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101 Nights

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01 / Night

Antinomies

Night - Antinomies / page 8

Mira ran as fast as she could down the densely wooded slope. From a distance, she heard voices and dogs barking. She didn’t look back, she just ran for her life. Occasionally, she slipped because the ground was already slimy from the heavy rain. This had the advantage that it made her slide down the slope even faster. Mira told herself that she had to pay more attention to the path. If she couldn’t find the way to the cave that the kind man had described to her, she would surely fall into the hands of her pursuers. She had kept as far west as possible the entire time, just as he had said. But hadn’t the big fork in the road already come by now? Had she maybe already passed it? Turning back was out of the question. So she had no choice but to keep running.

The longer she ran, the more uncomfortable she felt. She heard the voices and the barking of dogs growing louder and louder. She had slowed down because of her uncertainty. Now, she picked up speed again. She forced herself to think only about continuing to run. She stumbled through the forest, and her fear that she had strayed off the path was confirmed. It became increasingly difficult for her to move forward as there was so much undergrowth in the way. She fought her way forward over tree stumps, through thorny bushes, through muddy ground into which she sometimes sank up to her knees. Still, she made progress, and suddenly, she was back on a path, and from there, she saw the white rocks the man had spoken of. She had to go there. She put all her strength into the final sprint, and just before she reached the rocks, she saw the red shawl that was supposed to show her the entrance to the cave. She took the shawl and crawled through the narrow opening that appeared behind it. Then, she took the stone lying on the ground and wedged it into the hole through which she had entered the cave.

It occurred to her that her footprints would likely be clearly visible, leading her pursuers to conclude that she must be here, as the tracks ended right before the cave. The dogs wouldn’t move from the entrance anymore. She stepped back from the entrance. It was too late; she couldn’t do anything else but wait.

She held her breath when she suspected her pursuers right outside the cave. She listened to hear what they were saying: “Which way did she go?” One of them, standing at the entrance, shouted: “The footprints stop here. She must have climbed over the rocks!” “Hasso, why are you pulling? Come this way!” “Now we have to go mountain climbing because of this stupid girl. She’s going to regret it if I catch her.” “Stop talking, keep running, Harry. Yeah, a little exercise will do you good.”

Mira felt so glad and relieved. She hadn’t expected that the end of the footprints could be interpreted in this way. But of course, there were no footprints visible on the rocks anyway. At first, she still heard the footsteps above her, and then the sounds gradually faded, until it was completely silent.

She had made it. Now, for the first time, she looked around the cave. Mira’s eyes had adjusted to the darkness. It was quite dark, but a little light came in through some cracks. The cave wasn’t large, about the size of her bedroom at home. She thought about how nice it would be to be at home, curled up in her warm bed, reading a book, and listening to music. Instead, she was in this damp, cold cave. At the back of the cave, there was a small plateau, and there, lying on it, was a sleeping bag. Next to the plateau was a large wooden crate with a note attached which said: “Well done for escaping the silentarians! Enjoy the food!” Mira concluded that her pursuers were silentarians. Did this mean they wanted to silence her? She wondered what she was not supposed to talk about. Then she peeked inside the crate. It was full of canned food, water bottles, apples, oranges, crispbread, cheese, a can opener, a fork, a torch, and then there was something that particularly caught Mira’s interest: a book. She immediately switched on the torch to see what kind of book it was, because she was a real bookworm. While she eagerly grabbed the book, she hoped it wouldn’t be one she already knew. When she read the title, she was quite bewildered and disappointed. “On Logic” it said. What kind of book was that? Not a novel — how disappointing. She put the book down on the plateau and properly spread out the sleeping bag.

Then she saw that some clothes were wrapped up in the sleeping bag. That was good. She immediately changed, as the dress she had been wearing was completely wet and dirty, and she was starting to shiver. Nice that whoever had set up this cave had thought ahead to provide food, drink, and clothing, but they could have thrown in a good book too. She really didn’t want to be ungrateful, especially since she had just narrowly escaped who knows what terrible fate. Still, she was displeased and at the same time ashamed of her ungratefulness. She tossed her wet dress into the corner. It was torn anyway, and she wouldn’t need it anymore. Then she crawled into the sleeping bag. Not that she was tired—she was still way too excited by the events of the day—but she just wanted to warm up. A pillow wouldn’t have been bad either, she thought, as she lay down. Now that she was lying there relaxed, she only then noticed how much her arms and legs were burning. She unzipped the sleeping bag, rolled up her sleeves, and with her torch, inspected her arms, only to find that they were all scratched up. Then she rolled up her pants and saw that her legs were covered in blood. She kept running her hand over the bloody spots, then licking the blood off her hand until there was no more blood on her legs. So that was the result of the thorn bushes. Hard to believe she hadn’t felt any pain before.

She crawled back into her sleeping bag, but as soon as she lay down, she thought she could take a quick look at the book to distract herself. So, she crawled out of the sleeping bag again, grabbed the book, crawled back into the sleeping bag, and lay on her left side, propping herself up on her elbow. That was her typical reading position. She placed the torch beside the book in such a way that the text was easy to read. She flipped through the book a little and found that it was all about mathematics. Mira didn’t like mathematics, just like many other people. She never understood what the teacher was talking about and didn’t even want to understand. Her favourite subjects were German, English, French, Art, and PE. All the other subjects were a thousand times better than maths. But her parents didn’t like it when she came home with a bad grade, which led her to occasionally sit down with her friend Tina and did some intensive maths swotting, usually just before a test. Tina was incredibly good at maths; she was the best in the class. Maths came easily to her. Mira couldn’t understand that. She had a strong aversion to mathematics.

She was about to put the book down again when she read the following sentence: “What I am saying now is a lie.” This was a claim made by a Cretan named Epimenides, who had lived around 600 BC. Mira had to think about this strange sentence. If Epimenides was lying with this sentence, then his statement was false, and he hadn’t lied. If he hadn’t lied, then his statement was true, and he had lied. Had he lied or not? Mira was visibly confused.

She continued reading: “Here is a story from Proclus, who lived around 450 AD: Protagoras taught a student the law and made an agreement with him that the student would only have to pay the tuition fees after winning his first trial. Since the student never took on a case after completing his studies, Protagoras sued him for the payment of the fees. Protagoras argued, ‘If I win the case, I will receive my money because of the verdict. If I lose the case, I will receive the money based on our previous agreement.’ The student argued, ‘I do not have to pay the tuition fees under any circumstances. If I win the case, I do not have to pay because of the court’s verdict. If I lose the case, I do not have to pay because of the agreement we made.’” Mira thought that this was an even thicker egg to crack. Both Protagoras and his student felt they were right. In today’s world, only the verdict would be decisive. If the student lost the case, he would have to pay the tuition fees; if he won, he would not have to pay. The question was only how the judge would decide. Mira thought that, if she were a judge, she would probably refuse to rule on such a case. That meant Protagoras would have to find another way to make sure that his former student would accept a lawsuit and win it. On the other hand, Mira thought that the teacher had spent time and effort on the student, and the student should reward that if he had enough money. Oh, this was so complicated. It was not a nice thing that people had to argue so often. When her mummy and daddy fought, it always tore her heart apart. She would feel dizzy and sick. Until now, she had always preferred to give in rather than argue, but unfortunately, others often took advantage of that.

Mira wanted to continue reading and learned that a certain Grellin had divided the adjectives into two classes, in heterological and autological. But that was too dry for her, and her eyes closed over it.

The next morning, Mira was as hungry as a bear, and she started to dig into the canned food. She still heard the rain pattering outside and thought about the fact that she should stay here for three more days until the silentarians had given up looking for her and returned home. They would think that she was already far outside of their territory. The march out of the territory still lay ahead, and she didn’t know what to expect outside. She was just thinking about what she might encounter when suddenly she heard a voice shout: “Now I’ve got you!” She startled and trembled with fear. She looked around but couldn’t see anyone. Still someone shook her.

Interactive puzzle

Liar sentence check

The chapter introduces a sentence that turns back on itself. Decide what makes it a logic problem, not just an ordinary false claim.

What is the trap in the sentence 'What I am saying now is a lie'?
Choose an answer

Pick the option that best follows from the chapter.

02 / Day

Heterological

Day - Heterological / page 12

“Now, out! Come on, get up, you’ll be late otherwise!” it roared into her ear. Slowly, Mira recognized the outline of her brother Felix, who was leaning over her. “How can you be such a sleepyhead!” , he said, now a bit calmer, because he noticed that Mira was slowly waking up. Felix was a bit smaller for his age, but a very cheeky boy with freckles on his face. He was younger than his sister, at 14 years old. “Is it already so late?” , Mira asked. “I had a nightmare again.” “I almost thought that.” , Felix answered. “Why, what do you know?” , Mira questioned him and looked at him in surprise. “If someone is tossing and turning like that in bed, something is wrong. Come on, no time for long talk, get up, or we’ll miss the bus!” Meanwhile, he pulled the blanket away and pinched Mira in the waist. Mira squealed and jumped out of bed. Mira could be fast when it mattered, and it didn’t take long before she ran to the kitchen with her school bag, grabbed a sandwich, and marched on to the front door. “Where are you, Felix? We’re going to miss the bus!”, she shouted.Felix jumped down the stairs, and then they raced to the bus stop, which was only 200 meters away. The bus wasn’t in sight yet, but they ran anyway. They had been doing this every morning lately, simply because it was fun for them. “First,” Felix shouted with joy as he reached the bus stop pole first. Only shortly afterwards, but still after Felix, Mira reached the pole. She looked exhausted. “What’s wrong with you, little sister? Are the nightmares affecting your running ability, or is there another maths test coming up?” Right, Mira hadn’t thought about that at all previously. Next week, there was actually a maths test on the schedule, and today she planned to meet her friend Tina after school to study. She had immediately forgotten that she lost the race because she was only thinking about school, but Felix was happy the whole day, because it was the first time he was faster than Mira.

Mira liked going to school, except for maths class. The maths teacher, Mr. Friedhardt, was always mean to her. She wasn’t even the worst in the class. Still, he always had to make fun of her mistakes. Her best friend Tina suspected that he must have once been in love with a girl who looked like Mira and had turned him down. What made Mira even sadder was that some kids in her class laughed when he made fun of her. Of course, not Tina and her best friends. Today, fortunately, the maths class was cancelled, so the school day went quite well. Even the studying with Tina was pleasant, and Mira had the impression that she was making progress. After dinner, Mira sat down at her desk and replied to a letter she had received from her friend Ulla. Then she looked up the meaning of heterological in the Brockhaus encyclopedia. Where had she heard that word before? She couldn’t remember, but she wanted to know what it meant:

An adjective is heterological, if it is not what it means. Examples are the adjectives long, two-syllable, French. Long is a short word, not a long word. Two-syllable is a four-syllable word, not a two-syllable word. French is an English word, not a French word.

Autological adjectives are those that mean exactly what they are. Examples are the adjectives short, four-syllables, English. Short is a short word. Four-syllable is a four-syllable word. English is an English word.

Mira understood what she had just read and wanted to test if she could decide for herself whether an adjective was autological or heterological. So, what about the adjective autological? Autological was itself what it meant. So, autological was autological. What about the adjective heterological? Was it autological or heterological? If heterological were heterological, then it would not mean what it meant by definition. But that was exactly what heterological meant, that it did not mean what it was. So, heterological would be autological, which would be a contradiction. If heterological were autological, then heterological would be what it meant, so it would be heterological. This also led to another contradiction. One could really get a knot in their brain! So, heterological belonged to neither of the two classes. Homological, on the other hand, was clearly homological. Mira thought of more adjectives to see which class they belonged to. Whatever came to her mind, they were all words that were not what they meant. How could a word be smart, empty, faithful, thirsty, or free? For a poet, that might be possible, but for Mira, these words were heterological. Some might find the word funny funny or the word nice nice, but for Mira, these words were also heterological. The word new is not new, the word quiet is not quiet. For homological words, only separable and flawless came to her mind. The classification into these two classes was an interesting idea by Grelling, Mira thought, although the word heterological did not belong to either of the two classes. And now she remembered her dream with the story of the trial, which also led to a contradiction, just like with the adjective heterological. All this thinking made Mira very tired, as she had not been sleeping well lately due to her many nightmares. She wanted to read the book that the German teacher had assigned to the class, but Mira fell asleep after just a few lines.

Interactive puzzle

Heterological word test

Mira reads that an adjective is heterological when it is not what it means. Classify one example from the chapter.

Which word is heterological by the chapter's definition?
Choose an answer

Pick the option that best follows from the chapter.

03 / Night

Feather Logic

Night - Feather Logic / page 15

Mira sat in the cave. The rain had stopped, and she poked her head through the hole she had crawled through the day before. The sky was blue, the sun was shining brightly, and the world looked friendly and inviting. There was not a soul in sight or sound for miles. Mira didn’t want to stay in the cave any longer. She was bored. The three days she was supposed to stay in the cave weren’t up yet, but she no longer even remembered why she had been there. She couldn’t recall anything. She climbed out and continued down the path that led further down the mountain. Mira felt carefree, the birds were chirping, and she wasn’t even in a hurry. She even started whistling because she was in such a good mood. But then she heard the sound of barking dogs, and it wasn’t even that far away. Instinctively, she began to run as fast as she could, and everything came back to her — how she had been chased and how she had been warned beforehand.

She could already see the wall that she considered the boundary of the territory. She wasn’t far from it, but neither were the silentarians. She felt her pulse pounding in her neck. Would she get caught just before the border? Perhaps she was running straight into their hands, as there might be others waiting by the wall. It was too late; there was no turning back to the cave. The dogs would track her down if she tried to hide. She had to risk climbing over the wall. The barking of the dogs grew fainter, but Mira didn’t pay attention to it. She ran toward the wall, swinging her arms as if someone were holding her back, and she had to shake them off. Finally, she reached the wall. But there was no passage there. The wall was too high and smooth to climb over easily.

Nervously, she run along the wall, hoping to find an opening. She kept running, glancing nervously around, checking for any sign of the silentarians. Then she found a tree that was climbable and close enough to the wall. Skilfully, like a little monkey, she worked her way up, swinging from branch to branch, until she reached the height of the wall. Then, she jumped onto the wall, slowly lowered herself, facing the wall on the other side. But before she could even touch the ground, she was grabbed from behind, her hands bound with a rope, and her face covered with a cloth. “No!” , Mira screamed loudly, struggling wildly, without any chance to escape.

Interactive puzzle

Escape route check

At the wall, Mira has very little time. Use only the facts in this chapter to choose the move that follows from the situation.

What is the best-supported move from the facts Mira has?
Choose an answer

Pick the option that best follows from the chapter.

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