I think it depends on how you were taught the concepts in elementary school. I think a lot of it is based on things like bar charts[0] and visual representations at first, so it's possible you were never taught how it was repeated subtraction and addition, how powers are repeated multiplication and so on.

https://en.wikipedia.org/wiki/Singapore_math#Bar_modeling

At my kid's school they start teaching division as "sharing" - a kid has 10 pieces of candy he wants to share with 5 friends; how many pieces can he share with each friend. Later they describe it as repeated subtraction - how many times can his 5 friends take a piece of candy from the pile of 10 pieces.

Yep. I remember in college when I made that connection and realized you could create infinite "levels" of operation, with each repeating the previous one N times.

Up-arrow notation ftw.

I'm missing the context here. The only arrows I'm familiar with are vector notation and ion spin notation.

I think they're talking about this, which appeared in a front-page HN post from yesterday: https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation

Not that story in particular, it's a perennial story on HN - I first learnt about that notation through the "largest number you can write on a postit note" challenge.

If you do this, 2 and 2 will always make 4, no matter what level you go to.