The Unfathomable is Not Impossible

The practice of unconventional thinking.


I was six or seven when I first came across Alice Through the Looking-Glass in one of the rooms at my grandparents’ home. While the adults spoke over tea, I would sneak away into the backroom and lose myself in a world of peculiar characters.

One sequence always stuck with me. It occurs shortly after Alice meets the Red Queen and asks her age, to which the Queen answers: one hundred and one, five months and a day. iStock 000022261968Large BW

“I can’t believe THAT!” said Alice.
“Can’t you?” the Queen said in a pitying tone. “Try again: draw a long breath, and shut your eyes.”
Alice laughed. “There’s no use trying,” she said: “one CAN’T believe impossible things.”
“I daresay you haven’t had much practice,” said the Queen. “When I was your age, I always did it for half-an-hour a day. Why, sometimes I’ve believed as many as six impossible things before breakfast.”
- Lewis Carroll

It is a subtle exchange that can be easily overlooked. I love it for the outlandish proposition it makes: not only can we think about impossible things, we should do so on a regular basis.

Like Alice, investors today find themselves in a strange world. In the last year, the price of oil halved, Russia invaded Ukraine, central banks responded to the threat of deflation with massive stimulus, and the risk-free rates of Spain, Italy and Portugal fell below the equivalent yield in the United States. Even the yield on some of Nestle’s bonds turned negative. In short, many events transpired that were previously considered impossible by some in the investment community. This underscores that much of what is considered “unfathomable” is clearly not impossible.

But is there some way to practice thinking unconventionally? Can we train ourselves to think impossible things like the Red Queen?

In our view, the advantages of building this skillset are significant; not only is this type of thinking important to protecting against the downside—by helping individuals avoid large losses from negative scenarios—it is also critical in order to optimize the upside—by allowing people to make the most out of life.

When we open our minds to a wide set of possibilities—including ideas that initially seem impossible—we make it easier to put the odds in our favour over time.

Considering the downside

It was 2:58am when the electric clock stopped working. Jack lay awake, awoken by what he thought was thunder. The noise soon returned but this time with violent vibrations. This wasn’t thunder. He quickly ran to his wife, Olive, shouting, “Grab the children and get out!".

Torrential downpours throughout the summer had saturated the hills creating a loose layer of soil that hung tenuously to the mountain. Tragically, it all came down that night. Huge mounds of mud detached from the bedrock and came cascading down the mountain, gathering debris and destroying everything in its path. Jack’s mobile home lay directly below. As Jack and Olive scrambled to grab their children, a boulder the size of a small pickup crashed through their living room window, inches from where one-year-old Jo-Ann lay sleeping. The mountain above was coming down in a giant mudslide.

Only Jack and little Jo-Ann made it out that night; Olive and the four older children were lost. The community shuddered at the terrible misfortune. While the 1973 mudslide brought destruction to Harbor Breton, Newfoundland, most people walked away unscathed; only my great-uncle Jack lost a child. And he lost four.

The mudslide that took Jack’s wife and children may have seemed like a highly improbable event to those in his community, but the more facts we learn about that evening, the less far-fetched it seems. Not only was Jack’s home situated at the foot of a mountain under loose soil, it had rained for forty days straight before that fateful night. One doesn’t need to be a geologist to suspect that on the thirty-ninth day of rain, the risk of mudslides was elevated. The magnitude of Jack’s loss was enormous; but the probability of a mudslide was not altogether incredible given the conditions.

Negative events happen. They happen more often and with greater magnitude than we usually anticipate. This is why we must spend time considering the downside and building our resilience to it. Unfortunately, the majority of us seem to avoid actively considering the downside. This leaves us exposed to both “black swan events”—a term coined by Nassim Nicholas Taleb1 referring to the rare and unpredictable—as well as the large swath of fairly normal negative occurrences.

Why do we avoid the downside?

So why do we avoid thinking about the downside even when we know it’s important to do so? The obvious answer is that it can be unpleasant. Thinking about the downside can trigger anxiety, depression and the sort of kill-joy atmosphere that appeals to no one. But it is not only the feeling of discomfort that dissuades us: we also possess biases that prevent considering the downside.

One such bias is overconfidence. As psychologists Marc Alpert and Howard Raiffa demonstrate in A Progress Report on the Training of Probability Assessors, humans tend to systematically overestimate their knowledge and abilities.2 For example, the recent war in Iraq lasted for far longer than the estimated duration announced publicly by the U.S. government at the start of the conflict. Such overconfidence can be a barrier to thinking about the worst-case scenario because we assume, often with conviction, that we are right about a future outcome; therefore, we don’t bother wasting time contemplating possibilities that we believe have no chance of happening.

Another bias is our tendency to think myopically. People are notorious for focusing on short-term factors instead of long term implications—and many downside scenarios require long-term thinking.

As an example, Canadians consume an average of 110 grams of sugar per day, the equivalent of about 26 teaspoons.3 This is simply a staggering amount given the negative long-term consequences of sugar consumption. As Dr. Peter Attia from the Nutritional Science Institute highlights, after forty years of age, we have a greater than 80% probability of dying of one of four metabolic diseases, and ALL of these diseases are strongly related to diet!4

In other words, if you care about longevity: diet matters. Therefore, so does your sugar intake. And yet our short-term cravings for sweets often totally overrule any long-term thinking about the consequences.

Think more creatively about the downside

So how can we start to better reflect on the downside? Below are three tangible processes that may prove helpful in fleshing out the risks in your life:

1. Identify your assumptions and then imagine how those assumptions could be totally incorrect

Before our team makes an investment we have a clear thesis on why we believe it is attractive. This thesis must clearly articulate our core assumptions and the accompanying logic. For example, we believe that Google is an attractive investment because it has a very strong position in online search, a culture of innovation, economies of scale and is trading at an attractive price.

In order to think more creatively about the downside, we ask ourselves how our assumptions about Google could be completely wrong.

For example, let’s explore our belief that Google has a durable competitive advantage in search. Well, it assumes that governments will allow the Internet to continue as a marketplace of free ideas. If totalitarianism was to spread and countries follow, say, Russia’s lead, the internet would change dramatically. Internet regionalism could hypothetically break Google’s stronghold.

How might this apply beyond investments? Let’s imagine that your brother owns a retail business in Fort McMurray, a city notoriously dependent on the oil sector. Business has been steady for years and even though the price of oil has dropped, he believes he will still be able to retire in five years as long as oil eventually rises again. What assumptions could he be making that could be totally, wholly wrong?

One major assumption is that the price of oil rises in the future. While most energy CEOs in Canada contend that oil is going to return to the $70 range within two years, this may not be the case. What would happen to the Fort McMurray economy if it didn’t? Would your brother still be able to retire if oil stayed at $50 for the next ten years? Maybe. Or maybe not.

2. Consider your second-order risks

Charlie Munger once said that it’s not who you have sex with, it’s who they’ve had sex with. The longstanding business partner of Warren Buffett was referring to your risk exposure due to indirect events: second-order risks.

A recent occurrence in Azerbaijan is a good example of a second-order risk. A small economy in Asia, Azerbaijan is heavily dependent on its oil fields and has historically pegged its currency to the U.S. Dollar. But weak oil prices and a rising U.S. Dollar have now forced Azerbaijan to devalue its currency by a whopping 35%. The devaluation has caused stress on the country’s banking system and significantly raised the cost of living.  Impressively, this has occurred, in part, because some oil entrepreneurs on the other side of the world came up with technology that allowed them to access unconventional oil resources in a more cost effective manner.

Second-order risks often catch people by surprise. This makes the practice of brainstorming these risks a useful one.

3. Manage exposure to “Castles Built on Sand”

Let’s imagine you own a profitable hot dog business. Every week, a steady stream of customers buys your hot dogs. Business is thriving and the future looks rosy…until it is announced that the Quebec Nordiques are moving to Colorado and abandoning the stadium that attracted all your customers in the first place. Overnight, your steady stream of revenue dries up.

This is an example of a “Castle Built on Sand.” Everything looks good until the day you wake up and see that the whole structure was built on a shaky foundation. Unfathomably bad events often occur in these situations, as people often have a difficult time spotting such castles in advance.

Macau is a good case in point. A decade ago, very few people in the West anticipated that China would implement an anti-graft program that would stem the flow of Chinese tourists into the region. Yet this is precisely what is happening now. With the Chinese government cracking down on corruption, foot traffic is down 20-30% and many businesses including restaurants, casinos and hotels have been impacted.

It is not always feasible to fully avoid exposure to castles built on sand. For example, some people might live in cities that are dominated by one industry. When this is the case, effort must be made to manage overall exposure to that sector in your investment portfolio.

Consider ways to protect the downside

While you’re reflecting on the downside, it’s a good opportunity to simultaneously consider ways that you can de-risk. After all, what is the point of thinking about the downside if not to protect it? De-risking simply means limiting the losses you accrue if a negative scenario unfolds.

One individual obsessed with protecting the downside is Sir Richard Branson. Most people know Branson as the adrenaline-loving, long-haired billionaire who founded Virgin Group. Few people realize that he is also obsessively focused on de-risking his business ventures. For example, when Branson launched Virgin Airlines, he negotiated a deal in which he could return the airplane to Boeing in one year’s time if the venture didn’t work out.

“I think it looks like entrepreneurs have a tolerance for risk. But, having said that, one of the most important phrases in my life is ‘protect the downside.’ It should be one of the most important phrases in any businessperson’s life.

So okay, we made a big, bold move going into the airline business. But the most important negotiation with Boeing was that we had the right to give the plane back after twelve months. That meant I could put my toe in the water, I could see whether people liked the airline. But if it didn’t work out, it wasn’t going to bring everything else crashing down. I’d be able to look my record company bosses in the eye and we’d still be friends because they’d still have jobs.

Protecting the downside is critical. Make bold moves but make sure you have a way out if things go wrong.”
– Richard Branson5

Don't forget the upside

Daniel Kish leads a conventional life in many respects. An outdoor enthusiast with an athletic build, he often rides his bike around town or takes long hikes in the wilderness. He even enjoys climbing trees, despite his age of 49 and a physical condition that some would consider limiting: Daniel is totally blind.

Watching Daniel on his bike is somewhat unnerving. Not only does he cycle in busy traffic, he has done so since he lost his eyesight to retinal cancer at 13. In fact, Daniel routinely engages in activities that many people can’t do.

How he does it is phenomenal. By making clicking sounds with his mouth, Daniel is able to detect objects in his environment with remarkable accuracy through a process of echolocation. In fact, this process is so similar to what bats do with sonar that Kish is sometimes called Batman.

If Jack’s situation is an example of the unfathomable downside, Kish is an example of the unfathomable upside. For most of his life he has defied the expectations that people have had of him. Now he spends most of his time training other visually challenged people to do the same.

The benefits and challenges of thinking big

There are benefits to systematically questioning the upside assumptions of what is possible in life. Entrepreneurs depend on this ability to build new ventures and reach new markets, while investors who can see the potential in an investment are more likely to systematically find high-returning stocks. In virtually every domain where mastery is possible, the top competitors often got there because they believed in a vision that was deemed impossible by most. When we challenge the notions of our perceived limits, we can achieve far more than we ever originally envisioned.

Yet the nuances of thinking about the upside are rather different than that of the downside. While we often avoid thinking about the downside entirely, the challenge in dreaming big is to focus our attention productively.

According to a study by Harvard psychologists Matthew Killingsworth and Daniel Gilbert, adults spend over 45% of their day dreaming about something other than the task at hand.6 This thinking often involves some kind of fantasy outcome, such as an image of a warm beach or having an uber-fit body. In most cases this is a relatively harmless activity (some even argue it could help with cognitive thinking). However, it does become a problem when this is the only kind of “big-picture thinking” we do since daydreaming is almost always disconnected from taking any kind of action.

Dreaming about winning the lottery is an example of what happens when unproductive thinking is allowed to flourish unchecked. The lottery is one of the most horrendous ways to spend your money: you are more likely to be struck by lightning while being attacked by a shark than win the Powerball lottery. And yet a stunning 30% of high-frequency American lotto players believe it is a reasonable strategy to get rich.7 These individuals are dreaming unproductively: they are fantasizing about outcomes they want, without reflecting on the steps that could take them there.

The baggage we carry

When it comes to picturing the upside, people are often constrained by linear thinking
(a process following known cycles or step-by-step progression) and limiting self-beliefs. This seems to occur due to our evolutionary and social baggage.

As Peter Diamandis and Steven Kotler argue in Bold, humans evolved over thousands of years to think locally and linearly.8 Hundreds of thousands of years ago, the human experience was local, meaning that tribes were shaped by factors that existed in their direct environments. It was also linear in that generations would come and go with little progress being made.

Our needs are very different today, as our world is changing exponentially and the effects of one decision in Tokyo can be felt in Delhi. But the linear thinking and pattern recognition that served us well in the Paleolithic era, is still prevalent in humans today. And these skills are simply not enough to handle the massive complexity and rapidly-innovating nature that now dominates.

We can also be constrained by limiting self-beliefs. Our accomplishments in life often have more to do with our belief systems than our actual abilities. We are typically capable of far more than we realize. And this isn’t just positive thinking run amok; the power of our belief systems are strongly backed up by science.

Widely cited cognitive psychologist Albert Bandura postulated in the 1960s that individuals possess varying amounts of self-efficacy. He defines self-efficacy as the extent to which a person believes in his or her ability to complete tasks and reach goals. His studies show that higher levels of self-efficacy are associated with higher degrees of success in virtually all areas of life.

How to expand your thinking about the upside

Below are some processes that can be used to expand our thinking of what is possible:

1. Practice contrarian thinking

When we practice contrarian thinking, it becomes easier to break linear thought patterns and spot opportunities in the world that others miss.

As an example, Peter Thiel asks a useful question in his book Zero to One: What important truth do very few people agree with you on? Thiel explains:

“The question seems easy because it’s straightforward. In reality it is very hard to answer. Intellectually, the question is difficult because the knowledge that everyone is taught in school is by definition agreed upon. Psychologically, it’s difficult because to answer it is to say something that is unpopular.”9

Thiel argues that few people answer this well. Most people either come up with statements that reflect a commonly shared view—“our educational system is broken”—or statements that simply take one side in a familiar debate—“there is no God.” He notes that good answers usually take the form of: “most people believe in x, but the truth is the opposite of x.” For example, Thiel notes that most entrepreneurs in Silicon Valley believe in minimum viable products and designing opportunistically, whereas he believes that the best designers are strong visionaries that plan well.

2. The Skunk Works Principle: find the right environment

In 1943, the U.S. military had a problem: German jet fighters had appeared over Europe. In order to counter the Nazi threat, the U.S. military needed jet fighters of their own and they needed them fast. They approached aerospace giant Lockheed with an impossible challenge: produce a jet capable of countering German technology within 150 days.

143 days later (and seven days ahead of schedule), Lockheed delivered the U.S.’s first military jet to the pentagon. A large part of this success was due to the engineers’ work environment.
Lockheed’s chief engineer, Clarence Johnson, believed that highly motivated, brilliant people could achieve great feats if they were put in the right setting. So he assembled his best engineers, gave them total freedom and then…isolated them from everyone.

Johnson was militant about insulating his team both from distractions and the kind of existing beliefs in the organization that would steer them towards mediocrity. In fact, Johnson sought isolation so much that he stuck the engineers in a rented circus tent next to a plastics factory so abhorrently smelly that curious outsiders would be deterred. Over time, the operation became known as Skunk Works.
This strategy of isolation, tight timelines, smart people, and a compelling dream (in this case, defeat the Nazis) has been replicated time and time again.

When attempting to dream up the impossible, it is useful to carefully plan the environment in which you will do your best thinking.

3. Build up self-efficacy

When it comes to dreaming big about the future, the existence of high levels of self-efficacy appears to be a critical prerequisite. As Albert Bandura’s research shows, people with high assurance in their capabilities approach difficult tasks as challenges to be mastered rather than threats to be avoided. High levels of self-efficacy pave the way for more creative thinking about what is possible.

Bandura suggests self-efficacy is built in four ways10:

Personal mastery

The more accomplishments we achieve, the more we prove to ourselves that we are capable; therefore, we will hold higher levels of self-efficacy. Thus, there is some logic to the idea of focusing on many “micro wins.”

Vicarious experience

Seeing that others have accomplished a feat has a massive psychological influence on what we consider possible.

For decades, experts considered it physically impossible for a human to run a mile in less than four minutes—that is, until Roger Bannister ran the mile in 3.59.4 in 1954. Once Bannister smashed the record, a wave of athletes subsequently broke the four minute mark. 

Persuasion of others

People can be verbally persuaded that they possess the capabilities to master given activities. Parents, coaches and leaders can help individuals build up their confidence in their abilities over time. The challenge with persuasion is that it is more difficult to instill it than it is to undermine it. A coach that builds up efficacy in an athlete will quickly see it diminish if the athlete gets discouraged by disappointing results. Hence, a successful “efficacy builder” will not only use verbal persuasion, they will put the individual in situations where he or she will succeed.

Emotional and physical state

People rely on their physical and emotional states when they judge their abilities. For example, an athlete might feel incapable of a task when their muscles feel sore, while a writer might get writer’s block when they feel stressed. Thus, the ability to think big about an idea is influenced by our current state.

The thin line between moonshots and madness

As much as we believe in dreaming big in life, there is a difference between moonshots and madness. It is one thing to dream big; it is quite another to harbour delusions. And walking this fine line is not always easy.

Big ideas can be crazy and possible or crazy and delusional. It is not always easy to tell the difference. “The day before something is truly a breakthrough, it’s a crazy idea” says Peter Diamandis, Chairman and CEO of XPRIZE, a competition which uses large incentive prizes to drive radical breakthroughs that change the world for the better. A true visionary by definition must believe that what they are attempting is possible.

Yet just because someone believes an idea is possible, it does not mean that idea is sane. In fact, some ideas are clearly mad. The rub is to be clear on what madness looks like.

To us, madness is when we expect an outcome to occur, yet our logic is drastically flawed or when we ignore the fact that the odds of that outcome are incredibly low and we have no control over them.

Returning to the lottery example, let’s say your dream is to get very wealthy through Powerball. Not only are the odds against winning the lottery absurd, there is no way you can make them better, short of bribing lottery organizers. You completely lack the ability to improve your chances of success (something entrepreneurs can actually do, if they know how). Therefore, pursuing the lottery as a legitimate source of future income is both crazy and delusional.

We see madness manifesting all the time within asset markets. Every time you see someone trying to get rich from an asset bubble, there is some degree of madness happening. For example, when housing bubbles form, people usually start to believe that housing prices can never go down—despite considerable evidence to the contrary. Inductively, housing prices go up and down according to long cycles that usually move along with interest rates and credit. Deductively, there is no reason to assume houses as an asset class will shirk the typical forces of supply and demand that push prices both up and down. Thus, the outcome expected (getting rich) is based on faulty logic (house prices will always go up). This is madness.

Likewise, individuals who believe they can accurately and precisely predict currency prices in a repeatable manner are suffering from severe overconfidence bias. Currencies are prices that are the emergent properties of a massive, complex adaptive system. The history of anyone sustainably calling them with both precision and accuracy (versus simply directionally) is very poor. Arguably, anyone attempting to build his or her wealth using this approach (very low odds, no real control) would also be demonstrating a kind of madness.

But what about a currency forecaster who has had a string of good luck? Like the lottery winner, you can be lucky and still stark mad.

“But I don’t want to go among mad people,” Alice remarked.
“Oh, you can’t help that,” said the Cat: “we’re all mad here. I’m mad. You’re mad.”
“How do you know I’m mad?” said Alice.
“You must be,” said the Cat, “or you wouldn’t have come here.”

Final thoughts on mastering impossible thinking

Whatever your goal may be, it is only logical to ensure that you are doing everything in your ability to maximize the odds of your success. You might be looking to build a portfolio that allows you to retire or you might be building a business; either way, the task boils down to limiting your downside and maximizing your upside. We contend that this is easier to do when you expand your thinking on what is possible—and act accordingly.

Much of what is considered unfathomable in life is possible. We simply require the mettle to embrace an expanded mindset.

And it takes practice. There is a difference between having knowledge and possessing skill—we can know all about soccer without having any skill whatsoever on the pitch. Thinking about unconventional things is no different. Virtually everyone accepts how important it is to be able to think expansively…that doesn’t mean we are any good at it.


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Kara Lilly, CFA
Investment Strategist

March 2015


  1. Taleb, Nassim Nicholas, Black Swan. Random House: 2007.
  2. Alpert, Marc, Raiffa Howard, “A progress report on the training of probability assessors.” Judgment under Uncertainty: Heuristics and Biases. Edited by Daniel Kahneman, Paul Slovic, Amos Tversky. Cambridge University Press: 1982, pp. 294-305.
  4. Dr. Peter Attia on Life Extension, Drinking Jet Fuel, Ultra-Endurance, Human Foie Gras, and More. Interview with Tim Ferriss
  5. Diamandis, Peter, Steven Kotler, Bold: How to Go Big, Create Wealth and Impact the World. Simon & Schuster. New York: 2015.
  7. Diamandis, Peter, Steven Kotler, Bold: How to Go Big, Create Wealth and Impact the World. Simon & Schuster. New York: 2015.
  9. Thiel, Peter, Zero to One: Notes on Startups, or How to Build the Future (with Blake Masters). Barnes & Noble: 2014.
  10. Bandura, Albert. “Self-efficacy: Toward a unifying theory of behavioral change.” Psychological Review, Vol. 84(2), Mar 1977, 191-215.