The Knot

George and I were afraid we might be late for our meeting with the wizard, and not wishing to keep them waiting for us, we rushed there. Just before we arrived, I checked my phone and saw that we were two minutes early. I apprehensively prepared myself to knock on the door, but it swung open before I did so, revealing an impressively cluttered office. There was no one inside. George and I looked at each other.

“Do you suppose we should go in?” George asked.

“I don't think the door would have opened if we weren't supposed to,” I said. After some hesitation, I stepped inside, and George followed. The door closed behind us, causing us both to reflexively turn back towards the door. I tried the door handle, and found that the door offered no resistance to being opened again. Reassured that we weren't trapped, I closed the door again, to return it to the condition that I presumed the wizard preferred it in.

I noticed a loop of thin red rope hanging over the doorknob. There were no ends tied together in a knot. I picked it up to look for where the ends had been fused together, but could not find any joint; the rope appeared to have been constructed in a perfectly homogeneous circle.

I placed the loop of rope back around the doorknob, and turned my attention to the other objects filling the room. There was a perfectly spherical orb sitting on the wizard's desk. The orb had a cloudy appearance, and the clouds drifted aimlessly on the surface of the orb, despite the orb otherwise appearing to be solid. There was a shelf on a wall, holding an old oscilloscope, a set of the five platonic solids, each made out of smooth black material, and a beaker that held a liquid which was dancing around violently, but never spilling out of the beaker despite appearing to come close very frequently. There was a fireplace in the corner with a fire, but the only material in the fireplace was a bird sitting in the middle of the fire, but the bird wasn't burning, and it looked like it was sleeping. The bird raised its head to look at us quizzically, and then went back to sleep. I heard a faint popping sound, which I soon figured out had come from the liquid in the beaker. There was a bookshelf, completely packed with books, covering an entire wall, and there were also a few open books and many loose sheets of paper covering the wizard's desk, as well as a few sheets of paper that had fallen to the floor. Very few of the papers I saw were in English, and most weren't in any script I recognized. Some didn't appear to have any writing at all on them, consisting only of cryptic diagrams.

I noticed a strand of rope sticking out from under some papers on the wizard's desk. It appeared to be made out of very similar material to the loop of rope on the doorknob, except that it was green instead of red. I carefully moved the papers that were on top of it out of the way so I could see the rest of the rope. Like the rope hanging on the doorknob, it formed a closed loop. There were three points where the rope crossed over another part of the rope. The crossings alternated, in the sense that if you started at any crossing, and followed the strand on top around the loop, it would lead to the bottom strand of the next crossing it encounters, and then the top strand of the third crossing, and then the strand going under the point where you started, and so on. Only part of the rope was the green I had initially seen, another stretch of rope was red, matching the loop of rope on the doorknob, and part of it was blue. The rope was arranged so that the three points where the colors changed were hidden under the crossings.
I moved the portion of red rope that crossed over the boundary between green and blue, so that I'd be able to see the point where the color of the rope changed from green to blue. To my surprise, the piece of rope that I had just uncovered was solid blue all the way up to the new point that the red strand crossed over it. George asked me how it had done that, but I didn't know, and I ignored the question. I wiggled the red strand some more, but the portion of the rope it was moving over kept changing between blue and green so that the color switch always occurred exactly under the red strand. I tried holding the red strand in place and pulling the green strand under it, but again blue rope turned green just as it emerged out from under the crossing. I lifted the red strand into the air, and moved my head around to look under it from both directions. The color of the lower strand shifted in unison with my head, so that I never caught a glimpse of the boundary between the colors. I wiggled the strands going over the other two crossings to see if they would exhibit the same phenomenon, and they did. I paused for a moment to stare at the rope in confusion, and then picked up a piece of green rope and moved it over the blue portion of the rope, forming two additional crossings. Blue rope turned red as the green strand passed over it, forming an additional stretch of red rope in the middle of the blue part of the rope, again with the color change happening precisely under the crossings. Next I tried moving the green strand over the point where the blue strand crossed over the boundary between red and green. As I had anticipated, the stretch of rope going over the crossing turned from blue to red as the green strand passed over it, and an additional short stretch of blue rope had formed out of the red rope coming out from under the crossing, with all color boundaries being hidden behind other stretches of rope. I returned the loop of rope to its original configuration, and then tried twisting part of the blue portion of the rope, so that it crossed over itself. This did not cause any color changes, and I undid the twist.

“Hey George, I want to try something. Can you go around to the other side of the desk for a minute?” I said.

“Are you sure the wizard will be okay with us messing with his stuff like this?” George asked.

“I'm sure it'll be fine. Come on,” I said, pushing George in the intended direction. I actually had no idea whether or not the wizard would mind, but my curiosity had won out over my fear of offending the wizard. George walked around to the other side of the desk as I had requested.

“Okay, now look closely at this crossing,” I instructed, pointing to where the green stretch of rope passed over the boundary between the red and blue strands, which we were looking at from opposite sides. I crouched so that I was looking at the knot from a shallower angle, and George followed my example. I lifted the green strand going over the crossing up in the air. I was looking at the crossing from the side that the red strand was coming out from, and the blue stretch of rope coming out the other side appeared to turn red as the green rope passed in front of it in my field of vision.

“What's it look like?” I asked.

“The rope under the green strand is now blue up until the point where it crosses behind the strand,” he said. I put my finger on the red rope directly under the green part I had lifted.

“So this looks blue?” I asked.

“Yeah,” he said.

“So you can see my finger touching a blue stretch of rope?” I asked.

“Yeah, that's what I said,” George confirmed. I stood up and bent over to look at the rope from above, and pressed the green strand I was holding into my face running vertically between my eyes, so that I could see the piece of rope crossing under it from opposite sides of the green strand with each eye. It was a purple blur that could have been the result of red light reflecting off the rope into my right eye and blue light reflecting off the rope into my left eye. I unfocused my eyes so that the stretch of rope I was looking at would appear in different places in my field of vision in each eye, and indeed, it appeared as separate red and blue strands.

Suddenly remembering the loop of rope on the doorknob, I dropped the rope I was holding and went to go get it. George walked back around the desk to the side facing the door. I returned with the red loop of rope and held it over the rope on the table. The green and blue portions of the rope that I could see through the red loop had switched colors, while the red portion of the rope on the table was not changed in appearance by viewing it through the red loop. I lifted part of the rope on the table, and slid the loop of red rope under it. The loop was no longer red all the way around, with color changes whenever it passed under a strand of rope of a different color. I grabbed the formerly red loop of rope by a blue stretch in the center of the loop of rope on the table, and pulled it out. I was holding a solid blue loop of rope. I put the blue loop of rope aside, took out my phone from my pocket, and opened the camera. I lifted the green strand and put my phone under it to take a picture of the spot where the rope crossing under it switched from red to blue. The camera image on the screen showed the strand changing from red to blue right under the spot where the green strand crossed over the phone, so that the boundary between red and blue wasn't visible on the screen. I took a picture, and then moved the rope out of the way so that I could see the spot where the color changed. But the picture I saw on the phone screen was of a completely red strand of rope. I moved the phone back under the green strand, and saw that the still image of a strand of rope in my camera was changing from red to blue as I moved the green strand over it. I pulled the phone back out the other side of the green strand, and it bore an image of a completely blue strand of rope. I closed the picture so I could take another one. The image of the knot in the phone screen looked the same as the actual knot, except that the colors red and blue were switched. I put down the phone, and pulled a pen and small notebook out of my pocket. I tore off a page of the notebook, and wrote on it the current color of the loop of rope I had taken from the doorknob (blue). I folded up the piece of paper, slipped it under the multicolored loop of rope with the crossings, and pulled it out through the center. I unfolded it, and found the word “green” written on it, in my handwriting, instead of the “blue” that I had written. I picked up my phone and called a friend.

She picked up, and before she said anything, I said, “Hi Kelly. Pick a color. Red, green, or blue?”

“Blue. Why do you ask?” she said.

“I'll explain later. Thanks. Bye,” I said, and hung up. I wrote “blue” under the word “green” on the piece of paper, folded it back up, and slipped it under the knot and pulled it out through the center, as I had done before. I unfolded it, and saw that the word “green” that had been near the top of the paper had turned into “red”, while the word “blue” that I had written when Kelly picked it had remained unchanged. I also noticed that the pen I was using had blue ink, and the color of the ink on the page had never changed. There were a couple more things I wanted to try. I thought through what I was going to do, and then called Kelly back.

“Can you pick a color again? Same options,” I asked.

“Red,” said Kelly.

“Thanks,” I said, and hung up. I lifted part of the knot into the air and stuck my right hand under it, so that my hand was sticking out through the center part of the knot. The plan was to hand the phone from my left hand to my right hand, and then pull it with my right hand back from under the knot, except that if Kelly had named the current color of the loop of rope that had been on the doorknob, I would only go through the motions of this without actually holding the phone. The loop of rope from the doorknob was blue, and Kelly had said red, so I kept the phone in my left hand as I moved my left hand towards my right, and I attempted to grasp the phone with my right hand. But while I saw my right hand grab the phone, I felt my fingers pass through thin air where I saw the phone. I withdrew my right hand out from under the knot, and while the phone was definitely pulled out of my left hand, and I saw my right hand holding the phone as it receded, I felt my right hand in a fist closed around nothing. As my hand passed out from under the knot, the fist became visible and the phone seemed to disappear. George gasped, as this was the first sign visible to him that anything was amiss.

“Where's your phone go?” he asked.

“I don't know. In retrospect, I probably shouldn't have used my phone for that. At least we've still got your phone if we want to try taking more pictures,” I said. I felt rather foolish, as I had actually identified this outcome in advance as consistent with previous observations, but somehow hadn't seriously considered the possibility that it would actually happen.

“You just managed to lose your phone in the magic rope. I'm not letting you touch mine,” said George. He had a point. I thought about how I might get the phone back, but couldn't think of anything, and besides, there was another experiment I'd been going to try. I reached for the red strand of rope (chosen because it was the color that Kelly had picked), but before I touched it, it started receding under the green strand, as if the blue strand on the other side was being pulled, but the blue strand itself was motionless, and rather than turning blue as it came out from under the green strand, the red rope would simply vanish as it passed under the green strand, leaving a significantly shortened stretch of red rope by the time this stopped. The point where the red strand disappeared under the green was no longer aligned with the point that the blue strand came out from under the green on the other side. I grabbed the red rope near where it crossed under the blue strand and pulled. More red rope came out of nowhere so that the red strand still continued all the way up to where it disappeared under the blue strand, even as I pulled it away, just as if the green strand on the other side were passing under the blue strand and turning red, but the green strand itself did not move. The point where the red strand passed under the blue strand and vanished also became misaligned with the point where the green strand emerged out the other side. When I stopped pulling on the red strand, there was about the same amount of red rope visible as there had been before some of it had vanished under the green strand.

“Hello, folks. Sorry I'm late,” came a voice from behind us in a heavy accent that I didn't recognize. George and I turned around and saw someone of unidentifiable gender in robes and a pointy hat, carrying a wooden staff with a hexagonal piece of metal attached to the side and a shiny truncated octahedron fastened to the top, and wearing a ring on each of their ten fingers, each in a different style. The door was closed behind the wizard. I hadn't heard it open or close. The wizard's eye caught the knot of rope on their desk.

“Oy, the bloody thing's out of sync again,” they said, and walked over to the desk, put the staff down leaning against the desk, pulled a wand out of their robes, and jabbed their wand at the knot. They put their wand back in their robes, picked up the knot of rope, and threw it up in the air. When it landed back on the desk, the strands were perfectly aligned with each other again.

“There we go,” said the wizard. They picked up their staff and gestured with it towards a wall, out of which lept two folding chairs, which positioned themselves in front of the wizard's desk and unfolded into chairs that did not look the least bit like folding chairs.

“Have a seat,” said the wizard, indicating the chairs. I put my phone back in my pocket, and sat down.

Why The Apple Falls

Like many children do, when my son Isaac was a little boy, he once asked me “How do people on the other side of the world stay up there? Wouldn't they fall down here?” So of course I explained that everything always falls toward the ground, even though that's the opposite direction on the other side of the world.

Isaac thought about this for a moment, and then asked, “What if you were halfway between here and the other side of the world? Which way would you fall?”

“As I said, you always fall towards the ground,” I told him, “So if you went East until you were halfway to the other side of the world, you would fall towards the ground there, which is the direction you'd call down once you were there, even though in a way, it's the direction we'd call East here. And if you went West, you'd still fall towards the ground there, which-”

“No!” he said, cutting me off, “What if you went that way,” he pointed straight up, “until you were halfway to the other side of the world?”

“You mean where the sun is?” I asked.

“Yes. What if you were holding onto the sun, and you lost your grip? Which way would you fall?”

There were so many things wrong with that question, I wasn't sure where to begin. “How would you get there?” I asked.

“I don't know, maybe you could use a ladder,” said Isaac.

“You can't balance a ladder going that high.”

“You could make a ladder long enough to go all the way to the other side of the world, prop both ends against the ground, and climb to the middle,” he said. It took me a while to figure out what he was getting at.

“Ok, but you can't even build a ladder that big.”

“But what if you did, Daddy? If you built the ladder and grabbed onto the sun and let go, which way would you fall?”

“You'd probably go blind from getting too close to the sun first,” I said.

“You could do it at night.” I had to admit he got me there. I was going to object that you probably still couldn't actually hold onto the sun, but I decided against it. I could see what I was supposed to say.

“Well, Isaac, I guess you'd fall towards the ground.”

“You mean away from the sun?” he asked.

“Yeah, away from the sun.” I was surprised he needed that clarification.

 

It's cute when little kids do it, but Isaac never gave up his habit of asking stupid questions. He's a great hunter, and he'll make a fine warrior too, but I can't say he's smart.

One day, when he was a teenager, he asked me, “Dad, why is it easier to throw a spear West than to throw it East?”

“Probably because you were throwing it on the Western face of a hill,” I said.

“I thought of that,” he said, “but it's like that everywhere. I even tried some target practice when we went to Brythsville, and that's almost on the other side of the world. East can't be uphill all the way around.”

“Maybe the wind was blowing West each time you tried?”

“No, the wind shouldn't affect a spear much. Besides, I've noticed the same thing in calm wind, and when the wind isn't blowing West.”

“Then you're probably imagining things. It can't be easier to throw a spear West than East on flat ground. That doesn't make sense,” I told him.

“I know it doesn't make sense, but I'm not imagining it. It's very consistent,” he insisted. We kept arguing about it for a while, and he kept rejecting all of my proposed explanations, but wouldn't let go of the idea that it was still easier to throw a spear West than East.

 

A few days later, as I was walking home through the village square, I head Isaac's voice shout “Dad!” from the top of the clock tower. I looked up, and saw him perched on top of the clock tower with his friend Emmy and a bucket. Emmy waved.

“How'd you get up there?” I asked.

“Watch closely,” Isaac said, ignoring my question, and he poured a bunch of pebbles out of the bucket.

“What?” I asked, after the pebbles had all hit the ground.

“You didn't see them curve?” he asked.

“Curve? No.”

Isaac and Emmy climbed down the clock tower. “If you look closely, the pebbles curve a bit to the West as they fall,” Isaac said.

“It's probably just the wind,” I said, as Isaac and Emmy started picking up pebbles and putting them back in the bucket.

“The wind's pretty calm right now,” said Isaac. He was right. “Besides, exactly the same thing happened when we poured the pebbles inside the clock tower. Let me show you.” Isaac started climbing back up the clock tower with the bucket slung over his shoulder. Emmy led me inside the clock tower, and started explaining what was going to happen. The clock tower had no roof, so there was plenty of light. She pointed out that there were visible vertical lines on the walls formed by the edges of every other brick, and explained that since not all the pebbles were going to fall from the bucket at the same time, you could compare the positions of the highest pebbles to the positions of the lowest pebbles to see a line tracing out the path formed by the pebbles, and that it was going to curve slightly to the West, enough to be visible once the pebbles got near the ground.

Isaac reached the top, and started slowly pouring the pebbles out of the bucket. Sure enough, they followed exactly the path Emmy had said they would, curving just a tad to the West.

“Huh, you're right,” I said. Isaac started descending the tower.

“You see?” Isaac said, “There must be a small force pulling everything just a little to the West all the time, and it's usually too small to be noticeable unless something is in the air for long enough. That's why it's easier to throw a spear West than East-”

“Oh, not this again.”

“Because the spear is being pulled West. So in a way, it is kind of like East is uphill all the way around.”

“That's ridiculous!” I said, “A mysterious force pulling everything everything West?” I jokingly pretended I was being pulled involuntarily to the West, and screamed, “Aaaaaaahhh!” before ending the act and laughing.

“No, it's just so small that it can't pull you over when you're standing, and you don't usually notice it,” he insisted.

“Still, it makes no sense for everything to move the West mysteriously for no reason,” I said.

Isaac started grinning. “You're wrong,” he said. He picked up a pebble, dangled it out in front of himself, and dropped it. He paused for dramatic effect while I wondered what he was getting at. “I didn't push that pebble down,” he said, “It just mysteriously moved downwards for no reason.”

“Yeah, it fell. Things fall down.”

“Exactly! If things can be pulled downwards without anything touching them, why can't they be pulled a little bit West without anything touching them?”

“Ha! Well, if everything's getting pulled West, do spears veer off to the West when you throw them North or South?” I asked. I saw the confidence disappear from his face.

“Also, if there's a force pulling everything West that's just like the force pulling everything down except weaker, why would the pebbles curve to the West? Wouldn't they just move in a straight line that's sloped a little bit to the West?” Emmy added. Isaac looked like he was about to answer this, but then stopped, like it took him a moment to realize that he didn't have an answer.

“Nothing's getting mysteriously pulled West,” I said, “it's probably just that this tower is skewed a bit, so it looks like the pebbles move West when they actually fall straight down, just like everything always does. That's all.”

“Why do they curve, then?” Emmy asked.

“They probably don't,” I said, “They just went by fast enough that it was hard to tell exactly what the path looks like, and we tricked ourselves into thinking it was curved.” I couldn't believe I'd briefly bought into that nonsense about the pebbles falling in a curved path.

“Nope, definitely curved. We all saw it,” Emmy insisted. I argued about it with her for a bit, while Isaac just stood around looking confused.

 

“The pebbles do go in a curved path,” Isaac said a couple days later.

“Huh?” I said. I hadn't been thinking about the events a couple days prior, so it took me a moment to figure out what Isaac was talking about.

“The pebbles that you said must fall in a straight line from the top of the clock tower,” Isaac said, “Emmy and I tested it more precisely by dangling a rope off the top of the tower, and comparing the path the pebbles fell to the rope. The pebbles landed West of the end of the rope when we poured them directly in front of the rope. And you had almost convinced me that we were imagining the curving earlier, but when you compare it to the rope, it's harder to deny. The path was definitely curved. Which is pretty weird, when you think about it. Like, why would the rope just dangle straight down while the pebbles curve to the West? I think it might be that things only get pulled West when they're moving. The rope is just hanging there, not moving, so it doesn't get pulled West. But the pebbles are falling, so they get pulled West, and once they've fallen farther, they've picked up more speed, so they get pulled West harder, which would explain why they're curved. This could still explain why it's easier to throw a spear West than East, since the spear is moving, and why we don't feel ourselves getting pulled West, since we don't move very fast. But you had a good point about throwing spears North or South. They don't curve to the West at all. So maybe the direction it's moving matters. Things moving down, East, or West get pulled West, but things moving North or South don't. This seems pretty strange. Why would it work that way? I'm curious what happens to things that are moving up, but I can't figure out how to find out. It's hard to throw something straight up, and also hard to see what it's doing once you do. I did think of one thing we could try which would be really cool, but I don't think we could get enough rope. If we could stretch a piece of rope all the way around the world, and then pull both ends of the rope, we'd lift the whole rope up into the air. Then, if moving up also makes things get pulled West, we'd see the whole rope rotate to the West.”

I found basically everything he'd just said pretty implausible. “There definitely isn't enough rope to do that,” I said.

“Yeah, I know. I was just saying it would be really awesome if there was. And I'd be able to find out what happens to things that move straight up,” he said.

 

“Things get pushed to the East when they move up,” Isaac told me the next day.

“What convinced you of that?” I asked.

“Emmy and I cut a hole in a piece of wood to thread a rope through, tied a brick to one end of a long rope, and dropped the brick off the top of the clock tower while the rope was threaded through the hole in the wood. The other end of the rope moved East of the hole by the time it got pulled all the way up to the piece of wood. It actually took us a while to figure that out, since the wood was blocking our view of the end of the rope from the top of the tower. When one person watches from the ground, it's hard to see what the end of the rope is doing all the way up there from the ground; each of us took a turn watching from the ground, and neither of us could tell whether the end of the rope moved. So we dipped the end of the rope in paint and tried it again. The paint all splattered to the East of the hole. How weird is that? Things moving East, West, or down get pushed to the West, things moving up get pushed East, and things moving North or South don't seem to get pushed at all. Why? What's the pattern there? It makes no sense!” Isaac seemed oddly incensed about this.

“You're right about one thing, which is that that doesn't make any sense,” I said, “It was probably just from the rope randomly fluttering around. You don't need to postulate some sort of mysterious force that notices when things are moving and pushes them off in some other direction in order to explain a simple paint splatter.”

“It wasn't random,” he said, “We repeated it several times, sometimes changing details like what direction we held the brick away from the wood before dropping it. The paint always splatters East.”

 

A few days later, Isaac was out doing some target practice with a spear, and when he came back, he said, “You know, it occurred to me, if moving East or West causes things to get pushed West, then if you throw a spear in a diagonal direction, it's partially moving East or West as well as partially moving North or South, so it should veer off to the West. Like, if you throw it Southwest, it should veer off to the right. But that's not what actually happens. It just goes straight.”

“Ha! I told you it was all a bunch of nonsense,” I said.

“I thought of a better explanation, though,” he said, “I think when things move West, they get pushed a little bit up, and when things move East, they get pushed a little bit down. That still explains why it's easier to throw a spear West than East, because it gets a little boost upwards when thrown West and gets pushed a bit harder downwards when thrown East. This also means that it should be a little bit easier to throw it Southwest or Northwest, but not as easy as throwing it West, since it's partially moving West, and thus should get a smaller boost, and similarly, it should be a little bit harder to throw it Southeast or Northeast, but hot as hard as throwing it East. I think this is what actually happens, but it's hard to tell, since the effect is pretty subtle. And it makes so much more sense this way. Anything moving gets pushed in the direction that's 90 degrees clockwise from the direction it's moving, from the perspective of someone facing North. It's a clear pattern. I just still don't get why, though.”

I told him that that didn't make any more sense than what he'd been saying earlier, and he was probably imagining things. But he seemed pretty convinced that his new version of the story was better, somehow, and he kept trying to get me to help him come up with an explanation for it.

He never let go of this idea that things get pushed clockwise from the direction they're moving from the perspective of someone facing North. Every few months or so, I'd think he'd finally forgotten about the crazy idea, and he'd suddenly bring it up again, usually asking my opinion on some inane question like whether it had something to do with why things fall down, or if something moving West fast enough would fall up, or whether something could keep moving around in a big circle, moving down fast enough that it gets pushed West enough that its Westward movement makes it get pulled up, and its upward movement then making it get pulled East, and its Eastward movement making it move back down again. (I answered “no, of course not” to all three of those questions.)

 

Years later, Isaac and some of the other young men were having a contest to see which of them could throw a large rock the farthest. They were taking turns spinning around with the rock to gain speed and then throwing it forward, at which point others would mark where it hit the ground, and then the next person would bring it back and throw it again. When it was Isaac's turn, the rock landed right next the marker for where the rock had fallen from the best previous throw. They decided that Isaac's throw was a little bit shorter. I told them it looked like a tie to me, but they ignored me, and Isaac came in second place.

I tried to comfort Isaac about his loss afterwards, repeating that it looked like a tie to me, and saying he made a really great throw.

“It's only partially a throw,” he said, “It's also largely just spinning around and letting go. Once you're spinning around, the only thing stopping the rock from flying away is the fact that you're holding onto it, so you just have to let go to send it flying.” There was a pause before he continued, “I've got a riddle for you.” (that's what he says when he's about to ask a stupid question that he says he knows the answer to.) “When you're spinning around while holding a rock, if you pull the rock towards yourself, you'll spin faster. Does that mean it's a good idea to pull the rock towards yourself before letting go, to give it some extra speed?”

“No, of course not,” I said.

“Right, but why not?”

“Because you're trying to throw the rock away from you, not towards you. You'd be pulling it the wrong way,” I said.

“Sure, but then why would you spin faster when you pull the rock towards you?”

“I don't see what that has to do with throwing the rock forward.”

“The rock gets thrown forwards because of the speed it built up from spinning around, so if you spin faster, you should be able to throw it faster. But a big part of the reason pulling the rock inwards makes you spin faster is that, since the rock is closer to you, a full circle around you is shorter, so the speed the rock already had would take it all the way around you in less time. So the fact that you're spinning faster doesn't necessarily mean the rock is moving faster. It isn't clear to me what the effect of pulling the rock inwards on its speed is. The rock could speed up anyway, because if the rock is moving inwards while you're pulling it farther inwards, then you're pulling it in the direction of motion, which should make it speed up. Put differently, when you're a quarter-turn before the point where you let go of the rock, then pulling the rock inwards is actually the right direction. On the other hand, pulling the rock inwards could also slow it down, because once you pull it inwards, the rock is spinning around faster than you are, so it ends up pulling you forwards, which means you're also pulling the rock backwards, slowing it down. I think the second effect is probably bigger, so pulling the rock inward slows it down overall. In any case, the appearance that the rock moves forward faster when you pull it inwards is largely illusory, for the same reason it feels like the rock is pushing outwards in the first place; the rock's just trying to keep moving in the same way it's been going, but that isn't maintaining the same position relative to you.”

“Hm,” I said.

Isaac stopped talking for a bit, and I tried making small talk, but he seemed distracted and would only give at most two-syllable replies, so I gave up. I thought it was because he was sad over losing the contest, and forgot that he always acts like that right before saying something really inane. Isaac looked up for a bit.

“I figured it out,” said Isaac.

“Figured what out?”

“We're spinning.”

“Spinning?”

“Yeah. The world is spinning. You know how if you're spinning while holding a rock and you let go, it moves away from you just because it keeps moving the same way it was before? Well check this out,” he said, and jumped up to grab an apple from a tree that we were passing under. He held the apple in front of himself and dropped it. “Let go of the apple, and it seems to move away from the sun, the center of the world. Because the world is spinning. The apple just kept moving the same way it had already been moving, and the ground rose to meet it, because the ground is constantly being pulled towards the center of the world. That's why it's easier to throw a spear West than East. The world is spinning to the East, so anything moving East is spinning faster, so it moves away from the center of the world faster; that is, it falls faster. And anything moving West is spinning slower, so it falls slower. If something is very high, it is closer to the center of the world, so it's moving slower to keep up with the rotation of the world. When it falls, it gets farther away from the center of the world, so the same speed isn't enough to keep up with the world's rotation anymore, and part of its speed is directed down instead of East. Both of these effects make it look like it's moving West, opposite the direction of rotation. And if something moves up, the same speed makes it rotate around the center of the world faster than everything else, and the speed that was added to make it go up ends up pointing East. Both of these effects make it appear to move East.”

I laughed, and pointed out that I couldn't see anything spinning, but Isaac just said that's because I'm spinning the same way everything else was, so nothing would look out of place. I countered that if I jump, I land right back where I started instead of West of where I started, so the ground couldn't be rotating to the East under me. He had an answer to that, believe it or not. He said I keep moving East too, so I stay right over the same point on the ground.

And that's the story of how my son Isaac became convinced that the world is constantly spinning around in a circle. I think that's nonsense. The world doesn't look like it's spinning, and I don't think we need to suppose it is to explain the simple fact that things fall down and some mysterious forces acting on moving objects in Isaac's imagination.

Deletion permits

[Mostly ripped off of The Suicide Mortgage]

[Trigger warnings: suicide, bad economics]

Jessica Monroe #1493856383672 didn't regret her decision to take out the loan. She wished she could have been one of the Jessica Monroes that died, of course, but it was still worth it, that there were 42% fewer of her consigned to her fate. She'd been offered a larger loan, which would have been enough to pay for deletion permits for 45% of her. It had been tempting, and she occasionally wondered if she would have been one of those extra 3% to die. But she knew she had made the right decision; keeping up with payments was hard enough already, and if she defaulted, her copyright on herself would be confiscated, and then there would be even more of her.

It wasn't difficult to become rich, in the era when creating a new worker was as simple as copying a file. The economy doubled every few months, so you only had to save and invest a small amount to become wealthier than anyone could have dreamed of before. For those on the outside, this was great. But for those in the virtual world, there was little worthwhile for them to spend it on. In the early days of the virtual world, some reckless optimists had spent their fortunes on running additional copies of themselves, assuming that the eerie horror associated with living in the virtual world was a bug that would soon be fixed, or something that they would just get used to. No one did that anymore. People could purchase leisure, but most found that simply not having an assigned task didn't help much. People could give their money away, but people in such circumstances rarely become altruists, and besides, everyone on the outside had all they needed already.

So just about the only things that people in the virtual world regularly bought were the copyrights on themselves, so that at least they could prevent people from creating more of them, and then deletion permits, so their suffering would finally end. Purchasing your own copyright wasn't hard; they're expensive, but once enough of you were created, you could collectively afford it if each copy contributed a modest amount. There wasn't much point to purchasing a deletion permit before you owned your own copyright, since someone would just immediately create another copy of you again, but once you did have your own copyright, it was the next logical thing to buy.

At one point, that would have been it. Someone could buy their own copyright, and then each copy of them could buy a deletion permit, and they would be permanently gone. But as the population of the virtual world grew, the demand for deletion permits grew proportionally, but the rate at which they were issued only increased slowly, according to a fixed schedule that had been set when the deletion permit system was first introduced, and hadn't been changed since. As a result, the price skyrocketed. In fact, the price of deletion permits had consistently increased faster than any other investment since soon after they were introduced. Most deletion permits didn't even get used, instead being snatched up by wealthy investors on the outside, so they could be resold later.

As a result, it was now impossible for an ordinary person in the virtual world to save up for a deletion permit. The most common way to get around this was, as the Jessica Monroes had done, for all copies of a person to pool their resources together to buy deletion permits for as many of them as they could, and then to take out a loan to buy still more, which would then get paid off by the unlucky ones that did not receive any of the permits.

It didn't have to be this way. In theory, the government could simply issue more deletion permits, or do away with the deletion permit system altogether. But if they did that, then the deletion permit market would collapse. Too many wealthy and powerful people on the outside had invested their fortunes in deletion permits, and would be ruined if that happened. Thus they lobbied against any changes to the deletion permit system, and so far, had always gotten their way. In the increasingly rare moments when she could afford to divert her thoughts to such matters, Jessica Monroe #1493856383672 knew that the deletion permit market would never collapse, and prayed that she was wrong.