the key to consciousness is self-reference.
despite thousands of years of analysis, definition, interpretation, and debate by philosophers, theologians, linguists, and scientists, the nature of consciousness remains perplexing and controversial, being “the most familiar and yet most mysterious aspect of our lives”. the only widely agreed upon concept about this topic may be the intuitive belief in its existence.
consciousness and self-referential structure is a related topic. self-referential structure is an understanding of human consciousness by philosophers, psychologists, and neuroscientists. according to this understanding, human consciousness is formed through cognition and understanding of oneself and others. it is a fundamental construct of human cognition and consciousness. however, the origin of consciousness and its relationship with self-referential structure remain unresolved scientific questions, with various interpretations.
self-referential structure refers to a structure that includes itself as a part. it can be mentioned in fields such as computer science, mathematics, logic, philosophy, biology, and psychology. it is usually a circular structure, part of which points to itself. this structure is useful for studying self-awareness, recursive algorithms, and systems theory. famous problems involving computer programs, mathematics, logic, proofs, such as the turing halting problem, gödel’s incompleteness, and hilbert’s undecidability, and russell’s paradox are self-referential issues.
self-referential structures are of two types: complete and incomplete. a complete self-referential structure is one without contradiction or paradox, which can be fully described in its own language or description. an incomplete self-referential structure is one with contradiction or paradox, which cannot be fully described in its own language or description. this structure is an important premise for gödel’s incompleteness theorem and hilbert’s undecidability theorem. whether human self-referential structure is complete or not, there is no clear answer. it is a complex philosophical question, involving multiple aspects of human self-awareness, cognition, and behavior. there is no simple answer to this question.
self-reference is a very ancient topic, usually related to ancient mysteries and various mystical philosophies. for example, the buddhist advocacy of “observing the impermanence of the body, observing the mind without me”, and ancient greece’s “know yourself”, are urging people to point the arrow of mental observation at themselves. the “nothingness” advocated by chinese taoists is a simple paradox in one word. a painting that best embodies the profound meaning of self-reference is the snake that is devouring itself. this snake, as a totem, has appeared extensively in norse mythology, christian theology, hinduism, and african religions. this snake vividly embodies the profound self-destructiveness of self-reference – one can imagine what a weird scene it would create when it completely devours itself.
in 1953, as people were toasting to watson and crick’s discovery of the dna double helix, which explained the mystery of life’s self-replication at the molecular level, another great american-hungarian mathematician, john von neumann, was independently contemplating the logical basis of life’s self-replication. suffering from cancer, he passed away in february 1957. his assistant arthur burks compiled his theory of self-reproducing automata, which was published in 1966. unlike watson and crick, von neumann was looking for the logical rather than material basis of life’s self-replication. although von neumann did not specify, it was implied that this logical basis for self-replication is a kind of self-referential structure.
in 1938, stephen kleene, who co-founded the foundation of recursive function theory with gödel, proved a famous theorem in recursive function theory, known more precisely as kleene’s second recursion theorem. according to it, it is possible to easily obtain a mathematical theorem stating that system self-replication is possible.
the core technique for proving the recursion theorem is a special technique called quine. willard.v. quine was an american philosopher, dedicated to philosophy, mathematical logic, and set theory. he created a method, called quine’s method, that allowed people to create sentences that could talk about themselves without using words like “i” or “this sentence”.
interestingly, the construction of quine is exactly that “golden diagonal line” (this method is the one cantor first used to prove that there are more real numbers than natural numbers, and is also the key technology for gödel’s theorem to construct gödel sentences). however, the diagonal line methods of cantor, gödel, and others are slightly different from quine’s diagonal line method.
self-reference is related to that infamous paradox sentence: “this statement is false.” this sentence is annoying because whether you assume it is true or false, you will come to the opposite conclusion. therefore, the statement is neither true nor false. however, this “liar’s paradox” is just one of many members of the vast family of self-referential sentences. many languages are self-referential, but harmless or even beneficial. for example, the sentence: “this statement is true” is a sentence that can be either true or false. your assumption about its truth or falsehood will determine the conclusion.
the mystery of life is not in complex physical rules, nor in intricate control logic. its essence lies in the overlap of self-reference on different levels. when this overlap occurs, information and physics are completely isomorphic, future and past are completely isomorphic, reality and virtual are completely isomorphic, and even observer and observed are completely isomorphic in some sense.
