Douglas Richard Hofstadter is an American cognitive and computer scientist whose research includes concepts such as the sense of self in relation to the external world, consciousness, analogy-making, strange loops, artificial intelligence, and discovery in mathematics and physics. His 1979 book Gödel, Escher, Bach: An Eternal Golden Braid won the Pulitzer Prize for general nonfiction, and a National Book Award for Science. His 2007 book I Am a Strange Loop won the Los Angeles Times Book Prize for Science and Technology.
Martin Gardner was an American popular mathematics and popular science writer with interests also encompassing magic, scientific skepticism, micromagic, philosophy, religion, and literature – especially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton. He was a leading authority on Lewis Carroll; The Annotated Alice, which incorporated the text of Carroll's two Alice books, was his most successful work and sold over a million copies. He had a lifelong interest in magic and illusion and in 1999, MAGIC magazine named him as one of the "100 Most Influential Magicians of the Twentieth Century". He was considered the doyen of American puzzlers. He was a prolific and versatile author, publishing more than 100 books.
Nomic is a game created in 1982 by philosopher Peter Suber, the rules of which include mechanisms for changing those rules, usually beginning by way of democratic voting. The game demonstrates that in any system where rule changes are possible, a situation may arise in which the resulting laws are contradictory or insufficient to determine what is in fact legal.
Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research-and-application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited to being an endeavor for amateurs, many topics in this field require no knowledge of advanced mathematics. Recreational mathematics involves mathematical puzzles and games, often appealing to children and untrained adults and inspiring their further study of the subject.
Self-reference is a concept that involves referring to oneself or one's own attributes, characteristics, or actions. It can occur in language, logic, mathematics, philosophy, and other fields.
Gödel, Escher, Bach: an Eternal Golden Braid, also known as GEB, is a 1979 book by Douglas Hofstadter.
In analytic philosophy, a fundamental distinction is made between the use of a term and the mere mention of it. Many philosophical works have been "vitiated by a failure to distinguish use and mention". The distinction can sometimes be pedantic, especially in simple cases where it is obvious.
Skeptical Inquirer (S.I.) is a bimonthly American general-audience magazine published by the Committee for Skeptical Inquiry (CSI) with the subtitle "The Magazine for Science and Reason". The magazine initially focused on investigating claims of the paranormal, but evolved and expanded to address other pseudoscientific topics that are antithetical to critical thinking and science. Notable skeptics have credited the magazine in influencing their development of scientific skepticism. In the "Letters to the Editor", the most frequent letters of appreciation come from educators.
In economics and game theory, a participant is considered to have superrationality if they have perfect rationality but assume that all other players are superrational too and that a superrational individual will always come up with the same strategy as any other superrational thinker when facing the same problem. Applying this definition, a superrational player who assumes they are playing against a superrational opponent in a prisoner's dilemma will cooperate while a rationally self-interested player would defect.
An ambigram is a calligraphic composition of glyphs that can yield different meanings depending on the orientation of observation. Most ambigrams are visual palindromes that rely on some kind of symmetry, and they can often be interpreted as visual puns. The term was coined by Douglas Hofstadter in 1983–1984.
The interesting number paradox is a humorous paradox which arises from the attempt to classify every natural number as either "interesting" or "uninteresting". The paradox states that every natural number is interesting. The "proof" is by contradiction: if there exists a non-empty set of uninteresting natural numbers, there would be a smallest uninteresting number – but the smallest uninteresting number is itself interesting because it is the smallest uninteresting number, thus producing a contradiction.
In the platonia dilemma introduced in Douglas Hofstadter's book Metamagical Themas, an eccentric trillionaire gathers 20 people together, and tells them that if one and only one of them sends them a telegram by noon the next day, that person will receive a billion dollars. If they receive more than one telegram, or none at all, no one will get any money, and cooperation between players is forbidden. In this situation, the superrational thing to do is to send a telegram with probability 1/20.
The Planiverse is a novel by A. K. Dewdney, written in 1984 about a two-dimensional world.
Egbert B. Gebstadter is a fictional author who appears in the indices of books by Douglas R. Hofstadter. For each Hofstadter book, there is a corresponding Gebstadter book. His name is derived from "GEB", the abbreviation for Hofstadter's first book Gödel, Escher, Bach: An Eternal Golden Braid; the letters appear in his last name, permuted in his first name, and permuted again in his initials.
I Am a Strange Loop is a 2007 book by Douglas Hofstadter, examining in depth the concept of a strange loop to explain the sense of "I". The concept of a strange loop was originally developed in his 1979 book Gödel, Escher, Bach.
In the end, we are self-perceiving, self-inventing, locked-in mirages that are little miracles of self-reference.
Infinity and the Mind: The Science and Philosophy of the Infinite is a popular mathematics book by American mathematician, computer scientist, and science fiction writer Rudy Rucker.
Aronson's sequence is an integer sequence defined by the English sentence "T is the first, fourth, eleventh, sixteenth, ... letter in this sentence." Spaces and punctuation are ignored. The first few numbers in the sequence are:
Wheels, Life and Other Mathematical Amusements is a book by Martin Gardner published in 1983. The Basic Library List Committee of the Mathematical Association of America has recommended its inclusion in undergraduate mathematics libraries.
