Linear Minds in an Exponential World
Rethinking the Upgrade Equation
A good friend of mine, Joe Clark, recently posed a question that’s been rattling around in his head: “How do you create a policy playbook for tech upgrades when technological advances are changing by the week—sometimes by the day? When do you abort and upgrade? What should we even be thinking about?”
It’s a sharp question. One that deserves more than a checklist.
So in the spirit of thinking differently, I wrote the following. Joe was probably focused on business when he asked it—and rightly so—but I’ve taken the liberty to zoom out, bring in some personal experience, and reflect on the broader philosophy behind our decisions to upgrade. This might not be a playbook, per se, but I hope it offers some good fuel for your own thinking.
Enjoy the ride.
Not long ago, upgrading our gadgets or systems was an occasional event. The mentality was simple: use what you have until it breaks or becomes hopelessly outdated. Improvements in technology felt incremental, almost leisurely. But something changed. We now live in an era where each new release—each new smartphone, computer chip, or software update—leaps far beyond its predecessor. Underlying this shift is the kind of exponential progress famously described by Moore’s Law: the number of transistors on a chip (and hence computing power) was observed to double about every two years. Over decades, this consistent doubling has compounded to astonishing effect, driving sweeping technological and social changes. The result is a world where the pace of change has left our old “upgrade when necessary” mindset looking increasingly inadequate.
From the Flat Past to a Steep Present
For much of the last century, progress in technology really did feel linear. Years might go by between significant upgrades, and improvements were modest enough that our lives were only gently nudged by new inventions. In hindsight, we recognize that an exponential trend was quietly underway, but in its early stages it was so gradual that it looked almost flat. Indeed, exponential trends often masquerade as linear when viewed over a short term. During this “deceptively slow” phase, it made sense that one would only bother upgrading devices or systems when the old ones failed or broke down—there wasn’t a pressing need to change sooner. We comfortably fell into a pattern: if it ain’t broke, don’t fix it. Little did we suspect that this calm would not last forever.
Hitting the Knee of the Curve
At a certain point, imperceptible growth transforms into rapid advancement. On that conceptual graph, this is the moment the blue exponential curve shoots upward. In real life, we began to feel this in the past few decades. The classic example is the personal computer and smartphone revolution. Through the 1990s, a PC purchased one year might not be dramatically different from one bought a few years later. But as we approached the mid-2000s and beyond, the leaps became startling. Each new iPhone or Android phone model brought so many improvements—faster processors, better cameras, more storage, new features—that tech enthusiasts started counting down the days to annual releases. We went from an environment where upgrades could be skipped without much loss, to one where skipping even a single cycle made your device feel antiquated. The “knee of the curve” had arrived: that phase when exponential growth stops looking linear and starts to take off, rendering our old linear expectations obsolete.
That was certainly true in my own experience with the iPhone. As an early adopter, I used to mark the calendar and queue up virtually (or physically) just to get the latest model on release day. There was something magical about it—holding the future in your hands, watching the camera improve, discovering what new apps had been made possible. It was a ritual of wonder. Ironically, though Apple is now adding more features with each release than they ever did back then, I’ve simplified my approach. Today, I only ask one question: Is the camera better, and is it better enough to justify the change? I no longer need day one. The magic is still there, but I’ve redefined what I need from it.
Several forces conspired to bring us here. Computing power kept doubling every couple of years, as Moore’s Law predicted, and similar exponential advances took place in related domains (storage capacity, network bandwidth, sensor resolution, and so on). According to tech entrepreneurs like Peter Diamandis, many technologies today improve at an exponential rate, doubling in price-performance every 18 to 24 months. Changes that used to span a generation now unfold in a few years or even months. Think of how streaming video, social media, or cloud computing went from novel to ubiquitous in what felt like the blink of an eye. The effect of this acceleration is that the future starts arriving faster than our instincts expect. We find ourselves constantly on the steep part of the curve where something new is always around the corner. It’s exciting, but also a bit disorienting. Our once-reliable rulebook for planning and upgrading can’t keep up.
Linear Brains in an Exponential Era
Why do these changes catch us by surprise? The answer lies in our own psychology. “Humans are linear thinkers living in an exponential world,” Diamandis observes pointedly. Our brains evolved for a life that changed very slowly; for millions of years, there was little need to anticipate exponential growth spurts. We became very skilled at linear prediction—extrapolating tomorrow from the pace of yesterday. If you walked 10 paces every day, in three days you’d be about 30 paces away; our intuition handles that just fine. But ask someone to imagine doubling their steps each day (1, 2, 4, 8, 16, 32…), and intuition fails spectacularly—the mind boggles at how 30 doublings would circle the globe 26 times. In the modern era, this mismatch between our linear intuition and exponential reality leads to constant astonishment (and often, anxiety) at new developments. We struggle to comprehend how a decade of exponential progress can reinvent whole industries. No wonder many people describe today’s world as feeling “fast” or even too fast.
There is a human cost to this disorientation. Alvin Toffler, in his 1970 book Future Shock, famously warned that society could be overwhelmed by “too much change in too short a time,” leading to a kind of culture shock of the future. That once-distant warning now feels visceral and immediate. We wake up to new realities—technologies, platforms, ways of living—that didn’t exist just a short while ago, and it can be destabilizing. This is the psychological dimension of hitting the exponential curve: our linear minds grapple to absorb what feels like vertigo-inducing progress. We cling to familiar ideas of how things ought to improve (slowly, predictably) and can be blindsided when change is nonlinear. For example, a business that assumed last year’s market will grow at the same linear rate might be utterly unprepared when an exponential trend causes demand or competition to explode. Our linear thinking isn’t just quaint; in an exponential age, it can be a liability.
Rethinking the Upgrade Equation
All of this brings us to what we might call the new “upgrade equation.” In the past, the equation was straightforward: Upgrade = (Old Thing is Broken or Obsolete). But in an age of exponential advancement, waiting for something to break means missing out on vast leaps in capability. By the time your tool or skill “breaks” (i.e. becomes obviously outdated), the world may have moved on in a fundamental way. Upgrading is no longer just about fixing problems; it’s about continuously positioning yourself to leverage new possibilities.
Take accounting, for example. In a traditional business setting—especially within a family office where ownership structures and investment tracking are uniquely complex—accounting has always been a dance of compromises. The standard systems are designed for a universal model, which often fails to account for custom ownership allocations or layered equity tracking. For years, the answer was Excel. But spreadsheets have become a crutch, not a solution. In the past, building custom systems to replace this would be unthinkable for a small entity. Too costly. Too fragile. Too much overhead. But not anymore. With modern low-code platforms and the advent of what I’ll loosely call “vibe coding,” building a bespoke accounting system tailored to exactly what we need has gone from ludicrous to logical. The cost curve has been shattered. What used to be enterprise-only is now within arm’s reach of even the leanest operations. This is the upgrade equation rewritten—custom is now the new commodity.
Crucially, rethinking upgrades also means adopting a new mindset towards change. Instead of dreading or resisting the relentless pace, we can choose to embrace it. Futurologist Roy Amara put it well in his adage now known as Amara’s Law: “We tend to overestimate the effect of a technology in the short run and underestimate the effect in the long run.” In other words, we might get impatient when a new innovation doesn’t immediately change everything (a linear impatience), yet we remain unprepared for how drastically things can change over a decade. (Robotaxi is finally coming!) Rethinking upgrades means correcting this bias. It means training ourselves to look beyond the next minor iteration and perceive the broader curve of change. Business leaders and individuals alike have to ask not just “what does the next version bring?” but “if improvements keep doubling or compounding, where will we be in five or ten years, and how can I prepare for that now?”
This applies in no clearer place than artificial intelligence. While AI’s promise is vast, it’s also easy to become overwhelmed by it. The best mental shift I’ve made is to stop thinking of AI as a replacement and start seeing it as a multiplier. A tool that turns my own efforts exponential. Forget the mythical 10x engineer—AI lets me be a 10x operator in any domain I apply it to, from writing and research to organizing tasks or designing systems. When framed this way, upgrading isn’t a surrender to a tech replacing me. It’s a superpower.
This is easier said than done. Our linear minds need conscious effort to think exponentially. Peter Diamandis calls developing an exponential mindset one of our biggest leadership challenges. Failing to do so can have stark consequences: those who ignore exponentials may find themselves suddenly obsolete, whereas those who surf the wave of change can become the disruptors instead of the disrupted. The history of technology is littered with examples of companies and careers that fell victim to an upgrade equation stuck in the past tense—waiting too long to adapt, assuming tomorrow would be roughly like today. We don’t want to be in that camp.
So what does the new upgrade equation look like in practice? It’s proactive and continuous. It’s saying yes to the update not just to patch a hole, but to acquire a superpower that wasn’t available before. It’s shifting focus from preserving the status quo to constantly exploring how new tools could redefine what we do. In a sense, “upgrading” itself becomes a core activity, a constant in one’s personal or organizational strategy rather than a rare disruption. This could mean scheduling regular reviews of emerging tech relevant to your field, budgeting for ongoing improvements, or perhaps most importantly, upgrading our own knowledge and skills all the time. After all, it’s not just our gadgets that need upgrading—we do too, in how we think and learn.
Embracing Exponential Possibility
We stand on the other side of the exponential curve’s inflection point, gazing upwards at a steep climb of possibilities. It’s a world where simply doing the same things a little better is not enough; we are challenged to imagine fundamentally new directions. The upgrade equation for this era is about evolution more than maintenance. It urges us to be curious, forward-looking, and comfortable with continuous change. Yes, our Stone Age brains will sometimes recoil at the pace, but we can consciously cultivate a mindset to match the times. It’s worth remembering Alvin Toffler’s insight that in the 21st century, “the illiterate… will not be those who cannot read and write, but those who cannot learn, unlearn, and relearn.” In other words, adaptability is the new literacy. To thrive, we must be willing to upgrade not just our devices, but our ideas and ourselves.
The exponential age rewards those who can think beyond the next step and envision the trajectory of the whole curve. By reflecting on how far we’ve come—from the deceptively flat early days to the heady heights of today—we can better prepare for the wild ride ahead. Instead of being flustered by the rapid tempo of change, we can learn to dance with it. The next time you ponder whether or not to embrace a new technology or innovation, consider the exponential context. What new horizon might this upgrade unlock? In a world of accelerating returns, the real question is not whether to upgrade, but when—and the answer is often “sooner than you think.” Embracing that reality is key to not only surviving but truly prospering in a time when the only constant is exponential change.
