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PI in the Sky: Counting, Thinking, and Being Paperback – 1992
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From Publishers Weekly
British mathematician Barrow ( Theories of Everything ) here commands an elegant modern style in describing a more classical, structured grammar: that of numbers. This broad history of--and reflection upon--the role of mathematics in the human enterprise of figuring reality spans recorded civilization. Barrow examines hash marks made on bones that date from 9000 B.C., delves into numerology, observes mathematics in the depths of philosophy and the far reaches of cosmology, often utilizing playful headings to introduce substantive material (the section on early mathematics in the Near East is titled "The Counter Culture"). General readers who doubt that "numeracy" is as civilizing a pursuit as literacy will note how utterly human are some of the early-20th-century intuitionists' debates Barrow recounts in "Intuitionism: The Immaculate Construction." He does not justify the culture of mathematics as "fun" or as a separate, mystical realm but characterizes it as the modern manifestation of the oldest and most compelling human instinct.
Copyright 1992 Reed Business Information, Inc. --This text refers to an alternate Paperback edition.
About the Author
About the Author:
John D. Barrow is Professor in the Astronomy Centre of the University of Sussex. His is the author of several highly acclaimed volumes on the philosophy of science, including most recently Theories of Everything, which Publishers Weekly hailed as "a mind-boggling intellectual adventure."
--This text refers to an alternate Paperback edition.
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Top Customer Reviews
The books starts with an introduction that really grabbed me. It talks about how most scientific theories are expressed in the language of mathematics and then asks a simple question: Why? What is it about the world that makes it so mathematical? The introduction clearly lays out mathematics deepest secret: Beneath all the formulas and proofs there is something about math that is mysterious and profound. This was not something my high school teacher pointed out.
The following chapters present the history of mathematics in an style that manages to inform about important concepts without getting bogged down in formulas. The author strikes a delicate balance between writing about mathematicians as people and writing about their work and its importance.
In the end, he doesn't have any answers about the deep questions posed in the introduction. But after reading his book it didn't matter because at least I now understood better what the questions meant and could appreciate their profound, abstract beauty. Sort of like the difference between looking up in the night sky and seeing little points of light versus seeing the vast universe. Excuse my hyperbole, but that's the best I can explain it.
Anyway, I highly recommend the book to anyone who might read this review. I especially recommend it to students just beginning their math studies. This book will help them appreciate the subject in a way that no textbook ever could.
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 (firstname.lastname@example.org)
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