Time again for Shtetl-Optimized’s Mistake of the Week series! This week my inspiration comes from a paper that’s been heating up the quantum blogosphere (the Blochosphere?): Is Fault-Tolerant Quantum Computation Really Possible? by M. I. Dyakonov. I’ll start by quoting my favorite passages:
The enormous literature devoted to this subject (Google gives 29300 hits for “fault-tolerant quantum computation”) is purely mathematical. It is mostly produced by computer scientists with a limited understanding of physics and a somewhat restricted perception of quantum mechanics as nothing more than unitary transformations in Hilbert space plus “entanglement.”
Whenever there is a complicated issue, whether in many-particle physics, climatology, or economics, one can be almost certain that no theorem will be applicable and/or relevant, because the explicit or implicit assumptions, on which it is based, will never hold in reality.
I’ll leave the detailed critique of Dyakonov’s paper to John Preskill, the Pontiff, and other “computer scientists” who understand the fault-tolerance theorem much better than a mere physicist like me. Here I instead want to take issue with an idea that surfaces again and again in Dyakonov’s paper, is almost universally accepted, but is nevertheless false. The idea is this: that it’s possible for a theory to “work on paper but not in the real world.”
The proponents of this idea go wrong, not in thinking that a theory can fail in the real world, but in thinking that if it fails, then the theory can still “work on paper.” If a theory claims to describe a phenomenon but doesn’t, then the theory doesn’t work, period — neither in the real world nor on paper. In my view, the refrain that something “works on paper but not in the real world” serves mainly as an intellectual crutch: a way for the lazy to voice their opinion that something feels wrong to them, without having to explain how or where it’s wrong.
“Ah,” you say, “but theorists often make assumptions that don’t hold in the real world!” Yes, but you’re sidestepping the key question: did the theorists state their assumptions clearly or not? If they didn’t, then the fault lies with them; if they did, then the fault lies with those practitioners who would milk a nonspherical cow like a spherical one.
To kill a theory (in the absence of direct evidence), you need to pinpoint which of its assumptions are unfounded and why. You don’t become more convincing by merely finding more assumptions to criticize; on the contrary, the “hope something sticks” approach usually smacks of desperation:
There’s no proof that the Earth’s temperature is rising, but even if there was, there’s no proof that humans are causing it, but even if there was, there’s no proof that it’s anything to worry about, but even there was, there’s no proof that we can do anything about it, but even if there was, it’s all just a theory anyway!
As should be clear, “just a theory” is not a criticism: it’s a kvetch.
Marge: I really think this is a bad idea.
Homer: Marge, I agree with you — in theory. In theory, communism works. In theory.
Actually, let’s look at Homer’s example of communism, since nothing could better illustrate my point. When people say that communism works “in theory,” they presumably mean that it works if everyone is altruistic. But regulating selfishness is the whole problem political systems are supposed to solve in the first place! Any political system that defines the problem away doesn’t work on paper, any more than “Call a SAT oracle” works on paper as a way to solve NP-complete problems. Once again, we find the “real world / paper” distinction used as a cover for intellectual laziness.
Let me end this rant by preempting the inevitable cliché that “in theory, there’s no difference between theory and practice; in practice, there is.” Behold my unanswerable retort:
In theory, there’s no difference between theory and practice even in practice.