How Archimedes in a bathtub can help you solve problems at work

How do you solve hard problems?

Do you relentlessly and actively grind through the problem, trying to force the answer into existence? Or do you go play the violin and let the answer come to you?

Both methods are valid. I’ve certainly done a LOT of the former, but the latter can create bigger breakthroughs, and it’s called combinatory play.

I mentioned playing violin, but violins aren’t specifically required. Albert Einstein, who is credited with coining the term combinatory play in a 1945 letter to French mathematician Jacques S. Hadamard, was famous for playing the violin as a strategy to create breakthroughs.

Einstein credits music (playing violin and piano) with unlocking his breakthroughs in general relativity. Einstein worked at the very edge of physics for 20 years before he published his seminal paper on general relativity. That was a very hard problem to solve!

Thankfully most of us aren’t trying to solve something like general relativity. Even though combinatory play is a long game, we can thankfully make progress in fewer than 20 years. 👨‍🦳

Today I’ll walk you through examples of famous breakthroughs using combinatory play, a model of how it fits in with related concepts, and how you can put it into practice yourself.

Examples of Combinatory Play Breakthroughs

Once you know what to look for, you can find a TON of these examples throughout history and into modern day.

Archimedes and “Eureka!” - This tale, although a likely embellishment since no one wrote it down in 250 BC, is the most common example of the idea of combinatory play. Archimedes was tasked with figuring out whether a golden crown was counterfeit (there was suspicion that it also contained silver). Struggling with the problem, his eventual breakthrough came when he discovered the concept of buoyancy while noticing water displacement stepping into a bath. He ran down the street yelling, “Eureka!”, which translates into “I’ve found it!”

Leonardo da Vinci and Flying Machines - Leonardo combined his love of nature with mechanical principles to produce detailed diagrams of flying machines over 400 years before the technology for powered flight made it possible.

Charles Darwin and the Theory of Evolution - Darwin was influenced by his forebears, James Hutton, who had a conception of the vast expanse of time, and Adam Smith, who wrote theories of the free market, to generate his theory of evolution. Note that Darwin worked on his theory for 28 years before publishing “On the Origin of Species”!

George de Mestral, his dog Milka, and Velcro - In 1941, on a walk with his dog Milka, George noticed seeds sticking to his clothes and his dog. Curious, he investigated them under a microscope and noticed the hooks on the seeds connected to loops on his clothes. Ten years later he submitted his patent for what became Velcro.

Einstein’s Explanation of Combinatory Play

“…combinatory play seems to be the essential feature in productive thought…”

— Einstein in his 1945 letter to Hadamard (one source for the original text is here)

Einstein’s letter, although only 80 years old, is actually quite hard to parse! Here’s what I’ve been able to piece together as his explanation for it:

He has non-linguistic and abstract elements rattle around in his head. Very specifically these are not structured or verbal constructs. The elements are visual, audible, and muscular in nature.

He combines these elements and plays with them before trying to structure them logically or verbally. He keeps the visual and sensory experience first, later turning it into words to communicate with others.

The goal is finding logical connections, which means it’s not random. He’s putting some conscious guidance around it, while also letting his subconscious work.

This is why playing the violin worked for Einstein. He was doing something audible and muscular (moving around while playing) and letting his mind work on finding the connections he needed.

How it Connects to Other Concepts

There are some supporting concepts that make combinatory play more likely to be successful.

Exposure
The first related concept is exposure. Live an interesting life and expose yourself to lots of ideas.

Read outside of your field. Go to interesting places. Do new things. Talk to people. Be curious.

At the top of the research process I drew for this newsletter is “live an interesting life.” The more things you expose yourself to, the more raw materials you’ll have available to you in later steps. It’s also why I read a wide assortment of books; you never know what’s going to come in handy!

“As these examples show, to connect apples and oranges, you have to collect them first. The more diverse your collection, the more interesting your output becomes. Pick up a magazine or book about a subject you know nothing about. Attend a different industry’s conference. Surround yourself with people from different professions, backgrounds, and interests.”

— Ozan Varol in “Think Like a Rocket Scientist”

Cross-Pollinate and Think Laterally
Getting exposure to new ideas doesn’t help if you can’t figure out how to apply them to new areas! Humans throughout history have been getting sticker burrs stuck to them, but it wasn’t until it happened to George de Mestral that we get Velcro.

Think laterally. Reason through analogy. Be intentional about drawing connections between disparate domains. Teach yourself to be open to this way of thinking and over time it becomes more natural.

“Usually someone has often already found an answer to your problem – just in a different domain.”

— Rory Sutherland in “Alchemy”

“Don’t contain your learning to your own profession or major. Read and learn as broadly as possible.”

— Morgan Housel in this article on Active vs. Passive Learning

Combinatory Play
Einstein gave us his model for this already. Engage in something physical. Be intentional about drawing connections, but without being too forceful about it. That balance is a little weird, but the goal is to let your subconscious be part of the solution. You can’t do that if you’re consciously trying to force a solution.

Einstein would sit and play the piano, then pause to write down a note, then get back to playing. He’d do this over and over. I wasn’t there, but I can imagine him setting the intention to play, and if he got an insight - great - and if he didn’t, that’s okay, too. He knew he couldn’t control the outcome, so he created the space for the outcome to be possible.

Rest
Since the subconscious is involved, you need to give your brain time to let everything sink down into the deeper recesses. Get good rest. Go play. Build new connections in the background so that they’re available to you later.

“however you find the time, it’s vital to create space in each day to let your thoughts wander beyond your immediate job responsibilities, to turn things over in your mind in a less pressured, more creative way than is possible once the daily triage kicks in.”

— Bob Iger in “The Ride of a Lifetime”

Loop!
This is not a linear process, but an iterative loop. Exposure gives you new material, which you can then cross-pollinate for use in combinatory play, after which you rest. Resting makes a new insight in future combinatory play possible. Cross-pollinating ideas creates an opportunity for future exposure to latch on to it.

This loop also info informs why it can take years to get a breakthrough for a truly novel problem. You have to have the right exposure, with the right cross-pollination, and your subconscious needs to make the right connection.

How You Can Employ the Combinatory Play Loop

Explore unrelated things. An opera. A video game. Farming. Nature. Magazine design. You never know what’s needed, but you want to feed yourself lots of good high-quality information from diverse sources and walks of life.

Let your mind wander. This is tough for most folks today because of phones and social media, but it’s worth making space for. Instead of picking up your phone to scroll when you’re bored, just…be bored for a while. Stand in the checkout aisle and think for bit. It doesn’t matter what it’s about, you’re practicing making space for serendipity in brain connections.

Get physical. Move around. Go for a walk. Get up and use the whiteboard. Play a game like you used to when you were a kid. Climb a tree. Get dirty. The goal is to engage your physical body so that the mind is free.

Be musical and creative. Draw. Pick up an instrument. You’re trying to get away from the verbal and logical constructs that you’re used to, and give way to a different kind of thinking.

Set an intention. Remember that Einstein said the act of combinatory play wasn’t random; you have a goal in mind.

For me setting an intention looks like loading up a question I want to answer before going on a long walk. Yes, my mind wanders while I’m walking, but that’s the point.

Like in meditation, if I notice I’ve really lost the plot, I’ll bring my brain back to the question, but otherwise I’m okay with my subconscious taking over. What feels like wandering may be your brain trying to make a connection. You can’t force it!

Let your subconscious work, and gently redirect if needed.

Call to Action

Big breakthroughs are a long game, but you can start practicing today!

When was the last time you exposed yourself to an idea outside your domain? Go pick up a magazine or book that interests you in an unrelated field.

What big problem are you working on? Go for a long walk, and before you go, set an intention to work on that problem. See if your brain comes up with any novel ideas. Bring something with you for notes by the way! I’ve had lightbulb moments an hour away from my house without a phone or a notepad, and I spend the hour home worried I’m going to forget!

Let me know how this goes for you! What did you try? What did you pick up to read? I’d love to hear how this goes. Drop me a line at kevin@catalyst.group18.co 😁

Kevin