People have told me I was smart since I was a kid, but I can't remember for shit. I had a thought when I was fairly young that the only reason I was (maybe, sometimes) outperforming others intellectually is that I was habitually compensating for my poor memory by working things out on the fly, while others could rely more on rote memorization. Anyway, takes all kinds I guess!

Somewhat tangential, but this reminds me of when I took a certain Microbiology midterm in college. I hadn't put much effort into that class leading up to it, as I had some tough CS classes that consumed my focus that semester (also was admittedly not a great student in general). So when I finally went to take the midterm, after cramming like mad before the exam, I quickly realized I basically didn't know the answer to most of the questions, even what I crammed was only a small portion of the material.

The exam was huge, at least over 10 pages, and even when we technically ran out of time, the professor was kind enough to move the remaining exam takers to the neighboring lecture hall to continue taking it. I recall I spent a total of 2 hours on that exam.

Now mind you it was mostly short answer or multiple choice questions. The multiple choice questions were pretty sharp too, lots of traps and false but sounds right answers mixed in. But if it had been purely essay questions, I would have been screwed.

However with such a huge corpus of information in front of me, I ended up basically learning all the material on the spot. I just kept doing multiple passes through it, each time I noticed one of my answers contradicted one of the others, I would make adjustments to harmonize, which indirectly refined my understanding.

In the end I got B+ in the exam (which was curved to an A), and walked out understanding the material better than I did walking in.

Reflecting in the experience years later, I've wondered if a hypothetical LLM which was ignorant of microbiology could do the same thing if fed that exam. In some respects the traps they placed in the multiple choice questions actually were what helped me refine my understanding the most. Made me appreciate information theory more.

Same. I have bad "factual" memory, but very good "conceptual" memory. I might not remember exactly what someone told me, but I probably gathered a keyword, and a feeling and idea of what they told me. Almost like it takes what they said then compresses it into my mind in a nice little multi-key lookup table.

We sort kids into the smart and non-smart labels when they are young, and those labels tend to stick, even when what we're measuring isn't raw intelligence but just variance in childhood development that wash out in the long term. I don't think either group is well served by this.

I remember for math tests in high school/college it was easier for me to derive formulas than to remember it.

I can relate to this, but always explained it away in the opposite direction: I never trained my memory very much because I was able to work things out on the fly. Who knows, maybe there isn't much of a link between the two at all.

Same. I don't remember most things including my childhood. I have to relearn everything all the time just in a few months time. Maths, code, etc if I don't use it in 1 or more month, I have to relearn it though its always easier to relearn it. Comparing myself to others its extreme. What I find is the process of constantly relearning instead of relying on memories (which are in a way similar to assumptions) can lead to different ideas (often unique) than other people because everything even basic concepts is a open question. This however is tortuous in job interviews when people ask about problems solved in previous work or about a concept so there are trade offs.

I think the fact that ‘just work it out on the fly’ is a viable response to ‘I cannot remember things’ is what makes the intelligence right?

I relate to this; there are some things I remember very well, but in many areas I think my talent for improvisation stems from a ~mid long-term memory.

Memory isn’t only being able to recall things on demand.

Agree. Plus the dimension of synthesizing new ideas from existing knowledge. Different skill set from rote memorization.