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

By George Gamow | Go to book overview

CHAPTER I
Big Numbers

1. HOW HIGH CAN YOU COUNT?

THERE is a story about two Hungarian aristocrats who decided to play a game in which the one who calls the largest number wins.

"Well," said one of them, "you name your number first."

After a few minutes of hard mental work the second aristocrat finally named the largest number he could think of.

"Three," he said.

Now it was the turn of the first one to do the thinking, but after a quarter of an hour he finally gave up.

"You've won," he agreed.

Of course these two Hungarian aristocrats do not represent a very high degree of intelligence1 and this story is probably just a malicious slander, but such a conversation might actually have taken place if the two men had been, not Hungarians, but Hottentots. We have it indeed on the authority of African explorers that many Hottentot tribes do not have in their vocabulary the names for numbers larger than three. Ask a native down there how many sons he has or how many enemies he has slain, and if the number is more than three he will answer "many." Thus in the Hottentot country in the art of counting fierce warriors would be beaten by an American child of kindergarten age who could boast the ability to count up to ten!

Nowadays we are quite accustomed to the idea that we can write as big a number as we please--whether it is to represent war expenditures in cents, or stellar distances in inches--by

____________________
1
This statement can be supported by another story of the same collection in which a group of Hungarian aristocrats lost their way hiking in the Alps. One of them, it is said, took out a map, and after studying it for a long time, exclaimed: "Now I know where we are!""Where?" asked the others. "See that big mountain over there? We are right on top of it."

-3-

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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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