When Terror Fuels Transformation: The Hidden Trap of Linear Thinking

When Terror Fuels Transformation: The Hidden Trap of Linear Thinking

Many companies justify complacency as risk aversion. In truth, they risk more by staying the course. The best leaders cultivate healthy paranoia to spot shifting ground—and move before it’s too late.

Recently, I was talking with the head of strategy at a large industrial firm. She wanted help thinking through the next phase of her company’s transformation: how to move faster, innovate more deeply, and shift their focus from what they make to what they mean. It was a thoughtful, grounded conversation until she paused, almost apologetically, and said, “The problem is that we’re a very risk-averse company.”

“Everybody’s risk-averse,” I told her. “The real problem is that you’re not scared enough about the right things.”

She isn’t the only one. Again and again, I hear leaders explain away inertia as culture. We’re conservative. We’re cautious. We’re careful. But the challenge isn’t that they’re too cautious—it’s that they aren’t scared enough about the right things.

It’s fitting that this conversation happened the week of Halloween. Fear is underused as a tool for transformation. The world doesn’t need more ghouls or ghosts—it needs leaders who can face real fear. The kind that doesn’t come from monsters under the bed, but from shifts in the ground beneath our feet.

When we tell ourselves that the alternative to change is a slow, gentle decline, we’re comforting ourselves with a story that isn’t true. Our brains are playing tricks on us.

The Call for Exponential Thinking

Back in 2001, an inventor named Ray Kurzweil sat down in Boston to make sense of something he’d been watching for years. He had built reading machines for the blind, invented pioneering speech-to-text software, and created the first digital music synthesizers to rival an orchestra. He had a knack for spotting patterns others missed.

In his essay “The Law of Accelerating Returns“, Kurzweil describes how each breakthrough in human progress makes the next one easier. Innovation, he argued, compounds—and the pace of discovery accelerates with it. The future wasn’t just approaching; it was speeding towards us. It was the first clear articulation of what would later be called exponential thinking: the idea that change doesn’t move in a straight line but in a curve so steep it’s impossible for the human mind to grasp.

In the years that followed, Silicon Valley turned that idea into gospel. Venture capitalists spoke of curves instead of quarters. Founders built companies on 10X ambition and unshakable faith in technology’s upward arc. Exponential thinking became a creed.

The problem, of course, is that most people don’t naturally think of the world in exponential terms. We think linearly. Not because we’re dumb or lazy, but because our brains are just wired that way.

The Flaw in our Wiring

The human brain loves gradual change. It wants to imagine that the world moves in steady, predictable increments.

In the 1970s, two psychology professors at Leiden University in the Netherlands decided to test how well people could sense accelerating change. Willem Wagenaar and Joseph Sagaria built a simple experiment using number sequences that doubled each time: 2, 4, 8, 16, and so on. They asked their students to plot how the numbers would continue. Almost everyone drew straight lines instead of curves. When the pattern suddenly spiked upward, participants were genuinely shocked. Wagenaar and Sagaria realized they had stumbled upon something fundamental: our minds see the world in linear terms, even when the data in front of us is compounding.

Decades later, economists James Stango and Jonathan Zinman ran their own version of the experiment—this time with money. They asked people to estimate how savings would grow or debts would balloon over time, and the results were nearly identical to Wagenaar and Sagaria’s classroom curves. Even trained analysts underestimated the effects of compounding. Stango and Zinman published their findings and gave the bias its name: the “exponential growth bias.” Their experiments explained why disruption feels sudden, why opportunities feel distant, and why change always seems impossible until it’s happening in real time.

It turns out there’s biology behind this bias. The part of the brain that handles numbers—the intraparietal sulcusperceives change in proportions, not raw amounts. Our neurons represent numerosity in a way that makes big jumps look proportionally smaller as the numbers grow. That keeps us tuned to useful everyday differences, but it also makes big, accelerating shifts feel slower than they are—until they suddenly overtake us.

That bias for linearity explains why we’re often surprised when the world changes around us. Processing power doubles roughly every two years, giving us supercomputers in our pockets. Health outcomes improve faster than anyone predicted, from gene therapies to mRNA vaccines. Solar energy costs have plunged by 90 percent since 2010, turning climate pessimism into cautious hope.

These trends didn’t just beat expectations; they humiliated the experts who said they couldn’t happen. Paul Ehrlich spent half a century predicting a global famine that never arrived. The economist Robert Gordon argued that innovation was slowing to a crawl, but it never did. And Vaclav Smil, the brilliant energy theorist admired by Bill Gates, long insisted that transitions in our energy systems would take generations. Yet here we are, watching renewables surpass coal as the world’s largest source of electricity.

Exponential progress has a way of embarrassing our skepticism. When the curve bends upward, it feels miraculous. But for every chart that climbs, another curve is bending down.

When the Curve Turns Downward

Exponential logic works both ways. When a company, an industry, or a civilization starts to decline, the fall is never smooth. It feels manageable—until it isn’t. Then the bottom drops out.

In 2009, BlackBerry controlled nearly half of the U.S. smartphone market. Business people insisted the device was indispensable. Seven years later, it was gone. AOL once connected more than 26 million people to the internet; within a decade, nearly all of them had moved on. 

In 1996, Kodak was worth $28 billion. By 2012, it was bankrupt. Nokia went from selling more phones than Apple, Samsung, and Motorola combined to selling its handset division for scrap.

Pan Am was the symbol of global air travel: glamorous, powerful, and seemingly permanent. But after deregulation in the 1970s and a few strategic missteps, its fortunes reversed. The 1988 Lockerbie bombing hastened its fall, and within three years the once-dominant carrier was gone. From global icon to bankruptcy in barely five years—a reminder that even empires with wings can stall overnight.

These companies died from a failure of perception. They misread the shape of change. Their leaders saw the signals but couldn’t imagine the curve bending downward so suddenly.

Inside companies, our bias towards linearity only deepens. Management consultants want to look smart, so they deliver “reasonable” forecasts that smooth sharp edges into gentle slopes. CEOs want to project confidence, so they reassure investors and employees of what’s possible. Boards, several layers removed from reality, get information that’s averaged, sanitized, and stripped of urgency.

Future-focused companies operate differently. Microsoft, Amazon, and Netflix know that the same exponential forces that make unimaginable growth possible also make decline catastrophic. They live with the awareness that the curve doesn’t owe them an upward direction.

Recognition of how fast things can change should spark the right kind of fear—the productive kind. It wakes you up to what’s really happening and pushes you to act before the curve turns against you.

Productive Terror

That’s what makes terror so helpful. Not the paralyzing kind that freezes you in place, but the clear-eyed kind that wakes you up to what’s really happening—the kind that forces you to move.

Start by questioning your assumptions. Are you on the right side of history? Do you see a path of gradual growth or eventual decline? And what if that path is bending faster than you think? What if the real risk isn’t betting big, but underreacting?

When every chart in your board deck looks linear—in any direction—it’s not a sign of rigor. It’s a sign of potential blindness. Progress rarely looks smooth in real time. If your dashboards are calm, your sensors are broken.

Look for signals at the margins of your business: shifts in customer behavior, technologies nibbling at your advantage, new entrants that don’t play by your rules. Demand data that scares you. Future-focused leaders cultivate what you might call productive terror. They treat discomfort as data and stay close to the edge of uncertainty, because that’s where the signals of the future first appear.

And when they act, they do it decisively. Not because they know what’s coming, but because they know that not acting is the only guaranteed way to lose.

Most companies don’t die because they’re too conservative. They die because they assume that they have more time than they do. But exponential change doesn’t care whether it’s taking you up or down. It just accelerates whatever path you’re already on. The question for every leader is whether you can feel the turn before it’s visible, and move fast enough to beat the curve.

Halloween is the one night we practice being scared on purpose. Maybe that’s part of what future-focused leadership really is: the courage to lean into the darkness when everyone else wants to look away.

Dev Patnaik

CEO

Dev Patnaik is the CEO of Jump Associates, the strategy firm for future-focused leaders. Dev has been a trusted advisor to CEOs at some of the world’s most admired companies, including Starbucks, Target, Nike, Universal Music and Virgin.