[bazoom42]

Of course you can encode self-references in morse code, how could morse prevent that? Just use the same lisp syntax as in the article and then encode using morse code instead of Gödel numbering.

The purpose of Gödel numbering is to represent an arbitrary-length string of symbols as a single integer which allows you to manipulate it using Peano arithmetic.

But it is not like Gödel invented binary as you seem to suggest. Baudot code (a 5-bit character encoding) was in use in 1870’s.

In any case, Gödel-numbering is the least interesting part of the the theorem. The groundbreaking idea is creating statements about theorems.