The Gordian Knot Problem-solving Method

This short piece is here to introduce a problem-solving concept I’ve had and wanted to share.
The eponymous example deals with an outrageously sized knot. It was said that whoever could undo the knot would rule the world. When Alexander the Great happened upon it in his conquest of Egypt, he took out his sword and sliced through the rope.

One of the hardest things about solving tough problems is overcoming implicit rules. We limit the scope of potential solutions by unspoken convention and rules. In many cases, scientific discoveries have been the result of someone willing to discard a fundamental rule and see where their work led.
So here’s my method when facing with a difficult problem:

  1. Identify an extreme solution without regard for cost, risk, morals, convention, or unintended consequences.
  2. While maintaining a working solution, take those factors into consideration
  3. If you fail to come up with an acceptable solution, try a different extreme solution.

The point of this is to start with a solution and work your way back to an acceptable solution. Most people start from acceptable non-solutions and move to acceptable solutions. This method starts with solutions and moves to acceptable solutions.

By allowing both acceptable and unacceptable solutions until the end, more lines of thought can be explored.

Let’s do an example. There’s a road near my house which is perpetually busy and backed up, and it will probably never be fixed.

The problem is that it connects arterial roads and highways while also serving as an arterial roadway. The result is too many stoplights, too closely spaced, for the amount of traffic using it.

The Gordian Knot solution to this is simple: eliminate half the traffic lights(or more). Many of the lights serve areas that are interconnected via other roads. Make local traffic use those and minimize the stops thru traffic has to make.

That’s the Gordian Knot Solution. Now we need to factor in all of the other considerations. Local roads would need to be upgraded, widened and extended. Businesses at intersections would require easy access to the roads.

Cost is still an issue. However, I live in a county that has no debt aside from amortized capital expenditures and no year-to-year deficit. Getting the money is largely a matter of will.

Impact to traffic during the change is another concern. If it is done incrementally: upgrading nearby roads, then eliminating a light, then moving to another part of the area; it can be done with little impact.

So there you have it, a simple way to come to a solution to a difficult problem. The biggest trouble is it might not be a solution you can stomach.

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