"

"Yes, indeed!" David agrees. "As you know, I have this theory, con-structure theory, in which the fundamental laws are not reductive. It’s very crude theory at present, but you have to stick your neck out at first. In constructor theory, the low-level, microscopic laws are all emergent properties of the high-level laws, not vice versa."

"Have you ever heard of something called the causal exclusion principle?" I ask. “No."

"It seems to contradict what you just said," I explain. "So, in particle physics, we have this idea that if we combine small things to large things, then the laws for the small things tell us what the large things do. And we use the mathematical framework of effective field theory for this. This tells us that we do have a law for the macroscopic things already. The causal exclusion principle then says that, since we already have a law for macroscopic things, then any other macroscopic law is either derivable from the one we already have, orgone of them must be wrong."

David replies, "I have no quarrel with the idea that the dynamical laws for macroscopic objects are deterministic and can be derived from the microscopic laws. But this doesn't imply that that's a good explanation."

I am still not sure I understand this entirely. "So constructor theory is not reductionist in the sense that the explanations don't start with the small scales?"

"Yes," David says. "As an example, let us just suppose that under constructor theory one of the fundamental laws says that there exist universal computers. In fact, let us say there exist universal computers with arbitrarily large memories. This one"-he points to his lap-top again-"is an approximation to that, but in the future, there will be ones with larger memories, and in the unlimited future, there'll be computers with unlimited memory. And suppose, just for the sake of the argument, that that really is one of the fundamental laws, but that other fundamental laws are reductive, such as quantum mechanics and elementary particle interactions, and so on.

"Well, then the existence of universal computers plus the microscope dynamical laws translates into a statement about the initial state of the universe. But it translates into it in a highly intractable way. There would be no way of actually calculating all the properties the initial state must have, apart from saying it's such as to produce that end result: universal computers. Some people would rule this out; they would say it's a teleological theory. But it's not any old teleological theory. We have to explain why the universe is so that it has computers at all. The existence of even the type of computer we use today makes the laws of physics extremely unusual. It's as unusual as the existence of chemical elements. It's a feature of the world that we see and that we haven't explained."

I say, "But, of course, putting the thing that you want to explain into your theory doesn't explain it. If you say the universe is such that it goes on to produce computers, that doesn't explain anything. “Right," David says. "You might as well say that the reason we are sitting here, and you are looking skeptical of what I say, is that you are going to write a book which will say, 'And I was skeptical of what he said.' And that you will write this in your book is the reason why you are skeptical now. That is the same argument, yet it explains nothing. I had to put the example with the computer this way because we don’t yet have that theory which would explain it."

"OK," I say. "So you mean there could be a theory that has the property that it would go on to produce universal computers with unlimited memory and so on, but you don't know what that theory is."

"Yes," David agrees. "But what we do have of constructor theory is friendly to that kind of thing. It's not silly to imagine that an explanatory theory of that type exists."

Coming back to the question whether the future is determined, I ask, "You said you have no problem with the dynamical laws being deterministic. Would you say that for that reason everything is deterministic-not just computers but also human consciousness and behavior and so on?"

David says, "Yes, deterministic, in that as a matter of logic, the state at one time is determined by the state at any other time plus dynamical laws. But it may be that the later time is explained by the earlier time and not vice versa."

"But just because it's deterministic doesn't mean it's predictable, “I say. "Do you mean that it's actually predictable? “No," he says. "For three reasons. First, in quantum mechanics, we cannot measure the state perfectly accurately. Therefore, even if we knew what the evolution of each state would be, we don't know what the actual state is, because it can't be measured.

"Second, there is chaos. Now, quantum mechanics doesn't have chaos, ª but things like computers and brains do have it at the level that they work, so that means that changing even one bit in this computer will drastically change what it will do in the future. And because we can't measure our state of mind to anywhere near perfect accuracy, we are unpredictable.

"And there's a third reason, that's the most important, and that is that one can't predict the future growth of knowledge. No theory can be so good that it predicts the content of its own successor. Imagine you put a person into a glass sphere and do not allow interactions with the outside world and so on. You may think that in principle you can then predict everything that that person will do. But that's an illusion. Because if the person comes up with new ideas, such as a new law of physics, then there's no way you could have known that when you started the experiment. And if your computer works out what he’ll do (say the computer works out in one day what he does in seven-day), then you already have the new law of physics before he does, and the computation that the computer performed is actually a per-son: it is essentially him. So in order to calculate what he would do in the future, you really had to take him out of the sealed glass compartment and put him in a computer and run him in a virtual form. Oh, I should say that I think running someone in virtual form is exactly the same as running them in real form. Thinking is just a computation. “So you are saying it would no longer be a prediction, because then you’d have the real thing in your computer already?"

"Yes," David says. "We can't predict the future growth of knowledge, because if we could, we would have it before the moment that we are trying to predict. It's a feature of knowledge that it leads to unpredictability, even in a deterministic system."

"So to come back to what we talked about earlier," I say, "if we insist on reducing laws to more fundamental laws by going to smaller scales, then the growth of knowledge remains unexplained?"

"Among many other things, yes," David says. "Atomic theory was thought of without evidence. The problem that they had in antiquity was that if the world was a continuum, to get from A to B you need to pass through an infinite number of points. And if it's not a continuum, how do you get from one discrete point to the next? Both seem impossible. The theory of atoms was developed because they tried to find a way out. And that might seem so esoteric that it would have no practical implication at all. But [ideas like this] were the things that led to everything good. And this is my view of the role of particle physics, reductionism, and holism. They should all be subordinated to the task of explaining the world."

And I was skeptical of what he said.

>> THE BRIEF ANSWER

If you could predict the growth of knowledge, your knowledge wouldn’t grow