A strange loop arises when, by moving up or down through a hierarchical system, one finds oneself back where one started.
Strange loops may involve self-reference and paradox. The concept of a strange loop was proposed and extensively discussed by Douglas Hofstadter in Gödel, Escher, Bach, and is further elaborated in Hofstadter's book I Am a Strange Loop, published in 2007.
A tangled hierarchy is a hierarchical system in which a strange loop appears.
A strange loop is a hierarchy of levels, each of which is linked to at least one other by some type of relationship. A strange loop hierarchy, however, is "tangled" (Hofstadter refers to this as a "heterarchy"), in that there is no well defined highest or lowest level; moving through the levels one eventually returns to the starting point, i.e., the original level. Examples of strange loops that Hofstadter offers include: many of the works of M. C. Escher, the information flow network between DNA and enzymes through protein synthesis and DNA replication, and self-referential Gödelian statements in formal systems.
In I Am a Strange Loop, Hofstadter defines strange loops as follows:
The "strangeness" of a strange loop comes from our way of perception; because we categorize our input in a small amount of 'symbols' (by which he means groups of neurons standing for one thing in the outside world). So the difference between the video-feedback loop and our strange loops, our "I"'s, is that while the former one converts light to the same pattern on a screen, the latter one categorizes a pattern and outputs its essence, so that you get closer and closer to your essence the further you get down your strange loop (according to his book 'I am a Strange Loop').
Hofstadter thinks our minds can determine the world by way of "downward causality", which refers to a situation where a cause-and-effect relationship in a system gets flipped upside-down. Hofstadter claims this happens in the proof of Gödel's Incompleteness Theorem:
Hofstadter claims a similar "flipping around of causality" happens in minds possessing self-consciousness. The mind perceives itself as the cause of certain feelings, ("I" am the source of my desires), while scientifically, feelings and desires are strictly caused by the interactions of neurons, and ultimately, the probabilistic laws of quantum mechanics.
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