Openings and closures

What we think of as therapy usually includes two people.  One of them offers mainly their ears and the other offers their voice.  These two people speak and listen to each other, they have a conversation, and over time a relationship develops.   

In the background are two apparently neutral actors: space (a room, two chairs, perhaps a couch, hopefully a window, etc) and time (a regular time to meet, the length of the session, a dialogue about past, present and future, questions about how long this will take, etc).  

Space stays pretty still and constant, whereas time moves and plays tricks – this session seems to last forever, that session is over in a flash, even though each is the same length.

Great philosophical and scientific books have been written about how we experience time.  I think it is worthwhile to consider the strange and counter-intuitive ways that time operates in therapy. 

So this is something of a digression, but I hope you find it interesting.  It presents us with a problem – the problem of the three prisoners – and its solution.


The problem is this:

A warden tells three prisoners, “today one of you must be freed.  I have 5 disks – 3 white, 2 black.  I will attach a disk to each of you, where you cannot see it, and I will keep the other two disks hidden.  There are no mirrors.  You must not tell the other two what colour their disks are.  Not that you would want to, for whoever tells me what colour his disk is, and how he arrived at his conclusion, will be freed.”

In fact, a white disk is fastened to all three prisoners.  So what happens?

The psychoanalyst Jacques Lacan, who wrote about this problem in 1945, gave the following solution:

“I am a white, and here is how I know it.  Since I can see that both my companions are whites, I thought that, if I was a black, each one of them would have been able to infer the following: ‘If I too were a black, the other would have necessarily realised straight away that he was a white and would have left immediately; therefore, I am not a black’.  And both would have left together, convinced they were whites.  As they did nothing of the kind, I must be a white like them. At that, I made for the door to make my conclusion known.”

So, all three of them exit at the same time, and with the same reason.


Like me, you may have to read Lacan’s solution more than once to understand it. 

Let us call the “I” who speaks in Lacan’s solution A, and the other two prisoners B and C.

Note that A assumes that B and C think thoughts that A himself does not think.  A makes his deduction on the basis of thoughts which A attributes to B and C.  And B’s and C’s thoughts are clearly hypothetical, since they could only think these thoughts if A was black – which he is not.

If A was black, he would be right to attribute these thoughts to B and C, and they would have immediately left.  But as A makes his deductions, he notices B and C have not left.  They are still in the prison cell.

So, A concludes he is white.  

In most logical puzzles of this type, we have reached our solution and there is nothing more to say.  But in this puzzle, time provokes a complication.

Remember - B and C are also white, so they must be in exactly the same position as A, and must reach the same conclusion at the same time.  All three move towards the door.  But here’s the thing: their conclusion – I am white – was based on the lack of movement towards the door.  Now everyone is moving towards the door!  So now, each hesitates and thinks, am I black after all? Each rehearses his process of deduction, and we shall do the same.


There are three possible scenarios:


 They can all immediately see that (3) is impossible, because each prisoner can see two whites.

So is it (1) or (2)?  To work it out once and for all, A, B and C must use logic, but they must also observe each other’s reactions.  There are two pauses here which occur when A, B and C communicate with each other. Usually, logical problems of this kind can be seen “all at once”.  But the solution to this puzzle evolves as A, B and C find out about what they do not see – and they find this out over time.   

Time is essential to the logical process, and Lacan describes three “times of possibility”.


Something is impossible before the prisoners even open their eyes: three blacks.  This is a given.  So each would know if he saw two blacks, he must be a white. This would be an instantaneous realisation.  It takes only a glance to realise it, so Lacan calls is the “time of the glance”.

A’s next thought requires observing, reasoning and comprehending.  He observes the fact that B and C are both white, and reasons that if either had seen that A was black, they would each think: “if I, C, were also black, B would have left instantly” (or the other way round if B is doing the thinking).  The fact that nobody does leave instantly, that all three stop and think, means that each of them comprehend they are white.

This is a more complex process, and Lacan calls it the “time of comprehending”.

“Hoorah,” thinks A, “I had better declare myself as a white, and quickly, before B or C get there”.  This is the very urgent “time of concluding”.  In A’s mind, it takes B and C the same time to realise that if A were a black, they would be faced with a white and a black and would need to act accordingly.  

There’s a strange paradox here – for B and C didn’t (and couldn’t) actually think this; the thought was imputed to them by A.  But if the situation he considers (A = black) is correct, B and C would be ahead of him – they wouldn’t have needed to spend all this time thinking about it, they would have quickly realised they were a white.  So he has to be ahead of the other two.  If he is not – if B and C beat him to it – he will believe their speediness is because he is, actually, a black.

Lacan says: “It is thus not because of some dramatic contingency, the seriousness of the stakes, or the competitiveness of the game, that time presses; it is owing to the urgency of the logical movement that the subject precipitates [headlong] both his judgment and his departure”.


What does any of this have to do with therapy?  I think our puzzle illustrates something about the therapeutic process.  Our thoughts often belong to the “time of the glance” – snap-judgments, automatic deductions, reactions which happen to us without us quite being in control of them.  As we explore things with another person in the room, perhaps our thoughts become more of the order of the “time of comprehending” – there is something more reciprocal in the nature of these thoughts, as we observe the reactions of the other and let them influence our movements.

But it is only in the third “time” – “the time of concluding” – that a really assertive I emerges: I must be a white.  This is perhaps what therapy aims for, and what I think is fascinating is how this assertive I does not emerge out of nothing, or out of itself, but instead emerges from a movement between the self and the other, between the psyche and the external world.