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John D. Barrow

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PI in the Sky: Counting, Thinking, and Being Paperback – January 1, 1992

by John D. Barrow (Author)

4.8 25 ratings

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John D. Barrow's Pi in the Sky is a profound -- and profoundly different -- exploration of the world of mathematics: where it comes from, what it is, and where it's going to take us if we follow it to the limit in our search for the ultimate meaning of the universe. Barrow begins by investigating whether math is a purely human invention inspired by our practical needs. Or is it something inherent in nature waiting to be discovered?

In answering these questions, Barrow provides a bridge between the usually irreconcilable worlds of mathematics and theology. Along the way, he treats us to a history of counting all over the world, from Egyptian hieroglyphics to logical friction, from number mysticism to Marxist mathematics. And he introduces us to a host of peculiar individuals who have thought some of the deepest and strangest thoughts that human minds have ever thought, from Lao-Tse to Robert Pirsig, Charles Darwin, and Umberto Eco. Barrow thus provides the historical framework and the intellectual tools necessary to an understanding of some of today's weightiest mathematical concepts.

Print length

317 pages
Language

English
Publication date

January 1, 1992
Dimensions

6 x 0.75 x 9.25 inches
ISBN-10

0316082597
ISBN-13

978-0316082594
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Product details

Publisher ‏ : ‎ Back Bay Books; Reprint edition (January 1, 1992)
Language ‏ : ‎ English
Paperback ‏ : ‎ 317 pages
ISBN-10 ‏ : ‎ 0316082597
ISBN-13 ‏ : ‎ 978-0316082594
Item Weight ‏ : ‎ 1.05 pounds
Dimensions ‏ : ‎ 6 x 0.75 x 9.25 inches

Best Sellers Rank: #2,111,542 in Books (See Top 100 in Books)
- #1,090 in Mathematical Physics (Books)
- #1,270 in Mathematics History

Customer Reviews:
4.8 25 ratings

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4.8 out of 5

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Mark ER

Great Book, Good service

Reviewed in the United States on March 17, 2017

Verified Purchase

Very interesting book. Answers some of my questions, on how counting started and evolved.

One person found this helpful

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W Paul C Hamilton

Five Stars

Reviewed in the United States on July 28, 2016

Verified Purchase

A hard read but worth it.

One person found this helpful

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Mr. Richard M. Smith

Five Stars

Reviewed in the United States on April 1, 2017

thank you

Discusses the question -- A delite

Reviewed in the United States on November 25, 2018

I have BA and MS degrees in Mathematics and Statistics, respectively. I have therefore spent some time debating whether Mathematics is discovered of invented. This book provide more food for thought on the subject. It's a great read.

One person found this helpful

Helpful

Librum

Very thought provoking and challenging read

Reviewed in the United States on June 18, 2012

A popular treatment of the philosophy of mathematics (PoM) -- not a book I imagine would jump off the shelves. Yet, what a gem this book is. For anyone not in the know about what some of the great intellectual debates in the realm of PoM are, Pi in the Sky offers a very solid, and endlessly interesting, overview. It's not always an easy-going read, but it's certainly one that rewards persistence. Barrow does a brilliant job of linking abstruse PoM arguments to other branches of philosophy (philosophy of mind and metaphysics for instance). Throughout, he maintains a neutral stance vis-a-vis competing positions, laying them out in detail, and presenting a wealth of arguments both pro and con. Whether or not Barrow is, himself, a Platonist, is irrelevant. He does not press a particular agenda in this book, only raises questions that have worried generations of philosophically minded mathematicians, and discusses the different philosophical claims that have been staked in response to them. In addition, Pi in the Sky is packed with fascinating insights from anthropology and developmental psychology, and with wonderful thought experiments. In short, Pi in the Sky is an intellectual feast. Don't be swayed by the moronic review at the bottom of this page. If "A Customer" even read this book (I doubt he/she did) he/she completely missed both the forest and the trees.

6 people found this helpful

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Mr P R Morgan

Is mathematics real?

Reviewed in the United States on November 14, 2004

That may be a silly question. After all, most of us use counting and numerical calculations many times a day. However, the reading matter here digs below the surface, and asks such awkward questions. What is the nature of maths? Would there be any maths if there were no mathematicians?

Starting with theories of counting, and the origins of methods of enumeration, John Barrow plunges headlong into the philosophy of mathematics. Perhaps the book ought to carry a health warning, for it should not be read accidentally. Readers need to have a grounding in some of the great mathematical movements, and discoveries. (Perhaps it is a bit judgmental to even use the word "discoveries"; are mathematical ideas invented or discovered? That topic is part of the subject matter).

I liked the debate, but found the volume hard going. It is not the kind of book to read solidly from cover to cover. A great deal of re-reading is necessary, and picking it up on the train requires a conscious effort to remember what the current debate is about. Some of the arguments are very intricate for those of us who are not mathematicians.

The work of some of the pillars of mathematics are described in varying detail, together with the triple crises that hit maths in the early years of the 20th Century. The optimism of Hilbert on the one hand, or Russell and Whitehead on the other was washed away by the work of Kurt Godel. The Austrian Godel, by the way, has been described as one of the most innovative minds of that century.

There are some interesting insights into some of the characters from the history of maths. Leopold Kronecker did not believe in negative numbers. However, he had been a BANKER. How did he convince his customers that the problems caused by negative numbers (i.e. too little in their accounts) needed to be solved? There were also some disturbing questions raised by the work of Cantor on set theory. This gives rise to a wonderful paradox called "Hilbert's Hotel".

As with many works on philosophy, it is not the answers that are important, it is the questions. Does the entity pi exist, even if there are no mathematicians. Is there really a universal 'pi in the sky', external to any human thought? You decide.

Peter Morgan, Bath, UK (morganp@supanet.com)

19 people found this helpful

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Indikos

God created the integers, the rest is the work of Man

Reviewed in the United States on April 18, 2014

I really liked this book on the history of numbers.
Found it very well written and the story kept me hooked.
People who do not have much of an interest in math
will probably find this book rough going.
But it should grab those who have some interest in math,
particularly high school students.
The origin of our number system in India, the discussion of the
invention of the zero and negative numbers I really liked.
I also liked the stories about the mathematicians Hilbert,
Kronecker, Ramanujan, Godel and Cantor.
The discussion of the Russell paradox in set theory was very good too.
The book does not get into how modern mathematics creates
the numbers a la Peano -- but that may been going too far afield.

4 people found this helpful

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Top reviews from other countries

W Paul C Hamilton

I found this is difficult but most enjoyable read. ...

Reviewed in the United Kingdom on January 20, 2016

Verified Purchase

I found this is difficult but most enjoyable read. The first chapter on the ways human beings count was especially stimulating. To be honest I'm going to have to read the book a second time in order to completely understand what the subject matter is all about. Worth the effort however!

2 people found this helpful

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