Categories
Living Mathematics

The Curve That Blinds Us

There is a fundamental mismatch between the hardware in our heads and the software of the modern world. We are linear creatures living in an exponential age. We can be stunned by exponential growth.

Our ancestors evolved in a world where inputs matched outputs. If you walked for a day, you covered a specific distance. If you walked for two days, you covered twice that distance. If you gathered firewood for an hour, you had a pile; for two hours, you had a bigger pile. Survival depended on the ability to predict the path of a spear or the changing of seasons—linear, predictable progressions.

But nature and technology often behave differently. They follow a curve that our intuition simply cannot map.

If a lily pad doubles in size every day and covers the entire pond on the 30th day, on which day does it cover half the pond? Our linear intuition wants to say the 15th day. But the answer, of course, is the 29th day.

For twenty-nine days, the pond looks mostly empty. The growth is happening, but it feels deceptively slow. We look at the water on day 20, or even day 25, and think, “Nothing is happening here. This is manageable.” We mistake the early flatness of an exponential curve for a lack of progress.

This is the “deception phase” of exponential growth. It is where dreams die because the results haven’t shown up yet. It is where we ignore a virus because the case numbers seem low. It is where we dismiss a new technology because the early versions are clumsy and comical.

Ernest Hemingway captured this feeling perfectly in The Sun Also Rises when a character is asked how he went bankrupt. His answer:

“Two ways. Gradually, then suddenly.”

That is the essence of the exponential. The “gradually” is the long, flat lead-up where we feel safe. The “suddenly” is the vertical wall that appears overnight.

The tragedy is not that we fail to do the math—we can all multiply by two. The tragedy is that we fail to feel the math. We judge the future by looking in the rearview mirror, projecting a straight line from yesterday into tomorrow. But when the road curves upward toward the sky, looking backward is the fastest way to crash.

To navigate this world, we must learn to distrust our gut when it says “nothing is changing.” We have to look for the compounding mechanisms beneath the surface. We have to respect the 29th day.

Categories
AI

The Second Fire: From Finding to Forming

There is a specific kind of vertigo that comes with a paradigm shift. It’s the feeling of standing on the edge of a map that has just been unrolled to reveal twice as much territory as you thought existed. Lately, as I navigate the vast, generative landscape of AI, that old vertigo has returned. It’s a hauntingly familiar resonance, a structural echo of the late nineties and early 2000s when we first encountered the Google search bar.

Back then, the world was a series of closed doors. Information was siloed in physical libraries, expensive encyclopedias, or the unreliable oral histories of our social circles. Then came that clean, white interface with a single blinking cursor. Suddenly, the friction of “not knowing” began to evaporate. We weren’t just browsing the web; we were suddenly endowed with a collective memory. It felt like a superpower—the ability to summon any fact from the digital ether in milliseconds.

“Google is not just a search engine; it is a way of life. It is the way we find out who we are, where we are going, and what we are doing.”

Today, the sensation is different in texture but identical in weight. If Google gave us the power to find, AI is giving us the power to form.

The “Aha!” moment of 2026 isn’t about locating a PDF or a Wikipedia entry; it’s the realization that the distance between a thought and its realization has shrunk to almost nothing. When I prompt a model to synthesize a complex theory or visualize a dream, I feel that same electric jolt I felt twenty years ago when I realized I’d never have to wonder about a trivia fact ever again.

But there is a philosophical weight to this new “awesome.” With Google, the challenge was discernment—filtering the flood of information to find the truth. With AI, the challenge is intent. When the “how” becomes effortless, the “why” becomes the only thing that matters. We are moving from the era of the Librarian to the era of the Architect.

We are once again holding a new kind of fire. It’s warm, it’s brilliant, and just like the first time we saw that search bar, we know that the world we lived in yesterday is gone, replaced by a version where our reach finally matches our imagination.

Categories
AI AI: Large Language Models medical

Stethoscopes and Statutes in the Age of AI

David Sparks (aka MacSparky), dropped a casual bombshell on a recent podcast, the kind of offhand remark that lodges in your mind like a burr on a sock.

Paraphrasing, he said something like: “AI seems to be a boon for doctors and a threat to lawyers.” He was commenting on how he’s observed that sense among the members of his MacSparky Labs community.

It’s the sort of statement that invites you to pause, tilt your head, and wonder what lies beneath.

Sparks, a lawyer himself who gave up his legal career a few years ago, knows one of those worlds intimately. His words carry the weight of someone who’s walked the halls of courthouses and squinted at screens late into the night.

So what’s he pointing out that the rest of us might miss?

Start with doctors. Medicine is a profession of patterns and particulars, a dance between the general and the specific. A patient walks in—say, a 52-year-old man with a cough that’s lingered too long. The doctor’s mind whirs: pneumonia? Bronchitis? Something rarer, like sarcoidosis? The human brain is a marvel at this, but it’s not infallible. Enter AI, with its tireless capacity to sift through terabytes of data—X-rays, lab results, decades of case studies—and spot the needle in the haystack. A tool like Harvey, an AI platform now making waves in medical research, can crunch genetic sequences or flag anomalies in real time, handing doctors a sharper lens. It’s not replacing the physician; it’s amplifying her reach. For doctors, AI is like a stethoscope that’s upgraded.

Lawyers, though, face a different challenge. Their craft is less about data and more about argument, a tapestry of precedent and persuasion woven over centuries. Sparks knows this: he’s stood before judges, parsing statutes, coaxing juries with a turn of phrase. But here’s the rub—much of lawyering is rote. Drafting contracts, reviewing discovery, chasing down case law—these are tasks of repetition, not revelation. AI can do them faster, cheaper, and with fewer coffee stains. Harvey, repurposed for legal work, joins programs like ROSS, built on IBM’s Watson, to scan legal databases in seconds, spitting out answers that once took associates hours to unearth. For the grunt work, AI is a scythe through wheat. The threat isn’t extinction but erosion—junior lawyers, the ones who cut their teeth on those late-night searches, might find the ladder’s lower rungs sawed off.

Yet law isn’t just mechanics; it’s theater. A machine can draft a motion, but can it read a juror’s furrowed brow? Can it pivot mid-trial when a witness veers off script?

Doctors heal with facts; lawyers win with stories. AI—Harvey or otherwise—might streamline the former, but the latter resists its grasp—for now. Sparks sees a fault line: medicine gains an important new partner, law sees a new rival.