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. 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.
Strange loops in cognitive science
Strange loops take form in human consciousness as the complexity of active symbols in the brain inevitably lead to the same kind of self-reference which Gödel proved was inherent in any complex logical or arithmetical system in his Incompleteness Theorem. [1] Gödel showed that mathematics and logic contain Strange Loops: propositions that not only refer to mathematical/logical truths, but also to the symbol systems expressing those truths. This leads to the sort of paradoxes seen in statements such as "This statement is false," wherein the sentence's basis of truth is found in referring to itself and its assertion, causing a logical paradox.
Strangeness
Hofstadter argues that the psychological self arises out of a similar kind of paradox. We are not born with an ‘I’ – the ego emerges only gradually as experience shapes our dense web of active symbols into a tapestry rich and complex enough to begin twisting back upon itself. According to this view the psychological ‘I’ is a narrative fiction, something created only from intake of symbolic data and its own ability to create stories about itself from that data. The consequence is that a perspective (a mind) is a culmination of a unique pattern of symbolic activity in our nervous systems, which suggests that the pattern of symbolic activity that makes identity, that constitutes subjectivity, can be replicated within the brains of others, and perhaps even in artificial brains.
Downward causality
Hofstadter thinks our minds appear to us to 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:
"Merely from knowing the formula's meaning, one can infer its truth or falsity without any effort to derive it in the old-fashioned way, which requires one to trudge methodically "upwards" from the axioms. This is not just peculiar; it is astonishing. Normally, one cannot merely look at what a mathematical conjecture says and simply appeal to the content of that statement on its own to deduce whether the statement is true or false. (pp. 169-170)”
Hofstadter claims a similar "flipping around of causality" appears to happen 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.
Strange loops may involve self-reference and paradox. 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.
Strange loops in cognitive science
Strange loops take form in human consciousness as the complexity of active symbols in the brain inevitably lead to the same kind of self-reference which Gödel proved was inherent in any complex logical or arithmetical system in his Incompleteness Theorem. [1] Gödel showed that mathematics and logic contain Strange Loops: propositions that not only refer to mathematical/logical truths, but also to the symbol systems expressing those truths. This leads to the sort of paradoxes seen in statements such as "This statement is false," wherein the sentence's basis of truth is found in referring to itself and its assertion, causing a logical paradox.
Strangeness
Hofstadter argues that the psychological self arises out of a similar kind of paradox. We are not born with an ‘I’ – the ego emerges only gradually as experience shapes our dense web of active symbols into a tapestry rich and complex enough to begin twisting back upon itself. According to this view the psychological ‘I’ is a narrative fiction, something created only from intake of symbolic data and its own ability to create stories about itself from that data. The consequence is that a perspective (a mind) is a culmination of a unique pattern of symbolic activity in our nervous systems, which suggests that the pattern of symbolic activity that makes identity, that constitutes subjectivity, can be replicated within the brains of others, and perhaps even in artificial brains.
Downward causality
Hofstadter thinks our minds appear to us to 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:
"Merely from knowing the formula's meaning, one can infer its truth or falsity without any effort to derive it in the old-fashioned way, which requires one to trudge methodically "upwards" from the axioms. This is not just peculiar; it is astonishing. Normally, one cannot merely look at what a mathematical conjecture says and simply appeal to the content of that statement on its own to deduce whether the statement is true or false. (pp. 169-170)”
Hofstadter claims a similar "flipping around of causality" appears to happen 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.
