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The Knot: How to Think About Problem Solving

The way we think about solving problems is ineffective. Here's how we should think about them.

0xZakk
0xZakk
. 3 min read
The Knot: How to Think About Problem Solving

The way most people think about problem solving is unhelpful to their process of actually solving problems. Why? Because we tend to think of problem solving as a linear process in which we can work through a series of steps. However, in reality, we discover solutions to problems by iterating and experimenting.

When most people approach a problem for the first time, they expect to work through a series of three steps:

  1. Break the problem down into smaller pieces
  2. Solve each of those smaller pieces
  3. Bring the pieces back together for a final solution

When we finish the first step, we move on to the second, and then the third.

But problem solving is nothing like this.

Part of the issue is in the name, problem solving. Using a verb makes us feel like we have control of the process when we don’t. Really, we discover solutions to problems, so a more appropriate term would be problem solution discovery.

A Better Metaphor

We think of problem solving as walking through a series of steps. But a better way to think of problem solving is like untying a really big knot of string.

Imagine a really big knot. I’m talking really big here - like the size of your fist. The threads are tied back and looped through each other hundreds of times. If you had to untie that knot, how would you do it?

You’d start by picking it up and looking at it. You’d find a thread that looks loose and you’d pull on it. You’d pull on it for as long as you could. Then, when you couldn’t pull that thread any further, you’d find another to pull on. Eventually through this process, clumps of the knot would start to come untied.

But, just because you’ve made progress on one piece of the knot, doesn’t mean that is the side that will eventually lead the whole thing to unravel. More likely, you’ll hit a dead end and have to pursue untying the knot from another side.

Did you waste your time working threads on a part of the knot that eventually lead to a dead end? No, of course not.

Eventually, you would have an untied knot. But you’d get there through pulling at loose threads until the knot came undone. You can’t linearly work through breaking the knot into different pieces, solving those pieces, and bringing them back together. You could try, but you’d be fooling yourself.

Untying Knots

When you take a big problem and break it up into different pieces, you’re doing so based on your understanding of the problem and the context it is in, which is imperfect.

If you go through the thought experiment of imagining a really big knot and how you’d untie it, you can see how this doesn’t work. The threads go throughout the knot in ways that we can and cannot see. While we may be able to break a problem up into logical pieces, we generally can’t see all the ways these pieces interact.

Additionally, we can’t realistically look at this big knot, see how all the threads relate and know exactly which threads to pull on to untangle the thread. We have to discover the solution by picking at the problem until we make some headway.

So it is with any meaningfully big problem: a purely analytical thought process doesn’t work. But it is the only way we are trained to think in school, so it’s the way we approach all problems — big and small.

You see this kind of thinking when someone says it would cost $330 billion to solve world hunger1 or $300 billion to solve climate change2 — both real estimates, based on that kind of analytical, fragmented thinking. It won’t cost $330 billion. It might not necessarily cost more, but the problem is way too big and complicated to be reduced to a single number like that. It’s not as if someone with $330 billion could just spend it and solve world hunger.

It’s the same line of thinking that would lead someone to spend hours analyzing our metaphorical knot, identifying it’s different parts, looking for a single thread they could pull to unravel the whole thing. We can’t isolate the parts of a problem and solve them independently.

Footnotes:

  1. Ending world hunger by 2030 would cost $330bn, study finds, The Guardian, October 13, 2020
  2. How to Halt Global Warming for $300 Billion, Bloomberg, October 23, 2019
Learning

0xZakk

Zakk is a software engineer and writer. In 2021, he co-founded CabinDAO.