Yet another thought experiment:
So consider an observer $O$ falling directly into a static spherical black hole. Now $O$ can be viewed as a physical system consisting of different parts exchanging information, however once $O$ enters the Event Horizon, any pieces of $O$ cannot send information in a direction that doesn't have positive directional component towards the center of the black hole.
Furthermore suppose we have two pieces of system $O$, $A$ and $B$ such that $B$ is closer to the center of the black hole than $A$, then if $A$ transmits any information to $B$ it can never receive anything from $B$, because such a transmission of information would mean that SOMETHING is moving away from the singularity, yet inside the Event Horizon.
So given that, it's not clear to me if the notion of "3 dimensions" makes sense for observers that have entered a black hole. Since as they are making their transit towards the singularity, any motion in the radial dimension, must necessarily be forward, and cannot be "undone", and so they don't appear to have any mechanism for measuring this 3rd dimension.
But that is just weird for me to consider, so I wanted to ask: if the idea I just considered makes sense, and if this would be a relatively accurate picture of what goes on once is sufficiently deep past the Event Horizon.