One Two Three... Infinity

One Two Three... Infinity

First edition
Author	George Gamow
Illustrator	George Gamow
Language	English
Subjects	Science, mathematics
Published	1947 (Viking Press)
Publication place	United States
Media type	Print
Pages	340
ISBN	978-0486256641
LC Class	Q162.G23

One Two Three... Infinity: Facts and Speculations of Science is a popular science book by theoretical physicist George Gamow, first published in 1947, but still (as of 2020) available in print and electronic formats. The book explores a wide range of fundamental concepts in mathematics and science, written at a level understandable by middle school students up through "intelligent layman" adults. The book includes many handmade illustrations by Gamow.

Overview

The 340 page book has four parts and eleven chapters. The parts are 1 Playing with Numbers, 2 Space, time and Einstein, 3 Microcosmos, 4 Macrocosmos. In the preface the shortness of the last part is attributed to Gamow's previous books The Birth and Death of the Sun and Biography of the Earth. There are 128 illustrations that Gamow drew, "topologically transformed" from works by "numerous artists and illustrators", thanked by Gamow in the preface. Chapter 3 addresses topology and quotes a proof of Euler's polyhedral formula from a work by other authors. A four page index is included. In 1961 a new edition was published. In its preface Gamow says that by luck the 1947 edition was "written just after a number of important scientific advances" so that "relatively few changes and additions were necessary." For example, Heinz Fraenkel-Conrat and Robley Williams separated tobacco mosaic virus into lifeless molecules and then recombined them into active virus. A 1965 edition speculated on assembly of a "man-made virus particle".(p 267)

Beginning with an exploration of elementary numbers, the book opens with a description of the "Hottentots" (Khoikhoi), said to have words only for "one", "two", "three", and "many", and builds quickly to explore Georg Cantor's theory of three levels of infinity—hence the title of the book. It then describes a simple automatic printing press that can in principle (given enough paper, ink, and time) print all the English works that have ever been, or ever will be, printed (a more systematic version of the infinite monkey theorem). The author notes that if all the atoms in the Universe, as known in Gamow's time, were such printing presses working in parallel "at the speed of atomic vibrations" since the beginning of known time, only an infinitesimal fraction of the job could have yet been completed.

Gamow then explores number theory, four-dimensional space, spacetime, relativity, atomic chemistry, nuclear physics, entropy, genetics, and cosmology. The book is known for a quirky sense of humor and for memorable metaphors, such as a visualization of the periodic table of elements on a spiraling cylindrical strip.

Reception

Science writer Willy Ley praised Gamow's book, describing it as an "admittedly rare ... book which entertains by way of instruction". Kirkus Reviews declared it "a stimulating and provocative book for the science-minded layman". Theoretical physicist Sean M. Carroll credited One Two Three... Infinity with setting the trajectory of his professional life. Cognitive scientist Steven Pinker read the book as a child, and has cited it as contributing to his interest in popular science writing. Astrophysicist and science popularizer Neil deGrasse Tyson identified One Two Three... Infinity as one of two books which had the greatest impact on him, the other being Edward Kasner and James Newman's Mathematics and the Imagination.

In 1956, Gamow was awarded the Kalinga Prize by UNESCO for his work in popularizing science, including his book One, Two, Three... Infinity, as well as other works.