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The Gnarly Gnews

Published by the SMP Company, PO Box 1563, Santa Fe, NM 87504
Copyright 2008 by Montgomery Phister, Jr.
www.gnarlymath.com
Vol. 10, No. 6, July/August 2009
Gnews World Headquarters

Page 1

Please. Be Logical!!
In Which We Explain
How To Avoid Being Illogical

      Here's a bit of good logic:

    
      All elephants are mammals.
      I have a pet elephant named Earnest.
      Therefore, Earnest is a mammal.

      The orange circle on the right contains .. probably we should say includes .. all mammals. That means rabbits and humans and lions and elephants. And many other creatures.
      The greenish oval inside it is just the elephants. So the orange part outside the green has the rabbits and humans and lions and so on.
      And since my pet is an elephant, it must also be a mammal.

Good logic

      And here's a bit of bad logic.

    

Bad logic

    
      Some elephants are Indian elephants.
      I have a pet elephant named Earnest.
      Therefore, Earnest is an Indian elephant.

      The green circle on the left includes all elephants. The blue oval inside it includes all the Indian elephants. The part of the green circle outside the blue, then, includes all elephants which aren't Indian. Those would be the African elephants.
      But we can't conclude that Earnest is an Indian elephant. He might be African. we could say Earnest might be an Indian elephant, but we can't be sure.
      


      In this issue of the Gnews we're going to look at all sorts of ways we can be misled by errors in logic. Many times as we wander along in life we'll hear arguments which seem reasonable at first glance, but which are in fact NOT reasonable.
We don't know? Then it's true.
      Chloe was in perfect agreement with me about the perils of logic, and so we went for a stroll. Chloe said, The good old dogs
      "Bet those dogs up ahead will give us some ideas. Like, the three in front are talking? In English? It could be that dogs always get together when there's no human near, and have long conversations in the English language. About cats? And chasing cars? And who has the best master?"
      I chimed in. "And how to get what you want. And where's the best place to bury bones."
      Chloe agreed. "And who knows? Whether they're talking. They stop when any human might listen? So you can't prove that they're not talking? Why can't they be? That's the argument: We don't know, therefore it's true: dogs can speak English.
      "The UFO believers make the same mistake," I added. "They see something in the sky. Nobody knows what it is. Therefore it's a traveler from outer space."
Too few things to choose from.
      "And the two dogs behind could let us make what's called a 'false choice.' We might pretend to be logical, and say, 'All dogs are either black or white. My dog isn't white. Therefore it must be black."
      "It's, like, a perfectly logical argument. Except!! The first statement is of course, wrong," Chloe pointed out.
      "Seems hard to believe that such logic could really be used," I continued." But it happens all the time. The problem is, we don't notice. So the government tells us, 'We’ve got to spend trillions of dollars to support banks, homeowners, and other failing institutions. Otherwise the country will suffer a terrible depression.'"
      "The terrible depression is the white dog, and spending trillions is black," Chloe pointed out.
      "But there are thousands of other choices," I went on. "Like doing nothing. Or spending billions instead of trillions. Or not supporting the banks... We could go on and on."
      By this time we were wandering down a street and happened to notice that at the moment, all the cars we could see were blue.
Bad Gambles
      "A real gambler understands probabilities. If he gets 10 heads in a row when he's flipping coins, he knows the next flip has a 50% chance of being heads or tails. The previous throws make no difference."
      I continued, "But foolish folks, seeing all blue cars like the ones all around us know, will figure the next car that comes by will also be blue.
      Chloe agreed. "As if the car colors aren't random. But why shouldn't they be? Maybe there are 10 different car colors. If we assume any color is equally likely, then there's only one chance in ten the next car will be blue? Shouldn't bet on another blue. It's like a lady's been buying lottery tickets? And keeps losing? But she tells a friend she's going to take a trip to Europe. And her friend goes, 'How you gonna pay for it?' and the lady goes, 'I've been losing for years. I'm due for a win now.'" Street with cars
Jumping to Conclusions
      "And some other person," Chloe continued, "seein' the same cars? Might conclude that all the cars in the city are blue. Just because this small sample is all blue cars?"
      "Good thing we're so smart," I bragged. "Never make mistakes like this."
      "Hope not," Chloe replied, "but who knows? I've made mistakes. Just like everybody? A while ago I dated this blond guy? I thought he was really cool. And we had some buddies from the Italian part of town? And a couple of them were dealing in drugs? So then one day this blonde guy made it clear he though all Italians were dishonest. Just because of those few? And I gave him up. Just about concluded that all blonde guys are illogical?"
      I laughed. "So he jumped to a conclusion about Italians, and you jumped to a conclusion about blonde guys."
Poisoning the Well
      "My blonde friend reminds me of another mistake?" Chloe continued. "After I told him to 'get lost', I overheard a classmate? Talking to another boy in the class? And she goes, 'Did you know that Chloe dropped Harry? You sure don't want to take her out. She's just too fickle.'"
      "That's called 'Poisoning the Well," I said. "It started when there were terrible plagues in Europe in the 14th century. And it was said that certain people caused the sickness by poisoning all the wells. So you should shun those people. Your classmate told a story about you, and then warned the boy that he shouldn't trust you -- a conclusion that can't be drawn from what you told the blond boy."
      "Right," Chloe replied. "But I figured out how to get even? I'd tell everyone that she was a girl never told the truth. So then what could she do? If she said she always was truthful, kids would just figure I was right? That she wasn't telling the truth? That'd poison her well!"
The Red Herring
      "You've got to be careful," I said. "Now look at that cyclist. She's not wearing a helmet. They're trying to pass a law to make all cyclists wear helmets."
      "Right," Chloe said, "and there's this argument? Says nobody has to wear a helmet when he's driving a car? So why a helmet law about, you know, bicycles? So that, like, leads to an argument why car drivers don't need helmets because they have seat belts?"
      "And air bags," I agreed. "So you find yourself arguing about cars, when the real problem in bikes. That's a 'Red Herring'.... Wonder why they call a diversion a Red Herring?"
      Chloe knew. "A red herring was one that is dried and smoked. Ready to be eaten? And if you dragged one across a fox's path, then the dogs chasing 'em would go off in the wrong direction? Here's another example. There's this chess club? At school? And we're talking about schemes to attract new members. But this one girl goes, 'We hardly have enough chess sets now, for all of us to play. Why do we want new members?' And so chess sets was the red herring. Got us off the subject of new members? And onto arguments about chess sets."
Post Hoc, Ergo Propter Hoc
      "Careful of that ladder!" I warned Chloe. "Bad luck to walk under it."
      Chloe ignored my warning, and under the ladder she went. "And if tomorrow my dog disappears, it's because I walked under the ladder?"
      "Right," I replied. "B follows A therefore B was caused by A. That's what the old Latin saying says. Post Hoc, Ergo Propter Hoc; 'after this, therefore because of this.' Probably they saw that logical error back in Julius Caesar's days. But it's still going on today. I have a friend says his computer broke down at work one week, and he lost his job the next week. Says it wasn't fair to lose a job because of your computer. But of course a dozen people lost their jobs that week at that company, all because business was slowing down. The computer had nothing to do with his problem."
The Parts are Like the Whole
      "Hey, there's school up ahead!" says Chloe. "Big, isn't it?"
      I agreed. "A big building like that, all the classrooms must be big."
      "Whoa, now," says Chloe. "That's, like, bad logic? Just because the building's big, you can't conclude all the rooms are big."
      "Just checkin'," I said. "You're right. That's like saying 'My class is big, so all the kids in my class must be big.' Or 'The management of Company A cheated and lost a lot of money. Therefore all the people who work for that company are dishonest.'"
(Continued at top of right column at 'If everybody Believes it...')

Today's Gnarly Weather
      Today we will either have the worst blizzard in 100 years, or the worst flood in centuries. We know that because we polled both our local weather forecasters, and they both agreed.
This Month's Riddle
     Q. Why is a publicity hound like a character in the Wizard of Oz.
(Answer on the next page)

This Month's Puzzle
      This issue's Gnarly Weather contains two fallacies. What are they?
      What kind of fallacies are these?
      1. The local Superintendent of Schools announces that the school budget has been cut, and he'll have to close the Jameson Elementary School.
      2. You tell your mother that you've heard Clem's Uncle is a rogue, and she shouldn't believe anything he says.
      3. Yesterday your best friend was seriously hurt in a car crash, and you decide you'll never ride in a car again.
If Everybody Believes it, It's True
(Continued from the bottom of the left column)
Your school
      "Big soccer field just past the school," I pointed out.
      "Yep," Chloe said, "and everybody believes, you know, our soccer team will win the city championship this year."
      "But we know that's bad logic," I remarked. "It isn't true just because everybody believes it. And what does 'everybody' mean? Everyone in the city? Of course not. Other schools think their teams will win."
      "And even in our own school," Chloe added, "prob'ly there are some kids who don't believe. Who think the team's not all that good?"
      "It's like the argument that 'everybody' believes CO2 is causing the earth to warm up. All sorts of scientists disagree with that. Be careful when you hear the words 'everybody believes', or 'everybody agrees'. Ask yourself, Who is Everybody?"
All Samples aren't Good
      "See those kids?" Chloe said. "In front of the school? They're taking a poll. They're asking everybody. Do you eat a lunch you brought from home?"
      "I suppose most kids do. Maybe 2/3 or 3/4 them?"
      "I'd guess 70%?" says Chloe. "But of course there's a place for a logical mistake."
      "Right," I agreed. "Somebody might say from this sample that 70% of everybody in the US brings his or her lunch from home. But a sample in front of a school, where almost everyone who passes is a school-kid, is not exactly a fair sample of everybody in the US." Britney Spears
      "It'd be like if you went '100% of the people think Congress is doing a wonderful job', "Chloe said. "But then somebody asked you what your sample was? And you said it was all the Senators and Representatives in Congress. Not a random sample."
      I laughed. "Not a random sample."
The Straw Man
      "Here's another bad one," says Chloe. "Some kids at school? They say their favorite songs are 'Circus' and 'Rader'? But then other kids say that those are Britney Spears songs? And that she's not a singer? She's a publicity hound. So they say those are terrible songs?"
      "Baaaad," I agreed. "They're not talking about the songs. They're bringing Britney into the picture to change the subject. The fact that she sings them has nothing to do with whether they're good songs. She's like a figure made of straw, thought up to divert our attention from the songs themselves."
      "So when the Governor goes, 'We must raise taxes to pay for improving bad roads in the state'. And someone argues? Going 'Higher taxes will hurt the poor, who hardly have enough money to buy food.' Hurting the poor is the Straw Man? Gets us talking about the poor, instead of the roads. Typical (?) boys
The Middle Ground
      "Then there's the error of the middle position?", Chloe said. "Like, Harry is the heaviest guy in our class and he weighs 210 pounds? And Frank weighs 120? He's the lightest?"
      So I continued, "The average of 210 and 120 is 165. Therefore, that's what everyone should weigh."
      "Same thing," Chloe added, "if your local mayor says the city council is a bunch of idiots? But the city council itself says it's perfectly sane. So do we conclude the council is full of half-wits? Being half way between sane and idiotic?"
      We both laughed. Stamps and graduates
Connections and Causes
      "Did you hear," Chloe asked, "that the number of kids graduating from high school in the US each year was only 100,000 in 1900, but was 14 million in 2009? And about postage? In 1900 you could mail a first-class letter for 2 cents, but this year it'll go up to 44 cents?"
      I laughed. "So it's evident that high school graduates are causing postage rates to increase!"
      "So things are connected some way?" Chloe said. "Doesn't mean one causes the other. Our school football team won 6, lost 6 this year? And the girls' basketball team went undefeated. The football coach said he had a bad year because the whole student body was talking about the girls. So his 6 and 6 was caused by the girls' 13 and zero? No way!" Exploding soccer ball
Fallacies Coming from Startling Memories
      "A boy I know," Chloe said, "at school? He was out shooting goals one day. On the soccer field? And the ball exploded! BANG. Scared him to death? So he said he'd never play soccer again."
      "That kind of thing happens," I said. "Something really striking happens, that everyone notices, and somehow it makes you forget what's normal. The unusual becomes something very likely to happen."
      "Like when there's a really strong earthquake?" Chloe said. "In California? Lots of houses knocked down, and some folks hurt? And in the next year hundreds of people leave the state. Don't want to get caught up in one of those earth-shakers."

The Camel's Nose
School year
      "Then there's that old story about the camel," I said. "An Arab had a camel. One day he let the camel stick its nose into the Arab's tent. The next day he allows nose and head. Then head and humps. And before you know it, the whole camel is in the tent and can't be persuaded to leave.
      "So when the city council wants to add another day to the school year, the kids naturally worry that a week will be added next year, a month the year after, and before long there won't be any vacation."
      "It's, you know, like the old slippery slope?" Chloe said. "You get pushed over the edge just a little bit? And zoom, you're all the way to the bottom of the hill? Like, my father says, 'Don't buy that chocolate bar. Next thing you know you'll weigh 200 pounds!'"
Personal Disbelief
Flat and warped worlds

      "If we can't understand something" I said, "if it's really difficult for us to believe, then it can't possibly be true. Take Professor Einstein's theory that space is warped. One might say, 'That's crazy! If space was warped, my house, which is I hope in space, would be all twisted and bent. I wouldn't be able to open the front door. I simply don't believe it. Space is smooth.'"
      Chloe agreed. "And there may be some folks who don't believe the Earth is round? They'd go, 'Don't be silly. If the Earth was round, the folks on the bottom side would fall right off; and those on the sides would have to cling to something to keep from dropping into space. Clearly the Earth is flat -- a sort of oval plate with all the continents sitting on it.' It's, like, hard to argue? Have to explain about Newton and gravity..."
Personal Attack
      "One more," Chloe said. "I have this friend, Bill? And his father told him, 'Be careful how you choose friends. Try to choose people who are honest and kind. Kindness is particularly important. If someone helps strangers and respects you and your opinions and goes out of his way to get acquainted with shy and unpopular kids, then he's someone who is worth knowing.'
      "And another kid heard about that? He's sort of the class bully? And he goes, 'Don't pay any attention to that advice. Bill's father is town councilor, and you know all politicians are dishonest and disreputable.' So instead of talking about the advice, he attacks the advisor? Not logical at all."
      "It's very like the ad hominem fallacy discussed elsewhere in this issue under School Days," I said. But the Personal attack is different because it's mean and hateful. For example, if a school Principal disciplines George for shouting in class, Bill might attack by telling his parents that the Principal hates all boys, and never disciplines girls."

The Gnarly Gnews
Vol. 10, No. 6, July/August 2009
Gnews World HQ
Page 2
Sam'll Answer
DEAR SAM:
      The April 1, 2009, issue of the Wall Street Journal had an article about GM, the car company. The front-page illustration is shown below.
      I don't know what kind of logical error could describe it, but it sure looks hokey to me. Maybe an April fools joke?
      HOKEY DETECTOR.
WSJ graphs
DEAR HOKEY,
      The Wall Street Journal doesn't do jokes.
      But I see what you mean. In the first place, the size of the green and red arrows don't go along with the numbers in them, which is confusing. Next, the large 52% increase in the Chevy sales compared to the small 5.0% and 7.7% decreases for the Japanese cars make it seem that Chevy is doing much better than its rivals.
      But then you look at the actual vehicle sales: 177,088 for GM versus 372,786 and 436,617 for the Honda and Toyota. So even with the 52% jump, Chevy sales are only about half of Honda's and 40% of Toyota's. Seems strange.
      But if we read that the 177,088 was a 52% increase over 2007, the picture becomes a little clearer. We can calculate what 2007 sales must have been, for 177,088 to be a 52% gain. If S is 2007 sales, then S+0.52S=177,088. So S=177,088/1.52 =116,505
      Now, the Malibu was first sold in November, 2007. So in November and December GM sold 116,505 cars, or over 58,000 per month. In 12 months in 2008 they sold 177,088 cars, or less than 15,000 per month. That fact seems to make the Malibu sales disastrous.
      Finally, we should say the comparison isn't quite right because the WSJ is apparently comparing the most recent model of the Mailbu with all models of the Accord and Camry.
      Is this story a logical error? Well, our 'logical' look at it showed that the story is very misleading. But perhaps it can't be classified with the logical errors described in this issue of the Gnews.

Limerick
     There was a logician named Rose
     Who dreaded the old camel's nose.
        The mouse her kids craved
        Would soon find her enslaved
     To elephants lined up in rows.
Answer to last month's puzzle
        Last month we were in ancient Catalhoyuk, where they counted by twos. The puzzle asked how many ducks there were in the picture. A citizen of Catalhoyuk would say 'two twos and one two'. He could not, of course, say 'three twos', or 'six'.
School Days
Ad Hominem
      Miss Barnes says that the sum of the squares of the two sides of a right triangle equals the square of the hypotenuse.
      But Miss Barnes is a teacher, and everybody knows that teachers are just trying to confuse us, telling us about complicated things. Goodness knows what the sum of the squares really is.
      This is called 'ad hominen', which means 'against the person'. You don't talk about the real subject (in this case, the Pythagorean Theorem). Instead, you lash out at whoever brought up the subject (in this case, Miss Barnes).
      Here's another example. Jones, the new president of a troubled company says that he's discovered that the previous boss, Smith, spent millions of dollars on antique cars, for his personal use. Smith says that Jones's opinion is worthless because he has been divorced three times. But what does that have to do with the antique cars?
Pythagoras and broccoli
Appeal to Authority
      Miss Barnes says we should all eat broccoli and cauliflower.
      And Miss Barnes is a teacher, who knows all about vegetables and diets. Therefore I'm going to tell my Mom to cook those vegetable more often.
      It's quite right to appeal to authority to bolster your argument. But you must choose an authority who is really an expert in the field...which Miss Barnes isn't.
      Another example: a group of fishermen is trying to persuade the state to make the fishing season a month longer. The state Fish and Game don't want to do this because it would leave too few fish in the rivers. The fisherman quote a Dr. Richards, who says the longer season would be fine. But Dr. Richards is a medical doctor who is a fisherman. He's not in any way an expert on fisheries. The state should ignore his position.
Your Horoscope
(For persons having birthdays this year.)
      You will be president of the United States in forty years. Your whole family -- parents, siblings, uncles and aunts and cousins -- are sure of it. And if everybody says so, it must be true.
      But for heaven's sake, whatever you do, don't pay any attention to Horoscopes!
Answer to this Month's Riddle
      Q. Why is a publicity hound like a character in the Wizard of Oz.
      A. Calling Britney Spears a publicity hound is a straw man, which of course is what the Scarecrow was.
(Back to top of page)
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