We left of at this:
The player reads the dice, which adjusts (influences) the picture in his head. The player reads the picture in his head which adjusts (influences) the dice. Now, if that's happening just in his head, he might as well be playing on his own. The players need to communicate the pictures in their heads to others. Let's talk communication.
In some fucked up ideal world, play would look kind of like this. People all imagining the same thing together. But that's not how it works.
In reality this is more like what's happening. Each person is imagining her own thing. There is some overlap where their individual imaginings coincide more or less perfectly, but in general it's always going to be different mental pictures. It's more like a storm of pictures. However, there is a bare minimum of common understanding. You could say that the storm cloud supports this bare minimum [white cloud], but also that the shared understanding is the underlining picture, the fundamental building block that we all build on. My favorite example is this: "Imagine we're on a boat at sea.". Everybody is imagining a different boat, a different situation, different colours all. But there's still this shared fundamental assumption that we're on a boat at sea. That's where we start.
To be able to play we need to constantly communicate our mental pictures to others at the table. Maybe our mental pictures are different, but by sharing them we come to a shared understanding of what's going on, who's standing where etc. If Red is imagining a bright blue square and Blue is imagining a dark blue square, they're fundamentally still talking about a blue square. Yellow on the other hand is thinking about a yellow triangle, and not sharing, so it doesen't feature in the shared understanding of things. If I think the orcs smell of rotten meat, but I don't communicate it, then it doesn't exist.
The usual defense of this is usually "But your character wouldn't know what's down the corridors." which is a valid and fair stance of course as the character's perception is limited. But the character could gain clues, hints, even straightforward answers by analyzing the environment, questioning the locals, gathering rumors, using divination etc. So there is no reason why information vital to making a valid, meaningful decision would not be communicated. But that's a rant for another time.
That's all for now. What else should I draw?