Peter Mcloughlin's Reviews > Infinity and the Mind: The Science and Philosophy of the Infinite

Infinity and the Mind by Rudy Rucker
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This book written in the seventies is something I read as a teenager in the 80s and is one of my all time favorite non-fiction books. This book explores infinity a concept that has always been with humans but was revolutionized in the late 19th century by Georg Cantor. Cantor showed that the infinity of the natural numbers is the smallest of (wait for it) an infinite number of larger and larger infinities. Cantor opened up a paradise in the words of one mathematician that we shall never be banished.
Infinity is a necessary but troublesome concept in Mathematics and it may be (I hope) a feature of the Physical world. Infinities crop up in time and space and in principal dividing up a stick into smaller pieces indefinitely. They exist physically in equations for black hole singularities and electrons interacting with themselves in Quantum Mechanics as if a ouroboros is built into the world generating infinities while biting its own tail.
This same principle applies to set theory where the set of all numbers can magically be created out of the empty set. The creation of infinity ex nihilo like the book of Genesis. I am not a believer but contemplating the infinite is the closest thing for me to pious meditation on God. This book covers development in transfinite numbers and paradoxes of the infinite including Gödel's incompleteness paradox, Russell paradox and Berry paradox and most important twentieth century developments on the topic. I come back to this book every few years for inspiration and awe at the pregnant idea of infinity.
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Reading Progress

Started Reading
January 1, 1986 – Finished Reading
January 7, 2013 – Shelved
May 3, 2013 – Shelved as: mathematics
May 21, 2013 – Shelved as: philosophy
May 21, 2013 – Shelved as: favorites
December 19, 2013 –
page 9
2.45% "different people approach infinity with different attitudes. Blaise Pascal and the author talk about the terror of infinite times and spaces. I actually find endless time and space quite comfortable. I have never felt terror at the thought of being a tiny drop in and endless ocean. I like the idea of endlessness and would be quite happy if it turned out that this was the nature of reality."
December 19, 2013 –
page 53
14.4% "This chapter is on ways the universe can be infinite in time and space. The ways time and space can loop back on itself. It also covers higher dimensions. How to construct infinite from sets and numbers and recursion. How to cut up a line in infinite pieces. This kind of stuff I could think about all day and never tire of."
December 19, 2013 – Shelved as: 1890-1959
December 19, 2013 – Shelved as: 1960-to-1989
December 19, 2013 – Shelved as: complexity
December 19, 2013 – Shelved as: computers
December 19, 2013 – Shelved as: general-science
February 11, 2014 – Shelved as: owned-books
June 11, 2016 – Shelved as: 00000good-things

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WarpDrive Very nice review, Peter. I immediately bumped up this book to the top of my to-read list :)

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