------------------------------------------------------------------- F.A.C.T.Net, Inc. (Fight Against Coercive Tactics Network, Incorporated) a non-profit computer bulletin board and electronic library 601 16th St. #C-217 Golden, Colorado 80401 USA BBS 303 530-1942 FAX 303 530-2950 Office 303 473-0111 This document is part of an electronic lending library and preservational electronic archive. F.A.C.T.Net does not sell documents, it only lends them according to the terms of your library cardholder agreement with F.A.C.T.Net, Inc. ===================================================================== ------------------------------------------------------------------- ------------------------------------------------------------------- HOW DO YOU KNOW IT'S TRUE ? Discovering the Difference Between Science & Superstition HY RUCHLIS Prometheus Books Buffalo, New York How Do You Know It's True?: Discovering the Difference Between Science and Superstition. Copyright c 1991 by Hyman Ruchlis. All rights reserved. No part of this book may be reproduced in any manner whatsoever without written permission, except in the case of brief quotations embodied in critical articles and reviews. Inquiries should be addressed to Prometheus Books, 700 E. Amherst Street, Buffalo, New York 14215, 716-837-2475. 95 94 93 92 91 5 4 3 2 1 Library of Congress Cataloging-in-Publication Data Ruchlis, Hyman. How do you know it's true?: discovering the difference between science and superstition / by Hy Ruchlis. p. cm. Summary: Discusses the difference between science and superstition, the basic nature of science as a way of thinking, and the ways in which amazing events can be explained rationally. ISBN 0-87975~57-8 1. Science--Methodology--Juvenile literature. 2. Superstition--Juvenile literature. [1. Science--Methodology. 2. Superstition.] I. Title. Q175.2.R83 1991 507.2--dc20 90-28449 CIP AC Printed in the United States of America on acid-free paper. Contents PART ONE: SUPERSTITION AND FAIRY-TALE THINKING 1. Fiction or Fact? 11 2. The Nature of Superstition 15 3. An Experiment with a Superstition 25 4. Astrology: Science or Superstition? 35 PART TWO: SCIENCE AS A WAY OF THINKING 5. How New Facts Are Discovered 47 6. Science and Freedom of Thought 59 7. Developing a Theory: Probability 73 8. Unusual Events: Luck and Chance 83 9. Science Gives Us Real Knowledge 93 10. Science: Past, Present, and Future 101 5 Acknowledgments My deepest appreciation goes to my wife, Elsie, who not only undertook many additional family responsibilities that made it possible for me to write this book, but also suggested a number of improvements in the manuscript. Ruth Handel, who read the manuscript, offered several im- portant ideas that were incorporated into the book. Last, but not least, granddaughter Kathy Ember, age 13, found a number of explanations in the book that seemed con- fusing to her and were therefore improved in the final work. Finally, to my other granddaughters, Julie Ember and Annalisa Ruchlis, and to all other children who were the main motivation for me to write this book--to cope with the con- fusions of modern life they need to be able to recognize "fairy- tale thinking" and superstition whenever they encounter it. PART ONE SUPERSTITION AND FAIRY-TALE THINKING Fiction or Fact? Do you remember the story of Cinderella? Her fairy godmother waved a magic wand and changed a pumpkin into a coach, some mice into horses, and a rat into a man to drive the coach. Then, with another wave of her wand, she instantly dressed Cinderella in beautiful clothes and glass slippers. As a child, when this story was read to you, did you wonder how a tiny mouse could be instantly changed into a large horse? Or a small rat changed into a big man? You knew that this story was a "fairy tale," pure fiction that described imaginary people doing magical things that could not have happened. What you knew about the real world contra- dicted the events described in the fairy tale. Children enjoy fairy tales because imagination is stimulated by the game of "Let's Pretend." We encourage the telling and reading of fairy tales because this helps children learn to enjoy books and reading. But as young folk grow older they quickly learn that many of the events said to happen in fairy tales cannot happen in real life. Not all "fairy tales" are in books. We are all fond of the delightful story of Santa Claus bringing gifts to every child in the world on Christmas eve. Adults know we are playing a game of "Let's Pretend," but many young children think that Santa Claus really exists. They have not yet developed the reasoning power to realize the contradictions with reality. How could just one Santa bring toys for perhaps a billion children everywhere on earth in just one night? How does he get all those toys into one small sleigh? How do those reindeer 11 12 Part One: Superstition and Fairy-Tale Thinking manage to fly? How does a chubby Santa ever manage to get those bulky toys down the narrow chimneys described in story books, and somehow scramble out again? As children grow older and gain experience, they begin to understand that events described in the story of Santa Claus contradict what we know about the real world. They come to realize that he is a "symbol" for the joyous season of gift-giving and good will, but does not actually exist. Any adult who could not tell the difference between fairy- tale fiction and real-world facts would have a very serious problem. If someone insisted he was Napoleon, or that he was made of green cheese, we would immediately send him off to see a psychiatrist. He would need immediate help. We must be able to know the difference between what is true, and what is false. But how do we know that what we think is a fact is really so? FACTS MUST BE BASED ON OBSERVATIONS Some simple facts are easily observed and checked by others. For example, if someone tells you that a rubber ball costs one dollar at a local store, it is easy to check that fact by going there and seeing it on a price tag, or hearing the salesperson say, "It costs a dollar." Or, if someone tells you that a certain person lives at 65 Cloudburst Street and the phone number is 123-4567, it is not hard to check these facts. You could look in the telephone book, or hear the person talk on the telephone when you call. You might check the address by actually going there to see the person. Anyone can verify such facts by means of observations-- by using our senses: sight, hearing, touch, smell, and taste. Modern business could not exist without such facts as prices, catalog numbers, and descriptions for products; names, ad- dresses, and telephone numbers of customers and suppliers; bills, checks, profits, and money in the bank. There are many billions of such facts, necessary to maintain our modern society. Fiction or Fact? 13 SOME FACTS ARE HARD TO DISCOVER However, many kinds of facts, or what we think are facts, are difficult to discover. For example, someone may get a severe pain that he thinks is in his stomach and take some medicine for indigestion. But perhaps what he thinks is a "fact" about the pain "in his stomach" may not be so at all. If the cause of the pain is a heart ailment, or a diseased gall bladder, taking the wrong medicine, or waiting too long to see a doctor, could be fatal. The pain itself is an observation because it is something that we know exists. We actually feel it. But mistakes are easily made when we try to figure out what the observation means. We may reason incorrectly and "jump to a conclusion" that is wrong. For example, someone may feel a pain in the leg and think there is something wrong where the pain is located. The pain may actually be caused by pressure on a nerve in the lower back. In that case, a treatment for the leg is useless, and perhaps harmful. For such health problems it is best to see doctors who are experts in discovering the causes of illnesses by means of obser- vations. They can then usually prescribe remedies likely to work. Of course, doctors sometimes make mistakes in judgment. Perhaps the facts are difficult to get or knowledge about some diseases is limited. But what counts is that the facts doctors do know usually enable them to prevent or cure many diseases that once killed many people. As a result, today the average life span is much longer than a century ago. It has taken centuries for thousands of scientists to find the causes of a great many different diseases. It usually takes many years of research to discover just a single important fact. Then it may take more years of work for others to verify it, to be sure it is true and not a mistake in observations or reasoning. For example, the earliest microscopes in the 1600s revealed the existence of microscopic plants and animals. It took another two centuries before it was proved that many deadly diseases are caused by different kinds of these microorganisms. Doctors did not even know that they had to wash their hands before treating different patients in hospitals, just to remove deadly germs. They actually caused many deaths just by transmitting germs when touching people with infected hands. 14 Part One: Superstition and Fairy-Tale Thinking Discovery of new facts in science is not simple or easy. It takes careful observation and lots of hard work. Wrong ideas tend to continue for many years, often for centuries. But gradually, over the years, we have learned how to tell the difference between fact and fiction. We have been steadily improving the way we uncover new facts, not known before. We call that method of discovery "science." Science is much more than the facts that make up today's knowledge about the nature of the world in which we live. It is really a new and different way of thinking,--a way of knowing how to find new facts and prove them true. This scientific way of thinking has transformed our world and made it very different from what it was just a few centuries ago. This book is about the methods of science, the way it differs from superstitious "fairy-tale" ways of thinking, how it has changed our world, and how we might use it to solve many of the difficult problems of the world we live in today. But first, let's go back three centuries, to the year 1692, to see how the wrong, superstitious way of thinking of olden times was misused to execute innocent people in our country, wrongly accused of what was considered to be the "crime" of "witchcraft." 2 The Nature of Superstition In 1692 a mysterious sickness began to spread in the town of Salem, Massachusetts. Eight girls had frequent "convulsive fits" in which they thrashed about wildly while moaning, cry- ing, and babbling. During those fits they had hallucinations in which they imagined strange things happening. People in the community were frightened. If eight girls could get such a scary disease, then anyone else might get it, too. Parents began to worry about the safety of their own children. Physicians were called in, but in those days they knew very little about illnesses. They found this one especially mystifying. However, one physician wondered if the convulsive fits might have been caused by "witchcraft." WITCHCRAFt! This superstitious idea struck terror into the hearts of people. Word spread rapidly that there was a witch among them. Perhaps a gang of witches, possessed by the devil, were casting evil spells on the girls. Driven by ignorant fear, the townspeople started a "witchhunt" to find the witches in their midst. During their babbling the girls would sometimes utter the names of people they knew. The townspeople grasped these flimsy bits of "evidence" as clues to who might be witches. They put anyone named by the girls into jail. Soon there were 150 innocent people awaiting trial for the imagined crime of witchcraft, punishable by death! They were neighbors of the girls, farmers, storekeepers, housewives, servants, a former minister, and even parents of friends. The people of Salem had been driven wild with fear 15 16 Part One: Superstition and Fairy-Tale Thinking by a superstition about witchcraft that was totally false. The Governor of Massachusetts appointed some judges to decide which of the people in jail were the witches, and which were not. How did the judges decide? They used a "test of touch." The accused person had to touch one of the girls while she was having a fit. If the fit stopped immediately this was "proof' that the accused person controlled it, was therefore a witch, and had to be sentenced to death. However, if the fit did not stop then the accused person was considered innocent. (Fig. 2.1) Figure 2.1. In 1692, during the Salem witch trials, accused people were judged guilty of being witches and executed if a girl's convulsive fit stopped when touched by the person on trial. (Drawing by Albert Sarney) The judges tried to be merciful. They spared the lives of convicted "witches" if they confessed to the crime of witchcraft. As you might expect, many of the innocent people who were convicted, "confessed" to save their lives. Nineteen of them, however, refused to lie and paid for their honesty and bravery with death by hanging. This terrible tragedy occurred only because people believed in the false superstition of witchcraft. Witches were imagined to be making people sick by using magical ceremonies, perhaps The Nature of Superstition 17 by uttering special words to cast evil spells on people. Today, physicians know far more about the causes of disease than in 1692. Several possible explanations have been proposed for the strange illness that afflicted the eight girls. They might have had a disease known today as "convulsive ergotism." It is caused by a poisonous substance in a micro- scopic plant, a "fungus" known as "ergot." This fungus grows on crops such as rye, used for making bread. Eating bread con- taining ergot might have caused the girls to have those fits and hallucinations. Another possible explanation is that the events in Salem were caused by "mass hysteria." There are examples today of large groups of children, and sometimes adults, who become so anxious and fearful about some reported illness that they imagine they have it, too. The eight girls might have seen or heard about others having fits and their vivid imaginations might have caused them to behave the same way. It is possible that some, or all the girls, were playing a monstrous trick on grownups by pretending to have fits and hallucinations. Perhaps they enjoyed having the power of life and death over all those innocent grownups. SUPERSTITIONS TODAY A superstition is a belief that is held despite evidence that it is not true. Superstitions are based on the belief that some people, plants, animals, planets, stars, words, numbers, or special things have magical powers. They are supposed to be able to do aston- ishing things that no one truly observes happening anywhere, although many people imagine they are happening. These su- perstitions contradict what we know about the real world. Superstitions are examples of fairy-tale thinking. But, unlike fairy tales, which people know are imaginative fiction, super- stitions are wrongly believed to be true. Scientific thinking is very different. We seek facts and expla- nations of events based on careful observations and logical reasoning that must be checked by repeated trials to try to elim- inate the errors that often occur. Then the facts have to be verified by other careful observers before being accepted as true. This is not an easy or quick process and mistakes are often 18 Part One: Superstition and Fairy-Tale Thinking made. Very often it takes years of work by many people to reach the point where facts and conclusions are considered to be true. Because mistakes or exaggerations are easy to make we must be ready to correct, or even change our ideas about facts as new information becomes available. In sharp contrast, superstitious belief reflects a lazy way of thinking. Superstitious people just assume the "facts" and often believe whatever they imagine to be true. The way this happens will be described in chapter 4 when the superstition of astrology is analyzed in detail. Today, polls show that, despite all our scientific knowledge, one person in seven in the United States believes in superstitions like the one about witchcraft. One in four people believe in the superstition of astrology and more than 1,000 newspapers en- courage this superstition by publishing "horoscopes" which supposedly predict for people of different birth dates what they should or should not expect to happen to them. Some people have formed groups that perform special witch- craft ceremonies. There have been reports of animals sacrificed during such events to ward off bad luck, or to try to accomplish some other desired goal. In one tragic case a woman whose child was ill was told by a person, who claimed to be able to heal sickness by super- stition, that a demon had possessed the child, causing the dis- ease. The remedy proposed was to starve the demon by depriving the child of food. The mother actually did so, and the child starved to death! This poor woman was punished with a jail sentence of four years. The real cause of her child's death was ignorance, which led her to believe in an ancient superstition about demons caus- ing illness. Superstitious belief in witchcraft is more widespread in coun- tries with many uneducated people and few modern physicians. People then rely on traditional "witch doctors" or "medicine men" who try to cure diseases with ceremonies and magic that are supposed to drive out imaginary demons thought to cause disease. Witch doctors collect things like skins of snakes and frogs, skulls or bones of animals, unusual rocks, carvings of animals, and other objects, all supposed to have magical powers to cure people. They may use such materials as magical objects in their ceremonies, waving them around the sick person as they utter magic words and perhaps dance or make special motions. (F/g 2.2) The Nature of Superstition 19 Figure 2.2. This witch doctor performs a ceremony to drive out the demon, imagined to be causing an illness. Since most sick people get better, ceremony or not, the witch doctor takes credit for his "successes," even though undeserved. (American Museum of Natural History) Scientists are careful not to reject everything witch doctors do as worthless in treating illness and disease. Witch doctors often make medicines from parts of different plants or animals. Some of these medicines have been found to be useful in curing diseases. For example, quinine, the main medicine used by modern 20 Part One: Superstition and Fairy-Tale Thinking physicians for treating malaria, was originally discovered by Indian medicine men in South America. They made it from the bark of cinchona trees. Also, an important tranquilizer to make people calmer was originally used by witch doctors in Asia. Other medicines used today were discovered in a similar way. Of course, performing magical ceremonies and uttering spe- cial words do not stop germs from invading the body, nor do they cure vitamin deficiencies. However, ceremonies are often better than doing nothing because they give sick people the feeling that something is being done to help them. They feel more optimistic, and this mental attitude has been found to be helpful to the body in fighting off some diseases. Since people recover from most diseases by themselves, imagined "cures" by ceremonies and magic words seem to "prove" that the superstitions are effective. This is also true for some medicines sold today in pharmacies. When people get better, with or without the medicine, they may mistakenly think that the medicine did it. The best way to find out if a medicine really works is to test it with a controlled experiment. A number of sick people are given the medicine being tested, while others are given false medicines called placebos (pronounced pla-SEE-bose), which are harmless substitutes. Careful records of medical examinations are kept to see how these people recover from the illness. The medicine is considered to work if many more patients getting the medicine recover, or do so faster. In such experiments it is best if the doctors or nurses actually giving the medical examinations do not know which patients are getting the real medicines and which are getting the pla- cebos. People doing experiments often want the experiment to "succeed." If they know which patients are getting the real medicine, they may be biased and slant their observations to favor the outcome they want. The people getting the placebos serve as the control group that gives us a way to compare what happens with and without the medicine. Such experiments are very expensive because many people are involved, they often take a long time, and costly measuring instruments may have to be used. But it is the best way to be sure that any medicine or other treatment actually works. The lesson we have learned from witch doctors is that every belief we think is a superstition should not be automatically The Nature of Superstition 21 rejected. We should examine each superstition carefully to see if there is some truth to it. The evidence for or against it should determine whether we consider it true or false. OTHER SUPERSTITIONS People today sometimes do or say things because of customs based on ancient superstitions. For example, a friend may say something like, "I hope it doesn't rain Saturday and spoil our picnic." Then she interrupts the conversation, raps the wooden table with her knuckles, and says, "Knock on wood." Why did she do that? Your friend does not realize it, but she is knocking on wood because people in olden times believed there were elves with magical powers trapped in wooden objects in our homes. They were imagined to have originally lived in trees in the woods. But when trees were chopped down and made into furniture, the elves were supposed to still be in the wood, right in our homes. Ancient people were afraid that the elves were angry for being deprived of their beautiful homes in the woods, and were just waiting for a chance to get even. Today no one ever thinks about the elves, or explains how they manage to understand English, or why we never see them. But when your friend knocks on wood, it is as if she is really assuming, like people long ago, that some invisible elf trapped in the furniture has heard her remark about rain spoiling her picnic. "Aha," he is imagined to think. "Now I have a way to punish those mean people. I'll use my magical powers to make it rain on Saturday and spoil their picnic." The procedure of saying, "Knock on wood," and then ac- tually knocking on something made of wood is supposed to be a magical way of telling the elf, "Don't spoil our picnic or we'll punish you. Remember, we could make things difficult for you by chopping up this table and burning it in the fireplace." This superstitious custom makes as much sense as expect- ing a fairy godmother to wave a wand and instantly create a limousine and chauffeur to drive us to a big party. Today we know that saying words cannot stop any illness from developing. But in olden times people believed in the su- perstiition that saying the right words had the magical ability 22 Part One: Superstition and Fairy-Tale Thinking to make things happen. A witch was supposed to be able to cast an evil spell by uttering special curses. Special words, like "abra- cadabra," were imagined to have magical effects such as opening locked doors without keys or releasing genies from bottles. BLACK CATS AND OTHER SUPERSTITIONS Some people still believe that a black cat crossing one's path brings "bad luck." To avoid this "bad luck" a superstitious per- son might turn around and go back, or go another way. Superstitious people may do strange things to cancel "bad luck." An old-time remedy for a black cat's "bad luck" was to rotate one's hat around on the head, take nine steps and then rotate the hat back to where it was before. No one ever explains how they know the superstition is true, or how the black color of a cat's fur could magically cause someone to perhaps fall and break a leg, or why the rotated hat remedy is supposed to work. In fact, people think they "know" that the superstition is true because they were told about it by others. When we try to track down who started this superstition we find that it goes all the way back into ancient times, without a shred of reliable evidence that it is true. In England the superstition is just the opposite, with black cats imagined to produce "good luck," not bad! Some theaters actually keep black cats to bring them "good luck" in perfor- mances and newspaper reviews. How could a black cat be "bad luck" in the United States and bring "good luck" when sent across the ocean? The superstition may have arisen from the fact that in our society the color black is associated with funerals and death. Halloween drawings of witches usually show them with black hats, and often black cats are nearby. Perhaps the black cat is supposed to be a witch in disguise, or some kind of spy or helper for the witch. It may therefore have been imagined to possess the same magical abilty to cause harm. A similar superstition is that breaking a mirror brings "bad luck." This belief is based on the mysterious way people see their images in a mirror. In olden times people did not know about the way light is reflected by a mirror to produce an image. The mirror image seemed to appear as if by magic. When we The Nature o[ Superstition 2g Figure 2.3. The superstition about a broken mirror causing "bad luck" probably arose because of the mysterious way an image appears behind a mirror, even though nothing is actually observed to be there. Perhaps people thought a person's spirit could not return once the mirror was broken. (Drawing by Albert Sarney) look for it behind the mirror nothing is there. (Fig. 2.3) Perhaps the mirror was imagined to mysteriously capture a person's "spirit," which could then not return to the owner of the image when the mirror was broken. The grumpy spirit would thereafter try to get even by magically causing misfor- tunes to happen to the person who broke it. There is a superstition that stepping on an ant brings rain. Considering how many people everywhere on earth step on ants all day long, it ought to be raining all the time. This conclusion clearly contradicts our experience. "Voodoo," a superstitious form of magic, is practiced in some 24 Part One: Superstition and Fairy-Tale Thinking countries today, even in the United States. One of its beliefs is that a person can be harmed at a distance by using magical procedures. One method is to stick pins into a doll representing the person to be harmed. This is supposed to cause that person to get sick or die. Unfortunately, this can really harm intended victims who believe in the superstition and are told that evil spells have been put on them. Just worrying about an evil spell could make an intended victim sick, and perhaps even die. Belief in superstitions is widespread in countries where people are poorly educated and is greatly weakened when people become educated. But even in nations where everybody goes to school some people are still superstitious. Superstitions take a very long time to die out. Scientific thinking has gradually developed mainly during the past five centuries. It has transformed the world by sweeping away most of the superstitions that prevented people from learning about the world in which we live. Could we use scientific thinking to test a superstition to find out if there is any truth to it? The next chapter describes how that could be done. 3 An Experiment with a Superstition You step into the elevator of a tall building. The door closes and up you go. You watch the lights that show the number of each floor that is passed: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ú.. and what's this? There's 12, then 14, but no 13! Did somebody make a mistake in counting? No. The thirteenth floor is really there, right above the twelfth floor. It's just that the real thirteenth floor of about half the tall buildings in our country have been deliberately marked 14 in- stead of 13. Why has that been done? There is an ancient superstition that the number 13 brings "bad luck." Some people actually believe in that superstition today and therefore do not rent, buy, or visit apartments or offices on floors marked 13. (Figure 3.1) Some people who are not superstitious may also not rent or buy on the thirteenth floor because they know that super- stitious people would not work or visit thereú A strange thing about this superstition is that every build- ing with more than twelve floors has a thirteenth floor. Paint- ing the number 14 on floor 13 doesn't change it from being the thirteenth floor. So why should just a wrong number 14 on a wall make any difference? This logic is somehow lost on superstitious people. Someone told them that the number 13 brings "bad luck" so they simply believe it without questionú 25 26 Part One: Superstition and Fairy-Tale Thinking Figure 8.1. Some superstitious people will not live, work, or visit a floor marked 13 because they believe it would cause them "bad luck." Builders sometimes mark the real 13th floor with a false 14 so that superstitious people will not have to worry that the number 13 will haunt them. (Drawing by Albert Sarney) "CARDSTACKING" THE EVIDENCE FOR A SUPERSTITION Superstitious people say they "know" that the number 13 is unlucky because they claim to have observed examples when it seems to have been true. "Last month Sam Bungling, who lives in apartment 1303, fell off a bicycle and broke his arm. Then last week Mary Contrary, from 1307, had her car stolen. And don't forget, Bill Barker, in apartment 1310, was bitten by a dog yesterday. I told him not to rent that apartment on the thirteenth floor." Believers in the superstition claim that such "anecdotal evi- dence" (based on "anecdotes": stories about events) is based on observations. But the mere listing of misfortunes for peo- ple living or working on a thirteenth floor does not prove that they are the result of special "bad luck," because everyone has An Experiment with a Superstition 27 some misfortunes, including those living on any other floors. We could give as many examples of misfortunes on those floors as on floor 13. We can't tell whether the people living or working on a floor marked 13 are more "unlucky" than people living on other floors unless we can show this by careful observations. An experiment, based on a detailed investigation, would have to be performed. When people try to "prove" superstitions, or even opinions, with anecdotal evidence they often make a common error in reasoning called cardstacking. This word comes from the way some gamblers prepare ("stack") cards in advance of a game in special ways that give them better chances to win. People cardstack the evidence when they look for, or show, only those examples that are in favor of whatever they want to "prove," while hiding or ignoring all the examples that show it to be untrue. (Figure 3.2) Some people deliberately cardstack evidence to mislead others. But more often, people are so eager to "prove" them- Figure 3.2. Evidence is often "cardstacked" by presenting only the facts FOR while hiding or suppressing the facts AGAINST. People often fool themselves by ignoring or rejecting facts that may show their opinions to be wrong, (Drawing by Albert Sarney) 28 Part One: Superstition and Fairy-Tale Thinking selves right in their opinions that they ignore the evidence showing them to be wrong. AN EXPERIMENT TO FIND THE TRUTH ABOUT 13 Could we do a scientific experiment to see if there is any truth to the superstition that living on a floor marked thirteen brings "bad luck?" What would we have to do? Suppose a student named Eddie does such an experiment for his science project. He selects a tall building with a thir- teenth floor and decides to interview people living on that floor. He also needs a "control" for purposes of comparison, perhaps the twelfth fiooor, to see which one has people with more "bad luck." He plans to find out about the amount of "bad luck" by interviewing everyone on both floors. Eddie starts by ringing the bell for apartment 1301. A mid- dle-aged man appears. "Yeah. Whaddaya want?" Eddie explains his science project and asks the man if he will cooperate by listing the misfortunes he has had recently. The man glares at Eddie. "I ain't got no time for such nonsense. I'm watching a foot- ball game." SLAM goes the door. Now Eddie can't go there any more. He crosses 1301 off the list. This is serious. Missing one, or several apartments, distorts the comparison. Gruff people like the man in 1301 may be angry at the world because they have had a lot of misfortunes and don't want to talk about them. In that case Eddie would be missing many examples of "bad luck" and his records would be incomplete. In apartment 1302 he finds a nice lady who says, "That's a great idea. Sure, I'll be glad to help you with your project. Come in and have some cookies and soda." She begins a long account of lots of little misfortunes. "Let's see. On Monday I scraped my arm and it bled, so I washed it with peroxide, then put on a Band-Aid. And last Wednes- day my uncle Pete had a pain in his stomach. Would you be- lieve that the doctor sent him to the hospital right away? Thought he might be having a heart attack. So they took a cardiogram, but found nothing wrong. But they are keeping him for observation for a few days .... "And so on for half an hour. An Experiment with a Superstition 29 CAN WE MEASURE "BAD LUCK?" That night Eddie tries to figure out what to do with his scrib- bled notes about a number of interviews. He enounters a seri- ous problem. Which is a worse misfortune, a broken leg or pneumonia? How should he compare one person's loss of a job with getting a divorce? Or losing $1,000 in a bad investment? Or learning that a very good friend died? Researchers doing interviews of events involving what people say or do often set up a rating system from one to ten, which helps them compare answers or results. Eddie does the same by rating the smallest misfortune as one and the worst a ten. What rating does he assign to the misfortune of a broken leg? Five? Seven? Nine? How does he take into account the severity of the break, when some legs are as good as new in a few months, while others cause permanent crippling? What rating is assigned to losing a wallet with $1000 This is a big misfortune to someone with a large family who barely earns enough money to get by. But it's practically no misfor- tune to a millionaire. How does Eddie find out how rich or poor the loser may be? Different people are also likely to rate misfortunes differ- ently. Someone who has never known poverty may not give a high rating for the loss of $100, easily replaced (for him) by going to the bank. A poor person doing the rating is likely to be more sympathetic and rate the loss higher on the scale. Here's another problem: Eddie found ten people reporting minor cuts, easily fixed with Band-Aids. He gives each of these a rating of one, for a total of ten. But then he also rated a death in the family, reported by one person, with the highest value of ten. Yet that death is clearly a lot worse than ten separate Band-Aid cuts, also worth a total of ten. For these reasons the rating system for misfortunes is said to be "subjective," and not "objective." SUBJECTIVE OR OBJECTIVE? Judgments are subjective when they depend on differing opin- ions, beliefs, and personal experiences. Eddie's rating system is clearly very subjective. If Elsie, Bobby, or Sally were rating 30 Part One: Superstition and Fairy-Tale Thinking the same misfortunes, each one would probably assign very different ratings. Ratings of "bad luck," based on what people tell us about their misfortunes, are certainly very subjective. On the other hand, ratings are said to be objective if they are not based on personal feeYmgs or prejudice, but on some kind of easily repeated measurement that enables everyone to assign practically the same rating. For example, ten people trying to judge the length of a room just by sight would give many different estimates. But a measuring tape would enable all to agree on the length within a fraction of an inch. On the other hand, no instrument can measure the amount of "bad luck" because it is too vague and abstract. It has no length, width, height, volume, weight, or color that can be meas- ured. We can't see it, hear it, touch it, smell it, or taste it. It is not a thing but an abstract idea. Many imp{>vtant, hard-to-measure ideas about the world are very abstract: good, bad, better, worse, luck, democracy, freedom, love, hate, jealousy, and lots more. To get some kind of measure- ment to compare good and bad luck we have to invent a tricky, subjective rating system that depends on the ideas people have. The numbers people assign to ratings are deeply affected by their prejudices (pre-judgments.) Their ratings would be biased (slanted) in favor of what they think is better or worse. In such cases people tend to "cardstack" their records by not noting misfortunes they think are unimportant. Cardstacking also occurs if people have strong opinions about the outcome of an experiment. For example, if Eddie be- lieves that 13 is an unlucky number, he may give higher ratings to similar misfortunes on floor 13 than to those on other floors. People are usually not aware of bias in their strongly held opinions. It is subconscious (below the level of consciousness, or awareness). They feel better if their opinions are shown to be fight, and feel badly if shown to be wrong. So they often "see what they want to see." In such cases a subjective ex- periment to see if the superstition about "bad luck" on the thir- teenth floor is true, or not, is likely to end up "proving" whatever the person wants to prove. One way for Eddie to reduce the effect of his bias would be to have several other people rate the misfortunes on the two floors, without knowing whether they occurred on floor 12 or 13. But this greatly complicates his experiment. An Experiment with a Superstition 31 WHAT DO THE RATINGS MEAN? There are still more problems after the ratings of "bad luck" are assigned. Suppose Eddie adds up the ratings of all misfortunes for each floor and finds the total for floor 12 to be 217, while that for floor 13 is 249. To see how much greater 249 is than 217, he divides 249 by 217 and gets 1.15. This is the same as saying 249 is 15% greater than 217. Does this "prove" that people living on floor 13 had 15% more misfortunes than for floor 12, and therefore had more "bad luck?" No. There is too much variation with only ten families on each floor, and only for one month. If Eddie were to conduct interviews for another month or in another building, the mis- fortunes would certainly be different and the totals might go the other way, with floor 12 getting the higher total. There is some safety in having a greater number of inter- views, in more buildings, in different places, and for a longer period of time. How many interviews are enough? Scientists use a kind of mathematics called statistics to guide them in judging how often they shotrid repeat a measurement or rating to get enough observations to make a proper judgment. You can see that it would require a lot of time and money to do an experiment properly to find out ff people on floor 13 really have more "bad luck." No one has ever done this properly for the superstition about "bad luck" on floors marked 13, partly because of the time, ef- fort, and cost. But suppose someone actually did this. Those who disagree with the conclusions cotrid find plenty of reasons for saying that the experiment is unscientific because the rat- ings are so subjective, and therefore it doesn't prove anything. HOW TO SHOW THAT A SUPERSTITION IS NOT TRUE Although probably no one has done an experiment to find out if there is more "bad luck" on the thirteenth floor, there is good evidence to show that the general superstition about number 13 is not true. Records are kept by hospitals, police, fire and health de- partments, and insurance companies, for many kinds of mis- 32 Part One: Superstition and Fairy-Tale Thinking fortunes: fires, crimes, diseases, deaths, accidents in homes, car and airplane crashes. This information is quite reliable because it is based on objective observations by physicians, firemen, policemen, and other officials. These people have no reason to be biased about noting that somebody died, or that people were injured in auto accidents, and on what dates they happened. As a result, we can easily test the truth of a common su- perstition about 13, that Friday the 13th (or any other thir- teenth day of the month) is unlucky. We can simply total all the deaths, or accidents, or fires, or illnesses, or crimes on dif- ferent days of each month and compare these completely ob- jective numbers. These official records show that no more misfortunes oc- cur on Friday the 13th, or on any other thirteenth day of the month, than on other days. This is strong evidence that the superstition about the number 13 being "unlucky" is not true. USING OUR REASONING POWER We can also use logical reasoning to show that the supersti- tion about 13 is very unlikely to be true. Let's ask an impor- tant scientific question that superstitious people ignore: How is the number 13 supposed to cause misfortunes for people liv- ing on a thirteenth floor? Suppose someone who is superstitious gets off the elevator on a thirteenth floor and sees a big 13 on the wall. Does that number 13 somehow have invisible eyes that see and recognize a victim? Does the invisible spirit of that ghostly 13 then follow the victim around for the next few months? Does it arrange to have a banana peel on some steps to make the victim fall and break a leg to give him some "bad luck"? (Figure 3.3) Just asking these questions tells us how silly the supersti- tion is. There is nothing we have ever seen, heard, felt, smelled, or tasted, nothing we can observe, that could explain how a mere number 13 on the wall could do all those magical things. Such superstitions contradict what we know about the way the real world works. It is an example of fairy-tale thinking. For that reason we are quite sure that the superstition about 13 and "bad luck" is very unlikely to be true, as much as we can know anything else in this complicated world. Other superstitions about "bad luck" or "good luck" can An Experiment with a Superstition 33 Figure 3.3. Belief in the superstition that the number 13 causes "bad luck" implies that some kind of ghostly "spirit" of 13 follows people around and arranges some kind of misfortune to occur. There is no observable evidence that this is so. (Drawing by Albert Sarney) be analyzed in much the same way, by means of reasoning, as we have done for the superstition about 13. HOW SUPERSTITIONS CAN HARM US There is a way for the number 13 to harm a person. Suppose someone who strongly believes in the superstition about 13 causing "bad luck" happens to visit a floor marked 13. The fear that the evil spirit of 13 would pursue its victim, and in- evitably cause harm, could make a believer nervous and acc- ident-prone (likely to have accidents). Little misfortunes are then likely to be exaggerated and imagined to be big ones. Some people can worry themselves into illness, even death, by imag- ining the worst. In one recent trial for murder, a son was accused of kill- ing his father who had tyrannized the family and friends with the superstitious belief that he had an evil spirit in an urn. The reason the son gave for the murder is that he had to free 34 Part One: Superstition and Fairy-Tale Thinking the family from the terrible power of the evil spirit that they were convinced was in the urn. Even with the tyrannical father gone the family did not dare to throw it into a garbage dump because they believed the magical powers of the evil spirit would somehow find a way to harm them. The family solved their problem with the evil spirit by call- ing in an "exorcist" to get rid of the spirit by saying the right magic words and declaring it dead. Only then did they feel safe. Meanwhile, of course, the father was dead and the son was in jail awaiting his trial for murder. The best remedy for such fearful thinking is the knowl- edge that superstitions about "bad luck" or "good luck" are not true. There is no reliable evidence that there are invisible, supernatural spirits that can do magical things that contra- dict what we know about the real world. Of course, most people do not think that they could ever be taken in by such superstitious beliefs. But just a minute! Polls show that one out of four people in the United States believes in another superstition called astrology. Widespread belief in this superstition is also shown by the fact that over 1,000 newspapers in our country publish columns giving daily "horoscopes" that claim to tell people what kinds of events are likely to happen to them in the future, according to their dates of birth. How do we know that astrology is a superstition? The next chapter explains how we can analyze what astrologers say to show that their beliefs are based on superstition. 4 Astrology: Science or Superstition? Polls have shown that about one person in four in the United States believes in astrology. Many of them read the daily horoscopes in newspapers and try to follow the advice in those columns. In addition, many books on the subject are published and sold, and some people even pay astrologers a good deal of money to prepare personal horoscopes to help them make important decisions. Astrologers who prepare these horoscopes say that what they do is good "science," based on "facts." They claim to be able to tell from any person's time and date of birth what kind of character he or she has as an adult. They also declare that they can predict for anybody on earth whether a particular time is "favorable" or "unfavorable" for different kinds of activi- ties people want to undertake. For example, they advise people if any chosen day or time of day is good for a marriage ceremony, starting a business, going on a trip, or for anything else. Astrologers claim they can do all this by making a "horo- scope" for each time and place. They use astronomical tables to figure out exactly where the sun, moon, planets, and con- stellations were, or will be, in the sky for the particular moment and place. Then they apply very complicated rules of astrology to predict if the luck for the activity in question would be good or bad. If they decide that the moment is not a good one, they claim to be able to tell what time of day, or other days, would be better. This would be a marvelous service if true. So it is important to answer the question, "Is astrology really science, and can 35 36 Part One: Superstition and Fairy-Tale Thinking it predict good or back luck for any activity anyone is planning to undertake?" IS ASTROLOGY TRUE? A good way to answer such a question is to analyze what astrologers say and do. Let's do this for a famous astrologer, Joan Quigley, who for many years prepared horoscopes for well- known actors and actresses. For six years she was paid a large fee by Nancy Reagan, wife of President Reagan, to prepare horoscopes for many of the president's important appointments. We know this happened because Nancy Reagan says so in her book My Turn. Joan Quigley confirms this in her own book What Does Joan Say ? Consider just one of many examples Quigley describes of the kinds of changes she says she made in the president's schedule of important appointments. In 1987 President Reagan arranged to go to Bitberg, Ger- many, for a wreath-laying ceremony to honor the memory of Germans who died in World War II. This visit became contro- versial and Mrs. Reagan was worried, not only about the presi- dent's safety, but also about bad publicity. She asked Quigley to check the president's planned schedule and tell her if any changes should be made to avoid "bad luck." The ceremony had been scheduled for early in the morning. Quigley explains in her book how she prepared a horoscope for the scheduled time and decided that it was not a good-luck moment for the ceremony. She says that at 11:45 A.M. the planets and stars were in a much more "favorable" position for the ceremony. So, she says she insisted that the president's assistant change the time, even though that was difficult to do. In her book she explains why she made that change: At the time I chose, the Sun, which ruled the event itself, was in a very elevated position in the 10th house of great prominence and prestige. The sun and the proud, honorable and dignified Leo Ascendant described the nature of the event. Jupiter, the planet of benevolence and good will, represented the public. Two planets in the 9th house indicated global attention. And Mars in the 10th showed a kind of victory. Astrology: Science or Superstition? 37 This way of deciding on a "best" time for the president's ceremony raises many questions: Why should the sun high in the sky ("in a very elevated position"), and in a certain part of the sky ("10th house"), give the president's ceremony "great prominence and prestige"? Does the sun have a brain that can understand what is happening on earth at a ceremony in a certain place called Bitberg? Does the sun do the same for all the billions of other human events taking place everywhere on earth at the same time? Why should a chance collection of separate stars in a constellation called Leo, thousands of billions of miles away, be "proud, honorable and dignified." How could these enormously distant stars "describe the nature" of our president's ceremony in Germany? How does the planet Jupiter bestow "benevolence and good will," or "represent the public" for a ceremony in Bitberg, Ger- many, hundreds of millions of miles away? Where did Jupiter get that power? How does it transmit this "benevolence and good will" to earth? The president's ceremony was already getting top billing on TV and radio programs throughout the world. So, why should "two planets in the 9th house" give it any more "global atten- tion" than it had? And how does Mars give the president's ceremony "victory," whatever that means? Astrologers do not ask or answer such difficult "why" ques- tions because they are just blindly following the rules of a kind of very complicated game called "astrology"--somewhat like Monopoly. They learned the rules of this game by reading books or going to special schools. Nobody writing these astrology books, or teaching astrology courses, bothers to ask such ques- tions or tries to answer them the way scientists do: by means of careful investigations, usually with experiments. Most of the rules were invented by astrologers who lived more than 2,000 years ago. Ever since, other astrologers have been blindly following those rules without bothering to prove that what they are doing is true or false! Some of the more creative ones invent their own rules, put them into books, and then teach them to others. 38 Part One: Superstition and Fairy-Tale Thinking ASTROLOGERS DO NOT UNDERSTAND WHAT A FACT IS Consider Quigley's statement that "the Sun... was... in the 10th house of great prominence and prestige." And then she writes, "Two planets in the 9th house indicated global atten- tion. And Mars in the 10th showed a kind of victory." What are these "houses" in the sky that Quigley thinks are so important? They are just one of the many kinds of invented rules of the game, imaginary sections of the entire sky from north to south. Most astrologers divide the sky into 12 such "houses," but some have imagined there to be 8, 20, 24, or other numbers of sections. Using fairy-tale thinking, with no evidence at all, they have imagined each house to have some control over an aspect of human life. Astrologers differ in what they imagine belongs in each house. In the 12-house system that Quigley follows, the First House is imagined to influence human personality and temperament. The Second Itouse takes care of possessions and feelings. Other houses deal with travel, or family, or public affairs, etc. As the earth rotates on its axis the sky appears to revolve around us once every day, wherever we happen to be. Astrologers imagine that the sun, moon, planets, and constellations each steadily move from one house into the next. When the sun or moon, or a planet or constellation, crosses the fence (boundary) between one house and the next it leaves behind the qualities of the house it was in and picks up those of the new house. There have been as many as 50 different systems of houses in the sky. Any astrologer can imagine his or her own number of houses and what each should mean. But no one does any controlled experiments to find out if their imaginary houses in the sky really do affect people as they claim. With this fairy- tale thinking, whatever any astrologer imagines to be true is assumed to be true. Figure 4.1 illustrates how silly this fairy-tale kind of thinking really is. Should anyone delay a trip until the sun appears to move into an imaginary "house" in the sky that is supposed to control everybody's luck while traveling? Since there is no evidence whatsoever that any such "house" exists, why should anyone believe it? Astrology: Science or Superstition ? 39 Figure 4.1. Millie: "Why don't we start on our vacation trip." Billie: "My astrologer told me to wait until the sun gets into the House of Travel, or we'll run into bad luck." Millie: "Why didn't we leave an hour ago when it was in the house of wealth?" ANIMALS IN THE CONSTEILATIONS? Let's analyze why Quigley thinks that "the proud, honorable and dignified Leo Ascendant described the nature of the event." Leo is the name of a constellation. The word "Leo" comes from the word "lion" in Latin, an ancient language of the Romans. They had borrowed the idea nf ~ ]inn in fh~ ~b~, ~-,~rn 40 Part One: Superstition and Fairy-Tale Thinking Figure 4,2, This diagram shows the arrangement of bright stars in the constellation called Leo (meaning lion in Latin.) Do you see any lion in the accidental arrangement of stars, as ancient astrologers imagined they saw? When today's astrologers make horoscopes they assume that this ancient superstition is true, although they deny being superstitious. (Drawing by Albert Sarney) to work dreaming up what kind of influences on luck this lion would have on the lives of all people on our distant earth. They used their favorite method of reasoning by analogy. If two different things are alike in some way, then they might be alike in other ways. However, astrologers forget the "might be" and take it to mean "must be." They abuse this method of reasoning by analogy so badly, by changing "might" into "must," that we may describe it as stretched analogy. In olden times the lion was considered to be the "king of beasts." Kings are supposed to be "proud, honorable and dig- nified." So, by stretched analogy, the accidental group of sepa- rate stars in Leo, m'filions of b',llions of re'ties away, was also imagined to be "proud, honorable and dignified." And that's why Quigley imagines she knows that the group of stars some ancient astrologer happened to call Leo would transmit pride, honor, and dignity to the president's ceremony. What does Quigley mean by "Leo Ascendant." A planet or constellation that is near the eastern horizon and therefore beginning to rise in the morning sky is ascending, therefore "in the Ascendant." By stretched analogy, if a planet or con- stellation is rising it is getting more powerful. So "Leo Ascen- Astrology: Science or Superstition? 41 dant" gives the president's ceremony more of its qualities of pride, honor, and dignity. Quigley did some astrological "cardstacking" here. A lion can be very vicious when killing and eating an innocent lamb, but Quigley decided to ignore that violent aspect of the stretched analogy to lions. She chose to imagine that gentle Leo gave only his good qualities to the Bitberg ceremony. Another astrologer might have chosen to see the lion as violent and warned the president not to have the ceremony at the dangerous time of 11:45 A.M. when Leo was "in the Ascendant." Suppose ancient astrologers had imagined they saw a chicken in the sky for the constellation, instead of a lion, and therefore called it "Chickie," not Leo. In that case the constel- lation of Chickie might well be viewed by today's astrologers as influencing people and events to be more like chickens than lions--perhaps timid and cowardly rather than proud, honor- able, and dignified. ASTROLOGY IS BASED ON BELIEF IN ANCIENT GODS The Romans, borrowing ideas from the Greeks of ancient times, imagined that the god Mars caused the planet Mars to move through the sky. Similarly, the god Jupiter was supposed to move the planet called Jupiter; the goddess Venus moved the planet Venus; the god Mercury moved the planet Mercury; and the god Saturn moved the planet Saturn. The fact that ancient Roman astrologers used the same names for the gods as for the planets tells us that they thought of them as almost the same. For that reason it seemed reasonable to them to look for clues as to what the gods might be like from the appearance of the planets they caused to move. The planet Mars has a reddish appearance. That reminded ancient astrologers of blood, which reminded them of violence and war. Wars were fought by strong, brave men who hoped for victory. So, by stretched analogy, ancient astrologers imag- ined that Mars was the god in charge of war, violence, courage, manliness, soldiers, and victory--and any similar qualities they could imagine. That's where Quigley got her idea that "Mars in the 10th [house] showed a kind of victory." This reasoning tells us that 42 Part One: Superstition and Fairy-Tale Thinking she accepts as true the ancient Roman superstition that the god-planet called Mars controls human wars, bloodshed, violence, victory, and sim'fiar qualities of human life and events. Another astrologer could just as well have chosen the influence of Mars on the ceremony at Bitberg to mean violence. That would have matched the violent side of Leo, the lion. Such an astrologer could have come to an opposite conclusion from Quigley, that 11:45 A.M. should be avoided because it predicted violence. The planet Jupiter moves much more slowly across the sky than Mars or Venus. By stretched analogy, astrologers of old probably imagined Jupiter to be older, therefore the chief god. He was thought to be more mature, wiser, and beneficial. That's why astrologer Quigley says that Jupiter is the planet of "benev- olence and good will" and "represented the public." The planet Venus looks beautiful in the sky, so ancient astrologers imagined it to be a female god whose influence on people would be about beauty, love, and womanly matters. We now know that Mercury is the planet closest to the sun. For that reason it appears to move more rapidly in the sky than any other planet. To ancient astrologers this faster motion provided the clue that Mercury, the god, was young and speedy. That is why Mercury, the god, is often pictured as having winged feet, serving as the messenger for the other gods. (Figure 4.3) By stretched analogy, Mercury's fast motion in the sky led ancient astrologers to put him in charge of human transpor- tation, communication, business, and commerce. Today's astrol- ogers do the same. Saturn is the slowest-moving visible planet so it was thought to be the "bringer of old age" and "cold." These qualities re- minded astrologers of approaching death, so Saturn's influence on earthly things was often considered to be more harmful than beneficial. All this supernatural magic by ancient gods is an example of fairy-tale thinking. It has little to do with anything we observe in the real world. But that is the way astrologers of today think. What is the chance that any forecasts they make, based on these ideas, would be true? With such fairy-tale thinking and extremely stretched analo- gies it is clear that astrologers really do not know what a fact is.t They seem to believe that whatever they choose to imagine to be true is really so. Astrology: Science or Superstition? 43 Figure 4.3. Ancient astrologers pictured their god Mercury with magical winged feet, serving the gods as a messenger. This remains today as a modern symbol for speedy delivery. Today's astrologers still follow this ancient superstition when they assume that the role of Mercury (the god), as a speedy messenger, causes Mercury (the planet) to "influence" transportation and commerce on earth. (Courtesy of Florists' Transworld Delivery) Why should anyone believe in the predictions astrologers make with such fairy-tale thinking? 44 Part One: Superstition and Fairy-Tale Thinking How baffled the early astrologers must have been when they could not account for the deceptions, rumors, and drug or alcohol abuse caused by Neptune, or the overnight success or sudden collapse of fortune so typical of Uranus. Neptune and Pluto together in the air in the sign of Gem'mi were responsible for the miracle of flight in the early 1900s, and Pluto rules, among other things, that uniquely 20th century phenomenon, the media. According to such reasoning, why should we honor the Wright brothers for inventing the airplane when Neptune, Pluto, and Gemini really did it? Why blame drug dealers, liars, and rumor-mongers when Neptune really made them do it? And if something is wrong with the media--newspapers and tele- vision-why not blame it on Pluto? Unfortunately, the more than 1,000 newspapers that publish those daily, meaningless horoscopes do not tell their readers that it is all based on ancient superstition and fairy-tale thinking. Many people, especially children, believe practically everything they read. So why should we be surprised that so many people believe in the ancient superstition of astrology? In Part One of this book we investigated the nature of super- stition. We showed that it is based on fairy-tale thinking that ignores facts. In the remaining chapters of this book--Part Two--we examine the powerful scientific way of thinking that enables us to obtain facts about the world and has greatly increased our knowledge and abfiity to do things. Along with the many good things this scientific knowledge has brought to the world, it has also produced some harmful effects. As a result, a major task today is for people everywhere to learn how to use this powerful way of thinking to solve the many problems that now confront the world. We begin, in chapter 5, with some answers to the impor- tant question, "How are new facts discovered?" PART TWO SCIENCE AS A WAY OF THINKING 5 How New Facts Are Discovered There have always been some great thinkers who put facts ahead of superstitious, fairy-tale methods of thinking. We might call them the early "scientists." But it has been mainly in the past 500 years that the scientific way of thinking has been widely accepted. As a result, today we are able to discover important new facts about our environment very much faster than ever before. In the chapters that follow you will see how the scientific way of thinking developed and how it has changed our world. But first, in this chapter, let's examine how the scientific way of thinking differs from superstition and fairy-tale thinking, and how we use it to build our knowledge. AN EXAMPLE: CAN ROCKS FALL FROM OUTER SPACE? Before the year 1803 the idea that rocks could fall from the sky seemed utterly ridiculous. Where would the rocks be coming from? Is someone sitting up in the clouds with a pile of rocks throwing them down on us? Impossible! There had been occasional reports from distant places of rocks falling from the sky and hitting the ground with a loud crash. However, in 1803 there were no telephones, radios, cars, or airplanes, and it was hard to investigate sketchy reports from faraway places. So, there were no reports from trustworthy observers that rocks could actually fall from above. Such an 47 48 Part Two: Science as a Way of Thinking idea was considered to be just a product of imagination. Then, on August 26, 1803, many people in the village of Laigle in France saw fast-moving bright streaks of light in the sky. They heard crashing sounds. Afterwards, they found many new crater-shaped pits of different sizes in the ground near the village. Each crater contained a rock that people could see was quite different from those usually found in the area. Although it was hard to believe, the people of Laigle were quite sure of the fact that a shower of rocks had somehow fallen to earth. People elsewhere were skeptical about these incredible re- ports. But reports from so many people in Laigle could not be ignored so easily. So a team of scientists went to Laigle to investigate. In a large area, six miles long and three miles wide, they observed about 3,000 new crater-shaped pits in the ground, each containing a strangely shaped rock. From such strong evidence, based on many observations, the scientists concluded that a shower of rocks, moving at high speed, really had fallen from above. Where had they come from? The only explanation that made sense was that these rocks had fallen to earth from outer space. A report by the scientists about their observations, with a proposed explanation of what happened, was published world- wide, in newspapers and science magazines. At first, the idea that rocks could fall to earth from outer space was considered by many scientists to be a hypothesis, a reasonable guess for a possible fact, based on some evidence. Such a startling new hypothesis stimulated scientists to seri- ously consider the idea. Many of them began to look for fur- ther evidence for or against it. HOW OUR KNOWLEDGE GREW The discovery that rocks could fall to earth from above opened the door to a new area of knowledge in astronomy that grew very rapidly as many new observations were made. Today, the knowledge gathered since the event at Laigle in 1803 plays an important part in the picture scientists now have of the way the earth, sun, moon, planets, and all the stars were formed many billions of years ago. How New Facts Are Discovered 49 All of this knowledge is based on careful observations. For example, it was observed that before the rocks hit the ground, they were often seen by people hundreds of miles away, rapidly streaking across the entire sky as brightly glowing "fireballs." This observation showed that they were at a great height in the atmosphere and traveled at enormous speed. Astronomers have instruments that enable them to measure the height above ground and speed of these fireballs. They are found to be traveling at speeds of about ten miles a second and begin to glow in the upper atmosphere at a height of about 50 miles. Because of their resemblance in the sky to meteors, the falling rocks were called meteorites. We now know that the main difference between meteors and meteorites is their size. Meteors are very tiny; most are the size of grains of dust. When they hit the earth's atmosphere at enormous speed, friction with the air heats them and they glow for only a moment before the small amount of material is burned up or evaporates. Meteors may be seen on any clear, moonless night, far from city lights, as quick streaks of light that usually last for only a second or so. The larger the grain of dust (perhaps the size of a grain of sand), the longer and brighter the streak. Photography is one of the most important aids to astron- omers because it captures observations at a moment in time. Figure 5.1 shows how useful photographs can be. This one, taken while the lens of the camera was kept open for several hours, captured the image of a meteor that happened to flash across the northern part of the sky during that time. As the earth rotated, the circular streaks were produced by bright stars as they appeared to revolve around the North Pole. Note how the meteor streak widens and narrows at sev- eral places as parts of it burned, evaporated, or broke off be- cause of the heat caused by friction with the air at high speed. Some meteorites fell closely enough to where scientists r~ved so that they could be examined shortly after they fell to earth. It was observed that the outside of a newly fallen meteorite is very hot because of friction with the air. However, when broken open, the interior was found to be extremely cold because the meteorite had been in very cold outer space for a very long time. Some meteorites in museums are enormous. The meteorite shown in Figure 5.2 is just one piece of a huge meteorite that produced the crater shown in Figure 5.3. 50 Part Two: Science as a Way of Thinking Figure 5.1. This photograph of the northern sky was taken with the lens open for several hours. The circular arcs show the apparent motion of northern stars as the earth rotated. The straight line streak is the track of a meteor that flashed across the sky while the lens was open. (Photo by W. Lockyer, Lockyer Observatory, England) SOME GIGANTIC FALLS OF METEORITES The biggest fall of meteorites since the one in Laigle occurred one morning in 1908 in a remote area of Siberia, in Russia. Many people saw an immense fireball streak across the sky, then heard distant thundering sounds that ended in a loud crash heard up to 650 miles away! The impact was so powerful that people and horses 100 miles from the site of the crash were blown over by the wind, and some were knocked unconscious! Giant waves formed in rivers. In broad daylight, people living 250 miles from the crash saw a jet of flame about twelve mfies high. Earthquake shocks were How New Facts Are Discovered 51 Figure 5.2. The man's hand in this photograph indicates the large size of this meteorite. It is just one of many that had hit the earth at the same time and formed the huge crater in northern Arizona shown in Figure 5.3. Note the pock-marked surface caused by melting or breaking of outer parts of the rock as it hit the air at extremely high speed. (Courtesy of Meteor Crater Enterprises) reported on measuring instruments all around the earth. There were no cities or villages in the area where the rocks fell, so there were no known deaths. However, anyone who hap- pened to be within many miles from the center of that crash would probably not have survived to tell about it. The place where the meteorites fell was so remote that it was not observed by scientists until nineteen years later, and then only from an airplane. They saw a completely devastated area about 50 miles in diameter, with most of the trees knocked down, as though blown over by an incredibly powerful wind. Two hundred craters were observed from the air. There surely are many thousands of smaller ones that were not visi- ble from the airplane. 52 Part Two: Science as a Way of Thinking Whatever hit the earth was certainly a huge mass, perhaps as big as a large ship. The mass seems to have exploded into many pieces before reaching the ground. Such an explosion could have been caused by sudden heating and bo'fiing of frozen gases. We now know that comets are composed of rock, ice, and frozen gases. One of the many comets in orbit around the sun may have hit the earth, causing the devastation in Siberia in 1908. We do not know of anyone killed by meteorites, but there have been some close calls. In 1946, a hail of meteorites in Kenya, located in East Africa, flattened huts in many villages over an area sixty miles wide. One village was set afire and many cattle were killed. Fortunately, no people died in that incident. METEORITES IN THE PAST Can we figure out what happened in the distant past, even though no one ever observed the events? Yes, by using our marvelous brains and ability to reason logically. Like detec- fives, scientists search for clues to figure out what probably happened. We can infer (conclude from evidence) some details about events that probably happened in the past from what we observe in the present. There is very strong evidence that some very large meteor- ites fell to earth in the distant past. We find a number of circu- lar "impact craters" on earth, of many different sizes, up to many miles in diameter. One such crater, in Arizona, is shown in Figure 5.3. It is almost a mile in diameter and deeper than a 60-story building. Compare its size to that of the tiny road seen in the picture, taken from an airplane. From magnetic measurements we know that a large mass of iron, often found in meteorites, lies beneath the crater floor. The evidence indicates that this crater was caused by the im- pact of a gigantic meteorite many years ago. Geologists have several ways to estimate the ages of rocks. From their observations and measurements they estimate that this crater was formed about 12,000 years ago. A number of other large impact craters have been discov- ered, often by noting large circular features on maps or photo- graphs from satellites. Most of these were formed many mil- lions of years ago, as shown by the way they have been eroded (worn away by rain, wind, rivers, and ice) over a long time. How New Facts Are Discovered 53 Figure 5.3. Meteor Crater, almost a mile in diameter, was produced by the impact of a huge mass of rock about 12,000 years ago. The main mass buried itself underground, but many smaller meteorites are scattered around the site. (Arizona Office of Tourism) METEORITES IN THE SOLAR SYSTEM Other evidence about what happened in the distant past comes from observations with large telescopes of the surfaces of plan- ets and their moons. Many "impact craters" are observed on our own moon (Figure 5.4), on Mercury (Figure 5.5), and on most moons revolving around the other planets. The way some of these craters overlap indicates that they occurred at different times. Additional evidence for rocks in space came from discov- ery of many "small planets," called asteroids, that orbit the sun. They range in size from the largest, Ceres (pronounced as "series"), about 900 miles in diameter, down to some of irregular shape that are only about one m'fie long. There must be many more that are too small to be visible in our best telescopes. More evidence for rocks in space, of many sizes, came from the spaceship Voyager II, which flew past Saturn in 1984. Scien- tists planned an experiment in which radio signals were trans- mitted to earth through Saturn's rings. (Figure 5.6) From obser- vations of the way these radio signals were weakened astrono- mers were able to infer that they probably contain dust, rocks, and boulders of many sizes, all revolving in orbit around Saturn. Other evidence about the nature of materials in space came from a space probe sent up from Russia in 1986 to investigate Halley's Comet as it approached the sun from far out in space, on its elongated 76-year orbit. Close-up pictures revealed that 54 Part Two: Science as a Way of Thinking Figure 5.4. The moon's surface reveals many thousands of craters, of many sizes, caused by impact of gigantic meteorites in the distant past. (Lick Observatory) it was a peanut-shaped mass, about 8 miles long. A bright halo of vapors and dust streamed outward from the head of the comet. This is what formed the bright tail which always points away from the sun. Scientists have found in the laboratory that light exerts slight pressure on objects it strikes. Out in space, that pressure of sunlight on a comet's dust and gases pushes them in a direction away from the sun. Figure 5.7 shows the spectacular, bright "tail" of illumi- nated gases and dust from Halley's Comet as it appeared in 1910. It was an astonishing sight, stretching across one-sixth of the entire arc of the sky and estimated to be many millions of miles in length. Astronomers concluded from these and other observations that comets are composed of a central mass of rock, or perhaps loose groups of rocks, mixed with ice, frozen gases, and dust. The dust and gases released by comets, and perhaps small rocks that break free, wander off into orbit around the sun. Some of these materials eventually hit planets and moons, How New Facts Are Discovered 55 Figure 5,5, This photograph, pieced together from a number of separate pictures taken by Mariner 10 as it passed by Mercury, shows many craters similar to those on the moon. (National Aeronautics and Space Administration) perhaps our own earth. We then see them flash through the atmosphere as meteors, or reach the ground as meteorites. It is also likely that some of the dust and rocks that hit the earth have been orbiting the sun from the very beginning of the solar system. Scientists can identify many tiny bits of dust floating in the air as having come from meteors. They also find such particles in deep deposits of mud at the bottom of the ocean. This shows that the earth has been bombarded by a rain of dust particles from outer space for a very long time, probably from the beginning of the solar system. From all this evidence it is clear that there are an enormous number of pieces of material in the solar system. There are planets, moons, asteroids, comets, boulders, and rocks of all sizes. There are huge numbers of objects the size of grains of sand and particles of dust. There are also many separate atoms and molecules of different kinds of gases. This does not mean that outer space is crowded. The vol- ume of the solar system is so great that the chance of a rock, or even a sand-size particle, hitting one of our manned space 56 Part Two: Science as a Way of Thinking Figure 5,6, Saturn's rings are composed of huge numbers of different sizes of dust, larger particles, rocks, and boulders, all orbiting the planet. (National Aeronautics and Space Administration) ships is extremely small. At theft very high speeds (many miles a second) the impact of a sand-size bit of material could dam- age a spaceship and lead to the death of the astronauts inside. Fortunately that has not yet happened, but it is always a danger. On earth we are well protected from damage by our 50- mile thick atmosphere that stops all but the larger rocks that come from outer space. EVER-GROWING KNOWLEDGE What began as a startling observation of rocks falling from the sky near the town of Laigle in 1803 has led astronomers to a much deeper understanding of our earth and solar system. It has also provided important information about events that occurred billions of years ago. Today, such information, based on observations, plays an important part in theories about how the solar system was formed about four and a half billion years ago. Astronomers have good evidence that the solar system began as a huge cloud How New Facts Are Discovered 57 Figure 5.7. in 1910 Halley's comet produced this enormous tail of gases and dust more than a hundred million miles long. It stretched across one-sixth of the sky. When the comet returned in 1986, a space probe sent from earth revealed a peanut-shaped "head" composed of rock and frozen gases about 8 miles long. (Mount Wilson Observatories, Carnegie institute of Washington) of gas and dust in space that was pulled together by the force of gravity. Our own earth was probably formed in this way from the dust and rocks that fell into the growing mass. The knowledge gathered about meteors and meteorites since the fall of rocks in Laigle in 1803 is an important part of that evidence. We see in the history of our knowledge about meteorites an example of the way science grows, fact by proven fact. Dis- covery of one new fact often leads to discovery of others. This accumulation of experience and knowledge enables many thou- sands of modern scientists to increase our ability to solve problems that constantly arise in our world. This scientific way of thinking is widely applied in engineering, industry, and medicine. It is increasingly applied to economics and the social and political sciences. Today we have entered an information age in which knowl- edge has become power. Those who know how to use the scien- tific way of thinking, and therefore know how to get new in- formation and use it properly, are the ones who will create new inventions and solve the difficult problems of our time. As we shall discuss in chapter 10, there have also been some harmful results of such use of knowledge. One of the big problems of our time is to find ways to use our knowledge wisely to create a better world. Perhaps you will play a role in this important task. 58 Part Two: Science as a Way ol~ Thinking THE MAIN IDEAS IN SCIENTIFIC THINKING 1. Facts must be based on accurate, carefully checked observations, verified by many people. These are the main ideas in scientific thinking that make it so superior to the kind of fairy-tale thinking upon which superstition is based. 2. Scientists use imagination, as well as logical reasoning to build on the facts they have. They make hypotheses: reasonable guesses as to possible explanations for what we observe. But these hypotheses are not considered to be true until supported by very strong evidence. 3. Experiments are often designed to get new observations to test hypotheses. 4. Scientists are open-minded about new ideas, but also reasonably skeptical about accepting them as true too quickly. History is full of examples when people thought they were absolutely fight about facts and theories that later were shown to be wrong. The scientific way of thinking has meant much more to our society than just the gathering of facts about our environment. During the past 500 years it has deeply affected the way people think about many things, including the way their governments operate. Science has played an important role in the establishment of democracy in our nation and in many others in the world. How that happened is discussed in the next chapter. 6 Science and Freedom of Thought Get into your time machine and go back 2,000 years. Imagine that you are observing the sun in the sky with an astronomer of that time. At dawn you see the sun appear to rise in the eastern sky and then go higher and higher until noon. Then it seems to move lower and lower in the afternoon, setting in the west in the evening. Your ancient astronomer friend says, "I've watched this happen for many years. From these observations it is clear that the sun always moves in the sky from east to west. Someone with enormous power must be making it move. Only a god could do that. We believe it is Apollo, the god in charge of the SUll. "Some people say that he pulls it with his magical chariot, but I really don't know about that. All I know is that he gets the job done. Since we are not gods, we will never know how Apollo does it. It's not a problem for me, so I don't lose any sleep over it." This explanation upsets you because you learned in school that it is not true, so you say, "Excuse me for differing with you, but no god is pulling the sun. The sun only seems to rise and set. Actually, we live on a huge, round, ball-shaped earth that rotates on its axis once a day. The earth's rotation gives us the illusion that the sun is moving when it really is not. It's like being on a merry-go-round and seeing everything else go around us, when we are really rotating with the earth." The astronomer stares at you for a moment and says, "A very clever theory. But you and I both saw the sun move up 59 60 Part Two: Science as a Way of Thinking from the east in the morning. We watched it move across the sky all day, and then go down below the horizon in the evening. Are you doubting what you actually see? "Besides, we know that the earth is enormous. The known part of the earth stretches for thousands of miles from here in every direction. If, as you say, it is rotating once a day, this means that its surface must be moving at enormous speed fight now to complete that big turn. It might have to move a thousand miles an hour. We don't feel that impossible motion. So, your theory is obviously wrong." This stumps you because you never thought about it before. Now that this enormous speed is brought to your attention, it does seem strange that you don't feel that thousand-mile an-hour motion. "Furthermore," he continues, "about this crazy idea of a round earth. See that lake over there. Can't you see that it is perfectly flat? "Look. I'll make a diagram to show you." (Figure 6.1) "Here's some water in the ocean, at A. If the earth is round then all its water would flow downward, away from the top, and finally fall off the sides of the earth. It has to disappear somewhere, perhaps in Hades. But we don't see the water in the lakes and oceans moving that way. That proves your theory is wrong. "And here is a man walking around the earth. When he gets to B he would be sliding downhill all the way, and probably also land in Hades. "What about this poor man at the bottom of the earth, at C? How long could he hang on without also going to Hades?" Your eyes light up triumphantly. "No. No. Gravity will pull everybody towards the center of the earth and also keep water, people, and everything else from falling off." "Gravity?... Who is he? How does he do that?" "Gravity is not a person," you reply. "Gravity is an invisi- ble force that pulls everything down towards the center of the round earth." The ancient astronomer replies, with a tone of voice as though he thinks you are pretty stupid. "How does this god, this Mr. Gravity, do this? Does it pull people with ropes? Do you see or feel any ropes pulling you down? "Suppose I put a ten-foot-thick stone between me and the earth. Shouldn't that thick stone block whatever Mr. Gravity tries to do in pulling me down? Shouldn't I then feel lighter, Science and Freedom of Thought 61 C Figure 6,1, It was reasonable for people in olden times to think that a round earth is impossible. How could people, water, and ships keep from sliding off into Hades? It was very difficult to prove that an extremely mysterious "force of gravity" pulls everything toward the center of the earth. (Drawing by Albert Sarney) maybe float in the air? You want me to believe that this pull, this gravity or whatever, passes fight through solid rock with- out being stopped?" At this point it dawns on you that you really do not fully understand this peculiar theory about the force of gravity in a round, rotating earth, something you were taught in school. You accepted this idea at school without thinking deeply about it. This reminds you of the way young children accept the story of Santa Claus without being puzzled by any of its contra- dictions. Your talk with the ancient astronomer makes you realize that people in olden times were not so stupid when they thought the earth was fiat and did not move. You also begin to under- stand that if you had lived long ago you, too, would have 62 Part Two: Science as a Way of Thinking considered anyone a bit crazy to insist that what you see and feel is really not so. In olden times, when there were no airplanes or satellites that go around the world, it was very difficult to prove that the earth is round and moves around the sun. That's why it took so long to discover the true nature of the solar system, and centuries more until most people were convinced it was true. Today it is easy to prove that the earth is shaped like a ball. Just look at the photograph of our round earth, on the front cover of this book, taken from a satellite far out in space. Many airplanes have traveled around the world by constantly heading west, or east. If we make a telephone call at noon to India, on the opposite side of the earth, we find that it is mid- night there. Such observations prove that the earth is round. By far the best evidence that the earth and planets revolve around the sun comes from the amazingly accurate predictions astronomers now make about events involving the sun and planets. They measure orbits of the earth, moon, and planets with great precision, then predict, years in advance, exactly when and where eclipses will occur, and how long they will last. These predictions are accurate to a fraction of a second. We have sent spaceships to the moon and many planets on journeys that could not have been made without precise calculations that take into account the forces of gravity of the sun, earth, moon, and planets. For example, in 1977, scientists sent Voyager II on a twelve-year journey to fly past the planets Jupiter, Saturn, Uranus, and Neptune, all hundreds of millions of miles away. Voyager II passed near each planet on schedule and reached Neptune, the last planet on its trip, within four minutes of the time planned by scientists twelve years before! This is extremely strong evidence that our facts and theories about gravity and motion are true. THE DANGEROUS IDEA OF A MOVING EARTH In 1492 Columbus sailed to America and found a new continent. His ships did not fall over the edge of a fiat earth, as many had feared. This fact cast doubt on the old theory of a fiat earth. Then Magellan sailed completely around the earth by head- ing mostly west. The fact that sailing mainly in one direction brings a ship back to its starting place was strong evidence, Science and Freedom of Thought 63 based on observations, that the earth is round. When the Polish scientist Nicholas Copernicus proposed the theory that the earth revolves around the sun, this idea was much more difficult to prove, and even harder to accept. It was also more dangerous for scientists to declare that they believed it true because the idea of a non-moving earth had become an important part of religious belief in Europe. People firmly believed that God had created the earth as the center of the universe, just for the benefit of people. The Copernican theory shifted the center of the solar system to the sun. The other planets became equals with the earth because all of them revolve in orbits around the most-important sun. The earth was no longer the center of the universe. Copernicus knew that his theory contradicted religious belief of that time and that to publish it would be considered heresy, the crime of differing in religious beliefs, punishable by burning at the stake. For that reason he delayed publication of his book until after his death in 1543. However, some scholars read the book, became interested in his theory, and began to discuss it. Religious leaders of that time acted to suppress such discussion. In 1593 Giordano Bruno was imprisoned because he wrote books that favored the Copernican theory. He was found guilty of heresy by judges of the dreaded "Inquisition" and, in 1600, was executed by burning at the stake. One of Brano's "dangerous" ideas was that the stars were not on a fixed dome that revolved around the earth, as was believed at the time. He suggested that the stars are separate, bright objects, extending far off in space in every direction. Today we know this idea is also true. So Bruno was executed for having correct ideas. Brano's execution discouraged discussion by others and made them more cautious. But it did not stop scientists from continuing their observations of the skies. In 1609, nine years after Bruno was executed, the Italian scientist Galileo Galilei heard about a Dutch invention of a telescope. He quickly put together some lenses to make one of his own and used it to observe the sun, moon, planets, and stars in the sky. By greatly magn'ffying the images of the sun, moon, planets, and stars, the telescope made details visible that no one had ever been able to see. This opened up the view of an astonish'rag universe that no one at the time could even have imagined. 64 Part Two: Science as a Way of Thinking WHAT GAI ,ILEO'S TELESCOPE REVEALED For the first time people could see that those smudgy markings on the moon were really mountains, valleys, fiat plains, and huge craters. Galileo was even able to estimate the heights of the mountains from their shadows. People could observe that the surface of the moon was similar to that of the earth. Galileo's telescope also revealed dark spots on the sun that slowly moved around it, day after day. (Figure 6.2) If a huge body like the sun could rotate on an axis, why couldn't the earth also do so, as Copernicus claimed? Gallleo was surprised to see that the planet Venus often appeared with a crescent shape. (Figure 6.3) This shape is seen only if a moon or planet is closer to the sun than the earth. Only then do we see that most of its circular shape is dark. We then see only the narrow illuminated portion as a crescent. This observation confirms the prediction by Copernicus that Figure 6.2. Galileo observed "sunspots" that moved from day to day, revealing that the sun rotated on an axis. If the sun rotated, why not the earth? (U.S. Naval Observatory) Science and Freedom of Thought 65 66 Part Two: Science as a Way of Thinking Figure 6,4, Note the four small moons of Jupiter (two in the upper left corner of this photograph, and two in the lower right corner.) They line up closely with Jupiter's equator, marked by the bands of clouds that encircle it. This system of moons greatly resembles a small solar system. (Lick Observatory, University of California at Santa Cruz) the orbit of Venus is closer to the sun than that of the earth. Galileo observed the planet Jupiter as a disk. There also seemed to be four small "stars" nearby, all in an approximately straight line with the planet. (Figure 6.4) To Galileo's great surprise, the next night those four little "stars" had all changed position. This was an astonishing observation for that time because no stars had ever before been observed to move from their positions in the sky, which people imagined to be a fixed dome. Yet here were "stars" moving. Night after night Galileo drew careful diagrams of the changing positions of these little "stars." It soon became clear to him that he was observing moons revolving around Jupiter! He measured the time it took for each moon to complete a revolution around Jupiter. As with the planets revolving around the sun, the moons farthest from Jupiter moved most slowly and took the longest time to complete one revolution. For many people that was the most convincing evidence for the Copernican theory. They could observe in Jupiter a smaller model of the solar system, with its moons actually revolving Science and Freedom ol~ Thought 67 Figure 6.5. This telescopic view of a small section of the Milky Way reveals many details not observed with the unaided eye, especially the vast numbers of stars. Do you see any evidence for dark clouds in space? (Yerkes Observatory, University of Chicago) around the planet, just as planets revolve around the sun. Galileo's telescope also revealed about ten times as many stars as seen with the unaided eye. He observed the Milky Way to be far more crowded with stars than other parts of the sky. (Figure 6.5) This observation was strong evidence for Bruno's idea that the stars were not just attached to a dome around the earth, but were a vast number of separate stars, extending very far out into space. Old ideas in closed minds die hard. The religious authorities of that time refused to accept this powerful evidence that proved them wrong. They ordered Galileo to stop writing and speaking in favor of the ideas of Copernicus and Bruno. Galileo waited many years, but then, in 1632, he published a book about theories ~f the solar system. To avoid punishment for heresy he tried to disguise his views by writing the book as a "dialogue" between two people, for and against the Coper- nican theory. No one was fooled. The arguments for the earth revolving around the sun were so much more convincing than for a non- moving earth that everybody could tell that Galileo really believed in the Copernican theory. As happened with Bruno, GaVfieo was brought to trial for 68 Part Two: Science as a Way of Thinking heresy. The judges of the Inquisition found him guilty and he was imprisoned for the rest of his life. He was probably saved from execution only by his great fame as a scientist. Gallleo was open-minded and drew logical conclusions from facts that he actually observed. Facts based on observations meant little or noth'mg to the judges of the Inquisition. To them it was most important to stop anyone from spreading any ideas that challenged what the authorities believed to be true. They imagined that if a fact contradicted their beliefs then the fact had to be wrong! They really had no notion of what a scientific fact is. This persecution of Galileo did not stop his ideas from rapidly spreading throughout the world. With the aid of Galileo's remarkable new instrument, the telescope, scientists in many countries kept gathering observations and drawing conclusions. In time, the ever-increasing evidence for a Copernican solar system established it as today's proven fact. Many old ideas are true, so it is important that they be taught to young people and learned by them. But the big lesson from the persecution of Bruno and Gallleo for their new ideas is that some old ideas may be wrong. When new, observed facts are discovered that contradict the old ideas, we must view them with open minds. We have to seek more evidence until a proper judgment can be made as to whether or not the new ideas are true. USING INSTRUMENTS TO HELP GATHER FACTS In 1609 Galileo's telescope was one of the first of many mod- ern instruments that have made today's world possible. It greafiy enlarged our view of the universe and our place in it. Modern telescopes, far more powerful than the one used by Galileo, enable us to observe a fascinating variety of ob- jects in the distant universe. We know now that there are hun- dreds of billions of galaxies, each with many billions of stars. (Figure 6.6). There are gigantic clouds of gas and dust in space. Increas- ing evidence shows that new stars are forming in some of these clouds. With the aid of a color-measuring instrument called a "spectroscope" we can analyze what is happening in stars that exploded long ago, hurling gases into space. (Figure 6.7) We Science and Freedom of Thought 69 Figure 6.6. Modern telescopes reveal billions of very distant galaxies of many shapes and sizes. This spiral-shaped galaxy contains more than 100 billion stars. (Mount Palomar Observatory, California Institute of Technology) can even show that the universe is expanding and probably began with a "Big Bang" about 15 to 20 billion years ago. The development of photography during the past century has been extremely useful in sdence because it permanenfiy cap- tures images of what we observe at a moment in time. Then scientists can carefully study those observations, long afterward. At the same time that Galileo made a telescope from two lenses, he also put them together in a different way to make a microscope. Although he did not do much with this new in- strument, it was used by others to peer into the world of small things. This new instrument also led to the discovery of remarkable new information, mainly in biology. Scientists soon discovered that tiny cells were the building blocks for all life. They observed such cells in every part of plants and animals, each doing a different job to make the entire organism work properly. Scientists also discovered tiny one-celled plants and ani- mals. It took another two centuries for them to show that some kinds of these tiny organisms could cause deadly diseases. From such discoveries we learned how to control many diseases and 70 Part Two: Science as a Way of Thinking Figure 6,7. Astronomers have evidence that this "nebula" (cloud of gases and dust in space) was produced by the explosion of a star many thousands of years ago, (Mount Wilson and Palomar Observatories) to double the average length of life. Today an immense variety of new instruments enables us to accurately observe and measure many quantities, such as length, weight, mass, force, time, pressure, speed, electric cur- rent, magnetism, light, color, and much more. Instruments have made it possible to observe invisible radiation, such as x-rays, infrared and ultrav/olet rays, and radio waves. Such instruments provide today's scientists with an enor- mous body of factual knowledge, based on observations, that could not have been imagined in Galileo's time. Engineers have used this knowledge to create today's giant industries. Physi- cians use this knowledge to prevent and cure diseases, prolong- ing life. Special measuring instruments are also important in aiding our senses to know what is going on inside complex machines. A car has just a few of these instruments on the dashboard. An airplane pilot may have many more that give him vital information about the temperature of each engine, the air pres- sure above the wing, the speed of the airplane, the direction in which he is heading, the amount of fuel, and lots more. He can tell instantly when something goes wrong in a remote part Science and Freedom of Thought 71 of the airplane, and can usually make adjustments to prevent accidents. NEW WAYS OF THINKING Besides the important facts of science and the many inven- tions it has made possible, science has also given us a better way of thinking. The sacrifices that Bruno, Gallleo, and many others made to break through the brutal, closed-minded thought-control of the Inquisition were not in vain. They showed the world that authorities in power can be very wrong in what they insist are facts. Science has also helped to diminish ignorance. We noted what terrible things ignorance could do in the Salem witch tri- als when the minds of people were poisoned by superstition. Our Founding Fathers learned these lessons well when they created our Constitution and wrote the Bill of Rights in 1789. They put into the basic law of our land the ideas of freedom of thought, speech and religion, and democratic rights. These ideas have become an ideal for most of the world. Freedom of thought does not guarantee that everyone will know what is true or false. Every person has the right to hold opinions and to make them known to others without being pun- ished by authorities. But then we also have the responsibility to try to find out what the facts really are. That is where the methods of science come into play. They give us important guidelines for finding out what is true and what is false. The best way to learn about the scientific way of thinking is to actually use it. This need not require complicated, expensive equip- ment. For example, what can you learn from the simple act of tossing some coins to see if they come down heads or tails? In the next two chapters you will see how some simple experiments with coin tosses can lead to very surprising re- sults. They will help you to understand why we should expect very unusual events to happen to people. And such experiments have also led to the discovery of facts that are now the basis of our huge insurance industry. 7 Developing a Theory: Probability One day, wh'fie playfully tossing a coin, you suddenly wonder if the chance of getting heads or tails really is 50-50. Are half the number of tosses really heads and half tails? At this stage all you have is a simple problem that arises, as most real problems do, from some observations whfie toss- ing coins. Posing that problem required some imagination. Your dog, Sparky, would never think of it. But we humans have this unusual ability to think deeply, to play with ideas. Your powerful ab'fiity to reason logically now comes into play. You examine both sides of the coin. They appear to be much the same, except for the picture stamped on it. So your reasoning leads you to think it equally likely for the coin to come down heads or tails. You make the hypothesis (reason- able guess at a possible fact) that half the number of tosses should be heads and half tails. This hypothesis is not yet a fact, but only a possible fact that must still be tested. Many hypotheses turn out to be wrong. So, consider your hypothesis to be just the start towards es- tablishing a fact. The main way of testing a hypothesis in science is with experiments. In the case of tossing a coin the experiment is much easier than for most situations in life. Just toss a coin a number of times and observe what happens. There seems to be nothing to it, but note what happens when you actually start tossing a coin. Suppose you decide to start with 10 tosses. Your hypothesis 73 74 Part Two: Science as a Way of Thinking predicts that in 10 tosses you should get 1/2 x 10 tosses, or 5 cases of heads, and 5 tails. Is that true? The way to find out is to try it and observe the outcome for tossing a coin 10 times. You do this, but are disappointed when only 3 heads and 7 tails are observed. You expected 5 of each. Does this mean your hypothesis is wrong? Not yet. It's too soon to give up. Continue tossing the coin for another trial of 10 tosses. Suppose that this time you observe 6 heads and 4 tails. Now you have a problem. Which is it, 3 heads out of 10, or 6 out of 107 Aha! A new idea pops into your fertile brain. Your myste- rious intuition is at work producing fruitful new thoughts. Perhaps 10 or 20 tosses are too few to get good information about how often a coin comes down heads. So, you decide to combine the results of the two trials. You now have a total of 10 + 10, or 20 tosses. If your hypothesis is right you should get half to be heads, or 10. There were 3 heads for the first trial of 10 tosses and 6 for the sec- ond. That's 9 heads in 20 tosses, a bit better than getting 3 out of 10 when you expected 5. But it still is not exactly the 10 you expected. Your new idea about increasing the number of tosses is really a new hypothesis: the greater the number of tosses of a coin, the more likely it is that you will get half to come down heads. Your mind instantly grasps the idea that to test the hy- pothesis you should toss the coin many times. You decide to keep a careful record of your observations by counting heads and tails as they occur. Something very interesting is happening. The new hypoth- esis, added to the first one, is the beginning of a theory about probability. Think of a theory as a set of rules that describe the way events occur in nature. You are on the way to developing a theory about just one small bit of nature: what happens when a coin is tossed. Test the hypothesis by tossing a coin 50 times, then 100, perhaps 200 times. Does the probability of getting heads (or getting tails) equal one half?. This experiment has been done by many people and they have found that the greater the number of tosses, the greater the likelihood that the number of heads would be very close to one half. So we consider it a fact that the probability of getting heads is one half. This fact is based on observations. Developing a Theory: Probability 75 THE VALUE OF THEORIES As you do experiments and observe what happens, your imagi- nation will cause new thoughts to pop into your head when you least expect them. Your first experiment with tossing one coin at a time is likely to grow and push its way into new kinds of observations. Suddenly you wonder: What would happen if you tossed two coins at a time? Would both coins be heads half the time? One-third? Onefourth? Something else? Why only two at a time? How about three at a time, or four, or ten, or twenty? How many times in 100 tosses would all coins come down heads, or tails, or half heads and half tails, or some other combination? Most of the rest of this chapter describes a "Theory of Prob- ability" that gives us a way to predict the expected results of tossing coins in different ways. But not only for tossing coins. It has been found to work for predicting expected numbers of accidents, fires, deaths, results of card games, motions of atoms and molecules, chemical reactions, nuclear explosions, opinion polls, and much more. Knowledge about this theory is the basis for the huge in- surance industry and is also essential to all sciences. So, as you experiment with coin tossing you will be learning about the important subject of probability. So, why not continue doing those experiments with toss- ing coins on your own, as far as you can go, before reading the rest of this chapter to find out what others have discov- ered? You will then get an actual experience in developing a theory all by yourself. You will also see how theories in gen- eral are developed. We have theories in the sciences of physics, chemistry, biol- ogy, astronomy, geology, and in the practical uses of science such as engineering, architecture, and medicine. We have them in economics, education, and politics and in every other area of knowledge. There are theories about how the universe began, how the solar system was formed, how continents move, how living things change, and evolve over time, how wars are started, how peace may be achieved, how recessions begin, how to end them, how to educate children, and lots more. Such theories are a major way for getting new knowledge 76 Part Two: Science as a Way of Thinking because their many different hypotheses require testing and experimenting, which lead to new hypotheses, testing, experi- ments, observing, and reasoning. THETHEORYOFPROBABILITY In science and mathematics the word probability is used to describe the likelihood that some chance event would occur. For example, if you observe that for 100 tosses of a coin 50 of them came down heads, then the observed probability would be simply 50 divided by 100, or 1/2, or 0.5. If an insurance company finds that during one year in a certain town with 10,000 homes, there were 100 cases of roof damage from storms, then the observed probability of roof damage per year is 100 divided by 10,000, or 100/10,000, or one in a hundred, or 0.01. Most people would describe that probability as "one chance in a hundred." Suppose you toss two coins at a time. Before reading fur- ther use your reasoning ab'dity to predict the probability that both coins would come down heads at the same time. Make a hypothesis about what the probability should be. Try it before you read further. The two coins fall independently of each other. As one is falling there is no way it can affect what happens to the other coin. This is the key to predicting what will happen when both coins are tossed. The diagram in Figure 7.1 gives us a way to analyze what happens. Consider what happens to the "First Coin," as shown on the first line. There are only two possible outcomes: heads (H) or tails (T). First Coin H or T /\ /\ Second Coin H or T H or T Outcomes HH HT TH TT (Number) I 2 1 Both One Heads Both Heads And One Tails Tails Figure 7.1. All possible outcomes for tossing two coins at one time. Developing a Theory: Probability 77 The second line, marked "Second Coin," shows all the dif- ferent ways the second coin could fall for each way the first coin can fall. So the line labeled "Outcomes" shows all the dif- ferent ways two coins can fall heads or tails when tossed together. Note the four possible outcomes: HH, HT, TH, and 2~r. Each of these outcomes is equally likely. Only one of these four gives us the "successful" outcome we seek: both coins heads (HH). So we can see that the probability that two heads will appear is one out of four, or 1/4, or 0.25. In 100 tosses of two coins we would expect to see 1/4 x 100, or 25 cases when both coins are heads. Try tossing two coins at a time for 100 times. Do you get exactly 25 cases of both coins coming down heads? Is this enough to confifm the hypothesis that the probability is 0.25? How many times should you toss the two coins to get an exact answer? A simple way to get many tosses is to have everyone in a class do the experiment. Then combine all the observations to get one total for the entire class. How close does your "ob- served probability" come to what is predicted from Figure 7.17 The chart in Figure 7.1 gives us a way to predict the prob- ability for any outcome when both coins are tossed. For exam- ple, what is the probability that both coins would come down tails? We note in Figure 7.1 that there is only one successful case in four when both coins come down tails (TT). So the probability is one divided by four, or 1/4, or 0.25. This is the same probability as for getting both coins to come down heads. That makes sense because both sides of a coin are practically the same, except for the minor detail of the image stamped on it. So both coming down tails seems to be as likely as both being heads. What is the probabfiity of getting one heads and one tails? When we look at both coins after they have fallen, it doesn't matter to us which coin came down first and which came down second. Both cases appear to us to be "one H and one T." Fig- ure 7.1 shows two such outcomes (HT and TH) in four tosses, so the probability is 2/4, or 1/2, or 0.5. There is a quicker way to calculate that the probability of getting both heads is 1/4. Just multiply the separate probabili- ties (one-half) that each coin will come down heads. So, for two coins the probability for both being heads is 1/2 x 1/2, or 1/4, which is the same as obtained from Figure 7.1. 78 Part Two: Science as a Way of Thinking Why is this so? Only half of the tosses of the first coin will be heads, and we will get heads for both coins only if the second coin is also heads when the first coin is heads. So, the number of cases in which both coins are heads would be one- half of one-half, 1/2 x 1/2, or 1/4. All that is theory. But is it really true? The only way to find out is to test this prediction with an experiment. What do you find? With this information you should be able to solve many problems about tossing more than two coins, on your own. PROBABILITIES FOR TOSSING MANY COINS AT ONE TIME Try these problems. When possible, test your answers with experiments to see if your predictions are correct. A discussion of each problem appears at the end of this chapter. Don't peek until you have first trim to find the answers yourself. The chart in Figure 7.1 shows all the ways two coins can fall. You can make similar charts for the other questions, as needed. 1. Toss three coins together 100 times. a. How many times would you expect all three coins to be heads? b. How many times do you expect two heads and one tails? (Suggestion: make a chart for three coins like the one in Figure 7.1.) 2. When four coins are tossed together 100 times: a. How many times would you expect all four to be heads? b. How many times would you expect three heads and one tails? c. How many times would you expect the number of heads to equal the number of tails? 3. If you toss ten coins at one time, what is the probabil- ity of getting all ten heads? Are you likely to get one such outcome in 100 tosses of the ten coins? Developing a Theory: Probability 79 FACTS AND THEORIES In this chapter you have seen how new knowledge about chance and probability begins with observations. We think about what we observe and use our imagination and intuition to develop hypotheses that might explain what we see. Then we test those hypotheses with experiments. We reject any hypotheses which the experiments and observations show to be untrue and keep only those that are not contradicted by them. This process leads us to new facts, new hypotheses, new experiments, and new tests with new observations. Soon we may have a theory that we think explains some events in the natural world. In time, if we find that the theory continues to be applied without any contradiction by new observations, then the facts are considered proved. At that point we may refer to such facts as principles or laws of nature. Facts, principles, and laws of nature are not absolute. In other words, we never consider them to be absolutely true. Some day a new observation, fact, or experiment may contradict a theory, principle, or law that we thought had been proved. When that happens, the contradictory fact cannot be ignored. Sometimes a theory can be changed somewhat to explain or include the new fact. If that cannot be done, then the the- ory must be abandoned. For example, Isaac Newton's Laws of Motion and Law of Gravitation held sway for several centuries. They were consid- ered to be absolutely true because of great success in predict- ing eclipses with precision. Newton's Laws had even been used to predict where an unknown planet could be found in the sky. Astronomers found the new planet, Neptune, very close to the place in the sky where calculations had predicted it would be. After that remarkable feat most scientists thought Newton's Laws were absolutely true. However, in 1887 an experiment by Albert Michelson and Edward Morley seemed to contradict Newton's Laws. The mystery was solved by Albert Einstein in 1905 with his Theory of Relativity. Einstein made a number of predictions to test his theory, all of which were found to be true. Newton's Laws of Motion were not abandoned, but the meth- od of calculation was changed somewhat to take into account Einstein's Theory of Relativity. Newton's Laws still work very 80 Part Two: Science as a Way of Thinking well for most situations. But when objects or particles move at extremely high speeds (many miles per second), Newton's Laws have to take into account the changes Einstein described in the Theory of Relativity. That is the way knowledge in science grows. It is also the way all howledge must change to adjust to new facts. In- creasing howledge based on such scientific ways of th'mking and doing has given us greater power to solve many kinds of problems. We have applied this howledge in many ways to give us more control over the environment. We will also have to apply scientific thinking to solve many problems of our en- vironment that modern inventions have produced. In the next chapter you will see how the information about pmbabfiity, described in this chapter, makes it possible for us to understand and explain some unusual, rather mysterious rare events that many people believe are caused by supernatural spirits. You will see that it is unnecessary to assume a supernat- ural spirit as the cause for such events. You will also find out that some very unusual events are actually likely to happen. DISCUSSION OF QUESTIONS la. Probability of Three Tossed Coins Being All Heads. From Figure 7.2 we see that the three coins come down all heads (HHH) for only one of eight possible outcomes. Therefore the probability of getting all three heads is one out of eight, or 1/8. For 100 tosses of three coins we expect to see 1/8 x 100, or 12.5 cases. The probability could also have been calculated as: 1/2 ~ 1/2 ~ 1/2 = 1/8 First Coin H or T Second Coin H or T H or T /\ /\ /\ Third Coin H or T H oY T H or T H L~r T 0 u t c o me s HHH HHT HTH HTT THH THT TTH TTT Figure 7.2. All possible outcomes for three coins tossed at one time. Developing a Theory: Probability 81 The probability of each coin being heads is one-half. The second coin will be heads for only half of the cases when the first coin is heads. So for two coins the probability of both being heads is half of a half, or 1/2 x 1/2, or 1/4. The third coin will be heads for only half of the cases when the other two are both heads, or for 1/2 of 1/4, or 1/8. This is the same as 1/2 x 1/2 x 1/2. You can see that as a coin is added to the group being tossed the probability of getting all heads is reduced by half. For four coins tossed at one time the probability that all come down heads is 1/2 x 1/2 x 1/2 x 1/2, or 1/16. lb. How Many Cases of Two Heads and One Tail? From Figure 7.2 we see three possible outcomes with two heads and one tail: HHT, HTH, and THH. So the prob- ability is 3 out of 8, or 3/8. 2a. Probability That Four Tossed Coins Would Be All Heads. This has already been discussed in question la. The probability is 1/2 x 1/2 ~ 1/2 ~ 1/2, or 1/16. 2b. Three Heads and One Tail. Make a chart for four coins tossed at one time. (Figure 7.3) You can observe four cases when there are three heads and one tail (HHI-IT, HHTH, HTHH, and THHH). From the chart you can count 16 possible ways that four coins could fall. Therefore the probability of getting three heads and one tail is 4/16, or 1/4. 2c. Two Heads and Two Tails. From Figure 7.3 you may observe six outcomes in which there are two heads and Figure 7.3. Outcomes for four coins tossed at one time. 82 Part Two: Science as a Way of Thinking two tails (HHTT, HTHT, HTTH, THHT, THTH, and 2'rHH). The total number of possible outcomes is 16. Therefore the probability of two heads and two tails is 6/16, or 3/8. 3. Probability of All Heads When Ten Coins Are Tossed. As explained in problem la, each additional coin in a group of coins that are tossed at one time reduces the probability of getting all heads by one-half. So for ten coins together the probability is 1/2 multiplied by itself ten times, or: 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2, or 1/1,024. This means that we are likely to observe only about one case of all ten heads in 1,024 tosses of ten coins. This is a rather rare event. Tossing them only 100 times, about one-tenth as many as a thousand, is not likely to produce even one case of all ten heads. Can you calculate the probability of getting all heads when 20 coins are tossed at one time? 8 Unusual Events, Luck and Chance Here is the story of an astonishing event that the author of this book (Mr. R) knows is true because it actually happened Mr. R dialed the telephone number of his friend Sam. Af- ter a few rings someone answered the phone. "Is Sam there?" "Yes. Just a m'mute. I'll call him." Sam got on the phone and exchanged greetings with Mr. R, then asked, "How did you know I was here?" "Why? Aren't you home?" "No. I'm at my friend's house." INCREDIBLE! Mr. R had dialed the wrong number and reached the person he wanted to talk to, at that wrong nurnber.t This event is so unbelievable that many people assume it must have been caused in some supernatural way. A SUPERNATURAL CAUSE? An "explanation" based on supernatural magic raises more questions than it answers. Why would some supernatural be- ing, or spirit, want to do this? The telephone call was of no special importance, nobody's life or health depended on it, and no money was involved. Did the supernatural spirit merely want to play a prank, perhaps have some fun by watching Mr. R's surprised expression when he realized what an unusual event had occurred? 83 84 Part Two: Science as a Way of Thinking There doesn't seem to be any purpose in having a myste- rious supernatural spirit make the event happen. Think about all the facts a supernatural spirit would have to know, and the many magical powers it must have, to cause this unusual call to happen. 1. The spirit would have to want Mr. R to dial a wrong number in just the right wrong way so the call would reach Sam away from home. 2. The spirit would have to be able to read Mr. R's mind and know, before the call, that Mr. R wanted to talk to his friend Sam on the telephone. 3. It would have to know that Sam would not be at home to receive the call. 4. It would also have to know that Sam would be in a friend's house at the very moment Mr. R made his call, or it would have to arrange for Sam to be there, which is even more miraculous. 5. The spirit would have to know the phone number of Sam's friend without looking in a telephone book. 6. It would have to get inside Mr. R's brain to direct his fingers to make the right mistakes to produce the wrong tele- phone call in the right way. An "explanation" based on a supernatural spirit requires more unbelievable things to happen than the unusual event itselfi Nothing in our experience, and nothing we can observe, gives us any evidence that anything could have the remark- able ability to make the electricity in the telephone wires go to the right place in the wrong way. Some people might think they are explaining it when they say it happened because of "luck." This is another way of say- ing "by chance," but it does not explain how the unusual call might happen. Scientists think in a different way. They want to know why things happen. There is a scientific explanation for what hap- pened to Mr. R that is based on the theory of probability which you began to investigate in the previous chapter. To understand that explanation you need to know more about the fascinating nature of probability for events that occur by chance. Unusual Events, Luck and Chance 85 MANY KINDS OF CHANCE EVENTS From experience with tossing coins you know that we cannot predict in advance whether a tossed coin will come down heads or tails. It is an unpredictable event that occurs by pure chance. However, your experiments with tossing coins have also shown that we can predict approximately how many heads or tails to expect when a coin is tossed many times. There are many other kinds of chance events, each of which has its own probability of occurrence. For example, if you pick any card from a full deck of 52 cards the probability of getting a spade is one-fourth because 13 of the 52 cards, or 13/52, or oneffourth, are spades. Suppose you select a card from a full deck, and repeat this 40 times. You are likely to get a spade about 1/4 x 40, or 10 times. Test that prediction with an experiment. But be sure to re- turn the selected card each time one is taken from the deck, otherwise the pack from which you select would no longer have 52 cards. That would change the probability. Also, take cards from different parts of the deck. Do you get the number of spades you expected? Suppose you now decide to look for aces. How many aces would you expect to get when you pick a card from a full deck and repeat this 100 times? There are four aces in the deck, so the probability of picking one from 52 cards is 4/52, or 1/13. You expect to get 1/13 x 100, or 7.7 (about 8) cards. Try it. What do you observe? The probabilities for many kinds of chance events are very small. For example, in the previous chapter one of the problems was to calculate the probability of getting all heads when 10 coins are tossed at one time. The answer, as described in the section at the end of chapter 7, was 1/2 multiplied by itself ten times, or 1/1,024. In other words, we expect to see only about one case of all ten heads for 1,024 tosses of ten coins. An experiment to test this prediction would be very tedi- ous. However, a computer could be programmed to simulate (imitate) the chance events for coin tosses, and could quickly run a test of many thousands. Being hit by a meteorite is such a rare event that we do not know of anyone to whom this has happened. The proba- bility is practically zero, but still, it might happen some day. 86 Part Two: Science as a Way of Thinking Being hit by lightning also has a tiny probab'dity, but not as small as that for being hit by a meteorite. Yet it does hap- pen occasionally. Insurance companies keep careful records of many kinds of accidents. From this actual experience, based on observations, they can predict fairly accurately how many illnesses, deaths, car thefts, fires, car crashes, or home accidents are likely to occur each year. These figures can be used as "observed proba- bfiities" to estimate how much should be charged for insurance to cover the cost of claims, plus profits. In a simfiar way, Mr. R's unusual telephone call could happen, so there is a tiny probability that it might happen. We cannot tell who would make or get such a call, or when and where it would happen. However, we can estimate how likely it is to happen to someone in the world sometime in the future. EXPLAINING THE UNUSUAL TELEPHONE CALL Everyone occasionally makes a mistake when dialing or press- ing the buttons for a telephone call. It makes a big difference if the mistake is made in the last four digits of a telephone number, or elsewhere in the number. If the mistake is in the last four digits then the call reac