The idea that there is out there a physical world which just happens to lend itself to mathematical description has always seemed to me to be incoherent. There is only one world – the universe, in fact, and it has the essential properties of a mathematical model. For reasons that we cannot even begin to understand, that model interacts with out senses, and so without measuring devices, allowing us to pretty much confirm conclusions antecedently reached by pure thought.

But to tell you the truth, I’m not at all sure I understand my own views, remarkable as they are.
… I’m sure that in this you are not alone, Mr. Berlinski …

DB: No doubt. But it is odd, isn’t it, that we really have no good views about science itself. Its existence is as much of a mystery as the phenomena that it explains. I know of nothing like an imagined overall theory that even begins to explain the role of science in the universe. No theory explains itself, after all, even if it could explain everything else.

… I’m not sure what you mean …

DB: Suppose one had a fabulous final theory. The universe is made up ultimately of wriggling strings – or whatever. The theory would not explain itself in the simple sense that unless the theory is in some odd and perverse sense self-referential, it would leave something out – the reasons why it just happens to be true. For that, one would have to deduce the theory from something else, and so far as we know or understand, deduction is itself a relationship between theories.

… But how is this connected …

DB: Not to worry. It’s probably not.

… Mr. Berlinski, you have frequently been accused of being a crank, someone more generally participating in what has come to be called crank science. I know that …

DB: So?

… Well, is the accusation one that you accept? …

DB: Sure. It’s obviously true in essence, although I prefer to describe myself as an iconoclast, one whom history will vindicate …

… No doubt …

DB: But the point is the same, whatever the terms. But speaking of terms, maybe I spoke too soon. Look, it’s one thing to say that someone like me is a crank. That’s fine because it’s true. It’s quite another thing to talk about crank science.

… Surely crank science is what cranks do? …

DB: Surely. But that is not how the term crank science has come to be used. Look at someone like Jeremy Bernstein – a good physicist and a very good writer about physics. He means something quite specific by the term crank science, and that is a willingness to deny the cumulative structure of modern physics, the fact that each great physical theory represents an enlargement of its predecessors. This is terrifically important as a rhetorical strategy because it means that the burden of skepticism becomes impossibly high with each new theory. This is just another way of protecting the sciences from criticism. To go on the attack, it is not enough to say, hey look, this particular theory is wrong, or absurd, or preposterous. You must instead take on the entire history of a tradition. Not quite sporting, I say.

… Yes, but isn’t it true? Science is cumulative and the more it accumulates the greater the weight of evidence in its favor …

DB: Yes, this is the claim. Steven Weinberg has made it explicitly. He at least knows of no advance in physical theory that has really overturned previous developments.

… How could you possibly object to that? …

DB: How? By remarking that it’s just nuts, that’s how. Weinberg is a very good physicist, but as an intellectual historian he rather resembles a horse put to work in a glass factory. He can’t help it, of course, it’s just not his métier. He gives that pompadour of his a shake, and a dozen fragile figurines just topple. Far from being cumulative, it’s the reverse that’s more really true. Let’s try and be just a little bit more precise. What’s a theory, for example? Now I’m an old logic hand and the only answer I know is that a theory in the physical sciences is just like a theory in mathematical logic – a consistent set of sentences satisfied in a model. Not the best way of putting things, but so far as I know, the only good way. Now take Newtonian mechanics and compare it to general relativity. Is it true that GR is a consistent extension of Newtonian mechanics?

… Surely many physicists would say so …

DB: Yes, and they would be wrong. Newtonian mechanics is committed to the view that the spatial structure of the universe is classically Euclidean. Not so GR. Newtonian mechanics holds that if you accelerate a rigid rod, neither its length nor certain temporal intervals will change. GR holds the opposite. But why am I telling you all this. It’s obvious.

... But Mr. Berlinski, no one would deny these points? GR is an extension of Newtonian mechanics. It goes further and because it does, we see better …

DB: An extension, maybe, but a consistent extension? Never. Consistent? If so, then Newtonian mechanics and GR must be satisfied in the same model by the compactness theorem. But how can a single mathematical model satisfy the postulates of both theories? It just can’t be done. No, no, I’m not appealing to anything like a paradigm shift. It’s perfectly possible to compare Newtonian mechanics and GR. One theory is better than the other. It explains more. It reaches for deeper principles. It is more elegant. I’m talking about Newtonian mechanics, of course. But the intersection of the set of sentences in both theories is inconsistent and so satisfied in no model whatsoever. If this is so, then the whole image of science as a cumulative structure breaks down. What one really has is a collection of cathedrals on a kind of fruited plane. Some are taller and grander than others, others are smaller and more elegant. No one cathedral is really built on top of the other.