“The perfect is the enemy of the good”Voltaire
Have you ever wondered where to go next in life and have been asked “If you could do anything in the world, what would it be?” And you may have thought to yourself, “Well, I can’t do anything in the world anyways so my answer is meaningless.”
But the truth is, we can’t be afraid of visiting the depth of questions like this. While the premises, might seem unrealistic, we have to understand it is simply more unrealistic to make life choices while factoring in everything. There is simply too much information to process when we consider, say, what we want to do in life. So we intuitively simplify our problem to make it easier to solve.
But is this intuition correct? Perhaps we are right in thinking we are tricking ourselves by asking such an easier question. However, I believe this is the correct approach. And we can even show this from a technical standpoint.
The Dilemma of Efficiency
There’s an infamous algorithm problem known as the Traveling Salesmen. The problem is defined as a salesman who needs to visit a full list of cities. And he must cover as few miles as possible without going to any town twice. From this, we need to find a method for the salesmen to find this shortest path.
Short Answer: He can’t. So don’t bother trying to figure this out. Well actually, he can. It’s just that the only known solution at the moment is to check all possible paths and then choose the shortest one. The only problem with that solution is that, for a large list of towns, the number of possible orderings grows in factorial time (for 3 towns you need to check 3!= 6 possibilities. For 10 it is 10! = 3628800. Imagine how quickly this can grow!)
So does that mean the salesman can never start his journey if he has too many paths to compute? Of course not. We simply define the problem differently. Perhaps the salesman can visit towns twice, and there is no cost to him traveling backward. Then we can easily find what would be close to the shortest path in just one shot. While it isn’t the optimal solution, at least it is a solution.
And in fact, it’s not a bad one at all. The solution I’ve described is a common computer algorithm that traverses a graph to find what is known as the minimum spanning tree. And in fact it’s been used to find the shortest path to visit every single town on Earth within .05% of the optimal solution .
And the idea behind this is simple. It’s what computer scientists call “constraint relaxation”. Rather than finding the optimal solution, we relax the problem a bit to find the next best things. Something extremely useful when we have no idea how to find the optimal solution. But why am I telling you this?
The Freedom of Relaxation
I’m sure you’ve been in a situation that you just feel stuck in. Maybe you have work to do that just can’t seem to get done. Maybe you have errands that you don’t want to do. We ask why we have to do all things.
But the truth is, we don’t have to do anything. It’s just that there’s a cost to not doing certain things. We don’t want to sacrifice anything, so we strive for perfection. But maybe we are willing to accept that cost.
The truth is, the optimal solution to many of life’s hardest choices have inefficient, and likely impossible, methods to find them. But learning to give up this idea of perfection means we can analyze much simpler problems. We can learn to relax, just as computer scientists do.
So why is the question, “If you could do anything in the world, what would it be?” and its many variants important. Because it’s the closest thing we have to finding an optimal solution. It’s a question worth pondering because one can actually ignore other factors such as finance, feasibility, etc. and just distill one element: our passion. And maybe that element is more important than anything else.
The next time you face a difficult choice, where it seems like there’s too much to factor, trust in the algorithm. Just relax.
 Algorithms to Live By – Brian Christian and Tom Griffiths