by | Jun 23, 2026

The Waiting Function

Emergence in Systems Optimized for Resolution

by Mike Magee

An hourglass on a textured dark teal background, with falling sand gradually forming a human silhouette beneath the title The Waiting Function by Michael Todd Magee.

The Waiting Function: emergence often begins long before its final form becomes visible.

 

What Friend B’s Garage Door Taught Me About Discovery

A friend of mine spent about an hour trying to reprogram a garage door opener. The instruction manual had been translated from Chinese to English badly enough that it didn’t make sense. He searched. He tried things. He got frustrated. But he wouldn’t ask AI for help.

He’d absorbed a story about AI being untrustworthy, fed to him by sources he trusts, and that story was load-bearing enough that an hour of fruitless searching was preferable to testing it. So I asked for him. Sent him the result. His response was immediate: this is great, very clear. Then he asked me to ask it next time he had a question.

The tool worked. The story didn’t change.

I sat with that for a while. Not because it was surprising — people resist updating beliefs all the time, for all kinds of reasons that have nothing to do with evidence. What stayed with me was something narrower: he received disconfirming evidence and didn’t reopen the question. The loop closed the moment the door worked. He left the room. Whatever was sitting underneath his resistance to AI stayed exactly where it was.

I’ve been finding versions of this everywhere, for months, in contexts that have nothing to do with each other. And eventually the pattern across them became impossible to ignore. I just published a paper about it: The Waiting Function: Emergence in Systems Optimized for Resolution. It’s a companion to Continuity Burden Asymmetry, published earlier this month, and together the two papers are starting to sketch something larger than either one alone.

The Thing Measurement Can’t See

Most systems — institutions, AI architectures, the way we evaluate productivity, the way we evaluate intelligence — are optimized for one thing: resolution. Close the loop. Solve the problem. Answer the question. That’s not wrong. Closure is efficient, and a world where nothing ever closed would grind to a halt.

But there’s a specific kind of loss that resolution-focused systems cannot detect, because what’s lost is something that never appeared. You can’t put a number on the form that would have emerged if the first adequate answer had been refused instead of accepted. You can’t measure the discovery that didn’t happen because the loop closed five minutes too soon. Premature resolution and timely resolution look identical from the outside, right up until something fails to show up that should have.

That absence is the subject of this paper.

Three States, Not Two

The instinct is to think of unresolved problems as binary — either the loop closes or it doesn’t, either you have an answer or you don’t. That binary misses something important, and the garage door is exactly where I started to see it.

There’s premature resolution: the loop closes before whatever was trying to emerge had a chance to. There’s stagnation: the loop stays open, but nothing is actually happening inside it — no new evidence is landing, nothing is accumulating, the unresolved state is just sitting there going nowhere. And there’s a third state, the one this paper is named for: the waiting function. The loop stays open, and the unresolved state remains in active contact with incoming reality. New evidence keeps arriving. Some of it resonates with the underlying tension. Some of it doesn’t. The first adequate answer keeps getting refused — not through procrastination, but through recognition that it isn’t yet the right shape. Structural coherence builds slowly, and eventually a form emerges that couldn’t have been derived directly.

The distinction between stagnation and the waiting function isn’t visible in how long the loop stays open. Both can last years. Both can resolve in seconds. Duration is just the container. What matters is whether the unresolved state is actively colliding with new evidence, or just sitting inert.

This is why the waiting function can’t be manufactured through patience or extended deadlines. You can’t decide to wait your way to a discovery. The thing that has to happen is continued, honest contact with the phenomenon — refusing the adequate answer not out of stubbornness, but because something hasn’t arrived yet that fits.

A Pattern With No Common Address

The clearest evidence for this mechanism comes from places that share nothing except the underlying structure.

A government secretary, decades ago, filled out a purchase order for a box of business cards well under the dollar threshold that required one. The threshold had changed years earlier. The process hadn’t. Asked why, she didn’t hesitate: “Because that’s the way we’ve always done it.” That observation — a process outliving its justification, invisibly, while the world around it changes — didn’t resolve when I first noticed it. It stayed unresolved across years of encountering similar patterns in different contexts, accumulating contact with new evidence, until one day it surfaced, in milliseconds, as the precise mechanism needed to understand something completely unrelated: why a two-document AI interaction primer had quietly split in two and never been questioned. Same mechanism. Unrelated content. The retrieval was instant. The years of accumulation that made the retrieval possible were not.

A designer held an unresolved feeling for weeks before a curved mark arrived that no brief could have specified — the Nike swoosh wasn’t derived from requirements, it was recognized when it appeared. A sculptor insisted on a reflective, abstract, hundred-and-ten-ton form for a public plaza that made no logical sense as civic art until it existed — The Bean wasn’t engineered from first principles, it was waited for past the point where adequate alternatives were available.

None of these examples are about AI. They’re about bureaucratic inertia, graphic design, and public sculpture. What they share isn’t a domain. It’s a structure: an unresolved tension, kept in contact with the world, refusing easy answers until something arrived that the easy answers couldn’t have produced.

Why AI Made This Visible

If the mechanism predates AI by decades, why did I find it through AI interaction?

Because AI provided the sharpest possible contrast case. Large language models are built almost entirely around resolution — produce a response, close the sequence, resolve the prompt’s uncertainty. Hand a system an open-ended reflection with no correct answer, and it reaches immediately for the nearest available closure: a framework, a category, a tidy correction. It takes the escape route every time, because resolving is what it’s built to do.

Watching that happen, over and over, across thousands of hours, made something visible by contrast that’s nearly invisible in ordinary human conversation, where both people share some capacity for staying in an unresolved state. With AI, one side of the exchange consistently lacks that capacity. The asymmetry is total, and the consistency of it is what eventually made the underlying mechanism legible.

This doesn’t mean AI contributes nothing. In the process of writing this paper, an image for an earlier piece resisted twelve generated attempts before something else — an Escher self-portrait, found through frustration rather than through any prompt — unlocked the direction. The AI generated. The human refused, repeatedly, until refusal turned into recognition. That division of labor — AI generates, human evaluates and waits — is probably the most accurate description available right now of how discovery actually happens inside a coupled human-AI system.

AI didn’t create the gap. It made the gap visible, because it has none of the capacity it’s revealing the absence of in itself.

What Gets Lost, Quietly

The implications go past AI. Any system that rewards closure over incubation — and that’s most systems, most institutions, most metrics of productivity — has a structural blind spot exactly where this kind of discovery originates. An organization that takes eighteen months to arrive at something genuinely new looks, on a spreadsheet, identical to an organization that wasted eighteen months. The thing that distinguishes them — continued, active contact with the problem rather than passive delay — doesn’t show up anywhere that gets measured.

Which means the people who do this naturally, who refuse adequate answers and stay with a problem past the point where everyone else has moved on, usually look difficult, slow, or perfectionistic from the outside. From the inside, what’s happening is recognition: this isn’t the form the tension is waiting for yet.

An Honest Open Door

The paper doesn’t resolve everything, and I don’t think it should. The deepest question it raises — what makes some incoming evidence resonate with an unresolved tension while most of it passes through unnoticed — is still open. I don’t know the answer. The paper says so directly, in its own final section, because closing that question prematurely would be exactly the move the paper is arguing against.

What I can say is that the friend with the garage door, the secretary with the purchase order, the swoosh, The Bean, an AI-generated image that took twelve attempts to fail before the right reference appeared — none of these started out looking like they belonged together. They only do because something kept refusing to resolve until it had a chance to become what it actually was.

DOI: https://zenodo.org/records/20726644

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