Logic to the Rescue
Adventures in Reason
Kris Langman
Post Hoc Publishing
Boston, Massachusetts USA
Logic to the Rescue
Copyright © 2008 by Kris Langman
ISBN: 978-0-9820927-0-5
Smashwords Edition
Post Hoc Publishing
Boston, MA 02116
Email: posthocpub@verizon.net
Website: www.posthocpub.com
Smashwords Edition, License Notes
Thank you for downloading this free ebook. Although this is a free book, it remains the copyrighted property of the author, and may not be reproduced, copied and distributed for commercial or non-commercial purposes. If you enjoyed this book, please encourage your friends to download their own copy at Smashwords.com, where they can also discover other works by this author. Thank you for your support.
All rights reserved. No part of this book may be reproduced without permission of the author except for the inclusion of brief quotations in a review.
The purpose of Logic to the Rescue is to provide an introduction to logical fallacies. It supplements this with simple examples from chemistry and physics. Neither the author nor Post Hoc Publishing assumes any liability with respect to loss or damage alleged to have been caused by the information in this book.
Contents
Chapter One: A Debater Disappears
Chapter Two: The King Has Spoken - Logical Fallacy: Appeal to Authority
Chapter Three: Everybody Does It - Logical Fallacy: Appeal to Popularity
Chapter Four: Fortune Teller - Logical Fallacy: Lack of Evidence
Chapter Five: The Benighted Knight - Logical Fallacy: Ad Hominem
Chapter Six: This or That - Logical Fallacy: False Dilemma
Chapter Seven: Scarecrow - Logical Fallacy: Straw Man
Chapter Eight: The Wishing Well - Logical Fallacy: Counting the Hits
Chapter Nine: Before and After- -Logical Fallacy: Post Hoc
Chapter Ten: Plot and Counterplot
A Debater Disappears
Nikki wiped her forehead with the back of her hand. The spotlights shining on the stage of the high school auditorium felt like tiny burning suns. Under her Westlake Debate Team t-shirt her armpits were sticky with sweat. She twitched uncomfortably and tried to focus on what her opponent was saying.
“And in conclusion, I propose that the federal government should increase its budget for solar, wind, and bio-fuels research.”
Her opponent was arguing the affirmative position in the debate, which meant that Nikki was stuck with the negative position. It was the semi-finals of the Wisconsin State High School Debate Championships, and Nikki’s nerves were getting the better of her.
They were debating whether the Federal Government should spend more money on renewable energy. Nikki had spent the past two weeks stuffing facts and figures into her head. Solar power was expensive. That was her main point.
Nikki cleared her throat and nervously shoved her long dark hair away from her face. It was her turn. This was her second rebuttal, which meant that this round of the debate was almost over. “It is a well-known fact that solar power, a main component of renewable energy, is um, expensive.” Nikki winced. Jeez, that was a clunker. She had to get it together or she wouldn’t make it into the finals. She paused, fiddling with the note cards on her podium. Normally she didn’t need to refer to her cards at all during a debate, but today her brain seemed to have purged itself of all facts ever stuffed into it.
Nikki cleared her throat again, and then she made her fatal mistake. She looked at the audience. This was her first time at the state championships. At local debates the audience generally consisted of her mother and maybe a janitor sweeping the floor. Here at the state championships the auditorium was filled to capacity. Hundreds of people looked back at her as she stared out at the crowd. Her mind went blank. Nikki could feel the seconds ticking away as she struggled to pull herself together.
“And that’s time,” called the judge.
The clock had run out.
Nikki felt her face turning red. She couldn’t believe it. Her first time at State and she’d bombed. She gathered up her note cards with shaking hands and darted through the curtains at the back of the stage.
She heard her debate teacher calling her, but she ignored him and pushed through the stage door. She found herself in a noisy hallway filled with debate students practicing their arguments. She dodged through the crowd, looking for the girls bathroom.
“Hey, Nikki. Wait up.”
Shoot. It was Tina, the captain of their team. The last thing she wanted was a lecture from Tina.
Nikki ducked behind a group of boys who were folding their note cards into paper airplanes. At the end of the hallway she spotted a door marked “Utility Closet”.
She yanked open the door and darted inside, coughing as the smell of ammonia and wet mop hit her nose. She shut the door and stood in the dark, peering out through the tiny glass window cut into the door at eye-level. Tina’s frowning face swam into view, then disappeared down the hall.
Nikki let out a sigh and groped around for something to sit on. A cardboard box full of what felt like old newspapers was pushed against the wall. She lowered herself onto it and leaned her head against the wall, the cold cement wonderfully soothing after the hot lights of the auditorium.
Maybe she should just stay in here for the rest of the day, Nikki thought. It was better than facing the debate team. Her screw-up had probably kept the whole team from advancing to the finals. It was also better than facing her mother. Her mom was a chemistry professor at the University of Wisconsin, and she had set high standards for Nikki from the first grade onward. Nikki had been only six when her mom had first started to teach her how to do scientific experiments. How to create a hypothesis and support it with data. How to think logically, research carefully, and defend your point with valid arguments. She’d been so proud when Nikki had been put in her school’s Advanced Placement chemistry class even though she was only fourteen. And she’d been even prouder when Nikki had been selected for the high school debate team.
Nikki sighed. Her mom was going to be so disappointed in her. She was contemplating spending the night in the closet, when suddenly she jerked upright.
Voices. She’d definitely heard voices. Not from out in the hall, but from inside the closet, somewhere near her feet. She jerked her feet up onto the box and listened, her heart beating in her ears.
“You’ve woken her up. She’s gonna be mad. She’ll probably stomp on us with her big feet.”
“Shhhh. Be quiet, Fuzz. She’s not going to stomp on us. She’s a very nice young lady. I can tell. I’m sure she’s the one we’re looking for. I’ll address her politely and I’m sure she’ll listen.”
Nikki heard what sounded like a tiny female clearing her throat.
“Hello, madam.”
A sputtering sound hissed through the darkness. “Don’t call her madam,” said a tiny male voice. “She’s obviously a young girl. If you offend her she’ll stomp on us.”
The tiny female voice cleared again. “My apologies, Miss. My companion is better at seeing in the dark than I am. Just give me a moment.”
Nikki heard a scratching sound and breathed in a sharp whiff of sulfur. A flame appeared at her feet. Holding a flickering match was the strangest creature Nikki had ever seen. It was roughly two feet tall, with straw-colored hair, a very long nose, and pale skin. It wore a long dress made of grey wool with blue embroidery on the sleeves. Beside it stood a similar creature, slightly taller than the first, with short brown hair and darker skin. The second creature wore a linen shirt, an embroidered vest, and brown woolen trousers. He sported a precisely combed goatee.
The female creature bowed to Nikki.
Nikki pinched herself on the arm. The pinching didn’t wake her up, so she tried again. Nope, she was still sitting on a box of newspapers in a janitor’s closet, staring down at two extras from a Disney cartoon. Maybe it was all the cleaning chemicals she was breathing in. She was just about to bolt for the door when the male creature spoke.
“Cut out the bowing and just ask her already. I want to get back to the Realm before more people from this world come in here and stomp on us with their big feet.”
The female creature elbowed him in the ribs. “Pardon the rudeness of my companion, Miss. Let me introduce ourselves. My name is Athena, and this is Fuzz. We are imps from the Realm of Reason. We were sent here by the ruler of our land, King Tertullius the True, to seek assistance from the great thinkers of this world. The king’s all-knowing advisor, Maleficious the Wise, looked into his crystal sphere and saw that a gathering of great minds had congregated at this place of learning.”
“Great minds? Place of learning?” Nikki asked dazedly. “You mean the debate at the high school?”
“Yes, Miss. And we can see by your garment that you are one of the wise. One of the debaters.” The imp whispered the last word with great reverence. “You are just the person to help us. You must come with us, quickly, before all is lost.” She took a step toward a dark corner of the closet, gesturing for Nikki to follow her.
Maybe it was the ammonia fumes. Maybe it was just a strong desire to avoid facing her mother, her debate teacher and the rest of the debate team. Whatever it was Nikki found herself following the little creature into the darkest corner of the closet.
The imp held the still-burning match above her head. Its flickering light shone on the carcass of an old metal boiler, long ago replaced by a modern heating system. The coal door of the boiler hung open on its hinges. The two imps hopped into its dark interior.
Nikki watched the tiny flame getting smaller and smaller. She gave one last look behind her and then climbed through the boiler door.
The King Has Spoken
Logical Fallacy: Appeal to Authority
Nikki squinted, her eyes stung by bright sunlight. She had emerged from the boiler onto a cobblestone street crowded with people. The street was lined with stalls piled high with cabbages, corn, lettuce, and apples. People rushed to and fro, their arms weighed down with straw baskets filled with their daily shopping.
The first thing Nikki noticed about the Realm of Reason was that it reminded her of medieval England. The buildings had thatched roofs, there was an old stone church across the way, and a farmer was herding goats down the main street. The second thing she noticed was that most of the inhabitants were people of normal size like herself. Only rarely did she spot another creature as tiny as the imps.
The third thing she noticed was the socks. All the men wore long woolen knee-socks underneath short woolen tunics. The women wore thick socks peeking out from under ankle-length dresses. All their socks were in bright colors of sunflower yellow, deep violet, royal blue and acid green. And not one pair of them matched.
The imps beckoned to her. Nikki took one last look behind her at the dark mouth of the boiler which led back to her own world. She shook her head, took a deep breath, and followed the small figures of the imps.
The market roiled with shoppers, farm animals, and stall owners loudly hawking their wares. Nikki dodged through the crowd, jumping aside as a herd of pigs squealed past her. She nearly lost sight of the imps as a throng of shoppers engulfed her and steered her toward a stall selling live geese. The geese squawked loudly, as if they knew exactly what would happen to them at dinnertime. Nikki yelped as a frantic goose pecked at her. She rubbed the red spot on her arm and peered around for the imps, who had trotted ahead, ignoring both the townspeople and the geese.
She caught up to them at the last market stall, where the town’s cobblestone road turned into a rutted dirt track. The noise and crowds of the market disappeared. The buildings of the town gave way to pleasant green fields dotted with dandelions and grazing sheep.
Nikki was about to ask the imps where they were going, when a sound like thunder rushed up from behind them. Nikki jumped aside as a group of knights on horseback roared past them, kicking up clouds of dust. The male imp gave a hacking cough and spit out the dust, shaking his tiny fist at the knights.
Nikki wiped the dust from her eyes and looked up. The dirt track they were following wound up a grassy hill sprinkled with orange poppies and delicate bluebells. At the top of the hill towered a white marble castle, its walls gleaming in the sun, purple flags flying from its many turrets. Soldiers were stationed along the top of the wall, the sun glinting off their polished armor. A snatch of melody from the movie Sleeping Beauty ran through Nikki’s head, and she realized that the castle reminded her of the one at Disneyland. She followed the imps as they trudged in the dusty wake of the knights up to the main gate of the castle.
The female imp ran up to a spear-carrying guard in front of the gate. The tiny imp hopped up and down in front of the guard until he finally noticed her. The guard’s top half was covered in steel armor, while his legs were encased in mismatched socks – one leg was blue, the other bright red. Nikki didn’t know whether to be afraid or to laugh.
The guard’s armor creaked as he bent down and held a whispered conversation with the imp. After several suspicious glances at Nikki he finally waved at a group of men manning the gate. They hauled on a massive rope as thick as Nikki’s arm and slowly raised the portcullis which barred the gate.
Her steps echoed on the gate’s wooden drawbridge as Nikki followed the imps into the courtyard of the castle. She had expected a bleak stone space filled with knights in armor, horses, cannon, maybe even a catapult or two. But the area they entered was more of a garden than a military drilling field. Fountains splashed, sparrows hopped across wide green lawns, and wisteria vines drooped from trellises and swayed lazily in the breeze.
The imps headed toward the center of the courtyard, and Nikki followed, her feet crunching on the white gravel path. They halted at a fountain shaped like a leaping salmon. A jet of water spouted from the mouth of the fish, spraying a fine mist on a group of people gathered around it.
Nikki, in her jeans and debate team t-shirt, felt seriously underdressed as she stared at them. The woolen garments of the townspeople were nowhere in sight. The people here were decked out in silks and gleaming satin brocade. The women wore jewels in their hair, and the men had golden chains hanging from their necks. The glory of their finery was a bit diminished, however, as peeking out from under their silks and satins were the same heavy woolen mismatched socks that the townspeople wore.
One man, standing apart from the rest, wore an elaborately sculpted crown of silver topped with an emerald the size of a chicken egg. Nikki guessed that this was the king. He wore a tunic of brilliant sapphire silk worked with fine gold thread, a long dramatic black cloak . . . and mismatched woolen knee socks, one yellow and one Kelly green. The king was deep in conference with an elderly man with a long white beard. The elderly man had bushy, overhanging eyebrows which gave his face a mysterious cast, and was wearing a floor-length robe of deepest purple.
Nikki noticed that the elderly man’s robe was so long that it dragged on the ground, preventing anyone from seeing his feet. She wondered briefly if he was wearing matching socks and was trying to hide that embarrassing fact.
The female imp, Athena, marched up to the king and tugged on the end of his cloak.
“Ah, my ambassadors are back,” said the king. He scooped up Athena and Fuzz and set them on the rim of the white marble basin surrounding the salmon fountain. “Did you find one of the wise?”
Athena nodded, pointing at Nikki, who blushed and wiped a smudge of dust off her t-shirt.
The king strode up to Nikki and took her hand in his, pumping it enthusiastically up and down. “Wonderful. Wonderful. So good of you to come. Welcome to Castle Cogent. We expect great things of you, you know.”
Nikki wasn’t sure how to respond to this. Out of the corner of her eye she noticed the elderly man in the long purple robe staring at her. He didn’t look nearly as glad to see her as the king did. In fact, he was positively glaring at her.
The king waved him forward. “This is my most trusted and knowledgeable advisor, Maleficious the Wise. Any help you need on this little problem, you just call on him. He’ll be only too happy to assist.”
Nikki nodded politely at Maleficious, who stared back at her stonily. Nikki cleared her throat. “Um, your majesty, what little problem is this, exactly?”
A look of surprise passed over the king’s face. He glanced down at the imps. “I thought Athena had explained things to you.”
Athena blushed, twisting her hands in her skirt. “We thought that your majesty, who is so eloquent, so articulate, so gifted at the subtleties of speech, could explain much better than we could.”
Nikki thought the imp was laying it on a bit thick, but the king nodded in agreement, a satisfied smile on his face. She noticed that Maleficious was watching the king with amusement. She guessed that the king’s ego was something his advisor found very useful.
“Well,” said the king, “let’s get comfortable while I explain.” He sat down on the marble rim of the fountain and patted the spot next to him. Nikki joined him, with Athena hovering anxiously nearby. Fuzz sat down on the rim of the basin and paddled his bare feet in the water. Maleficious stood a few feet away, glaring down at them all.
“You see, my dear,” the king suddenly paused, looking appalled. “Goodness. You must forgive me. I’ve forgotten to ask your name.”
“My name’s Nikki.”
“Nikki,” repeated the king. “Lovely name. So, Nikki, the reason I sent our two ambassadors to search for you is that our wonderful Realm of Reason is rapidly becoming not so reasonable. For centuries we were the envy of neighboring realms, renowned for our iron-hard grasp of logic, for the hard-headed common sense of our citizens, for the exemplary way we would apply the rules of evidence to all our decisions.” The king paused, frowning. “But lately, we’ve noticed superstition and backwardness creeping up on us, especially in our outer provinces. Reason and rationalism have been abandoned, and the people have adopted all manner of foolery and nonsense.”
“Like the socks,” said Nikki without thinking. She turned red and mentally whacked her forehead. Maybe the mismatched socks were just the fashion here, and besides, the king himself was wearing them.
The king chuckled, not looking the least offended. “No, my dear, the socks are not foolery. They are the brilliant invention of Maleficious.”
Nikki glanced nervously up at Maleficious, who smiled coldly at her. “Er, invention?” she asked.
The king nodded enthusiastically. “Yes, they are truly a breakthrough. Mismatched socks. Who would have thought they were such miracle workers. I don’t know how Maleficious manages to think of these things. The mysteries of genius are impenetrable.”
“But,” said Nikki, “what exactly do the socks do?”
“Better to ask what don’t they do,” said the king, stretching his legs out in front of him and picking a miniscule speck of dirt off of his Kelly green sock. “They cure colds, dissolve warts, heal rashes of all sorts, abolish acne, soothe stomach upsets, and that’s just for starters.”
“Gosh,” said Nikki, trying to look impressed. Her inner skeptic was jumping up and down so frantically in her brain that she was getting dizzy. “Um, how do they work?”
“Only Maleficious knows, and he’s not telling.” The king winked at Maleficious, whose mouth curved into a pained smile.
“Okay,” said Nikki, watching Maleficious warily, “but, how do you know they work?”
Maleficious glared down at her. “Are you questioning the effectiveness of my discoveries?” His voice was as raspy as a rusty lock. “For I’ve spent many long years perfecting them.”
“No, no,” Nikki said quickly. “I’m not questioning them. Certainly not. I just, um, was inquiring about your methods.”
Maleficious frowned, looking not in the least bit appeased, but he cleared his throat importantly and addressed a spot above Nikki’s head. “As to the question of how I know the socks work, I have collected many responses from sock-wearers as to their efficacy. The wearer has, for instance, a cold. He dons the socks, and in an instant, three to four days at most, his cold has disappeared.”
Nikki wiped the incredulous expression from her face and tried to look respectful. “Colds, you know, can frequently disappear on their own in three to four days.”
Maleficious didn’t look at her. He addressed the spot above her head again. “In the case of rashes or stomach upsets, the person has only to wear the socks for a day and the problem will ease.”
“You have, of course, heard of the placebo effect,” Nikki said cautiously.
Maleficious looked down his long, pointed nose at her.
“The what?” asked the king. “Is this some wondrous technology from your own realm?”
“No,” said Nikki. “It’s just a very common bodily response. My mom told me about it. If people think a certain medicine, or cure, or, in this case, mismatched socks, will help their illness, then frequently it does. At least a little bit. The placebo effect won’t cure serious illness, but for minor complaints such as rashes or colds, it can help the body heal itself. Doctors think it triggers certain chemicals in the brain which then give the immune system a boost.”
The king looked impressed. Maleficious looked livid, his face taking on a dangerously red tint.
Nikki was thinking maybe it was time to find the entrance back through the boiler to her own world, when the king spoke.
“Wonderful stuff. Just wonderful.” He slapped his knee. “So, this placebo effect, this is what has actually been curing the people’s colds, rashes, and other sundry complaints?”
“Maybe,” said Nikki, avoiding Maleficious’ eye. “It’s hard to tell without doing a proper experiment. So far, all you’ve collected is anecdotal evidence, which is a big no-no. You’re putting too much faith in the stories a few people tell you. They could be lying, after all. Or you could be coming to the wrong conclusion, due to lack of evidence.”
Maleficious raised himself to his full height and glared down at her. “Meaning that I, advisor to the king, and the most learned person in the Realm, have come to a false conclusion.”
The king stood up and gave Maleficious a hearty pat on the back. “Not at all my good fellow. Not at all. We all have enormous faith in your abilities. Why, those daisies you had me tuck down my trousers to clear up my hayfever were a stroke of pure genius. I haven’t sneezed in several hours.” He paced back and forth in front of the fountain, kicking up bits of white gravel. “I think, however, this experiment our illustrious guest is proposing is a grand idea. The two of you can work together on it. Really do it up right.”
Maleficious tucked his hands into the voluminous sleeves of his robe. “I must decline, your majesty. I have important work to do back in my study.” He sneered down at Nikki. “I’m sure our guest can handle things on her own.” He spun on his heel and stalked away.
Nikki breathed a sigh of relief as Maleficious disappeared through a door in the castle wall. She turned to the king. “Um, your majesty?”
The king bent toward her, grabbing at his crown as it slid down his forehead. “Yes, my dear?”
“Well,” said Nikki, “I was just wondering how long you wanted me to stay here?”
“Stay here? Oh, you mean stay in the Realm?”
Nikki nodded. “It’s just that I don’t want my mother to worry about me.”
The king patted Nikki’s shoulder. “No need to worry about that. We here in the Realm have occasionally had dealings with other worlds. Through the gateways, you see. They are passageways leading out of the Realm. Athena and Fuzz used one to bring you here. When someone from outside the Realm uses one of these passageways to come here, we have found that no time, no time at all, passes in their world while they are here. So you see, your mother will not even notice that you are gone, no matter how long you stay in the Realm.”
“What is the first thing we must do, Miss?” asked Athena.
“Formulate a hypothesis,” said Nikki. She pulled a blank piece of parchment toward her and dipped a goose-feather quill into a pot of black ink. They were seated at a small, wobbly table in the room which the king had assigned to Nikki. The room was in one of the towers of Castle Cogent. It was small but comfortably furnished, with a four-poster bed, tapestries on the stone walls, and a spotlessly clean chamber pot. Nikki eyed the chamber pot nervously, thinking longingly of indoor plumbing. But with adventures came minor inconveniences she told herself firmly.
She chewed on the end of the quill, thinking.
“What’s she doing? Is she wasting time already?” Fuzz climbed onto an empty chair and poked his head over the edge of the table.
“Shhhh!” Athena waved a finger at him. “She’s formulating a hypothesis. Be quiet.”
Nikki took the quill out of her mouth and wrote on the parchment. When she was done the parchment was spotted with ink drops and dribbles. Writing with a quill was harder than it looked. Too bad she didn’t have a ballpoint pen with her. “Okay,” she said. “Here it is. See what you think.” She read from the parchment:
“Hypothesis: the wearing of mismatched socks does not cure or alleviate illness.”
Nikki frowned. “This phrasing means we’ll have to prove a negative: that mismatched socks do not cure illness. It’s usually better to state your hypothesis in positive terms.” She scratched a line through the words on the parchment and wrote a new sentence:
“Hypothesis: the wearing of mismatched socks cures or alleviates illness.”
Athena scurried around to Nikki’s elbow and read the new sentence. “But, Miss,” she said worriedly, “doesn’t this say that we agree with Maleficious?” She shuddered when she said the advisor’s name.
Nikki peered down at her, wondering why the imps seemed to dislike Maleficious so much. Admittedly, she hadn’t taken a shine to the man either, but the imps’ dislike seemed excessive. “Not necessarily,” she said. “A hypothesis is just a starting point. Kind of a guess about how something works. We haven’t formed a final opinion on the matter of mismatched socks yet. For now we’re going to keep an open mind, and use Maleficious’ claim as our starting point. We don’t have to agree with it.”
Athena looked unconvinced, but she nodded.
Nikki re-read the new hypothesis. “I’m going to change this slightly. Maleficious claims that mismatched socks cure illnesses. A very bold statement, which says that the socks banish the illness completely. He doesn’t mention anything about just helping with pain or symptoms.” She dragged her quill across the parchment. “I’ve scratched out the part about alleviating illness. So, here’s our final hypothesis:”
“Hypothesis: the wearing of mismatched socks cures illness.”
“What now, Miss?”
Nikki drew a line across the middle of the page. “Now we plan an experiment to prove our hypothesis true or false. There are a couple of important things to keep in mind here. One is to make sure our sample size is large enough. We must find as many people as possible to be our test subjects. Also, they must be different kinds of people. If I were to use only bakers, for instance, then it’s possible that something about being a baker is actually curing their illnesses. Maybe flour cures colds. Something like that. Our goal must be to use people from many different professions, many different age groups, both genders, etc.” She made a note on the parchment. “Also, I think we’ll limit our illnesses, just to make things easier. Maleficious seems to be claiming that the socks cure any illness, but that would be too hard to test. Maleficious could always claim that our test missed a rare disease which the socks can cure. There’s no way we can test every single disease. We have to narrow it down.” Nikki tried to think back to the conversation around the fountain.
“What illnesses did he list again?” She chewed on the quill. “I remember acne, and rashes. What else?”
“Colds and stomach upsets,” said Fuzz, climbing up onto the table and sitting cross-legged next to the parchment.
“Right.” Nikki wrote those down and studied her list. “To make our test as foolproof as possible I’m going to limit it to just colds. Acne and rashes can take a long time to heal. Colds will go away within roughly a week, making them easier to test. And stomach upsets, well, it may not be very scientific, but I don’t want to get barfed on.”
Fuzz nodded energetically in agreement.
“Okay,” said Nikki. “Since we’re going to limit our testing to colds, I’ll make another small change to our hypothesis.” Her quill scratched across the parchment.
“Hypothesis: the wearing of mismatched socks cures colds.”
“Everybody in agreement?” asked Nikki.
Athena nodded and looked at Fuzz, who was excavating his ear wax with the tip of his little finger. Athena elbowed him in the ribs and he gave a grumpy nod.
“The last thing to keep in mind is objectivity,” said Nikki. “We need to do a blind test.”
“What’s that, Miss?” asked Athena, primly smoothing her skirt out.
“It means that our test subjects can’t know about the test. Or at least they can’t know why we’re doing it. We can’t keep the test completely secret, because we’ll have to ask people questions about their colds, but we don’t have to tell them why we’re asking the questions. It keeps them from falsifying the data. For example, say they’re friends of Maleficious. If we told them we were testing whether or not the socks worked they might be inclined to lie and say yes, even if the socks hadn’t really worked for them. Or, if the test subjects were afraid of Maleficious, they might lie about the socks so that he wouldn’t get mad at them. Ideally, we’d do a double blind test, where even the testers don’t know the exact details of the test, but I don’t see how that’s going to be possible in this case.”
Nikki drew a grid on the parchment, consisting of two rows and five columns.
“What’s she doing now?” Fuzz whispered to Athena. “It looks like she’s going to play Tic-Tac-Toe. I knew she was a time waster.”
“It’s not Tic-Tac-Toe,” said Nikki. She labeled the rows and columns and turned the parchment so the imps could see it. “The two rows represent our test subjects. We have two types of subjects: people with colds who are wearing mismatched socks, and people with colds who are not wearing the socks. The columns represent the outcomes from our experiment. In column one we’ll record a check mark each time a person’s cold is gone in one day, in column two we’ll put a checkmark each time the cold is gone in two days, and so on.”
“Do you have any more parchment?” Nikki asked.
“Yes, Miss. One moment.” Athena hopped down from the table and pattered over to a carved wooden chest on the floor at the foot of the bed. She shoved open the creaking lid and dived into the chest, emerging with a roll of parchment.
Nikki reached down and scooped up the imp and her burden. “Thanks, Athena.” Nikki tore two sheets off the roll. “I’m just going to make a copy of this grid for each of you. That way we can split up and collect a lot more data.”
“Well, the socks must work, because Maleficious said so.” The farmer spat on the ground and wiped his runny nose on his sleeve for good measure. “He’s the big poobah ‘round these parts. King’s special pal and all that. He must know what he’s talking about.”
Nikki raised an eyebrow. “Have you heard of the logical fallacy called Appeal to Authority?”
“Logical What? Honey, I got a corn crop to get in the barn. Every year. And a wheat crop too. I ain’t got time for no book-learning stuff like logical thing-a-ma-gigs.”
“Appeal to Authority just means that you’re assuming Maleficious is always right about everything. You never question him.”
The farmer pulled a grimy handkerchief out of his sleeve and blew his nose. “Dang right I never question him. Don’t want to get hauled up in front of the Council, do I? They’re in his pocket, ain’t they? Everyone knows that.”
Nikki nodded tiredly and pulled the piece of parchment out of her jeans pocket. Maleficious certainly had a lot of power in the Realm. Almost as much as the king himself. Most of the people she’d talked to seemed afraid of him. She un-stoppered her little jar of ink and dipped in her quill. “Okay, so, just a couple more questions. When did your cold start?”
“Tuesday morn. I woke up with the most awful head pain. Put on my socks right away.” The farmer pointed down at his legs, which were encased in heavy wool, the right leg in royal blue, the left in bright yellow.
“And how are you feeling now?”
“Bit better. Still sniveling, but less.”
Nikki nodded. “Today is Friday, so that makes it four days.” She put a check mark in the appropriate box while the farmer looked on suspiciously.
“Okay,” said Nikki as brightly as she could manage, “that’s it. Thanks very much for your help.” She hurried away over the rough furrows of the corn fields, imagining that she could feel the wary gaze of the farmer between her shoulder blades. She did a quick count of the checkmarks on her piece of parchment. She’d collected data from forty different test subjects. Time to head back to the castle and compare notes with the imps.
“Sixty-four! Wow, Athena, that’s great. Good work.” Nikki spread Athena’s piece of parchment on the table next to her own. “Okay, Fuzz. How many test subjects did you find?”
“Eight,” said Fuzz, grumpily handing over his piece of parchment, which was mangled and scrunched and gave off a yeasty smell. “I couldn’t find any sick people in my part of town.”
“But you managed to find a tavern,” said Athena, wrinkling her nose. “You smell like the inside of an ale glass, Fuzz.”
Fuzz ignored her. He lay down on the table and closed his eyes.
Nikki un-scrunched Fuzz’s parchment and laid it next to the others. She tore off a new sheet from the roll and dipped her quill in ink. “Okay, I’m just going to make a new grid and combine all three of our counts into one. Give me a sec.”
Athena waited patiently as Nikki’s quill scratched across the parchment. Fuzz began to snore.
“Okay,” said Nikki, laying down her quill. “Let’s look at our results.”
Athena prodded Fuzz with her foot. Fuzz gave a loud snort and sat up, grumbling.
“Let’s deal with the outliers first,” said Nikki.
“What’s an outlier, Miss?” asked Athena.
“It’s a statistical term. It means something which doesn’t fit. Something so out of the ordinary that you should leave it out of your count. Our grids have two categories which I’m going to call outliers: the “Cured in one day” category, and the “Not cured” category.” She pointed to the grid, and Athena walked across the table to get a closer look.
“There is only one checkmark in each of these categories, Miss.”
“Exactly,” said Nikki. “That’s why I’m going to classify them as outliers and leave them out of our results. Mathematicians usually say that you shouldn’t exclude outliers unless you have a good reason, but in this case I think there is a good reason. We know from experience that colds are rarely cured in one day. That’s why only one of our test subjects fell into this category. We can’t be sure, but we can make an educated guess as to why the subject fell into this “one day” category. Maybe what they had was not a cold, but allergies. Same thing with the “Not cured” category. For a common cold it’s unlikely that there would be no improvement at all in five days, so we can guess that what the test subject had was not a cold, but something more serious, like bronchitis.” She drew a slash across the two categories. “There, we’ve excluded them. Now, let’s focus on the remaining categories.” She tapped the parchment with the end of her quill. “See anything interesting?”
Athena bent forward until her nose was almost touching the parchment. “Most of the checkmarks are in the category called “Cured in three days”, Miss.”
Nikki nodded. “I don’t know about you, but from my own experience with colds I’ve found that I’m mostly better by the third day after becoming sick. So, our data matches with previous experience, which is a good sign. If our data was way out of line with existing knowledge and experience we might have to conclude that something had gone wrong with our test, and we’d have to do it all over again. But, I think we’re okay.” She tapped the grid again. “This is what’s really interesting. There are forty-nine checkmarks in the box for “Cured in three days and wearing socks”, and there are fifty-one checkmarks in the box for “Cured in three days and not wearing socks”.
Athena frowned down at the grid. Even Fuzz got up and ambled over to take a look.
“What’s so interesting about that?” he asked.
“What’s interesting is how similar the counts are. We can form a conclusion from this. A conclusion which indicates that our hypothesis is false.”
Athena looked from Nikki to the grid in confusion. Fuzz scratched his head, unleashing a tiny shower of dandruff. “I don’t get it,” he said.
Nikki laid her original piece of parchment on top of the piece with the combined totals. “See? Here’s what our experiment was trying to prove:”
Hypothesis: the wearing of mismatched socks cures colds.
“Now, if our hypothesis was correct, then we should have seen a much bigger number of checkmarks in all of the “wearing socks” boxes. That would indicate that the socks were working – actually curing colds. Instead, there’s a total of one hundred checkmarks in the “Cured in three days column”, split between socks and no socks. We see an even split, almost fifty-fifty, between the two boxes.”
Athena began jumping up and down, rattling the wobbly table. “Oh, Miss. I see! I see! It means the socks made no difference! People’s colds went away in three days, whether they were wearing the socks or not!”
“Exactly,” said Nikki.
Fuzz nodded sagely. “It means that that doofus Maleficious is wrong. His stupid mismatched socks don’t cure colds. They probably don’t cure anything at all.”
Nikki nodded. “We’d better go present our results to the king.”
Everybody Does It
Logical Fallacy: Appeal to Popularity
“Did you see his face?” Fuzz laughed so hard that he stumbled and fell over. He rolled around on the leaf-covered path, holding his sides as tears ran down his cheeks and his ears turned red.
Athena primly picked up her skirt and stepped over him. “Yes, we saw it. It was very angry and purple, but that’s no reason to roll around in the mud like a pig.”
Nikki laughed and bent down to set Fuzz back on his feet. He promptly fell over again in a fit of giggles. Fuzz wasn’t the only one in a good mood. All three of them had been highly praised by the king for their debunking of the mismatched socks myth. He’d thrown them a party in the courtyard of Castle Cogent, complete with fireworks, swans gliding on the castle fountains, and a banquet table heaped with roast chicken, mashed potatoes, and pecan pie topped with whipped cream. The only person at the party not in a good mood had been Maleficious, who had glowered at Nikki from under his heavy eyebrows the entire time.
Nikki looked nervously over her shoulder at the dark wood behind them. Was it just her imagination, or had something moved in the shadow of the trees? She wondered if Maleficious was angry enough to send someone to follow them. He hadn’t been pleased when the king had announced that he was sending Nikki and the imps on a journey through the Realm to fight superstition and ignorance. Nikki peered into the trees, but the only creature she saw was a sparrow hopping along the ground, pecking for seeds.
“What is it, Miss?” asked Athena.
“Nothing,” said Nikki, pulling up the hood of the woolen cloak the king had given her. The cloak looked strange worn over her t-shirt, jeans, and muddy sneakers, but it was warm and it repelled the rain which was beginning to fall. “How much farther is it to this village?”
“Not far, Miss. Not far. The king sends us imps there frequently with messages to the town council. We make the trip in less than four hours.”
“Would one of you like to ride on my shoulders?” asked Nikki a little hesitantly. She wasn’t sure if this suggestion was violating some rule or other.
Fuzz stopped laughing and hurried eagerly toward her, but Athena waved her finger at him. “No, Miss,” she said. “Thank you, but we imps are used to walking. Don’t be fooled by our small size. We are proud to be the king’s messengers. It’s a tradition of our race, and we are great walkers because of it. My grandmother could walk non-stop for two days, right up to the day she died.”
“Huh,” said Nikki. Making an old lady walk for two days straight didn’t seem like a very nice thing to do, but who was she to judge? This was a different world, with different customs. She shivered and crossed her arms under the cloak. Night was falling, and she could see her breath hanging in the air like puffs of smoke. “What’s the name of the place we’re going to again? Popularity?”
“Popularnum, Miss.”
“Kind of a strange name. Does it mean that the village is a popular place to live?”
Behind her Fuzz let out a loud snort.
Athena ignored him. “No, Miss. It means that . . . well, I hate to be rude, but . . .”
“It means that the people who live there have kumquats for brains,” said Fuzz, running up to a pitcher plant growing at the roots of an oak tree. He tipped one of its bright green leaves toward him and greedily swallowed the dew which had gathered there.
“Fuzz, stop that at once!” Athena ran up and shooed him away from the plant.
Nikki watched Fuzz as he staggered away from the plant. He seemed to have a hard time following the path, and there was a goofy grin on his face. She glanced back at the pitcher plant, its bright leaves waving innocently in the evening breeze. “Um, Athena . . .” she said, pointing at Fuzz as he tripped over a tree root and fell face down into patch of mossy ferns.
Athena waved her hands in a flurry of embarrassment. “Never mind him, Miss. Never mind.” She darted on ahead, so that Nikki had to jog to catch up.
“The village of Popularnum,” continued Athena when they were a good distance ahead of Fuzz, “bears that name because its inhabitants have an unfortunate habit of following trends. Trends which become very popular.”
Nikki frowned down at her. “But, everybody follows trends. There’s a new trend every week at my high school. Just last week everyone was obsessed with Nirvana t-shirts. I practically got kicked out of the cafeteria at lunch time because I wasn’t wearing one.”
Athena shook her head. “The Realm has that kind of thing also, but Popularnum is different. The villagers there go to very great extremes. They will bankrupt themselves to follow a trend. I was there just last month. The nobility of the town had taken to wearing ostrich-feather hats. There are very few ostriches in the Realm, and they do not like having their tail feathers pulled out to make hats. They kick the feather-pullers, and, as you can imagine, ostrich-kicks can cause great injury. So, the hats were very expensive. Yet, all the people in the village of Popularnum had to have the hats. It caused much poverty and distress.”
“Appeal to Popularity,” murmured Nikki.
“Pardon me, Miss?”
“Appeal to Popularity. It’s the name of a logical fallacy. We learned about it in debate class. Those socks of Maleficious’s were an example of the logical fallacy called Appeal to Authority. Everybody was treating Maleficious as if he couldn’t possibly be wrong. As if he was the ultimate authority. Appeal to Popularity treats popular opinion as if it’s the ultimate authority. Something which should never be questioned.”
Athena looked up at her. “Are we going to question it, Miss?”
Nikki shook her head thoughtfully. “Appeal to Popularity is a tough thing to fight. Let’s wait until we see what’s going on in the town before we make any plans.”
The next morning dawned bright and clear. The rain-washed cobblestone streets of Popularnum shone in the sun as if each stone had been scrubbed with tooth-whitener. Nikki took a seat on a bench next to front door of the inn where they’d spent the night. She stretched out her legs and took a bite out of the pastry the inn’s landlord had given her. It was warm from the oven and oozed currants and brown sugar. Nikki devoured it in four bites and licked her fingers, wondering if she could scrounge another one. She was just about to head back inside on a pastry search when her attention was caught by a man passing by. Nikki’s mouth fell open, pastry forgotten.
Apparently the mismatched socks had not made it to Popularnum. The man’s legs from the knee down were both encased in plain grey socks. The rest of his attire looked similar to what she’d seen the men in Castle Cogent wearing. A forest green tunic covered most of him, with poofy pants that reminded Nikki of a Shakespeare play she’d once seen. So, none of this was particularly eye-catching. No, what had banished thoughts of warm pastry from her mind was the ruff.
And what a ruff it was. At least three feet to a side, it circled the man’s neck like a wagon wheel. A wagon wheel fashioned of silver wire and covered with what looked like very expensive embroidered lace. Twinkling ornaments dangled from the edge of the ruff. Silver, red, and shiny green, they made the man look like a walking Christmas tree.
The morning breeze caught the front edge of the ruff, and Nikki watched as the man struggled to stay upright. He tacked down the street like a sailboat before the wind, narrowly avoiding a horse hitched to a cart filled with turnips. Nikki could have sworn the horse rolled its eyes as the man passed.
“There you are, Miss.” Athena emerged from a tiny opening set into the front door of the inn like a cat flap. The innkeeper had built it for the use of the imps who often stayed there on business from the king. “Did you sleep well?”
Nikki nodded abstractedly. “Athena, look at that man. Quick, before he disappears around the corner. What on earth is he wearing?”
Athena darted into the street to get a better look, then returned, shaking her head. “It’s another fad, Miss. Just like the ostrich feather hats. Very expensive, this one looks.”
“Not to mention impractical,” said Nikki. “How on earth would you get through a doorway wearing something like that?”
Athena leaned forward, backward, and then bent herself sideways. "I believe you would need to go through the door sideways, Miss. Possibly while bending your head down to your knees at the same time."
Nikki stared at her. "That's nuts."
Athena nodded. "Yes, Miss." She climbed up the side of the bench, using tiny stair-like notches in the wood that Nikki hadn't noticed, and sat down. "If you'll take my advice, Miss, we should start by going to the town hall. The nobility of the town gather there most days to show off their finery. In this case, to show off their ruffs. The trends in Popularnum usually start with the nobility, and are then picked up by the rest of the population."
Nikki nodded. "Sounds like a plan." She stood and stretched. "Where's Fuzz? Is he still sleeping?"
Athena's cheeks turned red. "Yes, Miss. He is sleeping off the . . . I mean to say, he is a bit under the weather this morning. Perhaps we should go to the town hall without him."
It was ruffs galore. Big ones, bigger ones, and gigantic ones. Their wearers bumped into each other like ungainly circus clowns, nearly knocking each other over. Tinkling ornaments hanging off the ruffs crashed to the floor and shattered. Nikki and Athena pressed themselves against the wall to avoid the chaos. The central meeting room of the town hall was very impressive, with gold-leaf mosaics on the walls depicting swans gliding among reed-filled ponds. Its high, arched ceiling was also covered in gold. In the center of the roof sparkled a mosaic of a giant ear of corn done in gold coins and emeralds.
Nikki pointed at the ceiling. "What's with the corn?"
Athena craned her tiny neck upward. "Corn is the symbol of this area of the Realm, Miss. It is the most important commodity. This area exports corn to all the Realm, and has grown wealthy because of it, though the citizens tend to waste all the money they make from corn on frippery such as these silly ruffs."
"Hmm." Nikki gazed thoughtfully up at the giant ear of corn as it twinkled in the light from the torches scattered around the hall. "I'm beginning to get an idea."
Athena looked up at her in surprise. "Are you, Miss? From corn?"
"Yes, from corn."
“Fuzz, you are painting your foot.”
Athena set down the corn husk she’d been braiding and marched across the tabletop to Fuzz, who was covered in splotches of blue paint.
They were back at the inn where they had spent the night. They'd spent the morning collecting dried corn husks, and these were now piled high on a creaky wooden table in the inn’s common room. They had the room with its crackling fire all to themselves. Shiny copper pans hung from the rafters, and a moldy moose head with one glass eye looked down on them from its perch above the rough-hewn granite fireplace.
Athena tugged at one of Fuzz’s feet, nearly causing him to topple over into the half-eaten bowl of stew leftover from Nikki’s lunch. Grumbling, Fuzz motioned her away and stripped a sticky, paint-covered corn husk off the bottom of his foot.
Athena took the husk from him with a disgusted look and dropped it into the rapidly growing pile of rejects in the center of the table. She sat down again and with careful concentration continued braiding the ornate hair ornament she was making.
Nikki looked over at Athena’s delicate artistry and sighed. She could sympathize with Fuzz. Her own arms were covered in paint splotches, and she was leading Fuzz in terms of the number of rejects in the pile. Arts and Crafts had never been her strong suit.
She watched as Athena dipped a dried husk into a bowl of water to soften it, and then gently worked it into the braid. She tried to copy the imp’s hand motions, but her own husks insisted on turning to stringy mush instead of intricate braids.
Nikki sighed. “This just isn’t working. Athena, why don’t you do the braiding, and Fuzz and I will concentrate on the painting. We won’t be able to make as many hair ornaments as we’d planned, but at least the ones we do make won’t look so awful.” She held up her mess of husks. “No one is going to wear this.”
Athena nodded. “No, Miss. I will braid faster.” She held up her creation, which resembled a straw version of the large combs Spanish women put in their hair to hold up their lace mantillas. “This will look very nice in your dark hair, Miss. All the ladies in the town will want one.”
Nikki looked at her doubtfully. “Just because I'm wearing it?”
“Yes, Miss. You are an emissary from the king, which makes you a person of high importance and status. The people in Popularnum are very aware of status. The very minute after we checked into this inn last night I assure you that the innkeeper ran to the town hall to spread the news that we had arrived. And at the town hall today, people were watching you very closely. Yes, Miss. I can guarantee you that anything you do will be watched and copied.”
Nikki shrugged uncomfortably. “Okay, well, I guess if I wear your beautiful hair ornament the ladies of the town might copy me, but what about the men?”
“Medals, Miss.”
“Medals?”
Athena put down the hair ornament and picked up a brightly colored object she had left to dry. It looked to Nikki like a straw version of something she'd once seen on the uniform of an army general.
“Er, is that official? I mean aren't military medals usually made out of bronze?”
“Yes, Miss, but we will tell the townspeople that this is the latest fashion, that all the knights and courtiers closest to the king have been awarded these new types of medals. I assure you all the men of the town will be clamoring for them.”
A sputtering sound came from Fuzz. Laughing loudly, he rolled across the tabletop, holding his sides and nearly knocking over a pot of yellow paint. “New types of medals. A bald-faced lie! Hee-hee. I never thought I'd see the day.” He pointed a paint-covered finger at Athena. “Miss Priss is going to lie.”
Athena gave a dignified shrug. “Yes, I am. It is for a worthy cause. We can't allow the people of Popularnum to sink into poverty. Not if we can do something to prevent it.”
Fuzz snorted. “You might be able to get rid of the ruffs, but as soon as we're gone they'll be right back at it with something new. Buying useless, expensive stuff until they’re bankrupt.”
Nikki thought that Fuzz was probably right, but she refrained from saying anything. Athena was working so hard, it seemed a shame to have doubts.
“I simply must have one in pink.” The elderly lady wedged one of Athena’s creations deeper into her fluffy white hair and admired the effect in the gilt-edged mirror.
“Pink will look lovely on you, Ma’am.” Athena scampered across the dressing table to a pile of ornaments. “Try this one, madam,” she said to a jaundiced looking woman in blue satin. “It will look wonderful in your lustrous tresses.”
Nikki raised an eyebrow. Yikes. Talk about laying it on thick. Athena was getting a bit carried away by this lying business, but she had to admit that it seemed to be working. The corners of the dressing room were piled high with discarded ruffs.
They were in the ladies salon, an elaborately decorated room in the town hall. The female half of Popularnum’s nobility crowded in front of its gilt mirrors and ruffle-skirted dressing tables. Athena dashed here and there across the tops of the dressing tables, hopping over pots of powder and rouge, snatching up the corn-husk ornaments and flattering shamelessly as she tucked them into elaborate hairdos.
Seeing that Athena had things under control, Nikki quietly left the salon. Time to check on Fuzz. Hopefully he was doing as well with the men.
After wandering the corridors of the town hall she finally found the library, a dark and musty room paneled in knotted oak and decorated with heraldic shields where the men of the town's nobility had gathered to smoke cigars.
Nikki peered through the half-open door.
Fuzz was standing on top of a carved oak table in the center of the room, leaning casually against a marble inkstand and puffing away at a cigar nearly as long as he was. He waved at Nikki and lazily blew a smoke ring in her direction.
Nikki crossed the room to him. “Hey, Fuzz.” She surveyed the library. Just as in the ladies salon, the corners of this room were also piled high with discarded ruffs. “Looks like it's going great. Only one holdout.”
Fuzz nodded and pointed his cigar at a red-faced, pot-bellied man who was wearing an immense ruff and trying to look nonchalant about it. “Old McManus is the last. He's still wearing his cause he's made a bundle of money on the ruffs. He setup a workshop to make them when the craze first took off, and now he'll lose a bundle if people move on to something else.”
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