[xandrius]

I tried to think about this and came to a personal realisation that perhaps there is no strict "foundational knowledge" for most topics.

Pick programming, is knowing binary operations foundational? Is knowing compilers? Is it knowing bubble sort? Or perhaps knowing data structures?

I believe that if you have been using/working in a field, whatever you touch for your own goals that's enough.

And perhaps the difference between being an expert beginner and an expert is whether you still care about such a distinction? If you can achieve your current and future goals and can eventually learn new concepts then you're good.

I'd say a beginner might be someone who wouldn't even know where to begin.

Let's pick chemistry for myself: sure, I could follow some video but without the video I wouldn't even conceive how to get started with anything.

While, say woodworking, I wouldn't call myself an expert but I would be able to imagine starting a random project from scratch and eventually figure out all the parts.

So, maybe: - beginner: can't complete a project without help/support - mid: can complete but is unsure whether that's the best way - expert: has completed it before somehow

[rustcleaner]

I'd argue the principles Turing and Wolfram lay out in regards to universal computation and computational equivalence are the most foundational, and then various systems or architectures (flow vs stack, etc), etc, are important as there needs to be concrete examples implementing the fundamentals. If you really want to get esoteric, programming goes all the way back with society and religion. Just like how a machine can compute so too can a group of people through their actions, if they adhere as religiously to their tasks as the fablic of reality seems to adhere to its laws in governing the motions of matter. Programming is the building abstract structures which, when represented with matter in the right ways that can take advantage of the moment-by-moment Gets Things Done™ nature of the fabric of reality itself, produces useful transformations of its initial states. Very complex behavior arises from the simplest of mechanistic rulesets, and it's found universally in biology and in places all over reality. Computation is so foundationally fundamental to this place and your (dear reader) existence here, it is shameful it's not in standard middle/high schools' curricula right next to the fundamental theorems of arithmetic and algebra!