I'm being silly while poking fun at Chalmers! It's not an actual argument. I do appreciate the actual argumentation you supplied.

Regarding round squares, a circle is the roundest thing there is, and a circle of diameter d consists of all points a distance no greater than d/2 from the center. In contrast, a square of side d consists of all points within +- d/2 in every dimension.

In two dimensions, if we place our shapes at (0, 0) then our circle is all points x, y such that x^2 + y^2 <= r^2. The square is all points x, y such that -r <= x <= r and -r <= y <= r.

But in one dimension, we don't have any y. So it's just x^2 <= r^2 and -r <= x <= r, which is the exact same statement. So, we have a perfectly round square, in 1D.

(Interestingly, in high dimensions the corners of squares get sharper and sharper until the thing feels like a porcupine, while circles stay perfectly round. 10000-dimensional squares are incredibly not-round, which has important implications for machine learning and the like.)