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.
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?”
“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.
4 thoughts on “Why The Apple Falls”
“If you look closely, the pebbles curve a bit to the West as they fall.”
I think they should curve to the East, and that most of the directions mentioned in this story are reversed.
In this story, I think the world is spinning in the same direction as the Earth. The sun rises in the east. This is because the earth is spinning. So we are traveling eastward. The crust of the earth (at the equator), and the people sitting on it, are traveling east at a rate of roughly 25k miles every 24 hours (the earth’s radius being roughly 4k miles). If you imagine someone sitting on top of a pole (pointing out from the equator) another 4k miles high, still revolving with the earth once every 24 hours, they would be traveling more like 50k miles per day—hence they’re traveling east twice as fast as you. Now, if you imagine jumping up 4k miles from the surface (without changing eastward momentum), it becomes obvious that you would fall behind the pole’s eastward movement, and hence someone from the ground would see you going westward. Conversely, if you imagine sitting on the pole, and then suddenly zooming downward close to the ground (again without changing eastward momentum), you’d be traveling east twice as fast as the ground, and obviously be seen to move east.
Pebbles falling down should follow the second case and go east. The painted rope getting yanked up, meanwhile, should go west.
As for throwing spears, if we ignore air resistance (not sure if that’s the right idea), someone on the ground who throws a spear upward and in some direction will have the spear temporarily “fall behind the ground’s eastward travel” while it’s up high, and hence fall farther west than a flat earth would suggest. Technically, the spear was launched from “arm level” and not “ground level”, so there will also be a period between when it falls down to “arm level” and when it hits the ground, during which it will travel east more quickly; but for serious spear throws, it would spend much more time “above arm level” than “between arm level and ground”. Therefore “it’s easier to throw West” remains correct.
The characters live on the inside surface of a rotating body, not the outside. The effect on the position of the spear from the fact that it spends most of its time in the air above the point it was thrown from should move the spear slightly East, but this effect is probably much smaller than the effect of the fact that a spear moving East is rotating around the center of the world faster, so it moves away from the center of the world (downwards) faster, making it harder to throw the spear East.
Ohhhhhhhhhh. Wow. That thought did not occur to me. In retrospect, some of the phrasing near the start of the story hinted at that, but I interpreted them variously as “odd ways of stating things about our solar system” or “character being stupid” and dismissed the oddness.
I believe a uniform spherical shell will have net zero gravity on the interior. (Whether it is actually uniform is not established, but let’s run with it…) All “gravity” is consequently due to centrifugal force. If someone walked up to the “north pole”—one place where the axis of rotation intersects the ground—then they’d be effectively weightless, with neither force nor momentum pinning them to the ground, and they could jump towards the sun or anything if they wanted. This would go for inanimate objects, too. What would be the tendency of objects…
Actually, for anything that is sitting on the ground of the world, and not at the equator, centrifugal force (/momentum) presses it directly outward from the axis, and the ground presses back perpendicular to the ground, implying the net force is towards the equator. Everything would roll down into the equator. In which case, if there’s a substantial amount of dirt or something that’s not rigidly part of the spinning body, then that would collect at the equator. The stable thing is if the “ground” is close to cylindrical (again, apart from any rigid thing). If that‘s the case, then you can walk parallel to the axis of the cylinder, and move towards or away from the sun (unless the sun is a line).
Next we ask whether the ends of the cylinder are visible to the inhabitants, and, if so, what they see…
I was picturing the sun being a thin cylinder. The narrator mentions not being able to see anything spinning, so the ends of the cylinder are probably opaque.