The first hint:
The Gratifying Enigmatic Brainteaser referenced in the first hint points to Douglas Hofstadter's book Gödel, Escher, Bach, which is sometimes called GEB.
The second hint:
The linked music is from Bach's The Musical Offering, a collection of keyboard pieces. This may just be a hint to help one see the connection to GEB. After all, GEB opens with a discussion of a piece from the same collection.
There is a hint in the title:
The strange loop referenced in the title is an allusion to Hofstadter's concept of the same name, which is discussed in GEB.
GEB includes many dialogues between Achilles and the Tortoise.
-1 ¬engine ¬Greek
-1 may refer to the introduction of GEB, which appears before Chapter 1. In it there is reference to both the ancient Greeks (p. 19) as well as Babbage's dream of an Analytical Engine (pp. 24-25). Not sure what to make of the logical negations.
10-20 bankrupt louise
input: 10-28 loop victim
st = new String(out); st = StringBuffer(st).insert(1,"M").toString();
Java code to insert 'M' into a string after the first letter. (This may be a reference to the toy formal language MIU presented in GEB, but I doubt it since the Java code is inconsistent with the syntactic rules of the language.)
The life and times of
This may refer to the 41st figure in GEB: