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Mind Tools: The Five Levels of Mathematical Reality

4.03  ·  Rating details ·  124 ratings  ·  13 reviews
Now available in paperback, Mind Tools connects mathematics to the world around us. Reveals mathematics' great power as an alternative language for understanding things and explores such concepts as logic as a computing tool, digital versus analog processes and communication as information transmission.
Paperback, 328 pages
Published February 1st 1988 by Mariner Books (first published 1987)
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Gianni Adragna
Nov 04, 2015 rated it liked it
I found this book disappointing. The author makes a promise at the very beginning. The promise is that he will show how information theory connects to the four main branches of maths, numbers, space, infinity and logic. The result is quite chaotic, results are presented one after the other with the same logic used for showing items for sale in a charity shop, i.e. little if any. The promise is broken and the book ends quite comically with the author trying to explain in three sentences what the ...more
Tom Schulte
In my reading, something happened between considering a tetrahedron’s vertices labeled Disease, Death, Loneliness, and Struggle and the passage: “The symbol 0 seems egg-like, female, while 1 is spermlike and male. Can this really be an accident? …An egg is round, and a sperm is skinny. …Formally speaking, both zero and one are undefinable.” I began to wonder why Dover reprinted this peculiar work. Into “Number”, after a discourse on Pythagorean metaphysics heading toward numerology, the book tak ...more
Dan Ust
Mar 22, 2017 rated it liked it
I read this in high school, so this is my recollection years later. I found it interesting to divide math into different approaches. I was already deeply interested in math. Anyhow, this is more a beginners intro to the conceptual issues in math: whets the appetite, but isn't the final word (of course!).
Mar 29, 2009 rated it really liked it
Shelves: nonfiction
A really excellent work in this field. I'm by no means a math whiz but this explained the topic well for those who aren't whizzes. If my grade school math teacher had told me just a few of these things I might have grown up loving math.
May 20, 2019 rated it liked it
Shelves: nonfiction
Math nerds unite! This will thrill any math-o-phile. Me, not so much. I'm really good at geometry and I love algebra, but this book was way out of my league . . . and interest level. While I admire Prof. Rucker's obviously brilliant mind (although I couldn't tell you if the book were or were not fraught with errors as I barely could understand a word of it . . .), the subject didn't do much for me. From fractals to googols to caustic nephroids to polynomial quartic space . . . get the picture? A ...more
Richard Meese
Apr 16, 2020 rated it it was amazing
Turing, Goedel, Cantor, a great treatment of infinity and computer science. Puts forward the idea that any thing can be coded, including human thought--which leads to an idea of the possibility of machine intelligence.
Jan 29, 2008 rated it it was amazing

Rudy Rucker links mathematics to reality and explains 5 ways we can look at it: in terms of number, space, logic, infinity and information. The concepts explained are rather simple to understand and I'm pretty sure everyone will find some things they didn't know before. Later in a book he argues that "reality as information" may be the most correct view and our universe can indeed be a computational process.
I suggest people whose interest touches corners of math read the book, otherwise you may
Sep 17, 2015 added it
Overall good food for thought, touches on tons of topics (some better than others). The way he presents proofs and more formal stuff is hard to follow, or I just wasn't trying very hard.

Ends with a fun theory of what reality is
Feb 07, 2013 rated it it was amazing
This one is moving me out of my mathematical comfort zone and keeping me reading.
edit: Now I'm done reading it, I can wholeheartedly recommend it for your kids. Grab it if you see it, this author has a good way with words.
Ami Iida
Jun 21, 2015 rated it liked it
Recommends it for: Infinite
Shelves: math
the story about Infinite ∞

I finished reading it just now. I knew this book
from complex system . I reference Infinite relative with complex system
Christopher Gilmour
Oct 26, 2013 rated it it was ok
its a book for dull people
Feb 22, 2013 rated it it was amazing
Great survey of mathematics that reveals its importance as a pure philosophy for everyday use.
Carrie Felton
May 29, 2013 rated it it was amazing
Very interesting. Does a good job of making connections that I never would have seen on my own.
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Rudolf von Bitter Rucker is an American mathematician, computer scientist, science fiction author, and one of the founders of the cyberpunk genre. He is best known for his Ware Tetralogy, the first two of which won Philip K. Dick awards. Presently, Rudy Rucker edits the science fiction webzine Flurb.

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