happen in minds possessing self-consciousness. The mind perceives itself as the cause of certain feelings ("I" am the source of my desires), while according to popular scientific models, feelings and desires are strictly caused by the interactions of neurons. The parallels between downward causation in formal systems and downward causation in brains are explored by Theodor Nenu (2022), together with other aspects of Hofstadter's metaphysics of mind. Nenu also questions the correctness of the above quote by focusing on the sentence which "says about itself" that it is provable (also known as a Henkin-sentence, named after logician Leon Henkin). It turns out that under suitable metamathematical choices (where the Hilbert-Bernays provability conditions do not obtain), one can construct formally undecidable (or even formally refutable) Henkin-sentences for the arithmetical system under investigation. This system might very well be Hofstadter's Typographical Number Theory used in Gödel, Escher, Bach or the more familiar Peano Arithmetic or some other sufficiently rich formal arithmetic. Thus, there are examples of sentences "which say about themselves that they are provable", but they don't exhibit the sort of downward causal powers described in the displayed quote. Examples Hofstadter points to Bach's Canon per Tonos, M. C. Escher's drawings Waterfall, Drawing Hands, Ascending and Descending, and the liar paradox as examples that illustrate the idea of strange loops, which is expressed fully in the proof of Gödel's incompleteness theorem. The "chicken or the egg" paradox is perhaps the best-known strange loop problem. The "ouroboros", which depicts a dragon eating its own tail, is perhaps one of the most ancient and universal symbolic representations of the reflexive loop concept. A Shepard tone is another illustrative example of a strange loop. Named after Roger Shepard, it is a sound consisting of a superposition of tones separated by octaves. When played with the base pitch of the tone moving upwards or downwards, it is referred to as the Shepard scale. This creates the auditory illusion of a tone that continually ascends or descends in pitch, yet which ultimately seems to get no higher or lower. In a similar way a sound with seemingly ever increasing tempo can be constructed, as was demonstrated by Jean-Claude Risset. Visual illusions depicting strange loops include the Penrose stairs and the Barberpole illusion. A quine in software programming is a program that produces a new version of itself without any input from the outside. A similar concept