The Parable of the Optimization Algorithm

What should my first blog post be? I am sufficiently confident in this argument that I have presented it over the pulpit at church. And I think it also captures my personal peculiarities well.


Prerequisites: None.

Originally Written: September 2016.

Confidence Level: Core religious belief.



Suppose that the most important goal in your life is to find the point in the United States with the lowest elevation. What would you do?

You don’t have access to the internet or to any encyclopedias and you don’t remember the correct answer from elementary school. Or perhaps, there are encyclopedias, but they all say such different things that you can’t rely on them for the solutions. What would you do?

Figure 1: Where is the lowest elevation? Source.

One idea is to start where you are now and walk downhill. If you wish to get to the lowest elevation, decreasing your elevation seems like an excellent idea. Sometimes, as you travel, the path becomes too difficult, and you sidetrack a bit and go temporarily uphill, while still striving to lower you elevation. Sometimes, as you travel, the path becomes too easy, and you sidetrack a bit to go explore other features of the landscape that catch your eye.

There is an obvious problem with this plan: the final result of your efforts depends on where you start.

If you start anywhere in the eastern $ 2/3 $ of the country, your best efforts will lead you to the Atlantic or Gulf coast. There, you conclude, based on your experience and the experiences of countless others like you, that the lowest point is not unique. Even though different people end up at different locations along the coast, as long as they continually strive to walk downhill, they will eventually end up at their result.

This conclusion is wrong. There is a unique lowest point in the country. It is at latitude $ 36.5^\circ \text{N} $ and longitude $ 116.9^\circ \text{W} $ and is more commonly known as Death Valley, California. In order to get there, you not only have to walk downhill, but you also have to start in the right location. What locations are good places to start is not obvious unless you already known the solution. It might be wiser to start walking downhill from the lofty heights of the Sierra Nevada and to start on the banks of the Chesapeake Bay.

Before resolving this problem, let’s first begin to consider the interpretation of the parable.

If the Creator of the Universe cares about humanity, then the most important goal in your life should be to become as close as possible to this Creator. Lower elevations in the parable correspond to being closer to God.

The apparent way to draw closer to God is to look at where you are in your life and do the simple things that bring you closer to Him. We often call these the Primary answers because we learn them when we are still children. You should pray, read your scriptures, and go to church. These simple things correspond to walking downhill in the parable. Sometimes, when things become too difficult, so we stop doing these for a while and move further from God as a result. Sometimes, when things become too easy, we allow ourselves to pursue distractions that may distance us from God. However, as long as we return to praying, reading our scriptures, and going to church, we will continue to draw closer to God.

Although the Primary answers will draw you closer to God, how good the final result is depends on where you start. Even if you have done all of things that you are supposed to do and even if you have developed a closer relationship with God as a result, that doesn’t mean that you are as close to God as you might be. This (partially) explains why there are so many different religions. Even though all of these people are trying to get closer to God, the landscape is complicated. Their best efforts may lead them to dramatically different places. Even if two people started close to each other, there might have been a divide in between them and so they end up in different watersheds, following different religions to draw closer to God.

How do we overcome this problem? If we have spent our entire lives trying to get closer to the Gulf Coast, why would we climb the Rocky Mountains in the hopes of eventually finding Death Valley?

Doing so requires a great leap of faith: a major decision made on the hope that there is something better at the end of this journey. But how do we make the leap of faith? How do we know if we need to? How do we know which leap of faith to make?

A computer scientist familiar with optimization algorithms might suggest the following: Instead of starting with a single point, why don’t you start with a thousand points, randomly distributed across the country. Walk downhill from each one until you reach the bottom. Then, you can compare the results and determine which one is best.

This is not a good option for us. If we wanted to pursue it and we could start where we are, walk downhill for a while. After following this path until we think that we have reached its bottom, we could abruptly move somewhere else and start all over again. Even if we end up on a path that leads to Death Valley at some point, we would soon switch to a different path to check if anything else is better. Most of time would be spent at high elevations, restarting on new paths that may or may not lead where we want to go.

This option corresponds to trying out as many different religions / ideologies as possible during the course of our life. Every time we change religions, there is some sort of disruption in our relationship with God as we leave our old path and start a new one. Hopefully, this disruption will be brief and will soon lead to a closer relationship than was previously possible. However, if we are just randomly picking religions to follow, there is no justification for this hope. We will spend most of our time farther from God than we would if we had stayed with whatever religion we started with.

There is a better solution to our problem.

Luckily, we are not alone. We can look at the experiences of other people to help guide our decisions. When we interact with other people, we can see if they are happy, we can see how strong their families are, we can see how selfless and charitable they are, and we can see how they interact with their church. All of these things indicate how close their relationship to God is.

We should not make a leap of faith alone. Before leaping, we should look at the people who are already close to the destination and ask: Are they closer to God than I think that I could become if I stay on my current path? If the answer is yes, then we can have confidence in our hope that this leap of faith will lead to us having a closer relationship to God.

Our leap of faith could end up being the wrong decision. In that case, we can go back to where we were before and continue down our previous path. The only cost was a delay along the way. But if our hope and faith were well founded, then our leap will not be a mistake. We will continue to become closer to God, and to a greater extent than we could have if we had continued down our original path.

Thoughts?