[bwfan123]

> But then again, how often do humans actually reason outside their own “training distribution”? Most human insight happens within well-practiced domains.

Humans can produce new concepts and then symbolize them for communication purposes. The meaning of concepts is grounded in operational definitions - in a manner that anyone can understand because they are operational, and can be reproduced in theory by anyone.

For example, euclid invented the concepts of a point, angle and line to operationally represent geometry in the real world. These concepts were never "there" to begin with. They were created from scratch to "build" a world-model that helps humans navigate the real world.

Euclid went outside his "training distribution" to invent point, angle, and line. Humans have this ability to construct new concepts by interaction with the real world - bringing the "unknown" into the "known" so-to-speak. Animals have this too via evolution, but it is unclear if animals can symbolize their concepts and skills to the extent that humans can.

[perfmode]

> Humans can produce new concepts and then symbolize them for communication purposes.

Sure, but the question is how often this actually happens versus how often people are doing something closer to recombination and pattern-matching within familiar territory. The point was about the base rate of genuine novel reasoning in everyday human cognition, and I don't think this addresses that.

> Euclid invented the concepts of a point, angle and line to operationally represent geometry in the real world. These concepts were never "there" to begin with.

This isn't really true though. Egyptian and Babylonian surveyors were working with geometric concepts long before Euclid. What Euclid did was axiomatize and systematize knowledge that was already in wide practical use. That's a real achievement, but it's closer to "sophisticated refinement within a well-practiced domain" than to reasoning from scratch outside a training distribution. If anything the example supports the parent comment.

There's also something off about saying points and lines were "never there." Humans have spatial perception. Geometric intuitions come from embodied experience of edges, boundaries, trajectories. Formalizing those intuitions is real work, but it's not the same as generating something with no prior basis.

The deeper issue is you're pointing to one of the most extraordinary intellectual achievements in human history and treating it as representative of human cognition generally. The whole point, drawing on Kahneman, is that most of what we call reasoning is fast associative pattern-matching, and that the slow deliberate stuff is rarer and more error-prone than people assume. The fact that Euclid existed doesn't tell us much about what the other billions of humans are doing cognitively on a Tuesday afternoon.

[bwfan123]

> Formalizing those intuitions is real work, but it's not the same as generating something with no prior basis.

> The fact that Euclid existed doesn't tell us much about what the other billions of humans are doing cognitively on a Tuesday afternoon.

Birds can fly - so, there is some flying intelligence built into their dna. But, are they aware of their skill to be able to create a theory of flight, and then use that to build a plane ? I am just pointing out that intuitions are not enough - the awareness of the intuitions in a manner that can symbolize and operationalize it is important.

> The whole point, drawing on Kahneman, is that most of what we call reasoning is fast associative pattern-matching, and that the slow deliberate stuff is rarer and more error-prone than people assume

David Bessis, in his wonderful book [1] argues that the cognitive actions done by you and I on a tuesday afternoon is the same that mathematicians do - just that we are unaware of it. Also, since you brought up Kahneman, Bessis proposes a System 3 wherein inaccurate intuitions is corrected by precise communication.

[1] Mathematica: A Secret World of Intuition and Curiosity

[perfmode]

The bird analogy is actually a really good one, but I think it supports a narrower claim than you're making. You're right that the capacity to symbolize and formalize intuitions is a distinct and important thing, separate from just having the intuitions. No argument there. But my point wasn't that symbolization doesn't matter. It was about how often humans actually exercise that capacity in a strong sense versus doing something more like recombination within familiar frameworks. The bird can't theorize flight, agreed. But most humans who can in principle theorize about their intuitions also don't, most of the time. The capacity exists. The base rate of its deployment is the question.

On Bessis, I actually think his argument is more compatible with what I was saying than it might seem. If the cognitive process underlying mathematical reasoning is the same one operating on a Tuesday afternoon, that's an argument against treating Euclid-level formalization as categorically different from everyday cognition. It suggests a continuum rather than a bright line between "pattern matching" and "genuine reasoning." Which is interesting and probably right. But it also means you can't point to Euclid as evidence that humans routinely do something qualitatively beyond what LLMs do. If Bessis is right, then the extraordinary cases and the mundane cases share the same underlying machinery, and the question becomes quantitative (how far along the continuum, how often, under what conditions) rather than categorical.

I'll check out the book though, it sounds like it's making a more careful version of the point than usually gets made in these threads.