You are led into a room. The far wall is covered in levers, buttons, dials, flashing lights, oscilloscope displays, buzzers, and so on. The person who brought you there says "we need you to describe the mechanism behind this wall. You're not allowed to look behind the wall. Good luck!" They leave the room.

You walk up to the wall and press a button. A few feet away, a light flashes green. You press the button again. The same light flashes green. "Aha!" you think. "I have figured out what this button does: it causes that light to flash green." On a table to the side of the room is a notepad and a pencil. You jot down your discovery.

You walk back to the wall, and press a different button. Once again, the same light flashes green. You begin to wonder if all the buttons affect that one light. You press the original button to confirm your suspicions. The light flashes blue.

---

Months have passed. You have covered the three previously unadorned walls with notes, with diagrams, with layer upon layer of discarded theory. But you're so close! The machine you've designed perfectly matches everything you've observed. It's so vivid in your imagination that you can practically see it through the wall. There's just a single lever you're unsure about; you can't decide if it's part of a complex mechanical linkage, or if it simply closes an electrical circuit. It would all work either way. You draw both options and place a question mark between them.

You wander down the hall to an office, pop your head in and say to the person seated at the desk: "I think I've figured it out. Could you come take a look?"

---

THEM: "So you're not sure which one of these it is?"

YOU: "It could work either way, so I drew both. I couldn't find any way to determine the answer."

THEM: "Well, that's not very satisfying. Are you sure you tried everything? What about this button, how many times did you press it?"

YOU: "That one? Tens of thousands of times, cumulatively."

THEM: "Have you tried pressing it repeatedly? Over and over again, I mean, without anything in between."

YOU: "I have the notes over here... yes, one hundred times in a row to confirm my theory was correct."

THEM: "Only a hundred? What if it does something different after a thousand presses? You should try that; it might solve your dilemma."

YOU: "I... could, but that seems awfully time-consuming. None of the other buttons did anything different after more than a dozen presses."

THEM: "Yes, but couldn't this button be different?"

YOU: "Maybe, but there's a point where I have to assume I've got it right. After all, there's no way of knowing whether it does something different at ten thousand presses, or a million presses!"

THEM: "All the same, we would really like to know what's behind that wall. It's a bit disappointing to only know what will happen but not know what's really going on back there. Could you try it the thousand presses? Perhaps twiddle some other widgets at random, see if that creates any discrepancy?"

YOU: "But that might never end! If nothing comes up after a day of effort, you could ask me to do it for a week. If nothing comes up after a week, you could ask me to do it for a year. Can't you just accept that either option works?"

---

The moral of the story: there's a limit to knowledge gained by inference. The problem is even worse than the story described, because even if you resolve the dilemma of the lever:

-It's impossible to know that the 200 sextillionth press (and only the 200 sextillionth press) of that button does something slightly different. Your design is wrong, and you'll never discover the discrepancy.

-It's impossible to know that the first time you pressed the button (and only the first time), it lit up a yellow light in the corner that you didn't see. Your design is wrong, and the information needed to resolve it is lost to you forever.

In the real world, maybe we'll get lucky and produce a theory that has only a single interpretation. Maybe there is a discrepancy that rules out all but one solution. (And maybe we'll get extra lucky and it will be easy to visualize.) But even then, we can never be sure. I feel as though the author of the article isn't clear enough about this. You can never know what's behind the wall.