I read both "Godel, Escher and Bach" along with "I Am a Strange Loop", by Hofstadter, and they are good reads.
This issue of looping is not just limited to Hofstadter alone as it stems not just through language but various civilizations and culture which give foundation to language. This directive capacity of culture forming language and language forming culture follows this same form and function looping-cycle-alternation where cultures and their intellectual foundations reflect:
1. Pythagorean Monad / Hindu Bindhu.
2. Sun and/or moon Worship in Various Cultures, observed with the Egyptian Aten.
3. Presocratic and Socratic emphasis on the Divinity of the circle.
4. Stonehenge
5. Taoism
6. Muslim Dome of the Rock
7. Circle dance of many cultures, specifically Jewish culture and 3rd world tribes.
8. Philosophers such as Hall, or the Occult book the Kybalion.
9. The 24 philosophers definition of God, with one as sphere.
10. Marcus Aruellius meditations.
11. Platonism
12. Book of Ezekiel Wheels within Wheels
13. The golden rule / "you reap as you sow".
14. Reincarnation
15. Moderation as cycling of extremes.
16. Nichmachean ethics.
17. Ecclesiastes "For everything their is a season".
18. Moral reciprocation (to give x is to receive x)
This is further reflected in natural and artificial phenomena.
1. Orbit of planets and stars.
2. Atoms
3. Circulatory, Respiratory and Nervous system.
4. Alternating current.
5. Seasons and weather patterns of nature.
6. Migratory patterns of birds.
7. Hunting/foraging patterns of wolves, deer, Turkey, etc.
8. Ocean currents
9. Reproduction as cycling of genetic material.
10. Movement of water to clouds to rain.
11. Alternation of emotions.
12. Personal habits
13. Standard conversations.
14. Wheels
15. Flying Saucers
16. Various dance and martial art moves.
17. Cycling action of semi automatic weapons.
18. Ball/puck/marbles
19. Various sports.
20. Mirror Effect in psychology.
21. Eyes, breasts, buttocks, various facets of human body, specifically female. Joint movement.
22. Economic exchange in cultures and between cultures.
23. Alternation of common traits amidst various people (personalities, physical traits)
24. Evolution.
25. Genome.
26. Political Spin.
27. Revolver, rolling, bullet spin.
28. Centrifuge.
29. Gyroscope.
30. Movements of elements.
31. Tornado, whirlwind, whirlpool.
32. Forms of liquids, solids, and gases.
33. Bipolar disorder.
34. Multiple personality disorder.
35. Various rolls for meals or desert.
36. Etc.
X. ALL triads, dualisms, and monads.
To cycle back to the premises:
1. Isomorphism in math and logic.
2. Godel's incompleteness theorems
3. ALL definitons in dictionary cycling back to previous defintion.
4. Addition and multiplication.
5. Wittgenstein observation of sets.
6. Subject-predicate looping in paragraphs.
7. Noun verb alternation in paragraphs.
8. binary code
9. Word through word as sentence, sentence through sentence as paragraph, paragraph through paragraph as page, page as page through book, book through book as volume with all cycling back to words.
10. ALL numbers as cycling of 1, 2 and or 3.
11. ALL languages looping through each other.
12. Set through set, definition through definition, concept through concept, etc.
13. Etc.
The problem of any projective linear space follows the same..."form" considering a line projecting away from a point is directed towards a point. In a separate respect a point is directed towards a point through a line.
Even the line as an extradimensional structure, exists through a looping effect as a localization of it.