A universal way to solve problems, from a mathematical genius

Finding the true form of the problem is almost as important as the answer that comes after.
Finding the true form of the problem is almost as important as the answer that comes after.
Image: Reuters/David W Cerny
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It took Claude Shannon about a decade to fully formulate his seminal theory of information.

He first flirted with the idea of establishing a common foundation for the many information technologies of his day (like the telephone, the radio, and the television) in graduate school.

It wasn’t until 1948, however, that he published A Mathematical Theory of Communication.

This wasn’t his only big contribution, though. As a student at MIT, at the humble age of 21, he published a thesis that many consider possibly the most important master’s thesis of the century.

To the average person, this may not mean much. He’s not exactly a household name. But if it wasn’t for Shannon’s work, what we think of as the modern computer may not exist. His influence is enormous not just in computer science, but also in physics and engineering.

The word genius is thrown around casually, but there are very few people who actually deserve the moniker like Claude Shannon. He thought differently, and he thought playfully.

One of the subtle causes behind what manifested as such genius, however, was the way he attacked problems. He didn’t just formulate a question and then look for answers, but he was methodological in developing a process to help him see beyond what was in sight.

His problems were different from many of the problems we are likely to deal with, but the template and its reasoning can be generalized to some degree, and when it is, it may just help us think sharper, too.

All problems have a shape and a form. To solve them, we have to first understand them.

Build a core before filling the details

The importance of getting to an answer isn’t lost on any of us, but many of us do neglect how important it is to ask a question in such a way that an answer is actually available to us.

We are quick to jump around from one detail to another, hoping that they eventually connect, rather than focusing our energy on developing an intuition for what it is we are working with.

This is where Shannon did the opposite. In fact, as his biographers note in A Mind at Play, he did this to the point that some contemporary mathematicians thought that he wasn’t as rigorous as he could be in the steps he was taking to build a coherent picture. They, naturally, wanted the details.

Shannon’s reasoning, however, was that it isn’t until you eliminate the inessential from the problem you are working on that you can see the core that will guide you to an answer.

In fact, often, when you get to such a core, you may not even recognize the problem anymore, which illustrates how important it is to get the bigger picture right before you go chasing after the details. Otherwise, you start by pointing yourself in the wrong direction.

Details are important and useful. Many details are actually disproportionately important and useful relative to their representation. But there are equally as many details that are useless.

If you don’t find the core of a problem, you start off with all of the wrong details, which is then going to encourage you to add many more of the wrong kinds of details until you’re stuck.

Starting by pruning away at what is unimportant is how you discipline yourself to see behind the fog created by the inessential. That’s when you’ll find the foundation you are looking for.

Finding the true form of the problem is almost as important as the answer that comes after.

Restructure and contrast

In a speech given at Bell Labs in 1952 to his contemporaries, Shannon dived into how he primes his mind to think creatively when addressing things that are keeping him occupied.

Beyond simplifying and looking for the core, he suggests something else—something that may not seem to make a difference on the surface but is crucial for thinking differently.

Frequently, when we have spent a lot of time thinking about a problem, we create a tunnel vision that rigidly directs us along a singular path. Logical thinking starts at one point, makes reasoned connections, and if done well, it always leads to the same place every time.

Creative thinking is a little different. It, too, makes connections, but these connections are less logical and more serendipitous, allowing for what we think of as new thinking patterns.

One of Shannon’s go-to tricks was to restructure and contrast the problem in as many different ways as possible. This could mean exaggerating it, minimizing it, changing the words of how it is stated, reframing the angle from where it is looked at, and inverting it.

The point of this exercise is simply to get a more holistic look at what is actually going on.

It’s easy for our brain to get stuck in mental loops, and the best way to break these mental loops is to change the reference point. We are not changing our intuitive understanding of the problem or the core we have identified, just how it is expressed.

We could, for example, ask: What is the best way to solve this? But we could also ask: What is the worst way to solve this? Each contains knowledge, and we should dissect both.

Just as a problem has forms, it also has many shapes. Different shapes hold different truths.

Multiply the essence of every input

While it’s important to focus on the quality of ideas, it’s perhaps just as important to think about the quantity. Not just concerning total numbers but also how you get to those numbers.

To solve a problem, you have to have a good idea. In turn, to have a good idea, it’s often the case that you have to first go through many bad ones. Even so, however, throwing anything and everything at the wall isn’t the way to do that. There is more to it than that.

During the Second World War, Shannon met Alan Turing, another computer science pioneer. While Turing was in the US, they had tea almost every day. Over the years, they continued to keep in touch, and both men respected the other’s thinking and enjoyed his company.

When discussing what he thinks constitutes genius, Shannon used an analogy shared with him by Turing, from which he extrapolated a subtle observation. In his own words:

“There are some people if you shoot one idea into the brain, you will get a half an idea out. There are other people who are beyond this point at which they produce two ideas for each idea sent in.”

He humbly denied that he was in the latter category, instead putting people like Newton in there. But if we look beyond that, we can see what is at play. It’s not just about quantity.

Every input has a particular essence at its core that communicates a truth that lies behind the surface. This truth is the foundation for many different solutions to many different problems.

What Shannon is getting at, I suspect, is that generating good ideas is about getting good at multiplying the essence of every input. Bad ideas may be produced if you get the essence wrong, but the better you identify it, the more effectively you’ll be able to uncover insights.

Doubling the output of your ideas is the first step, but capturing the essence is the difference.

All you need to know

Much of life—whether it’s in your work, or in your relationships, or as it relates to your well-being—comes down to identifying and attacking a problem so that you can move past it.

Claude Shannon may have been a singular genius with a unique mind, but the process he used isn’t out of reach for any of us. His strength was in this process and its application.

Good problem-solving is a product of both critical and creative thinking. The best way to combine them is to have some process in place that allows each to shine through.

Thinking patterns shape our minds. The goal is to have the right thinking patterns doing so.

Want to think and live smarter? Zat Rana publishes a free weekly newsletter for 30,000+ readers at Design Luck.

This post was originally published on Medium.