'Trémaux's algorithm, invented by Charles Trémaux, is an efficient method to find the way out of a maze that requires drawing lines on the floor to mark a path, and is guaranteed to work for all mazes that have well-defined passages. A path is either unvisited, marked once or marked twice. Every time a direction is chosen it is marked by drawing a line on the floor (from junction to junction). In the beginning a random direction is chosen (if there is more than one). On arriving at a junction that has not been visited before (no other marks), pick a random direction (and mark the path). When arriving at a marked junction and if your current path is marked only once then turn around and walk back (and mark the path a second time). If this is not the case, pick the direction with the fewest marks (and mark it, as always). When you finally reach the solution, paths marked exactly once will indicate a direct way back to the start. If there is no exit, this method will take you back to the start where all paths are marked twice.'
Sunday, 9 June 2013
Trémaux's algorithm and a few simple rules
'Let families realise, as they start their journey, that all will not be fair weather. Each in his turn may be footsore and may straggle. There will be alluring shortcuts and by-paths down which they may wander and lose their way.' (Alcoholics Anonymous pages 122–123)
If you are in a maze, you will struggle to find your way out through intuition or common sense. What look like promising avenues turn out to be dead ends or to lead you back to where you started. Mazes cannot be thought through.
There are various methods of escaping mazes, each method suited to the design of maze in question. There is one method, however, which works on all mazes:
Make sense? Probably not, but this does work universally. One simply has to follow the instructions, even if they appear, in the moment, to be laborious or counter-intuitive. Each instruction, however, is indeed simple, in and of itself. Why this works as a method may not be self-evident, but work it does.
I have often tried to operate on emotional instinct in the moment, or on the basis of attempting to gain intellectual oversight of my situation.
As with mazes, emotional instinct can be very misleading; as with mazes, intellectual oversight can be gained only with full information. When you are in a maze, you have only what you can see in front of you plus memory. Even if you think you have generated rules for how the maze is laid out, the maze is at liberty to break its own rules. In any case, whatever you see and intuit falls far short of the overview required to plot the most effective and efficient course.
As with mazes, we may or may not be provided with a map, after the event, that plots the course we have taken. Future disclosure will not help us in the moment, however. I have sometimes understood only years later exactly how I navigated a particularly thorny period—only years later will the path typically make sense (page 100).
Mazes cannot be thought through; they can, however, be acted out of, on the basis of principle.
In AA, the principles can be boiled down in many ways, but what works for me is this:
Have a plan for the day—ask God for it (page 86); base my actions on giving, rather than getting (page 128); consult with others (page 80); do as I think God would have me and humbly rely on Him (page 68).
Make sense? Maybe not, but this does work universally. One simply has to follow the instructions, even if they appear, in the moment, to be laborious or counter-intuitive. Each instruction, however, is indeed simple, in and of itself. Why this works as a method may not be self-evident, but work it does.
The instructions are not the Higher Power but the method by why the Higher Power is accessed; they work not because the universe is a cold, dead, mechanism but because there is a higher order and design.
These are the principles I follow and which have solved every problem I have ever had ('Quite as important was the discovery that spiritual principles would solve all my problems'—page 42).
I do not need to think everything through obsessively; I do not need to navigate by emotions; I do not need to try to gain an overview of my entire life—for this is impossible and fruitless; all I need to do is follow these simple rules.