One Two Three ... Infinity
Encyclopedia
One Two Three ... Infinity: Facts and Speculations of Science is a 1947 non-fiction science book by George Gamow
, is a book about some fundamental concepts in mathematics and science, but written at a level understandable by middle school students up through "intelligent layman" adults. The book is illustrated by Gamow. it remains one of the most well received ever in the popular science genre. Gamow's writing style is informal and wryly humorous, showing a gift for memorable metaphors and analogies.
Beginning with an exploration of elementary number concepts, the book leads with the "Hottentots" (Khoikhoi
), said to have words only for "one", "two", "three", and "many", and builds quickly to explore Georg Cantor
's theory of levels of infinity
– hence the title of the book. It then describes a simple 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's explorations then wind from the mathematics of infinity, to topology
, the fourth dimension
, relativity
, atomic chemistry
, nuclear physics
, entropy
, DNA
, evolution
, cosmology
, and more. For a book originally written in the first half of the twentieth century, Gamow's work remains surprisingly relevant even in the twenty-first century. Gamow focused his writing on what he knew or suspected were fundamentals unlikely to change much, even as science advanced with increasing speed. As a result, very little of his book has become obsolete, and many of the key concepts he covered are even more relevant today.
, with the inscription, "Who would rather be a cowboy".
praised Gamow's book, describing it as an "admittedly rare . . . book which entertains by way of instruction."
George Gamow
George Gamow , born Georgiy Antonovich Gamov , was a Russian-born theoretical physicist and cosmologist. He discovered alpha decay via quantum tunneling and worked on radioactive decay of the atomic nucleus, star formation, stellar nucleosynthesis, Big Bang nucleosynthesis, cosmic microwave...
, is a book about some fundamental concepts in mathematics and science, but written at a level understandable by middle school students up through "intelligent layman" adults. The book is illustrated by Gamow. it remains one of the most well received ever in the popular science genre. Gamow's writing style is informal and wryly humorous, showing a gift for memorable metaphors and analogies.
Beginning with an exploration of elementary number concepts, the book leads with the "Hottentots" (Khoikhoi
Khoikhoi
The Khoikhoi or Khoi, in standardised Khoekhoe/Nama orthography spelled Khoekhoe, are a historical division of the Khoisan ethnic group, the native people of southwestern Africa, closely related to the Bushmen . They had lived in southern Africa since the 5th century AD...
), said to have words only for "one", "two", "three", and "many", and builds quickly to explore Georg Cantor
Georg Cantor
Georg Ferdinand Ludwig Philipp Cantor was a German mathematician, best known as the inventor of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets,...
's theory of levels of infinity
Infinity
Infinity is a concept in many fields, most predominantly mathematics and physics, that refers to a quantity without bound or end. People have developed various ideas throughout history about the nature of infinity...
– hence the title of the book. It then describes a simple 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
Infinite monkey theorem
The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare....
). 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
Big Bang
The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
, only an infinitesimal fraction of the job could have yet been completed.
Gamow's explorations then wind from the mathematics of infinity, to topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
, the fourth dimension
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...
, relativity
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
, atomic chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
, nuclear physics
Nuclear physics
Nuclear physics is the field of physics that studies the building blocks and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those...
, entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
, DNA
DNA
Deoxyribonucleic acid is a nucleic acid that contains the genetic instructions used in the development and functioning of all known living organisms . The DNA segments that carry this genetic information are called genes, but other DNA sequences have structural purposes, or are involved in...
, evolution
Evolution
Evolution is any change across successive generations in the heritable characteristics of biological populations. Evolutionary processes give rise to diversity at every level of biological organisation, including species, individual organisms and molecules such as DNA and proteins.Life on Earth...
, cosmology
Cosmology
Cosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...
, and more. For a book originally written in the first half of the twentieth century, Gamow's work remains surprisingly relevant even in the twenty-first century. Gamow focused his writing on what he knew or suspected were fundamentals unlikely to change much, even as science advanced with increasing speed. As a result, very little of his book has become obsolete, and many of the key concepts he covered are even more relevant today.
Dedication
The book is dedicated to his son, Igor GamowIgor Gamow
Rustem Igor Gamow , son of physicist George Gamow, is a microbiology professor and inventor. His best known inventions include the Gamow bag and the Shallow Underwater Breathing Apparatus.- Youth :...
, with the inscription, "Who would rather be a cowboy".
Reception
Willy LeyWilly Ley
Willy Ley was a German-American science writer and space advocate who helped popularize rocketry and spaceflight in both Germany and the United States. The crater Ley on the far side of the Moon is named in his honor.-Life:...
praised Gamow's book, describing it as an "admittedly rare . . . book which entertains by way of instruction."