merc

The interesting thing is that these days the maps people most use are digital ones. They can be updated instantly for everyone who uses them. But, even in that world you have problems.

In many countries it's a legal requirement that the maps reflect the country's definition of its borders. That means that in some cases Google Maps has 3 versions of a map, the one shown to users in country X (say India), the one shown to users in country Y (say China) and the one shown to users in the rest of the world, where the border is marked as disputed.

Changing the electoral system means passing laws.

The people who pass laws are elected representatives.

The current electoral system works well for the current elected representatives (kinda by definition, because it's what got them elected).

So, the laws won't get changed because the people who have the power to pass the new law aren't going to pass a law that disadvantages them.

Case in point, the Liberal Party of Canada promised that if elected they'd reform the electoral system and get rid of first past the post. But, of course, FPTP is a massive advantage for the two main parties, the Liberals and the Conservatives. So, when they won the election, they quickly backed out of that promise. The only parties still promising to get rid of FPTP are the smaller parties who would have a big advantage if FPTP went away -- but, of course, these small parties can't win elections because of FPTP, so their promises to get rid of it are empty because they will never be in a position to make that change.

Do they have ultra-stylized versions too?

The French symbols are either pure black or pure red, they're symmetrical, and they're fairly abstract. The "diamond" is just a rhombus. The Spade and Club are fairly abstract shapes that don't look like anything in particular.

In the image, all the other versions are multicolored, and still seem to represent real-world objects. But, I'm curious if there are "modern" decks where say the coin (oro) is just a circle, or the club is just a long thin rectangle, or something.

Even just the map of the world is outdated pretty much by the time it's taught.

In 2023 Micronesia made a fairly minor change from the former name, "Federated States of Micronesia". But, in 2022 Turkey now wants you to use its metal name: Türkiye.

Then there's the new country of South Sudan, Bougainville on its way to splitting from Papua New Guinea. And Kosovo shows another problem -- whether its an independent country or not depends on who you ask. That includes regions like South Ossetia, Transnistria, Catalonia and Taiwan.

Then there are things that students are taught that we've known are wrong for over a century, but the fully correct version is too complex for anything below a university course. Like, Newton's laws are appropriate for high school, but they're known to be incorrect and are simplifications of Einstein's refinements. But, they're close enough for most purposes, and understanding Einstein's stuff is pretty hard. Same with models of the atom.

And, history is another subject where the deeper you dig, the more the generalizations you're taught are shown to be wrong. The names and dates might be the same, but the reason X happened is often a whole lot more complex than the simple reasons given in high school.

However many the AI decides to give me.

I’m saying that by the time the wheel is rolling, the plane’s is already moving forward

The wheels are attached to the plane, so they move at the same time. There's going to be slight flex due to rubber and metal not being insanely stiff, but essentially as soon as the plane starts moving forward through the air, the wheels start rolling forward along the ground. Since the conveyor belt cancels the forward movement of the wheels, the movement of the plane ceases too.

The plane would continue accelerating even as the wheels reported weird rates of turning.

Initially, for a few tenths of a second, or a few seconds sure. But, during that time, the conveyor belt would be moving faster and faster as it matched the speed of the wheels. The faster the conveyor moved, the more friction there would be, and the more drag there would be from that friction. Eventually you'd reach an equilibrium where the drag from the wheels was equal to the thrust from the engine, and the plane would cease moving forward. It would be exactly like the plane being anchored to the ground, except instead of a stationary anchor, the anchor would be a spinning treadmill in contact with a spinning wheel. In a world without a magic conveyor belt that could instantly adjust to the speed of the wheels, there would be some slight forward and backward movement of the plane, but that's just like being attached to an anchor with a bungee rather than a rigid rope.

an affixed anchor does not allow the free motion that a wheel would.

The wheel doesn't have free motion. By definition, the conveyor is moving at the same speed as the wheel, so the wheel is locked in place. With a real conveyor belt there would of course be some lag as the motors of the conveyor accelerated the belt, but using the hypothetical as defined, the axle of the wheel couldn't ever move because every rotation of the wheel would be matched by a movement of the conveyor belt.

And one of a few things happen. Either the plane has enough engine thrust to overcome the acceleration induced by the wheels, and therefore takes off, or it does not.

The thrust would have to be infinite because, by definition, the conveyor is always going to match the velocity of the wheels. If the wheels were truly frictionless, then the conveyor belt would have no effect at all. But, any real wheel will have some friction that will increase with speed, so there will always be some speed where the force backwards from the friction of the spinning wheels matches the force of the engine.

As an aside, my guess is that most real airplane wheels would probably fail pretty quickly at just double the normal takeoff / landing speed. The centripetal force acting on the spinning parts of the wheel and tire increase with the square of the velocity, so 2x as fast means 4x as much force. 3x as fast and 9x as much force. So, if you did this with a real wheel, you'd destroy the wheel pretty quickly. Of course, the same applies to the conveyor belt, but I'm going to assume that it's specially engineered to survive this challenge.

the wheels would continue spinning in increasing RPM until the plane begins moving backwards

The plane wouldn't move backwards because if the wheels slowed down, the conveyor belt would slow down too. Of course, that's in a world where the conveyor belt could adjust its velocity instantaneously, but for this thought-experiment you can say that if the pilot cuts the engine or something, the wheels don't spin as fast, so the conveyor belt slows down, and the plane remains in one spot.

eventually it would take off anyhow. because the airflow over the wings would still generate lift

In the thought-experiment world, there wouldn't be any airflow over the wings because the plane would be stationary. In reality, there would be some airflow due to the movement of the conveyor belt, but the wheels would probably melt long before that was enough air to give the plane lift while stationary relative to the world around.

So, it's not really a good use case of an LLM.

Just to clarify; you understand that because the engines are pushing on the plane itself and not the wheels, by the time the wheels start moving, the plane is already moving relative to ground and air alike.

The wheels are attached to the plane so they move at the same time as the plane. But, I get what you're trying to say, that the wheels are effectively being dragged by the plane, they're not powering the movement. But, what you need to think about is that if you oppose that dragging by moving the conveyor belt in the opposite direction you can prevent the plane from moving at all. Yes, the wheels are merely dragging and there isn't a lot of friction there, but friction increases with speed. And, if you move the conveyor belt fast enough, you can stop the plane from moving relative to the ground, which can stop it from moving relative to the air, which can prevent it from taking off.

An anchor sufficient to keep the plane from rolling forward is different because the force it is apply is significantly greater.

No, by definition it's the same. The conveyor moves with however much speed is necessary to stop the forward motion of the plane. The conveyor would eventually go so fast that it generated enough force to stop the plane from moving, so it's indistinguishable from an anchor.

Sure, you can deflate the tires and increase the rate of spin on the wheels.

You don't need to deflate the tires, you merely need to increase the speed at which the conveyor moves to match the speed of the wheels.

if we assume the wheels are indestructible, which I’d argue is only fair, then even if what you’re saying is true and we ramp up the drag induced by the wheels sufficient to counter the engines… then the wind generated by the rolling treadmill would be producing a sufficient headwind for the plane to take off

That seems like an unfair assumption because you're assuming that the conveyor belt has second-order effects on the air (i.e. generating a "wind" over the wings of the plane), while ignoring the second-order effects the conveyor would have on the wheels (massive heat from friction leading to failure).

On the other hand, this entire conversation assumes the thrust to weight ratio is less than 1. If it’s more than one, well they just…. Go straight up.

I mean, the discussion is of a plane, not a helicopter or a rocket. Even jet fighters with a thrust-to-weight ratio of more than 1 typically have engines that only have that ratio once they're at high speed, not from a standing start. That's why even fighter jets on carriers need a catapult-assisted takeoff. A VTOL aircraft like a Harrier wouldn't need that, but then its takeoff speed is zero, and the myth isn't very interesting when the conveyor belt doesn't move.

If the conveyor moves at the same speed as the wheels, it is exactly like attaching an anchor. That isn't the myth they were testing, but it's a more interesting myth.

it can’t do that through the wheels- the wheels can only apply a force equal to their rolling resistance and friction in its mechanics.

It can do that if it can spin the wheels fast enough. Picture the ultra-light airplane from the episode with big, bouncy wheels and a relatively weak propeller. If the treadmill was moving 1000 km/h backwards, that little propeller could never match the force due to rolling resistance from the wheels.

The tricky bit is that the air within a few millimeters of the treadmill will move with the treadmill. The air slightly above that will be slightly disturbed and also move a bit in the direction of the treadmill. If you had an extremely long and extremely wide treadmill (say the length and width of a runway) it's possible that the air at the height of the propeller would be moving along with the treadmill, rather than staying still, or moving with prevailing winds.

But, even in that case, the plane could still take off. All the plane needs to do is move the body of the plane through the air at enough speed to allow the wings to start generating lift. If the air at propeller-height is moving with a treadmill that is moving at take-off speed, the plane might take off with zero forward speed relative to the non-treadmill ground. But, as long as you're not somehow preventing the propeller from moving the plane through the air, the plane will always be able to take off.

There are videos of planes taking off by themselves in high wind, and videos of VSTOL (very short take-off and landing) planes taking off and landing using only a few metres of runway.

at what point does this become true?

It's always true.

A stationary aeroplane on a treadmill will obviously move with the treadmill

What do you mean? The plane has its parking brakes on and moves with the treadmill surface? If you don't have parking brakes engaged and start up a treadmill under a plane, the plane's wheels will spin and the plane will stay pretty much in one place. Because the wheels are free to spin, initially that's all that will happen. The inertia of the plane will keep it in place while the wheels spin. Over time, the plane will start to drift in the direction the treadmill is moving, but it will never move as fast as the treadmill because there's also friction from the air, and that's going to be a much bigger factor.

I assume an aeroplane moving at like 1 km/h still gets pulled backward by the treadmill.

Moving at 1 km/h relative to what? The surface of the treadmill or the "world frame"? A plane on a moving treadmill will be pulled by the treadmill -- there will be friction in the wheels, but it will also feel a force from the air. As soon as the pilot fires up the engine, the force from the engine will be much higher than any tiny amount of friction in the wheels from the treadmill.

but how does it get lift if it is prevented from accelerating from 0 to 1 km/h of ground speed

It isn't prevented from accelerating from 0 to 1 km/h of ground speed. The wheels are spinning furiously, but they're relatively frictionless. If the pilot didn't start up the propeller, the plane would start to move in the direction the treadmill is pulling, but would never quite reach the speed of the treadmill due to air resistance. But, as soon as the pilot fires up the propeller, it works basically as normal. A little bit of the air will be moving backwards due to the treadmill, but most of the air will still be relatively stationary, so it's easy to move the plane through the air quicker and quicker until it reaches take-off speed.

I think the confusion is that the conveyor belt is running at a fixed speed, which is the aircraft's takeoff speed. That just dictates how fast the wheels spin, but since the plane generates thrust with its propeller, the wheels just end up having to spin at double takeoff speed. Since they're relatively frictionless, that's easy.

The more confusing myth is the one where the speed of the conveyor belt is variable, and it always moves at the same speed as the wheels. So, at the beginning the conveyor belt isn't moving, but as soon as the plane starts to move, and its wheels start to spin, the conveyor belt movies in the opposite direction. In that case, the plane can't take off. That's basically like attaching an anchor to the plane's frame, so no matter how fast the propeller spins, the airplane can't move.