[Here’s a little fable that I wrote today, while listening to a talk “showing” that a fault-tolerant quantum computer would need at least 100 physical qubits for every logical qubit. Physicists are welcome to shoot back with counter-fables, as are closet computer scientists like His Holiness.]
One day a group of physicists ran excitedly into the computer science building. “Guess what?” they cried. “You know how you’re always trying to prove lower bounds, but you almost never succeed? Well, today we proved a lower bound!”
“What did you prove?” asked the computer scientists.
“We proved that to pull a wagon through a forest, you need at least five oxen. It’s physically impossible to do it with four oxen or less, regardless of what other resources you have.”
“How did you prove that?”
“Well, we looked up the strength of a typical ox, the weight of a typical wagon, the size of every forest in a 30-mile radius…”
“Yeah, but what if you had an ox the size of a Brontosaurus? Or what if the forest was only two feet across? Or what if the wagon weighed less than a fingernail?”
The physicists snickered. “These are clearly unphysical assumptions. As long as you stay within a realistic region of parameter space, our impossibility proof is airtight.”
“Ah, but how do you know there couldn’t be some completely different method of pulling wagons — maybe even a method that’s not ox-based at all?”
“Look, we physicists are interested in the real world, not complexity-theory la-la land. And at least in the real world, when people want to pull wagons, oxen are what they use.”
The physicists weren’t heard from again until almost a decade later, when they once again barged into the CS building. “Guess what?” they cried. “We just discovered a loophole in the famous Five-Ox Theorem — the one we published years ago in Nature!”
“What’s the loophole?”
“Elephants! If you had an elephant pulling the wagon, you wouldn’t need any oxen at all. With hindsight it’s almost obvious, but what a paradigm shift it took!”
The computer scientists stared blankly.
“You see,” said the physicists. “This is why we never trust so-called impossibility proofs.”