Solving The Unsolvable In 3 Steps

Legend tells us that Alexander the Great visited the city of Gordia, in asia minor, before he conquered most of the known world. The shrine in the city held an oxcart that was fastened to a pole using an intricate knot with no loose ends. It had been prophesied that the one who could solve this Gordian knot would become the king of the world. The Alexander solution to the problem of the Gordian knot has become a timeless metaphor for the solution of intractable problems. It was, according to himself, his greatest victory.

There are actually two different solutions to the Gordian knot with somewhat different implications. Aristobulus tells us that Alexander removed the pole from the oxcart and thereby exposed the loose end of the knot. This implies that sometimes, the way forwards is to look for a clever shortcuts that cut through all the difficult steps. The other account, the classical one, from Plutarch tells us that Alexander used his sword and cut the knot in two. This would invite us to look for an elegant out of the box solution, simple and resolute or perhaps even a brute force solution. The key to either of these solutions is to look at the problem from a new perspective or to redefine the goal.

Neither of these example provides us with a guide of how to solve other intractable problems. But it tells us that the solution is often visible as a result of a single idea, a shift in the frame of reference. In a way the legend illustrates the hindsight bias, i.e. the answer always looks obvious after you hear it. What the legend does not highlight is a key component often required to solve an intractable problem. To fully explore this we want to look at the three step process of problem solving:

1. The first step is to make sure that you clearly know what the goal is. Often what you are trying to do is not getting you any closer to the intended outcome. What are you actually committed to accomplishing and how will you know that you have gotten there? If you do not know where you are going it is pointless to ask how to get there. Serendipitous breakthroughs are the only option when the goal is not set. In the classical account of the Alexander solution the goal was redefined from solving the knot to separating the oxcart from the pole and this made the problem much easier. As soon as the knot was cut, the cart was free.
2. Once the goal is clear, the second stage, is about outlining what specific known actions there are to take. These may or not be sufficient to accomplish the objective, but this is where we start. If you really think about it, there is typically a path forward right in front of you, straight and narrow. Do not make it too complicated.  Start with what you know. Thinking about a problem is important but nothing will happen until you take action. Do not get stuck in analysis paralysis, your plan will likely not survive the first encounter with an obstacle but it will send you towards your goal. The plan will have to evolve continuously to address the challenges of an ever-changing landscape. It is key to set out a plan and get moving.
3. The third step is typically the hardest part: doing what you set out to do and deal with the challenges and breakdowns that will occur. If you can manage to keep yourself on track you should be on your way to endless success, but please let the rest of us know how you did it. For everyone else, being a part of a team and having external project support and coaching are great tools. Find someone who will support you to do what said you would do at the time you said you were going to do it. The person should also invite you to rethink the strategy when things don’t go as planned and keep the goal in sight.

Now if we take a step back we see that the solution of the Gordian knot is best set in the larger context of Alexander’s grand campaign to conquer the world. This was the grand goal he identified (step 1) and to achieve this goal he had to set his plan in motion by first fulfilling the prophecy and solving (cutting) the Gordian knot (step 2). The big and possible unappreciated challenge was to go out and conquer the known world (step 3). Without actually fulfilling his grand goal few would have heard about a macedonian prince and his encounter with an oxcart.

This is a take home message, both humbling and empowering, that the initial solution you are looking for will most likely not prove as complicated as you fear but there will be no shortcuts to achieving your long term goal. In the end your greatest victory might not be to figure out how to find the first loose thread but to stay committed to your goal in the presence of challenges great and small and get the job done.

So let’s ask the question often, what is my Gordian knot, right now? In which step am I stuck? What distant objective would become one step closer if I just solved that one problem? Let’s focus on the objectives that really matter to you, the ones that you are passionate about and where there is nothing you would not do to achieve them. Let’s work towards them now and practice cutting some knots along the way. With each resolved breakdown, each knot solved, you will develop proficiency in problem solving and learn how to approach challenges and eventually reach your goals.