Comment by lutusp

Don't let specialists detract from your enjoyment of Quanta-level articles. This one is well-written, makes no egregious errors, and only omits one important fact. And that fact is ...

All this talk about exponentiation, tetration and pentation have their roots in Peano arithmetic, which for reasons of logical clarity, defines precisely one function -- the "successor function":

s(n) = n+1

Using just this function, Peano defines addition, multiplication and exponentiation with great clarity. Since Peano's time, people have been making adjustments, like including zero among the counting numbers, and by extending exponentiation into tetration, pentation and a few more exotic operations fully discussed in the linked article and elsewhere.

I personally would have liked to see a more complete exposition of the logical roots of the Busy Beaver challenge, and I think the missing parts would have made the article a better read, even for non-specialists. Maybe especially for those readers.

But Quanta articles are perfectly suited to their audience, people who may be inspired to look for more depth elsewhere.