And what about the concept of integers in the first place? That is, where does one banana end and the next begin? While we think we know visually, we do not have a formal mathematical definition.

I think the author is unaware of all the formal definitions of integers that exist. One can start with Hilbert's program ( https://en.wikipedia.org/wiki/Hilbert%27s_program ) as a first attempt at this problem. Then the work of Church and Curry created formal definitions in lambda constructions. But my personal favorite is the recent work in Homotopy Type Theory ( https://en.wikipedia.org/wiki/Homotopy_type_theory ), which proceeds to formally define integers with only 2 axioms, homotopy and univalence. This is in contrast to early formulations in ZF theory which (if I remember correctly) required 18 axioms.

To make a blanket statement that we don't have a formal definition of integers ignores the last 100 years of foundational mathematics work. While the article is interesting in some of the questions it poses, this demonstrated ignorance on the part of the author has me categorizing it as a fluff piece. The introduction and 1st chapter of Penrose's "Road to Reality" directly tackles the questions of the article in a far more elegant manner.