One of those loops is the Gödelian strange loop based on Gödel’s famous “Incompleteness theorem”, that arises in formal systems in mathematics and which allows such a system to discern itself…to become “self-aware”.
Coming back to our previous “self”, we know that one’s cranium is a “purely physical object made up of completely sterile and inanimate components, all of which obey exactly the same laws as those that govern all the rest of the universe.” They key doesn’t lie in those inanimate matter, the atoms the brain is made of, but in the patterns that exist inside the brain.
You get to an “I” from a bunch of meaningless primitives (atoms, molecules etc.) which don’t mean anything. So what is the connection between those two? BEG tries to answer this question by going back to our formal mathematical system . We start with a bunch of logical primitives ( 3+2=5, etc.) and we’ll get to a bunch of statements that refer to themselves. These two systems are somehow equivalent.