My previous provocation about Zachary’s article, where he digs into LLMs’ inability to make the genius leap into a solution, was just a first step in reinterpreting what happens behind the curtain of the genius mind. It was a bit harsh as a counterargument, because people do experience the jump. It is almost impossible to advocate that there is no quantum leap into a new state of awareness. Or is it consciousness?

A mathematician stares at a problem for days and suddenly sees the solution. A scientist wakes with an experiment in mind. A composer hears the missing passage. Einstein imagines a man falling from a roof and later describes what occurred to him as the happiest thought of his life. Before the moment, the answer is absent. After the moment, it is there. We call this insight, inspiration, eureka. Sometimes, genius. So when I recently responded to the argument in LLMs Can’t Jump by proposing that there is no jump, we left something important unresolved.

If discovery is a continuous trajectory, why does insight feel discontinuous? The answer may require separating two events that we habitually collapse into one.

The formation of a connection and the firing of a connection are not the same thing.

The first may be continuous. The second may be sudden, and the distance between them may contain much of what we have historically called genius.

The Flash Is Real

Our disagreement with the “jump” should not require us to deny the flash. Something does happen. A configuration that was previously unavailable becomes available. Relations that existed separately become connected. A problem that resisted formulation suddenly acquires a different shape.

At the level of conscious experience, this can be almost instantaneous. That phenomenology matters, but phenomenology does not necessarily reveal mechanism. Lightning appears suddenly. The electrical conditions producing it do not.

A phase transition can appear abrupt while depending upon an accumulation of preceding conditions. Likewise, the moment of insight may be discontinuous without the process producing it being discontinuous. This suggests a distinction: formation can be continuous while firing is discrete. The “jump” may therefore be neither illusion nor mechanism. It may simply be the visible threshold event of an invisible trajectory.

Return to Einstein

This becomes particularly interesting when we return to the same case used in LLMs Can’t Jump: Einstein’s development of General Relativity. Seen from far enough away, the story is irresistible. See Fig. 1.

But moving closer makes geometry change. Einstein’s path contained years of unresolved contradictions, physical intuitions, mathematical insufficiency, collaboration, wrong equations, abandoned approaches, failed constraints, and returns to ideas previously rejected.

His famous equivalence insight in 1907 did not produce General Relativity. It opened a trajectory. By 1912, Einstein knew that his physical intuition required mathematics he did not possess. Marcel Grossmann helped introduce him to the geometry required to express it. Einstein and Grossmann came remarkably close to the mathematical structure eventually needed… and then rejected it.

The Entwurf theory followed. It was wrong. Years of work were spent trying to make it work. Mercury remained troublesome. Rotational motion exposed difficulties. Arguments Einstein had constructed to defend the theory began collapsing. Then, in 1915, he returned to mathematical territory that had previously been abandoned. And the field equations emerged.

The Coherence-Bridging Event

This suggests another way to describe insight. Suppose a cognitive system contains many partially related elements: observations, memories, unresolved contradictions, concepts, bodily states, mathematical structures, conversations, failed attempts, environmental signals, and imagined possibilities.

Initially, the relationship between some of these elements may be weak. A connection is possible, but improbable. Continued interaction changes the field. Some possibilities disappear. Others gain relevance. Failures constrain the space. New information changes relationships among existing information. Previously distant elements become increasingly compatible. What looks like noise begins acquiring structure.

Eventually, a bridge that previously could not stabilize becomes possible. Then something happens. The connection fires. The system reorganizes around it. And consciousness receives what feels like an answer. I named this a Coherence-Bridging Event.

A coherence-bridging event is not creation from nothing. It is the moment at which sufficient organization allows previously separated structures to become functionally connected, and the resulting configuration to stabilize.

Genius Changes Location

This produces an uncomfortable consequence. We normally locate genius inside a person. Einstein was a genius. Mozart was a genius. Newton was a genius. The noun quietly transforms a class of events into an intrinsic property of an individual. But suppose we separate the person from the event, let’s see what happens:

“Individuals clearly differ in capacities relevant to discovery. Some may sustain unresolved problems longer. Some preserve weak signals others discard. Some tolerate contradiction without forcing premature closure. Some move unusually easily between representational domains. Some detect distant relationships. Some possess extraordinary technical or perceptual abilities.”

Those differences matter enormously. But none requires us to locate the breakthrough itself permanently inside the person. Perhaps what we call a genius is someone unusually capable of entering, maintaining, or constructing conditions from which coherence-bridging events can emerge.

Then “Genius” is not something a person contains. Genius is something that happens.

We can describe this even more precisely: what we call genius may be a coherence-bridging event attributed to the individual in whom the event became visible, rather than to the trajectory that made the event possible. This does not diminish Einstein. It makes Einstein’s actual accomplishment more interesting. His achievement was not that an inexplicable answer materialized inside an exceptional skull. It was his extraordinary ability to remain inside a problem for years while its organization changed.

Failure Moves Too

Once genius changes location, failure changes meaning. The Entwurf theory was wrong. Under the conventional success/failure distinction, it belongs on the unsuccessful side of Einstein’s biography. Under a trajectory model, that classification becomes less obvious.

The failed theory constrained subsequent search. It exposed assumptions. It forced mathematical confrontation. It created structures that could later be rejected, modified, or recovered. Failure changed the field. This does not mean every failure is productive. Nor does it mean wandering randomly eventually produces genius. It means something more precise:

A failed connection may still transform the conditions under which subsequent connections become possible.

Failure can therefore participate in coherence formation without itself being the solution. That distinction matters far beyond physics, because it changes how we think about learning, research, organizational problem-solving, and artificial intelligence.

DeepMind Found the Event. Perhaps Not Yet the Mechanism.

This brings us back to LLMs Can’t Jump. The paper makes an important distinction between induction, deduction, and abduction. Its central claim is that contemporary LLMs can perform increasingly sophisticated inductive and deductive operations but lack the grounded abductive mechanism necessary to move from experience toward genuinely novel axioms.

That is a serious problem. But perhaps the “jump” identified by the paper describes the terminal event at the wrong resolution. If a novel connection suddenly becomes available, it certainly looks like a jump. But the engineering question changes dramatically depending on whether the jump causes the discovery or merely marks the point at which an underlying organizational trajectory crosses a threshold.

In the first interpretation we need to engineer machines capable of jumping. In the second, we need to understand the conditions under which coherence bridges become possible. Those are different research programs.

A Necessary Scientific Caution

At this point, it would be tempting to turn the coherence-bridging proposition immediately into a neurological claim. We should not.

Brains operate through threshold-dependent electrochemical processes, changing network states, plasticity, synchronization, and enormously complex interactions across multiple temporal and spatial scales. It is therefore plausible that the phenomenological suddenness of insight could coexist with gradually changing neural conditions.

But the coherence-bridging event, as proposed here, is presently a conceptual model. It does not yet specify a demonstrated neural mechanism. That distinction is important. The proposition should therefore generate questions rather than borrow certainty from neuroscience:

• Can insight be empirically characterized as a threshold event preceded by measurable changes in network activity?
• Does prolonged engagement with an unresolved problem alter the probability of distant associations becoming functionally connected?
• Can failed hypotheses measurably reorganize subsequent search rather than merely eliminate alternatives?
• And can similar dynamics be reproduced outside biological cognition?

The last question takes us directly to AI.

Stop Asking Whether AI Is a Genius

Much of the contemporary debate asks whether an AI system can be creative, or whether an LLM can discover, or whether machines can become geniuses. Perhaps the unit of analysis is wrong.

Imagine instead: Human ↔ AI ↔ Problem Field. The human contributes embodied history, intention, valuation, perception, and the ability to recognize relevance in lived reality. The AI contributes an enormous accessible relational space, rapid recombination, persistence, alternative formulations, and the capacity to preserve and manipulate structures across extended inquiry. The problem contributes constraints. Reality pushes back. Failed propositions reorganize subsequent search. New connections alter the field. Something may eventually emerge that neither participant reliably produces alone.

Where, exactly, would the intelligence reside? In the human? In the model? Or in the organization of the relationship? If coherence-bridging events can emerge from such systems, then trying to determine whether the AI itself “possesses genius” becomes less interesting.

Can we organize human–AI–problem systems in ways that increase the probability of productive coherence-bridging events without prematurely forcing coherence where none exists?

That is a substantially different objective for artificial intelligence. We stop trying to manufacture an artificial Einstein. We begin studying the conditions under which discovery becomes possible.

The Spark

There is still a spark. There is still a moment when something that could not previously be articulated suddenly can. There is still surprise. There is still the extraordinary human experience of seeing something and wondering how it had remained invisible moments before.

The Matrix does not need to explain that experience away. It only changes where we look for its cause. Not at the instant alone, but at the trajectory. Not only at the neuron that fires, but at the conditions that made this particular firing possible. Not only at the person who announces the discovery, but at the field that became capable of producing it.

And perhaps this is why genius has remained mysterious for so long. We have been staring at the spark. The mechanism may have been accumulating in the darkness around it all along.