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

By George Gamow | Go to book overview

simply setting down a sufficient number of zeros on the right side of some figure. You can put in zeros until your hand gets tired, and before you know it you will have a number larger than even the total number of atoms in the universe,2 which, incidentally, is 300,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.

Or you may write it in this shorter form: 3·1074.

Here the little number 74 above and to the right of 10 indicates that there must be that many zeros written out, or, in other words, 3 must be multiplied by 10 seventy-four times.

But this "arithmetic-made-easy" system was not known in ancient times. In fact it was invented less than two thousand years ago by some unknown Indian mathematician. Before his great discovery--and it was a great discovery, although we usually do not realize it--numbers were written by using a special symbol for each of what we now call decimal units, and repeating this symbol as many times as there were units. For example the number 8732 was written by ancient Egyptians:

whereas a clerk in Caesar's office would have represented it in this form:

MMMMMMMMDCCXII

The latter notations must be familiar to you, since Roman numerals are still used sometimes--to indicate the volumes or chapters of a book, or to give the date of a historical event on a pompous memorial tablet. Since, however, the needs of ancient accounting did not exceed the numbers of a few thousands, the symbols for higher decimal units were nonexistent, and an ancient Roman, no matter how well trained in arithmetic, would have been extremely embarrassed if he had been asked to write "one million." The best he could have done to comply with the request, would have been to write one thousand M's in succession, which would have taken many hours of hard work (Figure 1).

For the ancients, very large numbers such as those of the stars

____________________
2
Measured as far as the largest telescope can penetrate.

-4-

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

Table of contents

  • 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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