How to Solve your Problem with more Problems

As an engineering student my college education can be summed up in one sentence: Here is a problem, now what is the solution?

The Classic Approach:

There are tons of methods and techniques you can use to find the solution but they are very specific. They only work on a very narrow type of problem resulting in all of this hard work and effort mastering a technique with limited value.

Problem Seeking Approach:

What if there was a technique that would work for all of your problems? A magical formula that gave you the solution to anything? Well, I don’t claim to know that, otherwise I’d be kayaking around my own private island right now.

What if, instead of looking for the solution, you look for another problem? Sounds counter-intuitive. You already have one thing to worry about, why make more? It’s all about framing; taking your initial problem that you don’t know how to solve, and 'morphing' it into a problem you do know how to solve.

Perspective

When given a problem, you will naturally look at it in a particular way. Take for instance this picture of a rabbit/duck. My eyes naturally look at its eyes making me see a rabbit. By becoming aware of my own subconscious tendency (I didn’t choose to look there initially, I just did), I can identify what I need to do in order to change my perspective. In this case, I simply have to look at the rabbit’s ears, which change into a duck’s bill, and now I see the duck.

This is a simple example but can apply to any problem. Have a machine break down? You will intuitively try to fix it a certain way, if that fails, identify what you intuitively focused your attention on and force yourself to focus on the parts/areas you didn’t.

Break it up

Let’s say you’re given a really hard problem, like generate more energy than you spend in a fusion reactor hard. The people working on these questions don’t just tackle that one big question, they break it up into 1000’s of easier questions that can then collectively solve the big question. This is something you can use with any question.

Here’s a fun example, Takeru Kobayashi and hot dogs. For those who don’t know, Kobayashi is a competitive eater, he makes a living by eating with speed and quantity. Nathan’s hosts a famous hot dog eating competition annually to see who can eat the most hot dogs in 12 minutes. In 2001, Kobayashi gave it a try, and DOUBLED the world record. How? He broke down the problem. The hot dog comes in two parts, a dog and a bun. He found that the bun was too dry to eat quickly, so he dunked it in water. He found that the dog was too long to eat quickly, so he snapped it in half to eat it. These simple, and now obvious changes, made him a legend in the competitive eating scene and go to show how splitting up a problem can generate a wonderful solution.

Final Thoughts

It’s important not to fundamentally alter the problem you are trying to solve. If you do, it’ll result in a solution that doesn’t work with the initial problem you had and you’ll be back at square one.

That being said, the next time you are given a problem don’t think, “Here is a problem, what is the solution?”. Think, “Here is a problem, now what is a better problem?”

Thank you to my Differential Equations/Linear Algebra professor Dr. Niloufer Mackey for inspiring me to write this article through her teaching of Eigenvalues and systems of DE’s.