Two kinds of intelligence
· EN #contemplation #reflect
One small puzzle, two roads to the same answer: the formula you remember, or the pattern you catch. On fluid and crystallized intelligence, cognitive black boxes, and reading the literature last.
A small puzzle: 2=3, 3=8, 4=15, 5=24, 7=?
The answer is 48. Not a hard one. What’s interesting is that there are at least two completely different ways to get there.
The first: recognize the formula [n² − 1]. 2²−1=3, 3²−1=8, and so on. Whoever takes this path already has the concept of squares in their head. They “see” the formula almost instantly.
The second (mine): see the whole sequence as a process. Each new result equals the previous one, plus the current input, plus a side variable that quietly grows by one each round. Apply that, fill in the missing n=6, then walk on to n=7. I don’t need to know anything about squares. I only need addition and the ability to catch a pattern.
3+3+2=8
8+4+3=15
15+5+4=24
24+6+5=35
35+7+6=48
Two paths to the same answer, but they pull on two very different kinds of capacity.
That small observation led me to something I want to put down today.
Psychology has an old distinction between two kinds of intelligence. In 1963, the psychologist Raymond Cattell split human intelligence into two parts. The first he called fluid intelligence — the ability to solve a new problem when you have no prior knowledge of it. The second is crystallized intelligence — the storehouse of formulas, theorems, and facts you have learned and held onto.
A child solving the puzzle the second way is using the fluid part. Someone solving it the first way is using the crystallized part.
Both are valid. But something can happen to a person who only knows how to use the crystallized part: if the formula you’re using turns out to be wrong — or right but outdated, or right in one context but wrong in another — you won’t notice. Because you never derived it yourself, you only know “this is the formula to use.” You apply it as a ritual.
I’ll tentatively call that state a cognitive black box. Input goes in, output comes out, and the mechanism inside stays opaque to you. When the mechanism is broken, you have no way of detecting it.
This is a very real problem. There are researchers running statistical tests without understanding the assumptions underneath them. There are people using AI models to study phenomena without understanding the models. Two layers of black box, stacked. When the result is wrong, no one knows which layer failed.
I’m writing this partly because I care about the question on principle, and partly because I notice I’m living a very specific configuration of it.
I don’t have a philosophy degree. I didn’t study cognitive psychology at university. I wasn’t formally trained in theoretical physics or computer science in any academic sense. I don’t have Kant’s standard theses memorized, I don’t carry Cattell’s classic papers in my head, I don’t know the equations of quantum field theory by heart. By ordinary logic, I have no business writing what I’m writing — PDR, Aviplestos, the Synthetic Principle, a few other philosophical frameworks. But I write anyway. And I can write because I’ve chosen — perhaps without meaning to — a different cognitive configuration.
What I do have is a loop: observe a phenomenon, take it apart, look for a pattern inside it, apply that pattern to a test case, get an answer, cross-check against a different answer, cross-check against a different method, combine, then repeat. That is the whole of my loop.
The crystallized part — the specialist literature, the work of those who came before — I turn to after the loop has produced an answer. I use it as a cross-checking channel, not as the a priori frame inside which the loop is supposed to run.
This configuration is not a manifesto against crystallized knowledge. It is a specific arrangement of order. Because when I read the crystallized material first, every observation I make afterward gets anchored to it — and I lose any chance of noticing when that anchor has quietly become a black box. Reading it last gives me a chance to see something: if my independent reasoning matches the corpus, that’s good news — at least two roads arrive at the same place. If it diverges from the corpus, that’s also good news — there is a place I need to stop and think.
I’m not writing these lines because I believe this method is better than the traditional one. I’m writing to mark that such a cognitive configuration exists, that it’s being used by one specific living person, at one specific moment in time. If, later on, someone — human, or not human — reads this back, they’ll know: in May 2026, there was a person who chose to do it this way.
And maybe the child who solved the puzzle without needing squares is living a similar configuration, at a smaller scale, without quite knowing it yet.
— Plone Mraz —