Task Complexity: Why Makers May Out-Think Scientists

Across eighty scored tasks, the ten creative-arts tasks — a novel, a film, a symphony, a typeface, an hour of stand-up — average an intensity of 2.96, meaning that across roughly twenty-four dimensions of demand, the typical demand sits just below frontier level.

The ten pure-science research tasks — proving a theorem, modelling beyond the Standard Model, sequencing a pathogen mid-outbreak, an IPCC-grade climate projection, defending a doctoral dissertation — average 2.86.

Creative arts beats pure science. Not by much, and the gap is well inside the noise of single-rater judgment, so the honest reading is a tie. But a tie is already a substantial result, because the folk hypothesis being tested here is not “they’re comparable.” It is that one of these is obviously the harder kind of human work, and everyone knows which.

The category that actually leads is neither: engineering, at 3.15. And report 1 explains why in a way that should make you discount it — engineering is the most coordination-dense, most constraint-dense, most institutional category in the catalog, and the instrument rewards breadth of demand. Strip that out and science and art are indistinguishable.

One more number, the one I find most persuasive. Eighteen of the eighty tasks are genuinely solo — one person, no orchestration. Rank those eighteen and the top five are: theoretical physics, a graphic novel, a body of abstract painting, a debut novel, a new statistical method.

Physics, comics, painting, fiction, statistics. Alternating.

So the folk hierarchy gets no support from these numbers. But I am not going to treat that as proof, because the numbers are one reasoner’s structured judgment rather than measurement, and a result I happen to like is exactly the kind I should trust least. What they are is a reason to look for a mechanism. And the mechanism, once found, turns out to be more interesting than the scoreboard — because it explains why the folk intuition exists, why it feels right, and why it is nevertheless measuring the wrong thing.

Difficulty is a relationship, not a property

Multiply CXLVII by XXIII.

Take a moment with it — not for the answer, for the feeling. There is a particular sensation of the mind reaching for a handhold and finding none. Roman numeral multiplication is genuinely hard. Medieval merchants hired specialists for it. There were manuals, and a profession.

Now multiply 147 by 23.

A nine-year-old does this. Not a gifted one — an ordinary one, in forty seconds, with a pencil.

Nothing changed about the world between those two paragraphs. Identical quantities, identical operation. What changed is the notation, and notation is not a description of a problem — it is part of the machinery that solves it. Positional notation with a zero performs most of the work the Roman system forces your skull to do unaided.

The difficulty was never in the multiplication. It was in the gap between the multiplication and the symbols available for it.

This is why the history of human capability reads as a history of people finding notations that made impossible things routine: Arabic numerals, algebraic symbolism, the Cartesian plane, calculus, double-entry bookkeeping, staff notation, the periodic table, Feynman diagrams. Each is a machine made of marks on paper that thinks part of the thought for you.

Which means the question “is science harder than art” has no answer in the abstract. Difficulty is a relation between a problem, a mind, and the representations that mind has been handed. And the crucial word in that sentence is handed — because the three parties do not hand out representations equally.

The master variable

One property determines who gets handed what.

Does the task come with a verifier? — some procedure that can look at a candidate answer and tell you whether it is good, without you already knowing the right answer.

The idea comes from computer science, where the complexity class NP is defined by it: problems agonizing to solve and cheap to check. A sudoku takes an hour to fill and twenty seconds to score. Carried into human work it explains things it was never built to explain.

Having a verifier buys four things.

Search works. If you can rank candidates you can generate a lot of them badly and let the ranking do the work — how evolution works, how drug discovery works, how chess engines work. Search plus a verifier is a machine that manufactures competence out of patience.

Work compounds. If I can verify your result I can build on it without redoing it. I take your theorem as a brick and put my floor on top. Mathematics is a four-thousand-year-old cathedral built from that single move. No living mathematician has checked more than a sliver of what they use daily; they don’t need to, because verification happened once and the result was cemented in.

Novices become trainable. Hand a beginner a problem, let them fail, tell them immediately and unambiguously that they failed. That loop is the engine of skill acquisition, and it is why chess produces thirteen-year-old prodigies and diplomacy does not.

And machines can enter. Every machine learning system is a search aimed at a verifier. A loss function is a verifier. Where we have one, we point compute at it and grind.

Now run all four backwards, and you have the situation of the artist.

What it costs to work without one

No procedure takes a novel and returns a verdict. Nothing tests whether a melody is good, whether proportions are right, whether a strategy was wise. Rittel and Webber put it precisely in 1973: for problems of this kind, solutions are not true-or-false but good-or-bad, and there is no immediate and no ultimate test.

So search stops working — a thousand plot outlines gets you no closer to a good book, because you cannot rank the thousand. Training loses its loop. And most importantly, work stops compounding.

A physicist starting a PhD inherits four centuries of verified structure. She does not re-derive Newton or re-check Maxwell. She receives them as bricks — pre-verified, load-bearing, free — and stands on them to reach something new. Her personal contribution can be modest while the altitude she operates at is enormous, because nearly all that height was built by others and certified by a process she can trust without inspecting.

A novelist starting her first book inherits technique. Structure, scene, dialogue — craft is real and it transmits. But she does not inherit the evaluation function. Nobody can hand her a working answer to “is this good.” She has to grow one inside herself, from scratch, over about a decade. And when she has it, she cannot give it to anyone. It dies with her.

That is the asymmetry. And notice what it is not: it is not that art is harder, which is the crude version and is wrong. It is that science is leveraged and art is not. The scientist stands on shoulders; the novelist stands on sand — not because sand is harder terrain, but because the shoulders are not available to her.

This is what the folk hierarchy is actually detecting. When people say physics is obviously harder than songwriting, they are comparing the total altitude of physics — four centuries of accumulated verified structure — against the personal climb of one songwriter. That is nonsense in the way that comparing a mountaineer at 8,000 metres to a swimmer at sea level is nonsense. The physicist is high up because the ratchet carried her there. That is no criticism of physics; the ratchet is the greatest thing our species has built. But “how high are you” and “how hard did you climb” are different measurements, and the folk ladder quotes the first while claiming to report the second.

The strongest objection

Here is the best case against all of this, and it is good.

Creative fields lack verifiers because their outputs don’t matter enough to be checked. Where being wrong has consequences — a bridge, a drug, a proof — reality supplies a verifier whether you want one or not. Where being wrong costs nothing, no verifier develops, because nobody needed one. Low verifiability is a symptom of low stakes, not high difficulty. The novelist isn’t working without a net because her problem is deeper; she’s working without a net because nothing falls.

Part of that lands and should be conceded. Some verifier-poor fields are verifier-poor because they are unserious, and their disagreements never resolve because nothing is at stake in resolving them. Mistaking that for profundity is a genuine failure mode.

But it does not generalize, and the counterexamples are decisive. Consider the tasks in this catalog with no usable verifier and enormous stakes: drafting a constitution, negotiating a peace treaty, sentencing a defendant, deciding custody, setting monetary policy. In every one, being wrong is catastrophic and irreversible. In every one, nothing can tell you at the time whether you were right.

So verifiability and stakes are independent. What actually produces a verifier is not consequence but a stable, fast, attributable link between action and outcome — the world has to answer, quickly enough to learn from, specifically enough that you know which choice it answered. Bridges have that. Constitutions never will, because the outcome arrives in fifty years, tangled with everything else that happened, with no counterfactual country to compare against.

Properly stated, then, the objection is not a refutation but a refinement: verifier-poverty comes in two kinds, one caused by triviality and one by genuine causal opacity. Telling them apart is most of the skill of judging which fields deserve respect. A poem and a monetary policy decision are both unverifiable, and only one is unverifiable because nothing rides on it — and it isn’t the poem I’d bet on.

Taste is a verifier you grow yourself

Take this seriously and something usually dismissed as soft becomes the hardest thing in the picture.

Taste is a verifier. It is a working evaluation procedure that reliably separates better from worse where no external procedure exists. It does the same job a proof-checker does in mathematics. The only difference is location: instead of sitting out in the world where anyone can use it, it sits inside one head where nobody else can reach.

That explains facts that are otherwise strange.

It explains why creative apprenticeships are so long. If there were genuinely “no right answer,” training would be quick and pointless. Instead the domains with no external verifier have among the longest formation periods in human activity — a decade is standard — because the only way to calibrate the instrument is to make thousands of things and slowly notice which ones were alive.

It explains why great practitioners so often cannot teach. Not won’t — cannot. Polanyi’s “we know more than we can tell” isn’t mysticism. Expertise is compression: ten thousand cases squeezed into instincts that fire in milliseconds, and compression of that kind has no decompression algorithm. The master genuinely cannot hand you what they have. An apprenticeship is not a transfer of knowledge; it is a supervised environment for building an instrument.

And it explains the specific dread of creative work. In verifier-rich domains you can be wrong and know it — unpleasant, survivable. In verifier-poor domains you can be wrong for years with no signal at all. The novelist three hundred pages into a book that isn’t working receives no error message. There is no compiler.

Where the line actually falls

The fault line does not run between the sciences and the arts. It runs between working inside an inherited evaluation function and having to supply your own — and that cut puts people on sides our institutions would find surprising.

Normal science is verifier-rich. The daily work of most scientists has strong verifiers: replication, statistics, peer review, the indifference of the apparatus. But paradigm-founding science has none. When Darwin was assembling natural selection, no procedure could tell him he was right. When Einstein was reconstructing simultaneity, there was no test he could run before the theory existed to be tested. That work is verifier-poor, and by every account from the people who did it, it felt like creative work feels: long stretches of not knowing, reliance on a privately grown sense of rightness, aesthetic criteria doing load-bearing work.

Einstein founding a framework and a novelist starting a book are on the same side of that line. A jobbing scientist running standard assays and an accountant closing the books are on the other side together.

That cut is more useful than the one our institutions make, and it explains why the folk ranking feels wrong to people who cannot say why. It sorts by subject matter when it should sort by whether anyone can tell you you’re wrong.

The verdict

Creative people are not smarter than scientists. Scientists are not smarter than creative people. The question was malformed, and the malformation has a precise shape: it compares inherited scaffolding with personal climb and reports the sum as though it were the second.

But the hypothesis has a real kernel, and it is now sayable exactly. Our picture of intelligence is anchored on the traits that are easy to certify — depth of codified knowledge, abstraction, symbolic manipulation — and those are precisely the traits that a verifier-rich domain makes certifiable in the first place. The traits that dominate verifier-poor work are, by construction, the ones no test can see. We built a meritocracy out of the legible half of human capability and then concluded the illegible half was decorative.

So when someone says creative people are the smart ones, they are pointing at something true through a bad instrument. What they have noticed is that the novelist is doing without help what the scientist does with four hundred years of assistance, and that nobody gives her credit for the difference. What they get wrong is the conclusion — that the scientist must therefore be coasting. Elite science is not coasting, and paradigm-founding science is among the hardest things anyone does. It is simply hard in the way we usually reserve for artists.

The ratchet is the greatest thing we ever built. It is also the reason we have never learned to see the people who work without one.

Category and solo-task figures computed from the 80-task matrix using the intensity measure defined in report 1, with the caveats set out there. Literature — Rittel & Webber, Polanyi, Cook, Hogarth, Kahneman & Klein, Ericsson, Boden — in the 104-source library/.