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  Text originally published in 1957 under the same title.

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  Publisher’s Note

  Although in most cases we have retained the Author’s original spelling and grammar to authentically reproduce the work of the Author and the original intent of such material, some additional notes and clarifications have been added for the modern reader’s benefit.

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  ONLY A TRILLION

  BY

  ISAAC ASIMOV

  TABLE OF CONTENTS

  Contents

  TABLE OF CONTENTS 3

  DEDICATION 4

  INTRODUCTION 5

  CHAPTER ONE—THE ATOMS THAT VANISH 7

  CHAPTER TWO—THE EXPLOSIONS WITHIN US 18

  CHAPTER THREE—HEMOGLOBIN AND THE UNIVERSE 28

  CHAPTER FOUR—VICTORY ON PAPER 42

  CHAPTER FIVE—THE ABNORMALITY OF BEING NORMAL 55

  CHAPTER SIX—PLANETS HAVE AN AIR ABOUT THEM 64

  CHAPTER SEVEN—THE UNBLIND WORKINGS OF CHANCE 77

  CHAPTER EIGHT—THE TRAPPING OF THE SUN 90

  CHAPTER NINE—THE SEA-URCHIN AND WE 105

  CHAPTER TEN—THE SOUND OF PANTING 114

  CHAPTER ELEVEN—THE MARVELLOUS PROPERTIES OF THIOTIMOLINE 123

  PART I 123

  PART II 130

  CHAPTER TWELVE—PATÉ DE FOIE GRAS 140

  REQUEST FROM THE PUBLISHER 155

  DEDICATION

  To

  GERTRUDE

  again

  INTRODUCTION

  One of the stories my mother likes to tell about me as a child is that once, when I was nearly five, she found me standing rapt in thought at the curbing in front of the house in which we lived. She said, ‘What are you doing. Isaac?’ and I answered, ‘Counting the cars as they pass.’

  I have no personal memory of this incident but it must have happened, for I have been counting things ever since. At the age of nearly five I couldn’t have known many numbers and, even allowing for the relatively few cars roaming the streets thirty years ago, I must have quickly reached my limit. Perhaps it was the sense of frustration I then experienced that has made me seek ever since for countable things that would demand higher and higher numbers.

  With time I grew old enough to calculate the number of snowflakes it would take to bury Greater New York under ten feet of snow and the number of raindrops it would take to fill the Pacific Ocean. There is even a chance that I was subconsciously driven to make chemistry my life-work out of a sense of gratitude to that science for having made it possible for me to penetrate beyond such things and take—at last—to counting atoms.

  There is a fascination in large numbers which catches at most people, I think, even those who are easily made dizzy.

  For instance, take the number one million; a 1 followed by six zeros; 1,000,000; or, as expressed by physical scientists, 106, which means 10 x 10 x 10 x 10 x 10 x 10.

  Now consider what ‘one million’ means.

  How much time must pass in order that a million seconds may elapse?—Answer: just over 11½ days.

  What about a million minutes?—Answer: just under 2 years.

  How long a distance is a million inches?—Answer: just under 16 miles.

  Assuming that every time you take a step your body moves forward about a foot and a half, how far have you gone when you take a million steps?—Answer: 284 miles.

  In other words:

  The secretary who goes off for a week to the mountains has less than a million seconds to enjoy herself.

  The professor who takes a year’s Sabbatical leave to write a book has just about half a million minutes to do it in.

  Manhattan Island from end to end is less than a million inches long.

  And, finally, you can walk from New York to Boston in less than a million steps.

  Even so, you may not be impressed. After all, a jet plane can cover a million inches in less than a minute. At the height of World War II, the United States was spending a million dollars every six minutes.

  So——Let’s consider a trillion. A trillion is a million million{1}; a 1 followed by 12 zeros; 1,000,000,000,000; 1012.

  A trillion seconds is equal to 31.700 years.

  A trillion inches is equal to 15.800,000 miles.

  In other words, a trillion seconds ago, Stone Age man lived in caves, and mastodons roamed Europe and North America.

  Or, a trillion-inch journey will carry you 600 times around the Earth, and leave more than enough distance to carry you to the Moon and back.

  And yet a good part of the chapters that follow ought to show you quite plainly that even a trillion can become a laughably small figure in the proper circumstances.

  After considerable computation one day recently I said to my long-suffering wife: ‘Do you know how rare astatine-215 is? If you inspected all of North and South America to a depth of ten miles, atom by atom, do you know how many atoms of astatine-215 you would find?’

  My wife said, ‘No. How many?’

  To which I replied, ‘Practically none. Only a trillion.’

  CHAPTER ONE—THE ATOMS THAT VANISH

  I think I can assume that the readers of this book all know that there are atoms which are unstable and which break down by ejecting particles from within their nuclei. Sometimes the ejection of one particle is sufficient to allow what remains of the nucleus to be stable. Sometimes a dozen or more particles must be ejected one after the other in order for stability to be attained.

  In either case, the original atom is completely changed.

  If you were to focus your attention on a particular one of these unstable atoms, it would be impossible for you or for anyone to tell when it would explode and eject a particle. It might do so the very next instant; it might stay put for a million years before doing so.

  Dealing with a large group of objects, however, is not the same as dealing with only one object. Once you have a large group, you can use statistics to predict the future. The larger the group, the more accurate (percentage-wise) the predictions.

  Given enough atoms, statistics will predict, for instance, that after a certain particular length of time, half of a quantity of a certain unstable atom will be broken down. After the same length of time, half of what is left will be broken down. After the same length of time, half of what is still left will be broken down, and so on as long as any of the atoms are left at all.

  Each kind of unstable atom has its own characteristic time for half-breaking-down. This time is called the ‘half-life’.

  Let’s see what this involves in a particular case. Suppose we take a kind of atom we will call Atom X and suppose that it has a half-life of exactly one day; twenty-four hours on the nose. Let’s suppose, further, that at noon on January 1, 1957, you have in your possession 1,048,576 atoms of Atom X. What will happen if statistical laws are followed exactly?

  The simplest way of answering that question is to present a table. For that reason, you are invited to look at Table I.

  Suppose that matters work out ideally and that we are down to a single atom by January 21. What happens to that atom? Statistics can’t say exactly, but it can predict probabilities. For instance, the odds are even money that a single atom of Atom X will last one day or less and be gone by noon on January 22. The odds are 2 to I that it will be gone by noon on January 23; 4 to I that it will be gone by noon on January 24; and over a million to I that it will be gone by noon on February 11.

  It’s pretty safe to say, then, that of the more than a million atoms you started with at New Year’s Day all would probably be gone within a month and almost certainly within six weeks.

  A very important thing to remember, incidentally, is that it doesn’t matter whether those million atoms of Atom X were heaped together in a pile to begin with, or scattered singly over the entire Earth. The end result is exactly the same either way.

  But what if we were to begin with more than 1,048,576 atoms? Take an extreme case as an example. There are about 1050 atoms in the entire planet, Earth. (The number, 1050, is a shorthand way of writing a number which consists of a 1 followed by 50 zeros. In other words, 1050 is a hundred trillion trillion trillion trillion.) We are going to suppose now that the entire Earth is composed of Atom X exclusively. How long would they last?

  The answer is about 5½ months.

  Of course, we don’t have to stop with the Earth. It has been estimated that the number of atoms in the entire known Universe (including the Sun, the Moon, the planets, the stars and galaxies, the interstellar dust and gas) is about 1075. If every atom in the entire Universe were Atom X, the whole supply would be gone in about 8½ months.

  So you see it is now possible to make a very comprehensive statement. When the Universe first came into being, a certain number of atoms of Atom X might have existed. If so, then no matter how many of them existed, not one of those original atoms of Atom X is left today.

&
nbsp; But certain radioactive (i.e. unstable) atoms do exist today. If you have heard of no other examples, you have surely heard of uranium. The question, then, is under what conditions can radioactive atoms, formed at the time the Universe came into being, still exist today?

  One way in which the existence of radioactive atoms can be stretched out is to have the individual atoms break down less frequently; that is, have longer half-lives.

  To give you an idea of what the effect of half-life on atomic existence is, consider Table II. Such a table points out the fact that if the half-life is only long enough then the atoms will last as long as is desired.

  Through several lines of evidence, astrophysicists have come to believe that some four or five billion years ago some kind of cosmic explosion took place, in the course of which the atoms, as we know them today, were formed. To have a round number, then, let us say that the Universe is five billion years old.

  In a five-billion-year-old Universe, even atoms with half-lives of a thousand years (the longest considered in Table II) couldn’t possibly have lasted to the present moment no matter how many had originally been formed. In fact, if we were to continue Table II onward to even longer half-lives, we would find that in order for even a single atom to be present today of a Universe-full of atoms five billion years ago, the half-life of those atoms would have to be twenty million years.

  That’s for a Universe-full. Actually, there could not have been that many radioactive atoms to begin with. Virtually all the atoms in the Universe are stable. It is extremely unlikely that more than one atom out of a billion was unstable to begin with (that is, after the first flush of creation had passed and short-lived atoms like Atom X had died out). If we restrict ourselves to that small proportion then in order for even one unstable atom to survive today, it must have a half-life of six hundred million years as absolute minimum.

  If the half-life is greater than six hundred million years, or, preferably, much greater than that, then some of the atoms could be existing today. That answers my earlier question.

  Few radioactive atoms have half-lives that long, but some do. The best known case, of course, is that of uranium. Uranium is made up of two types of atoms, uranium-238 and uranium-235. Uranium-238 is the more common of the two. Out of every thousand uranium atoms, taken at random, 993 are uranium-238 and only 7 are uranium-235.

  Uranium-238 has an extremely long half-life, four and a half billion years. Uranium-235 has a shorter half-life (yet still not what one would really call short); it is a bit over seven hundred million years.

  There are three other fairly common atoms (and several uncommon ones we won’t mention) that fall into the same class as these uranium atoms. One is the element, thorium, which is made up of only one type of atom, thorium-232. It is even longer-lived than uranium-238. Thorium-232 has a half-life of fourteen billion years.

  Then there is one of the varieties of potassium. Potassium is one of the most common elements in the Earth’s crust, much more common than either uranium or thorium. It is made up largely of two kinds of atoms, potassium-39 and potassium-41, both of which are stable. One out of every ten thousand potassium atoms, however, is a third variety, which is potassium-40, and this variety is radioactive. The half-life of potassium-40 is about one and a fifth billion years.

  Finally, there is rubidium. This element is much like potassium, but it is considerably rarer. Over a quarter of the atoms in rubidium, however, are a radioactive variety known as rubidium-87. This atom has the longest half-life I have yet mentioned; sixty-two billion years.

  Now since we know the half-lives of these five types of atoms and since we have a figure for the age of the Universe, it is possible to calculate what percentage of the original quantity of each atom is still in existence today. The results are shown in Table III.

  Naturally, the shorter the half-life, the smaller the percentage remaining today. Uranium-235, with a half-life close to the minimum allowed for survival, is well on the way toward disappearance. Five billion years ago, fully 280 out of every thousand uranium atoms were uranium-235. Now only 7 out of every thousand are.

  These five kinds of atoms account for almost all the natural radioactivity of the Earth’s crust. (The Earth’s crust may be defined as the ten-mile thick outermost layer of the Earth’s solid surface.)

  In Table IV, I present the latest data I can find for the occurrence of atoms of potassium, rubidium, thorium and uranium in the Earth’s crust. Notice that potassium is by far the most common of these elements. However, it contains so few of the potassium-40 variety that there are actually fewer of those than there are of rubidium-87, which forms a larger percentage of a rarer element.

  Merely the quantity of each atom, however, is not the whole story. There are over five and a half times as many rubidium-87 atoms in the Earth’s crust as uranium-238 atoms, true. Yet uranium-238 atoms are breaking down at fourteen times the rate that rubidium-87 atoms are. Furthermore, while rubidium-87 ejects only a single particle before becoming stable, uranium-238 ejects no less than fourteen particles before reaching stability. For both these reasons, uranium-238 is responsible for many more of the flying subatomic particles that crisscross the Earth’s crust than is the more common rubidium-87.

  In fact, making allowance for the rate of breakdown and the number of particles ejected in the course of breakdown, we can prepare Table V. The particles can be divided into two main groups, the ‘alpha particles’ (comparatively heavy) and the ‘beta particles’ (comparatively light). Figures for both particles are given in Table V.

  Let’s look at Earth’s radioactivity in another way. In the Earth’s crust there are roughly 6 x 1047 atoms (a 6 followed by 47 zeros) and of these about 3 x 1042 are our five radioactive varieties. If we consider all the radioactive atoms in the entire crust, it can be calculated that the total number of subatomic particles being shot out of atomic nuclei in the crust amounts to 2 x 1024 (or two trillion trillion) every second!

  Undoubtedly, this number is too big to grasp, so we’ll cut it down to size. Suppose the radioactivity of the Earth’s crust were evenly spread all over (which, of course, it isn’t) and suppose you owned an acre of land. The top ten feet of your acre would weigh about 38,000 tons, and in it there would be two and a third billion particles shot out by radioactive atoms every second.

  Still too big? Very well, then, consider a cubic foot of soil (about 170 pounds). If it contained its fair share of the radioactive elements, it would be bouncing to the tune of 5,000 particles ejected every second.

  Despite the fact that uranium-235 is almost all gone, atoms of much shorter half-life still exist on Earth. Radium, for instance. The longest-lived variety of that element, radium-226, has a half-life of only 1,622 years. This is far, far less than the six hundred million year minimum I set earlier as necessary for existence. Yet radium exists.

  If this seems contradictory at first sight, remember that I have been supposing that atoms were created only at the time the Universe was formed. Any radium atoms that were formed then have, indeed, disappeared many eons ago. But why should we suppose that no radium atoms have been formed since the beginning of the Universe; why should we suppose that no radium atoms are being formed right now?

  In fact, radioactive atoms can be formed and are being formed continuously. One natural method for producing unstable atoms in quantity involves cosmic radiation. This consists of extremely high-speed subatomic particles that originate from outside the Earth. They are the most energetic particles we know. They bombard Earth every second of the day and night. They plow into Earth’s atmosphere and when they hit some atom in the atmosphere, the atom goes smash.

  One quite interesting atomic change that takes place as a result is the conversion of occasional nitrogen atoms to an unstable variety of carbon called carbon-14. Carbon-14 has a half-life of only 5,570 years, but new formation by cosmic rays keeps pace with its breakdown and among the carbon dioxide molecules in the atmosphere, just over one carbon atom out of a trillion is carbon-14.