Is Douglas Hofstadter's version of Godel's proof utter nonsense?

Question

Is Douglas Hofstadter's version of Godel's proof, which he offers in his book Godel, Escher, Bach, utter nonsense? Hofstadter goes to great length to disguise the fact that there are two distinct variables designated as a'. One of the variables designated as a' is the arithmoquinification of equation u, and the arithmoquinification of equation u does produce G (Godel's equation). But, the variable a' that is within G (Godel's equation) is definitely not the same variable a' that is equivalent to G (Godel's equation).

Answer 1

See page 447 (Basic Books ed, 1979) : $u$ is not an equation; it is a number. It is the G-number of the formula called G's uncle (bottom page 446).

In formula G's uncle there is only one free variable : a''.

The "trick" is to substitute the numeral $\overline u$ [i.e.$S(S( ...S(0)...))$, where the symbol $S$ for the "successor" function is repeated $u$-times], corresponding to the above G-number $u$, into the formula G's uncle in place of the only available "slot", i.e.in place of the free variable a''.

The result is a sentence (i.e.a closed formula : a formula without free variables) called $G$.