SECTION VII Chapter 1. Misuse of Statistics to Portray "Amazing" Coincidences/Prophecy Definition of a Prophecy: "Two bull's eyes out of a possible million" --Mark Twain "If, of two astrologers consulted on the life of a child and on the weather, one says that the child will live to manhood, the other not; if one announces rain, and the other fine weather, it is clear that one of them will be a prophet." --Voltaire ("Astrology") "The first principle is that you must not fool yourself—and you are the easiest person to fool." – Richard Feynman "AMAZING" Coincidences in Everyday Life IN THE COURSE OF PLAYING A LARGE NUMBER OF CARD GAMES, almost everyone has experienced an amazingly wonderful (or simply atrocious) combination of cards being dealt to them. Statistics can accurately predict the ODDS of obtaining any combination of cards, over the course of a large number of games. The best professional gamblers apply the laws of statistics in their games, in order to net wins over the long term. These mathematical principles on random card drawings, apply in real life as well. Just as amazing hands can be drawn in a game of cards, AMAZING COINCIDENCES can also occur during the lifetimes of one or more individuals. Many people like to attribute these amazing coincidences to external forces watching over us that CAUSE these to happen. While it is agreed, that perhaps divine forces "could" be the cause of SOME amazing coincidences-- on the other hand it can ALSO be shown that PURE RANDOM CHANCE will guarantee that at least "some" amazing coincidences will also naturally take place over time. Coincidences are quite common. Amazing coincidences have occurred where people who have not seen each other for many years--say, find themselves sitting next to each other in the theatre, or run into each other in another city. Incidents such as these are striking!-- Still, the laws of probability would guarantee that over the course of many years and among large numbers of people, that some "amazing" coincidences such as these should happen--quite randomly. Coincidences may crop up within our daily conversation. Yet, many (if not all) of these may be expected, based upon the laws of probability. Take the following example. (I am quoting here from John Paulos' book entitled INNUMERACY): "Two strangers from opposite sides of the United States sit next to each other on a business trip to Milwaukee and discover that the wife of one of them was in the tennis camp run by an acquaintance of the other's. This sort of coincidence is surprisingly common. If we assume each of the approximately 200 million adults in the United States knows about 1500 people, and that these 1500 people are reasonably spread out around the country, then the probability is about 1 percent that they will have one acquaintance in common, BUT MORE THAN 99 PERCENT THAT THEY WILL BE LINKED BY A CHAIN OF TWO INTERMEDIATES.[emphasis mine]"(Paulos, INNUMERACY, p 29) It is important to note, this high probability only occurs if the two individuals know a fairly large number of people, and can match on ANY two people they know in common. Thus the more they talk about people they know--and people these people know, and on down the chain-- the more likely there will be SOMEONE they know in common. How Magicians and Con-Artists Can Appear to Have Great Prophetic Powers. To objectively judge a person's ability to make predictions, one must of course, tally up BOTH the successes AND the failures of the individual-- in order to compute an accuracy rate. Many con artists have created the DECEPTION of making accurate predictions by issuing a large number of forecasts AND ONLY COUNTING THE SUCCESSES. Or to state this another way, one way many con artists get away with making random events APPEAR to be magical, is to follow this simple rule: * ONLY COUNT THE "SUCCESSES" AND NEVER COUNT THE "FAILURES" (IE "MISSES")! This concept is elegantly simple--The trick is to either hide-- or distract attention away from the "MISSES". An excellent example of this technique can be seen in the "classic" Stock Market scam. The Stock Market Scam The Scam works like this: Say a con artist has a computerized mailing list of 32,000 names and addresses. He sends out 16,000 computerized letters predicting that a particular stock index will go UP, and to the other 16,000 he sends out a different letter that predicts that the stock index will instead go DOWN! He then waits for the index to either go up or down.--Now 16,000 thousand people have noticed the con artist "missed" his prediction, and probably doesn't care to hear from him again. However 16,000 people (who presumably are NOT aware of the other group) have now received a letter containing an "accurate" prediction. The con artist focuses on this latter group who received the "correct" prediction. He again hedges his prediction by sending 8,000 letters to half of these individuals, predicting the index will go UP--with the other 8,000 letters mailed to the other half which predicts that it will go DOWN. After the event occurs, there should now be 8,000 people who are starting to be impressed by TWO accurate predictions in a row! Again the con artist mails out to this latter group, 4,000 letters predicting the stock market will go up, with the other 4,000 predicting it will go down. Let's say he continues this process until after the sixth time, a group of 500 people will have received SIX CORRECT "PREDICTIONS" IN A ROW! If the con artist now sends out letters reminding this group of 500 people of his "successful predictions" and asks $500 for the next prediction, he could make $250,000 if everyone paid for this! (John Paulos, INNUMERACY, p 32) The "Psychic" Variation on the Classic Stock Market Scam. Psychics frequently use a variation of the stock market scam described above. Their trick is to issue out a LARGE number of predictions and hope the press will publicize ALL predictions that come true, while quickly forgetting about all false predictions. This technique has sometimes been called the "Jeane Dixon" effect, after the famous psychic Jeanne Dixon, who (presumably) employs this technique. Jeane Dixon and her "Gift of Prophecy" Jeanne Dixon has been credited with predicting the following "hits": The assassination of President Kennedy, that China would turn communist, that Russia would launch the first satellite--among others. "Misses" made by her include the following predictions: WW III would begin in 1954, the Russians would be the first to land on the moon, the Viet Nam war would end in 1966 (it ended in 1975), and her 1968 prediction that Jacqueline Kennedy was NOT thinking of marriage (Mrs. Kennedy married Aristotle Onassis shortly after this prediction.) Some analysis of her "hits" are revealing in themselves. For example, regarding Kennedy's term in office, a May 13, 1956 forecast made in PARADE MAGAZINE stated--"As to the 1960 election, Mrs. Dixon thinks it will be dominated by labor and won by a Democrat. But he will be assassinated or die in office, though not necessarily in his first term." The 1960 election was NOT dominated by labor, although it was won by a Democrat. It was also NOT so remarkable an event for a president to "be assassinated" or "die in office"--for during the twentieth century President McKinley was assassinated, and both Warren G. Harding and Franklin D. Roosevelt died in office. It is also a fact that Ms. Dixon had apparently changed her mind before the 1960 election, that Kennedy would even win the presidency. According to her forecast that appeared in Ruth Montgomery's syndicated column in January 1960: "the symbol of the Presidency is directly over the head of Vice President Nixon"--although "unless the Republican party really gets out and puts forth every effort it will topple." As can be seen by the above, there was so much creative HEDGING on the part of Mrs. Dixon, that she probably could've claimed SOME credit for prophecy--regardless of WHO won! Thus, Mrs. Dixon was well poised for a "heads I win, tails you lose" strategy. As long as no one focuses on the "misses", this kind of strategy works only too well (as her popularity will attest). Another example of Mrs. Dixon flip-flops: In February 1962, she predicted: "A child, born somewhere in the Middle East shortly after 7 A.M. on February 5, 1962 will revolutionize the world. Before the close of the century he will bring together all mankind in one all-embracing faith. This will be the foundation of a new Christianity, with every sect and creed united through this man who will walk among the people to spread the wisdom of the Almighty Power..." According to her biographer, Rene Noorbergen, Mrs. Dixon was much criticized for this prediction. Consequently she modified her prediction, stating that this individual was not a goodly person, but was instead- the "Antichrist". (Josh McDowell, JOSH MCDOWELL'S A READY DEFENSE, Here's Life Publishers, Inc, 1990, pp 388, p.s. I thought McDowell did an excellent job in this section of his book.) How "Good" Psychics Avoid Exposure Occasionally a psychic will be confronted by a skeptic or two, regarding their "misses". Of course, the mark of a really "good" psychic, is how well they can find a creative, but acceptable LOOPHOLE out of their earlier "prediction". For example, when skeptics once confronted one famous psychic as to why the state of California had NOT fallen into the ocean in the previous year as earlier predicted--the psychic defended herself-- by saying that she had "ONLY" promised that the California coastline would "change" during the year. Presumably she must have meant, that the GRAINS OF SAND along the coast would be "rearranged" by the tides from the ocean during the course of the year! Witchdoctors and other self-proclaimed practitioners of magic have employed this same technique for thousands of years--to give them the appearance of healing powers. If there is ANY improvement in the patient's condition, this is attributed to the powers of the magic worker. Any deterioration in the patient's health (ie "failure" or "miss") is "EXPLAINED" by other causes-- the patient waited too late for treatment, evil spirits interfered with the cure, etc. Thus, once again, only the "hits" are counted. The Fraudulent "Faithhealer" Version of the Stock Market Scam. There are fraudulent television faithhealing evangelists who use the principle of the "classic" Stock Market scam. During a dramatic moment, the fraudulent faithhealer will touch, or pronounce a person cured. In the drama of the moment, this can actually create a powerful emotional experience for the believer. Psychologists have documented numerous cases whereby believers (of all faiths and backgrounds) can in moments of ecstasy and hysteria call forth great surges of strength. (See Chapter 3). Psychologists will also tell you that the effects of this "hysteria" are temporary--often lasting hours or mere days. Typically though, the FRAUDULENT faithhealer is not held accountable for failures--because he has WARNED the believer that it was through THEIR OWN FAITH that they will be cured! That is, if the cure doesn't last--then it is the FAULT of the "believer"--because s/he LACKED enough faith to invoke a cure! Thus, after the person later realizes that they are NOT cured, s/he feels such terrible guilt, that they do not wish to publicize their plight.-- For to do so, would announce to the world that they FAILED to have enough faith. Most of these people would rather suffer in silence.--For to question their cure would, in itself, mean they had "failed" the test in having enough faith--not to mention they would lose all hope in a cure! The above technique thus basically works by suppressing "MISSES" from being publicized. The "Large Numbers" Game--or The "Someone, Somewhere" Scam Another fraudulent statistical technique is to make general predictions that have a good chance of occurring-- at least once-- among a LARGE population base. For example, one famous psychic used the following trick: He got on the radio and announced that he was emanating "psychic" waves that would cause broken clocks to start working again. Sure enough, someone called in who excitedly reported that he had just looked up at his broken clock and it was now working. James Randi, a professional magician, gave the exact same performance on another radio station in another city. He KNEW he wasn't even trying to send out psychic waves-- yet he ALSO received callers that announced that their clocks started working again. Randi explained that broken clocks are commonplace. Not only that, but SOME broken clocks will start running again. Therefore, he knew that he had good odds that SOMEONE, SOMEWHERE had not noticed that their broken clock had begun working again --- until prompted to look at it by the radio broadcast. According to James Randi's book, THE MASK OF NOSTRADAMUS (New York: Charles Scribner's Sons, 1990) the famous prophet Nostradamus also had figured out this trick when he lived way back in the sixteenth century. That is, he made a LARGE number of cryptic predictions, which the "believer" could interpret almost any way he wants to. When one compares Nostradamus' prophecies with the official event that is supposed to fulfill the prophecy, one can see where the Nostradamus scholars have twisted the interpretations to try and make their case. According to Randi, the "highly fanciful interpretations" of scholars reading Nostradamus' predictions "were arrived at only after diligently searching through history for something--anything" that could possibly be construed as matching it. A few predictions might still seem to come true. Of course one has to be careful that later individuals had not KNOWN of a prediction--and purposefully acted to make them come true. This is known as a "self-fulfilling" prophecy. (For example, some have claimed that the Jews built the Temple in Jerusalem following the Babylon Captivity-- because they KNEW of the prophecies and hoped its construction would initiate a new age.) As of today, a large number of Nostradamus' prophecies remain yet "unfilled". The believer must have faith that this was not due to the "large numbers" game, but represents those prophecies which will be fulfilled at some later date. Fraudulent "Faithhealer" Version of the "Someone, Somewhere" Scam Another technique used by fraudulent psychics and faithhealers is the "Someone, Somewhere" Scam. Fraudulent faithhealers apply the "Someone-Somewhere" scam as follows: Instead of focusing solely on one individual, they pronounce that cures are working somewhere among a large group of people. Random chance would predict that SOME individuals would naturally improve-- REGARDLESS of the faithhealing session. That is, it is a known fact that some people's illnesses naturally improve over time from being treated by doctors--or even by the action of their own immunity system (such as the remission of some cancers). Just as with psychics, if a large number of people are pronounced cured, and just ONE appears to have really been cured, then typically only this ONE success (ie not the large list of failures!) are greatly advertised. This has its parallels with the "broken" clock that started working again, That is, just as the psychic promised that SOMEONE, SOMEWHERE will have a broken clock that starts working, the faithhealer promises that SOMEONE, SOMEWHERE will be sick who gets well. Any ONE person who calls in and states their health improved, is now considered a miracle. (Televangelists have a special advantage with this technique because television allows them to apply this technique against a very large population base of believers.) But what about the Honest Psychic/Faithhealer? Now, the above analysis was directed clearly towards FRAUDULENT psychic/ faithhealing practices. Surely, it can be argued there MIGHT be cases where humans can invoke great powers. I personally believe that a person should be open to considering the possibility of miraculous happenings. However, because of the presence of con artists it is also important to use one's rationality to try and distinguish the genuine article from the con game. Regarding faithhealing, there is an actually an easy test for this. Any real faithhealer should eagerly ask impartial medical professionals to validate the cure. As with the rest of the population, MOST doctors are religious-- and want to believe in miracles like every one else. Likewise, the national media is always eager for sensational stories. The reason why so few "miracles" are reported in the press, is because they so often fall apart under rational, critical examination. (Footnote: For a good publication on this (dedicated to primarily examining psychic claims and not religious ones) this author would strongly recommend any interested reader subscribe to the SKEPTICAL INQUIROR magazine whose charter is to rationally research the existence of psychic, paranormal, and religious phenomenon. Founded by the Committee for the Scientific Investigation of Claims of the Paranormal (CSICOP), their quarterly magazine routinely lists dozens of exposes on fraud, deception, and sometimes just an honest misapplication of science in everyday life. Here are some examples of articles: *Magicians in the PSI Lab *Loch Ness Evidence Reassessed *Poltergeists *Retest of an Astrologer *Medical Quackery *Psychic Vibrations--Mermaid sightings, Pyramid Crystal Energy, etc) The interested reader is strongly urged to read James Randi's book, FLIM-FLAM--Psychics, ESP, Unicorns, and other Delusion, and Martin Gardner's FADS & FALLACIES. (These subjects are obviously beyond the scope of this book) The "AMAZING" Trend I had the good fortune to sit in on a college statistics class, where the professor knew how to make statistics exciting. For example, he designed the following experiment to illustrate the concept of RANDOM CHANCE for the class: Everyone had to stand up, one at a time, and announce BOTH their height and how much pocket change they had on them. The professor then plotted this information on a chart before the class. After the first FOUR students stood up and announced their height and Pocket change, an "amazing" trend was seen to exhibit itself. For in every case, the TALLER the person was, the LESS pocket change they had on them. Everyone became excited, and our teacher asked us (almost with a straight face), if we believed we had "discovered" some unknown, mysterious force operating on our college campus. By the time we got to the sixth student, our "amazing" trend line was broken up some. And by the time all fifteen students had posted their results, our beautiful straight line had become a RANDOM display of dots. The professor explained that the purpose of the demonstration, was to illustrate how fairly LARGE numbers are needed to detect a TRUE trend! With SMALL numbers, (such as in our case where the first four people kicked off an "amazing" trend), one can ERRONEOUSLY believe that a CAUSE AND EFFECT has been discovered. That is why statistical predictors insist on having a fairly LARGE number of data points-- before promising any reliable trends! The Example of the Astrology Believer In the above example, we saw how based on the first four students, that there APPEARED to be a strong connection (or correlation) between a person's height, and how much pocket change they carried on them. However, after more data was gathered, it was shown that there was NO "real" cause and effect between how tall a person was--and how much pocket change they carried on their personage. There is a Latin phrase that describes this common rational error in confusing CAUSE and EFFECT--ie "POST HOC: ERGO PROPTER HOC" ("after it, therefore because of it"). This "seeming" cause and effect can convince some individuals to believe in the paranormal. For example, I once knew an individual who strongly believed in astrology, because he believed it had so ACCURATELY predicted his love life. He was basing this on two events in his life surrounding women. He briefly lived with a woman whom "he was madly in love with". They parted after terrible fighting. He next fell in love with (and married), another woman--and described this as a good relationship. After checking out the astrological signs of both women in his life, he found that the sign of the first women was INCOMPATIBLE with his, while that of the second showed COMPATABILITY. This seemed to him to be "proof" that astrology worked--ie that their astrological sign was a good predictor of compatibility with him. After I listened to his story, I agreed this was indeed a coincidence. However, I also pointed out that there was a 25% RANDOM chance of obtaining this same result, (that is, the same probability as flipping two coins twice in a row and getting two heads.) When I related to him the example of the "amazing" trend story above, the concept "clicked" with him. He later thanked me for showing him the error in his thinking towards astrology. Examples of "False" Trends, Incorrectly Reported by the Far Right There are numerous examples, of how people see "false" trends at work: Several years ago, there were several articles that claimed that a connection existed between teenage suicides and the playing of the game "Dungeons and Dragons." Apparently, twenty-eight teenagers who played the game, later committed suicide. The theory was that these teenagers, in their obsession with the game, lost contact with reality and killed themselves. A deeper analysis showed that there was not necessarily any cause and effect relationships here. For the fact is that twenty eight teenagers is a SMALL number of the TOTAL teenagers who have been estimated to play the game (maybe as many as 3 million teenagers). This means that roughly .00093% (ie 28 divided by 3 million) of teenagers playing the game committed suicide. This number is actually smaller than the national average of teenage suicides of .012% (or 12 out of a 100,000 teenagers). (Paulos, INNUMERACY, p 126.) Another example of a false trend, has been the claim by the Far Right-- that since prayer was removed in 1962 from public schools, that this CAUSED the decline in public school performance in the late 1980's! This statement ignores some basic differences: In 1962, the SAT exam was taken primarily by middle and upper class, well-educated students. In the late 1980's, more diversified groups of students from a broader social-economic background were taking the tests. This had the effect of pulling down the AVERAGE scores. (Some studies, have indicated that the UPPER percentiles of Americans may still outperform their European and Japanese counterparts in some areas.) Another problem with this type of analysis, is that it only considers the observations that would "prove" its cause and effect relationship--while ignoring other points that would disprove it! Thus, using the above example of SAT tests, one should consider if Europeans and Japanese have improved too in this same period. If so, was it Christian prayer that "caused" the difference? If Japanese students perform better than American students, is anyone willing to apply this to its full limits to mean that the Japanese religion (Shintoism/Buddhism) is superior to Christianity? I think not. Sometimes, the Far Right claims that removing prayer out of school has also LEAD TO THE MORAL DECLINE OF OUR SOCIETY. Again, this assumes that previous periods in our history were moral than today. Yet, in the previous century, the slavery of blacks, and the eradication of Indians--is generally conceded to be wrong and even immoral by most moderate groups today. However, there periods are also considered more religious than in modern times. Of course, it is the definition of MORALITY that is crucial here to make such a judgment. (This subject is further discussed in Section VIII under Ethics.) But let's tackle this charge on another front. For, if the decline in public prayer had lead to the moral decline of society, one might think that OTHER (more measurable) areas of society had declined as well. Yet, between the 1960's and the 1980's, one can see other areas that actually IMPROVED. Life expectancy had increased from the 1960's to the 1990's (largely due to improved medical advances). The average standard of living also improved during this time, along with technological advances. Thus, if there were a true "cause and effect" from the decline of public prayer, then one should be prepared to explain exactly WHY these factors had not declined as well. (It can, of course, be counterclaimed that these periods of economic improvement are unrelated to public morality. But, as we have seen with the example of slavery, moral standards have not remained absolute in society over time.) Again, what is important--is to consider more than a "few points" in determining a trend--as these can so easily turn into FALSE trends! Thus, if public prayer was truly an important factor in society, then Medieval Times SHOULD have been a "Golden" Age, as opposed to a "Dark" Age. And the long time span for this period--ie a thousand years-- should have been a more meaningful indicator, than a relatively "short" time span of a mere thirty years. The Catholic Church's "Cause" or Explanation for Sex-Offender Priests In 1993 the Vatican sought to diffuse criticism of recent child abuse scandals involving clergymen, by counter-arguing that this is instead due to the RECENT, moral laxity in modern society. Chief Vatican spokesman, Joaquin Navarro-Valls defended the Church, saying: "One would have to ask if the real culprit is not a society that is irresponsibly permissive, hyperinflated with sexuality and capable of creating circumstances that induce even people who have received a solid moral formation to commit grave moral acts." Of course, the fact is that there have been sex-offending priests--as far back as the Dark Ages (as can be seen in penitential for sex-offending priests dating back to these times). Some modern accounts of sex crimes also occurred during conservative, religious periods in U.S history--such as in the 1950's. (The Catholic Church was silent on this aspect.) It has been estimated that in 1992 the Catholic Church had already paid out more than $400 million to individuals who accused clergymen of abusing them sexually when they were children. According to Jason Berry in his book, LEAD US NOT INTO TEMPTATION: CATHOLIC PRIESTS AND THE SEXUAL ABUSE OF CHILDREN (Doubleday,1992), the Catholic hierarchy often knowingly covered up cases of abused children. Even worse, they often sent sexually molesting priests to other communities, without alerting them of the priests' past--so that repeated offenses could occur. The official Church statements generally IGNORED the complicity of the Catholic hierarchy in covering up the crimes of sexually offending priests, preferring to blame it on a permissive environment. The result? In 2002, the scandal erupted again. This time with evidence that church authorities had not only covered up past abuses, but allowed it to continue, possibly on a larger scale than before. Now the estimated cost of paying off lawsuits have been estimated as much as a billion dollars. But let's go back to the claim of the Vatican in 1992 and evaluate this within that period's context: There was a major shift in how the local media PUBLICIZED sex-abuse stories between the 1950's and the 1990's. For in the 1950's the press typically co-operated in keeping sex-abuse stories SECRET from the public-- as such subjects were considered taboo. Thus, what is more likely is that this change in the attitude of the public and press in PUBLICISING sex-related stories was what had changed – not the promiscuity of a small minority of their priests. Still it is important to keep in proper perspective – that the vast majority of Catholic priests (now and then) are good, law-abiding citizens! The Catholic Church needs to put proper procedures in place to catch and stop the small minority that do act criminally, without covering it up within the church hierarchy and blaming "their" problems on the rest of society. The Tendency to Romanticize the Past One must recognize that the tendency to ROMANTICIZE the past, can cause one to simplistically state that only the current times are bad. Many generations have thought they lived in decadent times, sinful times. Indeed, it is a myth that the past was EVER free of violence or family abuse! According to Stephanie Coontz in her book, THE WAY WE NEVER WERE: AMERICAN FAMILIES AND THE NOSTALGIA TRAP, ALL historical periods--even the much idealized Victorian period, and the 1950's Good Times--had serious problems with alcoholism, child abuse, violence, poverty, and prejudice. She notes, in one example, how during the 1780's and 1790's in rural New England, roughly one third of all brides were pregnant. One reason divorce was less common, was because life expectancy was lower. (For example, the average marriage lasted only 12 years, because of heavy mortality rates during childbirth). Conclusion In conclusion, the problems experienced in American society today are due to a myriad of complex social-economic factors. Many sociologists HAVE noted a serious increase in violence and divorce within modern society, compared to the recent past. However, OTHER powerful forces (other than lack of "prayer" sessions) are at work too--such as the easy availability of dangerous mind-altering drugs, media violence, and greater population pressures. Indeed this has already been shown in one study on the subject (footnote as reported in EDUCATION WEEK, April 29, 1987 by sociologist Peter L. Bentson to the annual convention of the National Catholic Educational Association) which compared 16,000 high school seniors who went to public vs. Catholic school. Interestingly, it found that the more affluent students who had nearly twelve years of daily group prayer AND religious instruction, were more prone to use alcohol or drugs, and to steal-- than students in public schools, where no daily prayers were invoked. (As reported in the VOICE OF REASON--THE NEWSLETTER OF AMERCIANS FOR RELIGIOUS LIBERTY, Winter 1994, No 48, PO Box 6656, Silver Spring, Md 20916, Edd Doerr, editor, p 2). The study DID find that daily prayer helped instill religious beliefs in the students, but was NOT "as good at preventing adolescent behavior we want to prevent." Thus, it is likely simplistic thinking to believe that any one item (such as prayer in school) can be the ONLY cause of our problems in society today. However politicians, theologians, and other members of society often refuse to address the real roots of complex problems---instead promising easy solutions. Why? Because people like to believe in simple, solutions. Adolf Hitler knew of the power of this technique--and used it to proclaim that the Jews were the "cause" of ALL of Germany's problems. Hitler made sure that his message was kept in simplistic, black vs. white terms, stating at one point: " The great majority of a nation is ... ruled by sentiment and emotion rather than by sober reasoning. Its sentiment, however, is not complicated but simple and consistent. Devoid of multiple shadings, it has only negative and positive notions: love and hate, right and wrong, truth and falsehood; never half this or half that..." (In Section VII, Chapter 7, this subject will be taken up again, when we look at the question of whether the human mind is constructed in such a way--as to be "naturally" terrible at statistics.)