A statistical case for human thinking

Perception maps inputs into internal representations. A comparison between human thinking and LLM generation has to account for the variation in that mapping. Especially when the comparison is about compute.

An input does not enter the mind as a stable representation. It may come from the world or arise within the mind. It is transformed by a particular projection function, a mapping through which a person at a particular moment turns input into something they can think with. The shape of the projection function is unknown but we can pretty confidently speculate that memory, attention, expectation, physical state, context, and many other parameters influence it. Crucially, the function is not only personal but temporal and sequential.

I am stretching the schematics here for sake of intellectual enjoyment, and in doing so oversimplifying a quite complex process, but every projection may also invoke a residual function. It can be thought of as an effect that persists after the projection itself and alters the conditions under which later inputs are received and perceived. Residuals, to add to the complication, may vanish, decay, or amplify with or without a lag. The thought itself is fascinating. The projection function operates on a state partly produced by the residuals of its own previous invocations, each involving different inputs and parameters and perhaps even a different topology.

I should stop abstracting here. My statistical argument only needs to establish that the function has effectively limitless variation.

People shaped by similar environments might develop partially overlapping perspectives and representational structures. From the way our outputs cluster, we can speculatively infer that our projection functions cluster into regions of similarity. External conditions seem to condition us toward certain thought trajectories.

I think these inherent clusters do not eliminate variation. Their existence is what makes collective thought possible. This gives us shared language, concepts, disciplines, categories, or simply put common structure to exchange ideas without underlying identical internal representations.

No two people, however, receive exactly the same sequence of inputs. Not even the same person does at different points in time. Even where the inputs overlap, they arrive in different orders, against different prior states and with different residuals already in motion. The conversation before the conversation matters. The book read before the book matters. A detail noticed yesterday changes which detail becomes important today. Each new input is therefore projected through a function already shaped by the particular sequence that preceded it.

So the variance is not only across people. It is across versions of the same person too. Something obvious to one person may be invisible to another, and something invisible to you today may feel almost embarrassingly obvious tomorrow. And we do not drift in isolation. Our outputs become each other’s inputs, constantly perturbing, en masse, the projection functions that produce the next round of outputs (although it is not a turn-based game, for sake of argument I conceptualize it as such).

This is at best half the story. The downstream transformation from representation into an association, idea or solution may itself vary across people and time, but the statistical argument does not require it to. It only requires that differences in representation are not completely erased downstream.

That already produces an unusually productive statistical regime. Human thinking samples from a constantly evolving distribution of partially correlated representational spaces. The same problem is therefore encountered under many different projections, most of which lead nowhere. Occasionally, one makes previously distant variables adjacent and an improbable association locally obvious. A change in representation can therefore change how much search an association requires. At the scale of society, this starts to resemble an uncoordinated form of computational brute force. A breakthrough may be exceptional to the person having it while remaining statistically unsurprising for the society applying enough different lenses to the same problem.

Almost none of the trajectory behind a human output survives as data, nor is it directly observable. What survives is the surface-level output at the end of it. The sentence, proof, equation, paper, painting, design. By the time an idea becomes legible enough to enter a corpus, an enormous hidden sequence has already occurred. Perceptions were filtered, associations formed and discarded, importance shifted, representations mutated, mistakes redirected attention, and eventually one trajectory stabilized enough to be expressed.

The output can tell us a great deal about the process that produced it, but it most certainly does not let us recover the process itself. The missing information is concentrated precisely where the generative process happened. Human artifacts are terminal states sampled from volatile cognitive trajectories. We preserve the output and lose the years that made its abstraction conceivable.

Language is already downstream of this machinery. By the time an experience, perception or idea becomes a sentence, it has been projected, transformed and compressed into a form other people can exchange. A corpus is therefore not reality, nor even the internal representations produced from reality. It is a simplification of what survived far enough downstream to become communicable.

An LLM begins from that point. It can form rich contextual representations over it and generate remarkable variation from what was preserved. More modalities and more training signal widen what goes in. They do not multiply the function doing the projecting. Its variants are copies of one inheritance, not a population that drifted apart. The asymmetry remains. The corpus contains the outputs of human cognition after perception, representation, thought and social exchange have already done their work. It contains the successful associations, abstractions and categories far more readily than the volatile trajectories that made them reachable in the first place. Elegant argumentation can mimic ideation closely enough to pass for it.

I want to be careful here. None of this makes LLM output inferior by virtue of who or what created it. The statistical argument is about the compute that runs before an output exists, not about the output itself.

The statistical case for human thinking, friends, is this. Humanity is a vast, path-dependent and self-perturbing distribution of representational processes, continuously projecting reality differently and exchanging the results. LLMs can generate extraordinary variation but much of that generation can still resemble a form of permutational search over a representational inheritance already filtered through human perception, abstraction and language. The permutation may be new. The machinery that defined what could be permuted was inherited, already projected down to a lower dimension from a vastly higher-dimensional reality. Human thinking operates upstream. It keeps altering the representation, changing which variables become adjacent, which distinctions survive, what counts as noise, and sometimes what the problem even is. Humanity has not been out-computed. Its representational variety is not in the calculation that says otherwise.