Infinity And The Mind: The Science And Philosophy Of The Infinite (Penguin Science)
A quite interesting, intellectually challenging, vibrant book which describes the concept of infinity both from mathematical (transfinite numbers) and philosophical standpoints.
Some ideas, like the concept of "Absolute Continuum", are very interesting; several subjects (like Godel's incompleteness theorems, Set Theory and its foundational importance in mathematics and in other disciplines, the Continuum Hypothesis, Godel's Neoplatonic philosophical approach to mathematics) are absolutely brillia ...more
Some passages and even some ideas were a bit obtuse/confusing, e.g. the concept of (circular) scale, which I only half understood. Quite ...more
Author of one of the very few books that changed how I think, Rudy Rucker is a mathematician who also writes fictionalized autobiographies and histories using science fiction tropes; hallucinatory, sublime, filled with scientific references and social observations, curiouser and curiouser.
A wizard of numbers and their philosophical meanings, he spins stories which may or may not be fictions in the usual sense; and the discovery of his nonfiction works can ...more
There is puzzles at the end of every chapter but they are not merely new information, most of them are differentiations of the idea in that topic.
I cannot go without mentioning the paradoxes. They are everywhere in the book. 'Even in my comment, which is false' If the sentence is true then my comment includes a ...more
Of course I didn't read the lengthy extra math excursions at the ...more
*Infinities and indivisibilities - I just appreciate this string of words
*Finite but unbounded - my favourite part of the book in chapter 1 which help me put the 4th dimenesion into perspective
An overview of the mathematics and philosophy of the infinite.
This book touches on many subjects including the transfinite numbers, Godel's Incompleteness Theorems, the possibility of machine intelligence, the limits of human intelligence, the ultimate reality of mathematics, and the concept of the Absolute.
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