№ 032Deep DiveAug 6, 202612 min read

AIAI LaborAI Models

Interpolation vs Extrapolation

Why AI is revolutionary in the library, but not outside of it

By Akram Ayyash

Note: this is my first thought piece on AI. As with many of you, artificial intelligence continues to occupy a disproportionate share of my thoughts. I will be writing more articles on this topic in the future.

ChatGPT is almost four years old, and as of July this year, its maker, OpenAI, said its models now reach more than a billion people. The four largest American cloud companies plan to spend roughly $700 billion this year on the infrastructure behind systems like it, a testament that no consumer technology has been adopted faster. On the question of whether AI is revolutionary, the bulls and the bears stopped arguing a while ago. No one seems to deny that this is the smartest technology we have ever had, and we have had it for quite some time now.

So here are a few uncomfortable observations, as of August 2026. No drug designed by AI has been approved by any major regulator; the furthest along entered Phase III trials only this July. AI has not yet discovered any new laws of physics. We have not yet seen any new theory of the cell, or of inflation, or of anything else that would justify the word "revolution" as a scientist would use it. We handed a machine nearly the sum of all written human knowledge, backed it with those hundreds of billions of dollars, and yet, the mysteries of the universe are sitting exactly where we left them in November 2022; still undiscovered.

The technology is genuinely revolutionary. And your life has not materially changed. For the past few months, I kept trying to reconcile these two statements.

I think the distinction that resolves this paradox is the most useful mental model (no pun intended) I have found for thinking about AI, and it came from working with these systems every day rather than from any research paper. It is also the reason this essay, every word of which was written by an AI, exists at all.

Two Kinds of Work

Nearly all knowledge work belongs to one of two categories.

The first is interpolation. You take a new situation and match it against the existing, codified body of human knowledge. A doctor sees a set of symptoms and maps them to the medical literature. A lawyer takes a fact pattern and maps it to statute and precedent. An engineer takes a design problem and maps it to physics that has been settled for a century. This work is hard. It takes a decade to get good at it, it pays well, and mistakes have real consequences. But notice what the work does not do: it does not create knowledge. The knowledge already existed, sitting in textbooks and case law. The skill, and the salary, is in the matching.

The second category is extrapolation. You push the body of knowledge outward, into territory where there is nothing to match against. A new material. A drug mechanism nobody has described. A rule for a domain that has no rules yet. The mathematician who proves a theorem is not consulting the answer key; there isn't really one. They're the one making it. Extrapolation is rare. Across the whole economy it is a sliver of professional output, and most of us, if we are honest, have gone entire careers without producing any.

Hard is not the same as new. That is the whole distinction, and almost every argument about AI runs the two together.

This distinction between interpolation-like work and extrapolation-like work matters, because a large language model is, mechanically, an interpolation engine. It was trained on the written corpus, and it produces answers by relating new questions to that corpus across more dimensions than any human librarian could hold. Researchers have argued for years about whether that description understates what is happening inside the models; the debate is technical and unresolved (when you interpolate over a sufficiently high dimension, aren't you in a way extrapolating?). I would argue, though, that you don't need to resolve this debate. Let us just look at where AI has actually worked, because the pattern is hard to miss.

The Revolution in the Library

The most successful legal AI company, Harvey, is inside roughly half of the hundred largest American law firms as of mid-2026, doing contract review and research memos. Microsoft's CEO said in April 2025 that AI writes as much as 30% of his company's code. EY's audit platform now reads every journal entry a client books, the full population, where a human team had time for a sample. Tax preparation, customer support, marketing copy, junior research: the same story with different letterhead.

Every one of these is a codified-corpus domain. Contract review is matching language to precedent. Most code is matching intent to programs that have been written a thousand times before. An audit is matching entries to rules. The machine went where the library was, and inside the library it has been everything the capex implies.

I cut my teeth on Wall Street, at two of the more sophisticated institutions in the business, and the honest version of the majority of what we did all day is this: we matched situations to a playbook. A new deal ran on the last deal's documents. A new crisis got the old crisis's hedges with wider spreads. The colleagues I watched become legends were, with almost no exceptions, the best matchers; they were very good at recognizing repeatable patterns and trading them. The person who invented a genuinely new structure came along maybe once a cycle, and we told stories about them for years afterward.

I say this while still believing that finance is a brilliant industry staffed by brilliant people, and yet it is overwhelmingly an interpolation business. So is medicine. So is law. I mean no insult by that; it is simply what professional work is, and it is why the machine came for white-collar work first, and why the disruption feels enormous from inside an office and invisible from inside your kitchen.

The AI revolution is real, but it is confined, so far, to the library.

Beyond the Walls of the Library

So let's now step beyond the metaphorical library, and watch where the machine stalls, because it stalls in the same place every time.

OpenAI is backing an animated feature film called Critterz, produced in about nine months for under $30 million, a fraction of studio economics, with a market debut staged at Cannes this year. Read the credits, though. The screenplay was written by humans, the team behind Paddington in Peru. The machine collapsed the cost of production, the rendering and the in-betweening; the one thing its own backers did not hand it was the story. A story worth telling is, almost by definition, the thing that is not already in the corpus; that story was not AI generated.

In July 2025, a Johns Hopkins robot removed eight gallbladders with no human hand on the instruments, a seventeen-step procedure, performed flawlessly. The fine print: the patients were pig cadavers in a controlled lab setting. No robot operates autonomously on a living human anywhere in the world, because living bodies are not standardized, and the moment the anatomy deviates from the training set is the moment surgery stops being pattern-matching.

Driving is the cleanest case, because we have run the experiment for a decade in public. In October 2016 Elon Musk promised a Tesla would drive itself from Los Angeles to New York, "without the need for a single touch," by the end of 2017. The drive never happened. Driverless rides at scale arrived nearly a decade behind that schedule, and they arrived through Waymo, which crossed half a million paid rides a week in early 2026 across roughly ten American cities. How they got there, however, is the tell. Waymo did not teach cars to reason their way through novel situations. It recorded and mapped the long tail of the road, city by city, mile by mile, until there was very little novelty left to encounter. The 99% of driving that is pattern was automated almost immediately. The last 1% took an extra decade, and it was not conquered by thinking; it was converted into pattern by brute force, so that the interpolation engine could handle it after all.

Even mathematics, the machine's best domain, tells the same story if you read it carefully. In October 2025 an OpenAI executive announced that GPT-5 had solved ten unsolved problems posed by Paul Erdős. It had actually retrieved solutions already published in the literature that the problem list's maintainer had not logged; that mathematician, Thomas Bloom, called the announcement "a dramatic misrepresentation," and the post came down. Interpolation, mistaken for extrapolation, by the people who built the machine. Seven months later the real thing happened: an OpenAI model produced a counterexample that disproved a long-assumed bound on a 1946 Erdős problem, verified by outside mathematicians, including Bloom. Genuine frontier movement, and worth taking seriously. But notice the domain where it happened: pure mathematics, where a candidate answer can be checked mechanically, in seconds, without touching the world. Where verification is free, the machine can guess a million times and keep the one guess that survives. Where new knowledge requires contact with reality (a patient, a road, an experiment) it has produced essentially nothing, because reality is the one dataset you cannot download in advance.

Klarna learned the shape of this boundary on its own payroll. In early 2024 the company announced its AI assistant was doing the work of 700 customer service agents; by May 2025 it was rehiring humans, with its CEO admitting that "what you end up having is lower quality." The machine kept the codified majority of tickets. People took back the tail, the complicated and unprecedented cases. The AI did not fail at customer service. It found the edge of the corpus, and the company reorganized itself around that edge.

The On-Ramp Problem

If you agree with my thinking so far, about interpolation and extrapolation, and how AI is good at one and fails at the other, then the impact of AI on the labor market becomes easy to determine: AI will continue to compress the interpolating jobs, and it is currently compressing the bottom of that layer first. The closer a career is to extrapolation, the lower the risk of AI taking it over.

Stanford researchers tracking payroll data found employment for 22-to-25-year-olds in the most AI-exposed occupations down about 16% relative to trend through October 2025, while older workers in the same occupations held steady. At firms adopting AI fastest, senior roles grew five times faster than junior ones over the past year, and total headcount at heavy adopters grew rather than shrank. The promised unemployment apocalypse has not arrived. What has arrived is a composition shift. The work that is disappearing is the codified work, and the work that is expanding is judgment: deciding what the machine should do, evaluating what it produced, owning the consequences when it is wrong, and handling the one-off edge cases.

I think this is not news. The uncomfortable part, which few are discussing, is what this does to the on-ramp. Every profession trains its young the same way: years of supervised interpolation. The pitch book, the document mark-up, the audit sample, the residency. That grind was never busywork; it was how you internalized the corpus, and internalizing the corpus is the precondition for ever pushing past it. You cannot extend a field you have not absorbed; you cannot extrapolate if you don't know how to interpolate.

But this grind is exactly what the machine absorbed first, which means the training ground for the valuable work is the work that stopped paying. Education has the same exposure, because a degree is, structurally, a certificate of supervised interpolation. Society has not begun to price this, and I do not think anyone knows yet what the new on-ramp looks like. School was never about rote memorization; it was about teaching students how to think. AI memorizes facts better than any student can, so now how do we train students to think?

One Explores, One Cements

So what does that mean for the future of human/AI interaction? To answer that, let's look at the past. In 1986 an information scientist named Don Swanson noticed something strange about the scientific literature: it contained discoveries nobody had made. Reading medical journals by hand, he found that one literature knew dietary fish oil changed blood viscosity, and an entirely separate literature knew blood viscosity mattered in Raynaud's syndrome, and no human had ever stood in both rooms at once. He published the hypothesis that fish oil might treat Raynaud's; a clinical trial later confirmed it! He called the phenomenon "undiscovered public knowledge," and he spent the rest of his career arguing that the library was full of it.

Swanson had to do it by reading, one paper at a time. This is precisely the work a high-dimensional interpolation engine was born for. The nonprofit Every Cure now scores every approved drug against every catalogued disease, some 75 million combinations in under a day, hunting for existing medicines aimed at the wrong target. Not new knowledge; new bridges between old knowledge. Somewhere in the world's libraries, there are cures already paid for, connections already implied, sitting unjoined the way fish oil and Raynaud's sat unjoined for a generation. The machine that cannot leave the library turns out to be the ideal tenant for it.

I believe the durable settlement looks like this. Humans push the frontier outward: run the experiment, meet the patient, form the question, decide what ought to be true next. Our innate desire to explore is something fundamental to our humanity. We crossed oceans and built planes to see what came next; we love pushing the frontier.

The machine cements what we bring back: organizes it, cross-references it, and finds the connections inside it that no individual reader has the years to see. We explore, the machine consolidates the territory. We expand the body of knowledge, the machine makes the body of knowledge actually usable, perhaps for the first time in history.

Which brings me back to the beginning. Every word of this essay was written by an AI. But here is the thing: every idea in it, the distinction, the taxonomy, the argument you just read, came out of walks I recorded on my phone, thinking out loud. I fed these thoughts to the machine, asked it to organize them, and then asked it to gather the evidence and check the numbers against sources. I asked my AI agent to interpolate my spoken thinking into structured and substantiated prose, and it did it in hours instead of the weeks it would have cost me. With my direction, it executed beautifully. It contributed no new idea that was not already in my recordings: I extrapolated, it interpolated. The division of labor this piece describes is the division of labor that produced it.

The mysteries of the universe are still sitting where we left them. The machine will build us a better library, but we still have to leave it.

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