Late vs Too Late

The white rabbit forgot himself, and all desire not to be seen, preoccupied by the fact he was late, he became restless.  He ran towards the rabbit hole, forgetting all manner of caution and precariousness, this was ultimately the reason Alice spied him and gave pursuit.  The white rabbit was in a panic, brought on by a fixation on something that was going wrong.  Alice on the other hand was in no panic, she was merely a curious child, who saw someone else in a panic and sought to help, ultimately that was the reason that led her to tumble down the rabbit hole.

When we are late we forget ourselves and our logic and reason, overcome with pressure of the impending, we rush.  There's a fine line between late and too late however.  The white rabbit was late, but he wasn't too late, he still believed he could salvage something.  That mentality is one that I find fascinating because the line between late and too late, whilst very fine, and very clear in hindsight, is not one that is easy to predict.  It is almost always the case that you do not know when the line will be crossed, until it has been crossed.

How late is too late?  That is the question, and it doesn't apply only to schedules and organisation, it extends far beyond.  When time and effort must be devoted to any endeavour, no matter the context, there is always a point at which time concedes defeat, and like a student with an exam paper rushing to fill in the last few answers before time is up, it is often the case that the paper is taken away or that we are forced to stop not by our own accord but by outside forces.

Alan Turing devised a number of tests and theories in his life that were devised to distinguish between human intelligence and artificial intelligence.  The most famous of these tests is the imitation game, where 1 person interacts with 2 entities, one is a human, and one is a computer.  The computer is said to pass the test if you are unable to determine it is a computer.  While this test is fascinating it is not the area of his work which interests me most.  Instead the area that interests me most is the Halting Problem - this is an area of study concerning machine intelligence.  Specifically the halting problem tests whether a machine intelligence can identify when to stop, when faced with a problem for which a solution is certain to exist, but it is not clear how long the solution will take to find. 

For example, assume I have a locked door and a key ring with an infinite number of keys, there exists one key in the set which will open the door.  How many keys do you try before you stop?  A program which defines only the objective to open the door will try every key until the end of time.  A human will try so many keys before they stop.  Even though the solution is certain, and the process is easy, the time taken eventually reaches a point where you realise the effort is not worth any potential gain.  The halting problem is essentially the ability to make a program realise when late becomes too late.  When the line is crossed.  When it's not worth it to keep trying.

So the question is, how do you know when to stop?