Please learn from our mistakes

No-bullshit lessons in business and careers. One mail every day. 15k+ readers love it. Join in?

Oops! Something went wrong while submitting the form.
5 Apr

Thinking in negative space

I'm sure that by now, most of us have seen this illustration and know what it's meant to convey.

Yeah yeah, it is for representing survivorship bias. For those who do not know the story, here it is, in short:

During the World War, when American fighter planes returned after fighting battles over Europe, they were riddled in bullet holes around certain areas, like the fuselage. Naturally, the obvious suggestion by people working on those planes was to armor and reinforce those areas where there was a high density of bullet holes for added protection.

But as Abraham Wald, the mathematician commissioned to work on the problem saw it, that was the wrong way to think about the armouring problem.

“The armour doesn’t go where the bullet holes are. It goes where the bullet holes aren’t: on the engines.”


Wald reasoned that if the damage had been distributed evenly across the planes, the engine casing too would have been riddled with bullet holes. But this wasn't the case. He realized that the missing bullet holes around the engine were on the planes that didn't make it back.

The planes were returning with fewer hits to the engine because the ones that did get hit in the engine didn't survive to make the journey home. On the other hand, the planes that made it back with numerous bullet holes in the fuselage provided strong evidence that hits to the fuselage were tolerable.

But the dead planes didn't register in the data. So, the unquestioned axiom others went ahead with was that maybe planes were likelier to get hit around their extremities in general.

Wald questioned this unquestioned belief and factored in what was missing in the data: the planes that didn't make it back.

However, this essay isn't about survivorship bias.

It is about something more fundamental that helps people like Abraham Wald arrive at non-obvious insight consistently and repeatedly.

I like to call it Thinking in Negative Space.

Let's say, for example, you run an online survey via email, asking your customers how often they open their email.

Now, if you were to go by the survey results only, you would think that most of your customers open their emails quite often. You would generalize this finding to all customers. But that would be a mistake. Just by virtue of conducting this survey via email means everyone who responded to it is likely to check their email often.

But the negative space — the customers who do not open their email often — never took the survey so you didn't account for their preferences. Only looking at survey results, in this case, would have been quite misleading. To get a clearer picture, you also need to hear from people who never took the survey and thus never recorded their preferences.

I see a similar thing happen when someone conducts a poll on Twitter asking people what social media platform they use more: Twitter, LinkedIn, Facebook, or Instagram.

Just by virtue of conducting the poll on Twitter, you're skewing poll results in favour of people who use Twitter often. Because people who don't use Twitter as often would probably not be answering your poll to begin with.

If you were to run the same poll on LinkedIn and Instagram, you would find them both winning on polls conducted on their own respective channels.

You see, as humans, we like clean patterns.

Clean patterns make thinking easier. And we often make the mistake of treating the first pattern we spot as an unquestionable axiom. But by doing that, we risk losing out on great alternatives.

Here's another example to establish the point I'm trying to make. The following is an account by Ricki Tarr who used to work at Apple during the early days of the iMac.

“Steve worked in a tight knit group of close confidants. So the engineers he was meeting often were outside of that circle. He would go from back to back to back meetings with people he had maybe met a couple times before. He needed to figure out whether they knew what they were doing, so would often take an extreme position. If you could argue him in you were probably “ok”, if not, maybe you were a bozo.

I demoed speakers in the first flat panel iMac to him in a lab in IL5 years ago, early in the product development. We prepped two physical models one with forward-firing speakers and a grille in the chin, and one with downward-firing speakers. I stacked the demo and showed him the good one first. Forward firing. Sounded great. Best sounding iMac ever. Really.

Then I demoed the downward-firing speakers.

It sounded crappy, sound comb filtering off the hard surface of a lab bench. Pretty nasty. He winced. Made a comment about the sound. Demo in the bag — I thought we were doing the great sounding forward-firing speakers.

Someone asked “Which model Steve?”

“The last one.”

Wait. What!??!?

I blurted out “But you said they sound like crap.”

“They do. Your job is to make them sound good enough so customers don’t bring the product back.”

Then he did the SJ pure-gold move.

“The thing is that anyone who cares about music, will plug in external speakers. And then they will be looking at the product wondering why there is a grille on the front. I want the design to be clean.”

We shipped the downward-firing speakers.

Steve had a holistic vision for the entire product. If something was harder to do, but it made the product better, do the hard thing.

He did this thousands of times. He helped people do better work by challenging assumptions and explaining what he wanted.”

Again, what happened here?

Ricki assumed that speaker quality, i.e., how they sounded was the only variable that mattered. But Jobs was able to reason in negative space; he was able to see that speakers on an iMac, no matter how good, can never beat a conventional pair of desktop speakers. It was simple physics.

Because he was able to see this, he reasoned that why not do the design well instead, and make sure the speakers are just passable in quality so the customers don't think they're broken.

By thinking in negative space and stepping outside the frame, he challenged the unquestioned belief that speaker quality was paramount. Naturally, he was able to prioritize aesthetic as the more important variable to focus on.

This isn't a novel concept.

In fact, if you observe, you will find all disruptive businesses using some variation of thinking in negative space.


Instead of using two sensors, LIDAR and cameras and increasing operational and design complexity, just use cameras. The best part is no part.

The company challenged the conventional belief that both sensors were required for self-driving.


Instead of owning real estate, help people use real estate they already own to earn money and make money from them instead.

The company challenged the conventional belief that you need to own real estate to run a hospitality business.

Saral Designs’ menstrual pad-making machine

Prior to Saral, there were only two options available:

  • Multinational centralized manufacturing units with high machine setup costs that also increased pad costs
  • Low-cost manual pad-making machines that produced poor quality and inconsistent pads due to low production capacity and lack of automation

Saral challenged this false dichotomy between centralization/automation vs. quality, by pursuing decentralization as a viable option to achieve both quality and affordability.

Stoa Daily

At the start of Stoa Daily, we had to challenge the unquestioned belief that it wasn't possible to publish high-quality business writing on a daily cadence, with the small team we had.

By challenging that belief, we were able to prioritize our constraints quite differently from traditional newsletters.

Thinking in negative space is quite similar to thinking in counterfactuals or just moonshot thinking. This means, asking yourself,

“What if this wasn't true?”
“What if this is just a limiting belief?”
“What if we could have both?”
“What if we chose to not focus on X at all and focus on Y instead?”

Every “What if” is a counterfactual, that when entertained in all honesty, can sometimes lead to pretty remarkable breakthroughs.

It can help you break out of the frame.

It can help you think of an Option C and D, as compared to constraining yourself to just options A and B.

So, the next time you find yourself making decisions with an unquestioned and unchallenged axiomatic belief, think in negative space. You might suddenly find yourself in a much more creative state, opening up avenues yet unexplored.

Feeling Lucky?
Subscribe to get new posts emailed to you, daily. No spam.
Oops! Something went wrong while submitting the form.
15k+ business professionals act on our advice every day. You should too.
Subscribe to get new posts emailed to you, daily. No spam.
Oops! Something went wrong while submitting the form.
15k+ business professionals act on our advice every day. You should too.