From Here to Infinity
One Two Three . . . Infinity by George Gamow is a classic that has introduced generations of readers, laymen and professionals alike, to the pleasures of mathematics and science. The experience of Sheldon Glashow, who shared the 1979 Nobel Prize in physics with Abdus Salam and Steven Weinberg, is typical: "One book, which I found in 1947 when I was 15 was the book by George Gamow called One, Two, Three - Infinity, which I still re-read from time to time. It's just a book describing the wonders of nature and, to the extent that a high school kid could understand, how we understand things about nature. That was one book I really appreciated."
First published in 1947 and revised in 1961, Gamow uses far-ranging knowledge, humor, imagination and his delightful and idiosyncratic pen-and-ink illustrations to explain the challenges and discoveries of science. His conversational writing style draws the reader in, and even thought parts of it have become dated, his book succeeds in achieving that most elusive of goals: kindle our sense of wonder at nature's mysteries.
Gamow begins with the strange yet familiar number infinity. How does one count it? Are there different types of infinities? Can two infinities be compared? Gamow calls Georg Cantor (1845-1918) the founder of the "arithmetics of infinity" and explains how his idea of Sets gave us a new way of grasping infinity's significance.
(Random associations appear unbidden. Gamow calculates that the number of sand grains necessary to fill up the visible universe would be over 10100, that is, 1 followed by 100 zeros. The mathematical term for 10100 is Googol. That is what Larry Page and Sergey Brin wanted to call their start-up but through a misspelling, the company they co-founded became known as Google.)
Gamow devotes several chapters exploring the properties of space and time using nothing more than middle/high school arithmetic, and gives a good overview of the ideas that led to Einstein's Special and General Theory of Relativity. He "uncovers" atomic and nuclear physics by tracing their historical roots from the Greeks, progressing all the way to the "modern alchemy" of radioactivity, fission, fusion and elementary particles. The discovery and implications of nuclear chain reactions are particularly well-told.
The value of Gamow's narrative on the foundation of modern physics lies not in its completeness (it is obviously not) but in its capacity to inspire readers to explore the subject in greater detail on their own.
Perhaps the most masterful chapter is "The Law of Disorder." This physical law is also known as "The Law of Statistical Behavior" and Gamow goes through various examples, including the "Drunkard's Walk," to show how scientists can draw profound conclusions about nature by looking at seemingly ordinary problems "a little more attentively" than the average person. Two examples he cites are Brownian motion and diffusion. There is also a discussion of probability and the Law of Entropy that is instructive and entertaining.
"The Riddle of Life" chapter reflects Gamow's interest in biology, a field that he took on as a physicist and to which he ended up making fundamental contributions. The last chapters deal with the study of planets, stars, galaxies and beyond.
One would not know by reading One Two Three . . . Infinity that Gamow made seminal contributions to nuclear and quantum physics, and that he was one of the chief architects of the Big Bang Theory, the idea that the universe began in a terrifyingly hot explosion that flung the stars and galaxies in all directions in an expanding universe. As far back as 1948, Gamow predicted that the radiation from the Big Bang must be filling the universe. Many physicists believe that he deserved a Nobel Prize for his daring theory and prediction. However, it was not to be. Arno Penzias and Robert Wilson won the physics Nobel Prize in 1978 "for their discovery of cosmic microwave background radiation." In 2006, John Mather and George Smoot won the physics Nobel Prize for "increased support for the Big Bang scenario for the origin of the universe."
Be that as it may, Gamow's reputation as a scientist is secure, not only because of his original contributions in many areas (an anomaly in our era of narrow specializations), but also because of the way he popularized science and inspired generations of readers to tune in to the wonders of the "microcosmos" and the "macrocosmos." One, Two, Three - Infinity reflects the spirit of this brilliant scientist and master storyteller.