One, Two, Three ... Infinity: Facts & Speculations of Science

By George Gamow | Go to book overview

CHAPTER III
Unusual Properties of Space

1. DIMENSIONS AND CO-ORDINATES

WE ALL know what space is, although we should find ourselves in a rather awkward position if we were asked to define exactly what we mean by the word. We should probably say that space is that which surrounds us, and through which we can move forward or backward, right or left, up or down. The existence of the three independent mutually perpendicular directions represents one of the most fundamental properties of the physical space in which we live; we say that our space is three- directional or three-dimensional. Any location in space can be indicated by referring to these three directions. If we are visiting an unfamiliar city and we ask at the hotel desk how to find the office of a certain well-known firm, the clerk may say: "Walk five blocks south, two blocks to the right, and go up to the seventh floor." The three numbers just given are usually known as coordinates, and refer, in this case, to the relationship between the city streets, the building floors, and the point of origin in the hotel lobby. It is clear, however, that directions to the same location can be given from any other point, by using a co-ordinate system, which would correctly express the relationship between the new point of origin and the destination, and that the new co-ordinates can be expressed through the old ones by a simple mathematical procedure provided we know the relative position of the new co-ordinate system in respect to the old one. This process is known as the transformation of co-ordinates. It may be added here that it is not at all necessary that all three co-ordinates be expressed by the numbers representing certain distances; and, in fact, it is more convenient in certain cases to use angular coordinates.

Thus, for example, whereas addresses in New York City are most naturally expressed by a rectangular co-ordinate system

-41-

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One, Two, Three ... Infinity: Facts & Speculations of Science

• Other Books by George Gamow ii
• Title Page iii
• Preface v
• Contents vii
• Illustrations viii
• Part I - Playing with Numbers 1
• Chapter I - Big Numbers 3
• Chapter II - Natural and Artificial Numbers 24
• Part II - Space, Time: & Einstein 39
• Chapter III - Unusual Properties of Space 41
• Chapter IV - The World of Four Dimensions 64
• Chapter V - Relativity of Space and Time 84
• Part III - Microcosmos 113
• Chapter VI - Descending Staircase 115
• Chapter VII - Modern Alchemy 149
• Chapter VIII - The Law of Disorder 192
• Chapter IX - The Riddle of Life 231
• Part IV - Macrocosmos 267
• Chapter X - Expanding Horizons 269
• Chapter XI - The Days of Creation 298
• Index 336
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