Why This Project Exists

The Limit Case is named after a technique from calculus: push a trend to its logical endpoint — the limit — and examine what the math implies. When you do this with the major technological and economic trends of the past 150 years, the implications are striking. They’re also almost universally underestimated, because human beings are structurally bad at reasoning about exponential change.

This isn’t a character flaw. It’s a cognitive limitation. And it’s the single biggest obstacle to productive conversation about the future of the economy, work, and society.

The Problem

Humans think in straight lines. Given a trend, we instinctively project it forward linearly — same rate of change, extended into the future. This works fine for most of daily life, where the things we interact with do change roughly linearly over the timescales we care about.

But the major technological trends driving economic transformation are exponential, not linear. And exponential curves have a property that makes them deeply unintuitive: they look flat for a long time, then they look vertical. By the time the change is obvious, most of the curve is behind you.

The AlphaGo Moment

In May 2014, Rémi Coulom — one of the world’s leading computer Go researchers — estimated in Wired magazine that it would take “a decade” before a computer could beat a professional Go player without handicap. Go was considered qualitatively different from chess: too abstract, too dependent on intuition and pattern recognition, too combinatorially vast for brute-force computation. Coulom wasn’t a pundit making a casual guess; he was the person building the best Go programs in the world at the time.

In October 2015 — roughly 18 months later — DeepMind’s AlphaGo defeated Fan Hui, the European Go champion, 5-0 in tournament conditions. In March 2016, it defeated Lee Sedol, one of the world’s strongest players, 4 games to 1. The “decade” had collapsed to under two years.

The formal data is equally striking. In 2016, Katja Grace and collaborators surveyed hundreds of machine learning researchers at the NeurIPS and ICML conferences — the premier venues in the field — asking when AI would achieve various milestones (“When Will AI Exceed Human Performance? Evidence from AI Experts,” arXiv:1705.08807). Their aggregate predictions for milestones like language translation (2024), high-school essay writing (2026), and truck driving (2027) have been dramatically outpaced by actual progress. The survey itself has become one of the best primary sources for the exponential blind spot: a snapshot of what the world’s top AI researchers believed just as the curve was going vertical beneath them.

The people building the systems — the domain experts closest to the work — underestimated the rate of progress by large factors. Not outsiders. Not pundits. The researchers themselves.

This matters because it demonstrates that the exponential blind spot afflicts even domain experts. If the people building AI can’t correctly extrapolate the curve they’re on, the general public has essentially no chance of doing so without better tools for thinking about exponential trends.

The Pattern

The AlphaGo moment wasn’t an anomaly. It’s a recurring pattern:

• Expert consensus on timeline → actual arrival far sooner than predicted
• Initial dismissal (“that’s science fiction”) → rapid normalization (“obviously that was going to happen”)
• The window between “impossible” and “obvious” shrinks with each cycle

In 2017, mainstream estimates for artificial general intelligence (AGI) ranged from 40-100 years. Applying the pattern — experts consistently underestimate by large factors on exponential curves — suggested a timeline of 5-15 years. We are now inside that window, and the estimates have collapsed accordingly. The Grace et al. survey has been repeated (2022, 2023), and each time the predicted timelines have shortened dramatically — the researchers themselves are updating faster than they expected to.

Why It Matters for Everything Else

The exponential blind spot isn’t just about AI. It applies to:

• Automation of labor — the rate at which human tasks become automatable
• Energy technology — solar cost curves, battery density improvements
• Biological science — genomics, drug discovery timelines
• Computing — processing power, storage cost, network bandwidth

Every economic model, every policy proposal, every personal career plan that assumes linear rates of change in these domains is making the same error the AI researchers made about Go. The question isn’t whether the trends will continue — it’s whether our institutions, policies, and personal plans are calibrated for the actual rate of change or for a comfortable linear projection.

The Equilibrium Problem

One common response to concerns about rapid technological change is the equilibrium argument: markets will adjust, labor will reallocate, new industries will emerge to absorb displaced workers. This argument is mechanically correct. Free markets do tend toward equilibrium. New technologies do create new forms of work.

But equilibrium models have a hidden assumption: that the rate of change is slow enough for the adjustment mechanisms to keep pace. Retraining takes years. New industries take time to emerge and scale. Institutional and regulatory adaptation is slower still.

When the rate of change exceeds the system’s adaptation speed, you get dislocations — periods where the old equilibrium is broken but the new one hasn’t formed yet. The question is not whether equilibrium will eventually be restored, but how long the transition takes and what happens to the people caught in the gap.

If the curve is steep enough, “eventually” might not be fast enough.

An Invitation

This is not an argument for pessimism. The trends, if handled well, point toward genuine abundance — less toil, more creative freedom, higher material standards of living for more people. The technology is good.

But “if handled well” is doing a lot of work in that sentence. Handling it well requires seeing the curve clearly — not the linear projection we’re wired to see, but the actual exponential trajectory we’re on.

The Limit Case project exists to build tools for seeing that curve. Not to tell you what to conclude, but to help you do the math yourself.

Questions for the Reader

• Think of a technology that changed your daily life. How far in advance did you see it coming? How far in advance could you have seen it coming with better information?
• If the major AI capabilities of 2026 arrived 5x faster than experts predicted in 2020, what does that imply about expert predictions being made today about 2030?
• What personal or professional plans are you making based on an implicit assumption that the rate of change will be roughly linear?