Here, however, Lacan points out how this solution requires a double delay and a hindered, interrupted gesture. That is to say, if all three prisoners are of equal intelligence, then, after the first delay, i.e., upon noticing that none of the others is making any move, they will all rise at the same moment — and then stiffen, exchanging perplexed glances: the problem is that they will not know the meaning of the other’s gesture (each of them will ask himself: “Did the others rise for the same reason as me, or did they do it because they saw on my head a black hat?”). Only now, upon noticing that they all share the same hesitation, they will be able to jump to the final conclusion: the very fact of the shared hesitation is a proof that they are all in the same situation, i.e., that they all have white hats on their heads. At this precise moment, delay shifts into haste, with each of the prisoners saying to himself “Let me rush to the door before the others overtake me!”*
* And, perhaps, the (future) master is simply the one who takes a chance and is the first make the move, i.e., to say “I am white”: he becomes a new master if his bluff pays off.
Slavoj Zizek 1993 Tarrying With The Negative
–can a flag or a gesture pass by itself as a synthetic a priori judgement?