alt.hn

1/10/2025 at 11:10:56 PM

Very Wrong Math

 https://www.charlespetzold.com/blog/2025/01/Very-Wrong-Math.html

by breadbox

1/11/2025 at 6:11:04 AM

I have seen a very similar (incorrect) argument used to justify the idea of a flat earth. A builder on youtube made the argument (with a similar out of scale drawing of the earth) that if he drops a plumb bob and makes a right angle so he has a straight horizontal line and then goes across that line for a bit and drops another plumb bob, the two lines he has dropped are parallel, "proving" that the surface of the earth must be parallel to the horizontal line and therefore flat and not curved. If the earth's surface was actually curved he argued then the two lines he has dropped should tilt slightly inward towards each other. Which of course they do. The earth is just much much much bigger than in the diagram so the effect is within the margin of error for the measurement he was taking.

As a meta point, our intuition often fails us hilariously when we are dealing with stuff that is out of the scale we have commonly seen in our lives. We joke about LLMs hallucinating but I'm not convinced we are so superior when we are outside our personal "training data".

by seanhunter

1/11/2025 at 10:52:09 AM

The earth is just much much much bigger than in the diagram so the effect is within the margin of error for the measurement he was taking.

It's actually measurable on a human scale:

https://www.mathscinotes.com/2017/01/effect-of-earths-curvat...

1 5/8" difference over 693', or slightly less than 1 part in 5 thousand --- definitely measurable on a smaller scale with accurate machinists' tools.

by userbinator

1/11/2025 at 4:15:00 PM

One can also watch a boat leaving shore descend "under" the horizon with a telescope

by pvillano

1/11/2025 at 4:50:56 PM

You don't even need a boat or a telescope. Just watch the sun set on the ocean while lying down at the beach just in front of the water. The moment it disappears completely, stand up. You'll see part of it again. If you measure the time it takes disappear completely again and know your own height, you can even get a rough estimate of earth's radius.

by sigmoid10

1/11/2025 at 9:01:21 PM

Unless I'm picturing it wrong, wouldn't this still happen even if the world were flat?

by yen223

1/11/2025 at 7:46:50 AM

Ah, but would they actually be parallel on a flat earth?

Say the earth is disc-shaped. Then the center of gravity is only directly beneath you if you're standing at the exact center. You get ever-so-slightly not parallel lines, just like on a round earth.

The fun part of a disc-shaped earth comes as you move towards the sides, and gravity, still pointing towards the center, makes you stand at an increasingly acute angle to the surface. The ground beneath you will then appear like one big endless mountainside, with an increasingly steep slope the further away from the center that you get.

by munch117

1/11/2025 at 8:21:59 AM

Depends what causes things to stick to the flat Earth. IIRC flat earthers have various explanations for gravity, including the disc continuously accelerating upward; in that case you'd experience the same force everywhere on it.

by tempestn

1/11/2025 at 10:23:14 AM

If this mysterious disc-accelerating force also accelerated the people and things on the surface, we'd all be weightless.

I guess it must be a pushing force from below.

So, who's doing the pushing? I'm thinking a big turtle.

by munch117

1/11/2025 at 10:51:41 AM

They mean it is actually accelerating constantly.

My math might be wrong, but if we were accelerating at 9.8m/s/s for at least 4000 years (roughly as long as we have continuously recorded history and the minimum time “gravity” has been observed) then we ought to currently be traveling through space at over 1,000,000,000,000m/s.

Now I’m no physicist, but I reckon that might end up violating causality.

by nkrisc

1/11/2025 at 2:11:27 PM

Some of them think that.

The problem with trying to "explain" this is that fundamentally, flat-earthers, to the extent that they could be said to have a coherent world view at all, are usually a kind of occasionalist[1]. They don't _believe_ in natural laws or cause and effect. For the most part, they believe that god is in complete control of all events, and things go down because god wants them to go down. There's no required explanation for _anything_. The sun moves across the sky because god wants it to, and he could stop it or make it go backwards if he wanted it to, etc.

Indeed, that a flat earth is incompatible with physics is part of the appeal of believing in it to begin with. They _want_ to overthrow Newton, because a clockwork universe is incompatible with their belief system.

It's also sort of immune to any kind of argumentation. The result of any experiment is simply that god wants it that way, that they're predictable and testable doesn't _prove_ anything, because you can do an experiment a million times, and god could still cause it to fail any time he wants to. God just doesn't want to argue with Netwon right now, for his own reasons, you see.

1: https://en.wikipedia.org/wiki/Occasionalism

by empath75

1/11/2025 at 11:15:34 AM

Nah, when you move that fast, further acceleration stops increasing speed and starts squishing time instead, so you asymptotically approach C.

So I guess what I'm saying is I see absolutely no problem with the flat earth arguments?

by jbeninger

1/11/2025 at 2:36:58 PM

We should see this as all the celestial bodies traveling "down" at relativistic speeds by now. Unless maybe they are also experiencing 1 G in the same direction as us in addition to whatever other accelerations.

by plagiarist

1/11/2025 at 11:03:22 PM

I imagine whatever magical force has been constantly accelerating the disc Earth for 4,000+ years also magically accelerates everything else uniformly in the exact same direction, at the exact same speed, and also magically solves every other hole in the theory.

by nkrisc

1/11/2025 at 1:41:47 PM

Can’t argue with that, I guess.

by nkrisc

1/11/2025 at 12:00:39 PM

wait, is the flat earth theory going to make me immortal?

by bryanrasmussen

1/11/2025 at 12:02:19 PM

Only if you truly believe in it. Then you create a belive field, shaping your reality in any form you desire.

by lukan

1/11/2025 at 11:03:22 AM

The theological argument I recently heard is, the creator just made up and down. And things move down. But it is not gravity.

by lukan

1/11/2025 at 4:02:09 PM

> And things move down.

It's not a bad way to look at it for a start. Things move down because it is their nature to move downwards. And this kind of empirical law is what we rely upon for most thought.

It takes a lot of work to get to a theory that makes more general predictions.

And even after having that, 98% of the time my thought is effectively just "things move down." Another 1.5% it's "things move down at 9.8 m/s/s". It's an extreme edge/special case when I'm thinking "massive things are attracted to each other, with a force proportional to their masses and inversely proportional to the square of their distances".

And even with "massive things are attracted to each other, with a force proportional to their masses and inversely proportional to the square of their distances" ... if you ask me why, it's because "uh, they just do that?"

by mlyle

1/11/2025 at 6:46:30 PM

"with a force proportional to their masses and inversely proportional to the square of their distances" ... if you ask me why, it's because "uh, they just do that?""

To be fair, that is somewhat the current scientific consensus on gravity. It just is. We can meassure it and determine a general constant and calculate with it (and even though some people claim to have understood way more, it is highly debated terrain as far as I know)

And in general, I was actually arguing with flat earthers recently a lot, I even met a flat earther in real life. It is an interesting intellectual challenge debating them. Basically rebasing all the physical theory I have. (Main summary is, they have a high ego, but lack understanding of everything and make up for it with make believe.)

If I found a school one day, one of the lessons will be the teacher telling the students: "The earth is flat! Proof me otherwise." Or more advanced, model a flat earth on a computer. Flat earthers try that for real - it gets weird very quickly, so much that I could not believe anyone taking it serious and it all is just satire. But they are for real (but with a very different concept of reality).

by lukan

1/11/2025 at 6:53:45 PM

> To be fair, that is somewhat the current scientific consensus on gravity. It just is. We can meassure it and determine a general constant and calculate with it (and even though some people claim to have understood way more, it is highly debated terrain as far as I know)

Sure, and if we come up with some fancy unified theory, and ask "why" once more, the answer will still be "uh, because they do?."

> But they are for real (but with a very different concept of reality).

We think ourselves so advanced. I wonder what big counterfactual scientists believed in the 1900s and 2000s will be laughed at a few hundred years from now.

And, of course, some of that will be libel; e.g. that we thought the world was flat "just like Christopher Columbus's compatriots" [who didn't].

by mlyle

1/13/2025 at 10:28:28 AM

A huge thing about flat earthers is that they don't care if their explanations are self-consistent. They happily accept explanations for one thing that directly contradict their explanations for another thing.

by UltraSane

1/11/2025 at 2:47:45 PM

"A wizard did it"

by cratermoon

1/11/2025 at 10:39:02 AM

We can give them points for creativity.

by f1shy

1/11/2025 at 8:19:46 AM

Standard flat-earther response is to scornfully deny the existence of gravity. It's all density/buoyancy you see... Gravity is a hoax promulgated by the notorious cabalist Newton, in service to his Illuminati/Papal masters, etc, etc.

by thombat

1/11/2025 at 1:22:51 PM

Why do we still talk about these people? The more we stand in awe of their calculated ignorance, the more satisfied they are.

I feel like there are better things to do with my time than be as fascinated by it as some people.

by mp05

1/14/2025 at 1:19:08 PM

I periodically suffer the delusion that some of the nonsense-adjacent people may benefit from seeing that sensible answers can be found. Of course there's effectively no chance of reaching the proudly loudly ignorant, wearing their refusal of any good-faith discussion as a shibboleth, but perhaps their recruitment can be stayed.

by thombat

1/11/2025 at 1:50:07 PM

> and gravity, still pointing towards the center, makes you stand at an increasingly acute angle to the surface. The ground beneath you will then appear like one big endless mountainside

That’s why you never hear of people who went to the edge of that dis: they slid down that mountainside, and dropped off :-)

Alternatively, you can postulate that disc to be arbitrarily thick.

That will decrease the deviations. If that’s not enough to make them immeasurable, postulate that the stuff “deeper down” has higher density.

In the limit, just postulate that there’s an enormous black hole millions of light years below the center of the earth.

Flat-earthers probably won’t accept Newton’s theory of gravity, however, so you can make up anything.

by Someone

1/11/2025 at 12:55:03 PM

Even physicists have a hard time with disks and gravity. I can't tell you how many times I've seen them use the shell theorem on galaxies (does not apply). The only dark matter is in their head ;-)

by phkahler

1/11/2025 at 8:14:03 AM

I'm considering what flat-surfaced shape you could construct with equal gravitational pull at all points. Maybe something where the center is thin as a point, the edges have a lot of depth, and they curve towards the center either convex or concave. Might run some calculus to figure it out.

by jimmaswell

1/11/2025 at 9:01:52 AM

That way you should be able design a disc-shaped earth with constant strength of the gravitational force on the whole surface. But it would still have a center of mass (likely lying outside the shape you're describing, in the void beneath the center point), and the direction of the force should still be pointing towards that center, no? So the problem the GP has described, that you're starting to tilt as you move towards the edge, should remain in principle.

by t_mann

1/11/2025 at 10:17:48 AM

I believe the strength of gravitational force would not be constant either, as your center of mass would still have a fixed location, so every point on the disc have different distances to that center of mass (in addition to not being orthogonal to the surface). But maybe it might be approximated with an infinitely long cylinder, so the center of mass is infinitely far away below the surface ?

by benterris

1/11/2025 at 7:37:41 PM

The thinking in the other post, that the mass increases as you move away from the center, in a manner that the two effects cancel out, intuitively seems like it should be feasible. Remember that the center of mass is just an abstraction, you need to take the full integral over all mass to get the force vector at each point. And if you're closer to more mass further away from the center, which a shape like the one described above should give you, it might work. But one would have to do the math to be sure.

Edit: come to think of it, maybe that effect would let you adjust the direction of the force, too. Thinking about center of mass can be treacherous with more complex shapes...

by t_mann

1/11/2025 at 9:55:50 AM

yes, we call it a sphere.

I am just joking with you, I know what you mean, however the fruit was hanging too low not to pick.

by somat

1/11/2025 at 7:46:30 PM

A sphere is only locally approximable by flat surfaces, but it's nowhere actually flat, which was a requirement in the previous post.

by t_mann

1/11/2025 at 8:00:23 PM

Eh, the original post wanted a convex disk that would have a uniform gravitational pull, flatness was already thrown out as a design requirement. Once convex disks are allowed, a specific category of convex disk that provides a uniform perpendicular gravitational field comes to mind. The sphere. The very object we were trying to avoid. It is one of those it's funny because of the irony things.

by somat

1/12/2025 at 11:23:00 AM

The post clearly described a non-convex shape, and "flat-surfaced shape" should be a pretty clear instruction as well. The shape described may be visualized as a cylinder with a cone cut out, where the base of the cone aligns with one of the bases of the cylinder, and its tip with the center point of the other cylinder base. Except that the cylinder may be modified so that, seen in a cross-section, the line going from the base to the tip on either side may be a (convex or concave) curve. It makes sense as a starting point in the search for a shape with the desired properties. And it can immediately be seen to be non-convex in both described configurations, given that there's a cavity cut out.

by t_mann

1/11/2025 at 10:19:32 PM

You misunderstood, I mean for the top to be flat but the "underground" to have some kind of shape to compensate for the gravitational pull at all points on the flat surface. For a 2Dish example in the ballpark, you could think of one of these wooden toy bridge blocks: https://thumbs.dreamstime.com/b/natural-wood-blocks-364582.j...

I think you could construct a curve such that the mass's gravitational pull on the right cancels out the pull on the left, for any point on the surface.

by jimmaswell

1/11/2025 at 12:17:56 PM

Doesn't the flat earth extend infinitely in all directions?

by rendaw

1/11/2025 at 3:49:49 PM

"We joke about LLMs hallucinating but I'm not convinced we are so superior when we are outside our personal "training data"."

In all seriousness one of the things about LLMs that most impress me is how close they get to human-style hallucination of facts. Previous generations of things were often egregiously and obviously wrong. Modern LLMs are much more plausible.

It's also why they are correspondingly more dangerous in a lot of ways, but it really is a legitimate advance in the field.

I observe that when humans fix this problem, we do not fix it by massive hypertrophy of our language centers, which is the rough equivalent of "just make the LLM bigger and hope it becomes accurate". We do other things. I await some AI equivalent of those "other things" with interest; I think that generation of AI will actually be capable of most of the things we are foolishly trying to press hypertrophied language centers into doing today.

by jerf

1/11/2025 at 11:08:27 AM

> We joke about LLMs hallucinating but I'm not convinced we are so superior when we are outside our personal "training data".

Every time I see the phrase "common sense", I expect to see an example of the human failing you describe.

by ben_w

1/11/2025 at 2:45:59 AM

Related Wikipedia article: https://en.wikipedia.org/wiki/String_girdling_Earth#Implicat....

The takeaway is that the extra length of the arc is likely much smaller than one would intuitively expect. The problem is usually framed like so: If you wrapped a rope around the earth, how much more rope would you need to add so that it would be 1 meter above the ground at all points? The answer is only 2π meters!

by BalinKing

1/11/2025 at 5:11:54 PM

> The takeaway is that the extra length of the arc is likely much smaller than one would intuitively expect.

Maybe it’s because I’m a pilot and we never account for altitude when measuring distance, my intuition puts the difference at “effectively zero”. I also have it internalized that the earth’s atmosphere is very thin.

by travisjungroth

1/11/2025 at 6:59:32 AM

This could be why dimensional analysis is one of the few things from physics class that can't be drilled enough..

Without forcefully dumping the geometric "intuition", this would still feel counterintuitive to me!

by gsf_emergency

1/11/2025 at 3:23:07 AM

(2pi * (n + 1)) - (2pi * n)

-> 2pi * (n + 1 - n)

-> 2pi * 1

-> 2pi

If I remember my algebra correctly. Someone else check my work I'm a dropout

by shortrounddev2

1/11/2025 at 4:22:43 AM

For convenience, we set τ=2pi. :-)

x = τ(r+1) - τr = τ(r+1-r) = τ(1) = τ

by freeopinion

1/11/2025 at 6:30:30 AM

How do you pronounce that symbol?

by shortrounddev2

1/11/2025 at 3:35:54 AM

The only issue I see with this is that as a classic physics trope, we've approximated the earth as a sphere.

If, instead we approximate it as a fractal... then the distance is infinite, or at least highly dependent on the thickness of the rope!

The error in the original is assuming that the radius is proportional to the height above the earth (Earthradius=0?).

by kurthr

1/11/2025 at 6:03:06 AM

We actually model the earth as a very large spherical cow. This is approximately the same for most purposes but ends up being more convenient.

P.S. Not a physicist, but my child is studying maths and physics at Uni at present, so I have it on good authority that this is still going on. They told me in their first week one of their classes had a worked example where the lecturer used the phrase "Assume the penguin's beak is a cone".

by seanhunter

1/11/2025 at 10:23:44 AM

> I have it on good authority that this is still going on

Do you mean making simplifying assumptions to make a problem tractable? Of course it’s still going on. It has to be, otherwise you just cannot do anything.

> Assume the penguin's beak is a cone

It is impossible to consider the true shape of a penguin’s beak for several reasons:

- you’d need to go all the way down to the electron clouds of the atoms of the beak, at which point the very concept of shape is shaky

- every penguin has a different beak so even if you describe perfectly one of them, it does not necessarily make your calculation more realistic in general.

There is a spectrum of approximations one can make, but a cone is a sensible shape at a first order. It’s also simple enough that students can actually do it without years of experience and very advanced tools.

What do you think they should do instead?

by kergonath

1/11/2025 at 10:49:34 AM

Bet you’re fun at parties as they say.

I totally understand why simplifying assumptions are helpful in modelling and definitely don’t need you to explain that. It also is a bit ridiculous if you think literally about it which makes it something that is fun to laugh about as here.

by seanhunter

1/11/2025 at 11:32:54 AM

Yes, sure, I get the jokes. I just found it puzzling that someone would think it stopped.

And I don’t talk about work at parties anyway :)

by kergonath

1/11/2025 at 1:55:17 PM

But nobody in this thread thought it (simplifying assumptions) stopped. You seem to be making an assumption that someone thought that and then posting long explanations that nobody asked for. I read the "P.S." of grand-grand-parent comment as good humor. Nothing there implied that they really thought that simplifying assumptions would/should stop.

Imagine a world where every bit of humor is interpreted literally and then refuted pedantically! What kind of a world would that be?

by eminent101

1/11/2025 at 9:10:11 AM

A spherical cow /in vacuum/

by davrosthedalek

1/11/2025 at 3:45:30 AM

> infinite, or at least highly dependent on the thickness of the rope

The latter. But that's only if it's not somewhat taut. Some tension brings it closer to a circle and makes the actual thickness pretty unimportant.

But I like the idea overall. It means that lifting up the string makes it smoother and it actually needs less length. How's that for being unintuitive?

by Dylan16807

1/11/2025 at 3:59:56 AM

Exactly, if you're only 1cm off the surface you follow every nook and cranny. If you're 10km off the surface only Everest is a blip.

by kurthr

1/11/2025 at 8:07:54 AM

Just because your initial fractal path is infinite does not imply that a line offset from it is also infinite (even for an infinitely thin rope), at least if the offset version is not self intersecting.

by aardvark179

1/11/2025 at 6:47:48 AM

Even if the math of the arc length was correct (and you don't need to be a math professor to figure out it isn't) there's another logic misstep.

Implied in the caption is that the speed is the same at all heights (given that an increase in distance is implied as an increase in time.)

This is again obvious nonsense - speed is a function of thrust versus drag, and it's safe to say that both of those are affected by air density.

It becomes even less true once one gets to space. There height is a function of speed which means that to "catch up" something in front of you, you need to slow down.

by bruce511

1/11/2025 at 7:15:26 AM

> It becomes even less true once one gets to space. There height is a function of speed which means that to "catch up" something in front of you, you need to slow down.

Can you expand on this? My brain is not connecting the dots.

by mastermedo

1/11/2025 at 7:31:38 AM

He is talking about orbital mechanics, rather than free space. When you are in an orbit, the shape of the orbit is determined by your speed. At every distance from the center of the object you are orbiting (such as the Earth), there is a speed that makes your orbit a circle. If you are going at any other speed then your orbit will be an ellipse instead. Too fast and your orbit rises higher above the Earth. Too slow and it dips back down closer to it. If you try to “catch up” with an object ahead of you in your orbit by speeding up you will only turn your orbit into an ellipse that gets further away from the Earth, and thus further away from the object you were trying to catch. Instead of catching it you’ll go up and over it. As Niven wrote, “forward is up, up is back, back is down, and down is forward”. It’s rather counterintuitive at first. Playing KSP can help you get a feel for it, especially once you start docking multiple craft together.

by db48x

1/11/2025 at 9:19:05 AM

It’s even worse than that. By speeding up you end up actually getting further behind your target because in your new higher orbit you actually move slower on average, and as your average orbital radius gets longer, so does the circumference, so you end up on a "detour" trajectory compared to your target!

Whereas if you slow down, you drop to a lower, shorter, higher-speed orbit.

by Sharlin

1/11/2025 at 9:14:25 AM

Just to point out here what's different between "space" and "not space": "Space" assumes no "height control",i.e. ways to exert force "down or up" along the earth-object direction. That's obviously not true for a plane. If you can exert force in that direction, you can change speed and keep the shape of the trajectory around earth constant.

by davrosthedalek

1/11/2025 at 8:50:51 PM

Wait, why wouldn't an orbiting satellite not be able to apply its thrusters "down"?

by falcor84

1/12/2025 at 8:19:59 AM

They could. The point is that if you allow for that (and it they would need to be constant on), the more speed -> either higher orbit or more elliptic orbit doesn't hold. But no satellite has enough fuel to keep its thrusters on indefinitely.

by davrosthedalek

1/11/2025 at 9:22:02 AM

This is called Kepler's Third Law, right? Radius^1.5 :: Period

by nyc111

1/11/2025 at 10:26:14 AM

You are literally going way and beyond what the target audience of that post (the original with bad math) was for.

by f1shy

1/11/2025 at 8:54:34 AM

I think the funny thing about this article is this numeric error (though not so egregious as the one that caused the article!):

> The mean radius of the earth is actually 3,459 miles or over 18 million feet.

That’s off by 500 miles; the correct figure is 3,959 miles. That makes it almost 21 million feet, and yields a ratio of about 1.0013378, even smaller than the quoted 1.0015.

by chrismorgan

1/11/2025 at 10:30:07 AM

Don't know if anyone mentioned this yet, but presumably the flight path does not follow a normal vector to gain height, but generally something more diagonal in the direction of travel.

by n4r9

1/11/2025 at 9:31:38 AM

One question I've always had with this: How does the rotation of the earth affect an airplane's flight time, if any? And how does this change with altitude?

by prmph

1/11/2025 at 10:30:38 AM

Simple answer: Zero. Because the planes move inside the atmosphere, which moves with the earth.

A more nuisance would be that earth rotating generate all sorts of things in the atmosphere, including winds and Coriolis effect on the winds, and you can account for that considering the winds. Btw a flight from Chile to France and back, will have a leg significantly shorter (up to 2 hs in a 13hs flight) and which leg it is, depends on the time of the year.

by f1shy

1/11/2025 at 12:18:01 PM

Interesting to know about the Coriolis effect.

I get that what really matters is the relative motion, but it still seems to me that there might be a gravitational/inertial effects at play, even if tiny.

Consider this thought experiment: Planes cannot really fly into space, but assume they can. At a certain altitude, it cannot be said the the plane is moving perfectly in step with the gravity of the earth. At infinite altitude, that certainly cannot be the case.

So that tells me there is some deviation due to the inertia of the plane, even at low altitudes. Like I said, the effect might be tiny, but would be interesting to learn more about it nonetheless.

by prmph

1/11/2025 at 12:31:55 PM

I meant coriolis effect on the wind. Not sure if noticeable in a plane.

by f1shy

1/11/2025 at 11:23:52 AM

In general, the air moves with the ground, so the earth's rotation does not affect airplanes.

However, rotation of the earth imparts a coriolis force on the air, which results in jetstream winds. Aircraft routes are optimized to use/avoid jetstreams for shorter travel times.

by Derbasti

1/11/2025 at 10:30:15 AM

It does not really, at least not directly. What matters is relative velocity compared to the starting and final locations, and relative to the air around the aircraft. It just happens that there are very powerful atmospheric currents that go west to east (those are due to the earth’s rotation, among others phenomena).

So, when flying towards the east, catching these currents can significantly reduce flying time. When flying towards the west, we want to avoid them by flying below or elsewhere.

by kergonath

1/11/2025 at 12:24:04 PM

Thanks for this explanation; quite interesting.

But it still seems to me that there might be a gravitational/inertial effects at play as well. At a (hypothetical) infinite altitude, it can no longer be said the the plane is moving perfectly in lock-step with the gravity/rotational acceleration of the earth. This implies the inertia of the plane relative to the rotation of the earth still has an effect at lower altitudes.

The effect might be tiny, but would be interesting to learn more about it nonetheless.

by prmph

1/11/2025 at 8:22:01 PM

What gravity/rotational acceleration ?

Something like this does exist under general relativity :

https://en.m.wikipedia.org/wiki/Frame-dragging

However,

> This does not happen in Newtonian mechanics for which the gravitational field of a body depends only on its mass, not on its rotation.

by BlueTemplar

1/11/2025 at 9:27:30 PM

Yes frame-dragging seems to be the name of the concept I was thinking of. Cool.

by prmph

1/11/2025 at 11:10:58 AM

I would do it like this:

Approximate Earth as a flat line. (The 5000ft path is close enough that it is also represented by the flat line. This is the 5000ft path.)

Then make the 33000ft path which is a slightly looser line on top of this line.

This new path is not 4 times longer. Just a little bit raised, because 33000 ft is “nothing” compared to Earth. (To become 4x longer we would go deep into outer space and back.)

by lynguist

1/11/2025 at 8:28:11 AM

just 2piR and then extra h change the result very little fraction. How is that counter-intuitive :)

by syntex

1/11/2025 at 11:08:00 AM

Seems intuitively obvious. On a flat Earth the two distances would be the same, and while the Earth isn't flat, its close enough to approximate a flat surface for most purposes, so you'd expect the differences in the two arcs to be ~0

by simplicio

1/11/2025 at 10:49:59 AM

Does "Remember the high you go the further it'll have to travel" really need to be debunked? Did the "design and construction firm" spell "drill" with one "l"?

by pessimizer

1/11/2025 at 5:34:07 PM

Earth in the picture is scaled to roughly 300,000 feet per pixel; Earth's surface and both flying altitudes would be the same pixel if drawn to scale.

(~42M feet diameter shown in ~134 pixels).

by jodrellblank

1/11/2025 at 5:28:46 AM

Curious, does the air being thinner affect flight time?

by kubb

1/11/2025 at 6:10:10 AM

There's no straightforward answer because there are many factors that affect flight time and fuel economy, including the aerodynamics of the plane and the engine technology. I hazard a guess that for commercial airplanes these are chosen primarily for reasons of fuel economy per seat and then that determines the model's designated cruising altitude.

For a particular model, flying above the model's cruising altitude should lead to lower fuel efficiency.

by jhanschoo

1/11/2025 at 6:14:57 AM

From what I've learned reading AdmiralCloudberg's plane crashes analysis [1]: altitude heavily matters in fuel consumption. Jet planes use a lot less fuel at a higher altitude, up to the point that a plane on the verge of running out of fuel at a medium altitude might manage to squeeze in 50 or 100 more miles of flight by climbing 5000 feet, even accounting for the increased fuel consumption during climb. I guess that correlates with speed as well. Turbofan engines, on the other hand, are more fuel efficient than jet engines at lower altitudes, hence they remain common for interstate transit. The difference seems to be directly caused by the effect of air "thickness" on the engines.

[1] https://admiralcloudberg.medium.com/

by aja12

1/11/2025 at 5:47:50 AM

I think in a way that’s why planes fly so much further up than you’d think they’d need to. They want more consistent and minimal atmospheric conditions. Less air means less energy means less turbulence, I think?

If you’re talking about friction… oooh that’s an interesting one. Intuitively yes. But is it also negligible?

by Waterluvian

1/11/2025 at 10:41:53 AM

Yes, because friction depends on the air density. You can think of this as the molecules in the air colliding with a moving object and pushing it backwards, thus slowing it. If there are fewer molecules, there is less friction and the object can move faster with the same thrust.

Thrust itself decreases because there are also fewer molecules to push against, so it can get quite complicated if you want to account for everything. But overall it is easier to fly faster higher up in the atmosphere. Also, atmospheric currents are important.

There is a useful discussion here: https://aviation.stackexchange.com/questions/57209/how-does-...

by kergonath

1/11/2025 at 11:31:26 AM

"the high you go" reinforces my initial assumption that this is self-filtering clickbait.

by wittjeff

1/11/2025 at 4:24:59 PM

All models are wrong, but some are useful. ⇒ Some models are wrong and useless.

by 1970-01-01

1/11/2025 at 4:09:04 PM

Charles Petzold.. His c++ book stood on the shelf behind me. 30y ago. heh :)

by svilen_dobrev

1/11/2025 at 6:23:09 PM

Holy crap is one drop of stupid consuming a lot of mental energy. This is after the drop of stupid that was Terence Howard's "1 x 1 = 2" physics rant fell on everyone's head. Individual drops quickening into rain would drown us all, apparently. Do serious people like Charles Petzold (here) and in other venues address this stupid out of fear that the stupid spreads, or because they just can't stand someone being wrong somewhere like a cognitive itch that must be scratched? If one troll flooded the zone with 30 of these over a month, mayhem would ensue. Absent knowing the true origin for this diagram, we don't even know if was stupid or malicious.

by quantified

1/11/2025 at 6:32:53 AM

And of course pi = 22/7! ;)

by teo_zero

1/11/2025 at 8:17:23 AM

That's actually a lot closer to the actual value of pi than the implied difference in the article vs the 0.15% actual difference in path length.

As in, the illustration would be less wrong if it only used 22/7 for Pi and correctly portrayed dimensions of Earth and flight heights.

by necovek

1/11/2025 at 5:13:00 AM

Are we talking spacetime?

by nejsjsjsbsb

1/11/2025 at 4:41:27 PM

i've seen that exact image posted semi-regularly on various reddit and facebook groups. (it's one of 500 things i hate about those sites. but for some communities that's where the information lives, that's where marketplace lives, etc., so i'm stuck with it)

these kind of things are intentionally wrong "puzzles" that are designed to get hundreds of people mad and post rebuttals to "drive engagement" or whatever. the pictures of a wheel with sledgehammers and chains and jacks with lugnuts plainly still in place and a post "how can i get this off it's stuck and i've tried everything". sigh... it's just another form of trolling.

sure enough, notice the sibling comments here. how many nice people took the time to patiently explain the fallacy(ies) for the 1000th time. then the pedants who correct the grammar/math/etc. in the 98% correct explanations. then the "true believers"/trolls who don't get it and argue back. and so on.

https://xkcd.com/386/

by fargle

1/11/2025 at 5:16:11 PM

haha crazy

by juresotosek

1/11/2025 at 2:43:39 PM

[dead]

by JimmyWilliams1

1/11/2025 at 9:48:46 AM

[dead]

by 752963e64

1/11/2025 at 3:05:10 PM

xkcd.com/386

by mppm