Infinity and the Mind
Encyclopedia
Infinity and the Mind: The Science and Philosophy of the Infinite is a theoretical mathematics book by American mathematician, computer scientist, and science fiction
writer Rudy Rucker
.
, have very austere covers suggesting an academic work.
, and a number of related topics. These include Gödel's incompleteness theorems
and their relationship to concepts of artificial intelligence
and the human mind, as well as the conceivability of some unconventional cosmological models. The material is approached from a variety of viewpoints, some more conventionally mathematical and others being nearly mystical. There is a brief account of the author's personal contact with Kurt Gödel
.
An appendix contains one of the few popular expositions on set theory
research on what are known as "strong axioms of infinity."
Science fiction
Science fiction is a genre of fiction dealing with imaginary but more or less plausible content such as future settings, futuristic science and technology, space travel, aliens, and paranormal abilities...
writer Rudy Rucker
Rudy Rucker
Rudolf von Bitter Rucker is an American mathematician, computer scientist, science fiction author, and philosopher, and is one of the founders of the cyberpunk literary movement. The author of both fiction and non-fiction, he is best known for the novels in the Ware Tetralogy, the first two of...
.
Marketing
The dust jacket of the original (Birkhäuser) edition had a picture of a star over a mountain and appeared to be a religious or mystical work. Subsequent paperback reprintings had covers suggesting that the publishers wished to appeal to a "new age" market. The most recent editions, from Princeton University PressPrinceton University Press
-Further reading:* "". Artforum International, 2005.-External links:* * * * *...
, have very austere covers suggesting an academic work.
Synopsis
The book contains popular expositions (accessible to readers with no more than a high school mathematics background) on the mathematical theory of infinityInfinity
Infinity is a concept in many fields, most predominantly mathematics and physics, that refers to a quantity without bound or end. People have developed various ideas throughout history about the nature of infinity...
, and a number of related topics. These include Gödel's incompleteness theorems
Gödel's incompleteness theorems
Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of...
and their relationship to concepts of artificial intelligence
Artificial intelligence
Artificial intelligence is the intelligence of machines and the branch of computer science that aims to create it. AI textbooks define the field as "the study and design of intelligent agents" where an intelligent agent is a system that perceives its environment and takes actions that maximize its...
and the human mind, as well as the conceivability of some unconventional cosmological models. The material is approached from a variety of viewpoints, some more conventionally mathematical and others being nearly mystical. There is a brief account of the author's personal contact with Kurt Gödel
Kurt Gödel
Kurt Friedrich Gödel was an Austrian logician, mathematician and philosopher. Later in his life he emigrated to the United States to escape the effects of World War II. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the...
.
An appendix contains one of the few popular expositions on set theory
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
research on what are known as "strong axioms of infinity."