A child you made deaf like that would still discover sound as the vibrations that distorted the lenses on the eye once detection got sensitive enough.

I dispute the very notion that it's possible to cut someone off from the basic nature of reality, because you must fundamentally have constructed the cage from that reality and thus their interaction with their cage will reveal its mechanics (and hence the mechanics of reality) to them.

You can only make it take more time by suppressing noise, but eventually the "errors" will carry accurate information inside. (And someone inside can accelerate this process by causing noise in certain manners.)

> lacking outside interference

Depending on your interpretation of quantum mechanics, this is either impossible (Bohmian; maybe all of them) or insufficient (Copenhagen, MWI) -- in either case, small "errors" will reveal information about the actual nature of reality.