Line that is straight in two dimensions.
Today on the internet: Fun with spherical geometry.
I feel like this is related to the can’t measure the coast’ thing.
Like if you zoom in enough you are always traveling in a straight line.
You just discovered the field of calculus! If you look closely enough at any smooth function it looks locally linear, and the slope of that linear function is it’s derivative
Not quite what’s happening here, here the problem is if you consider geodesics on a sphere to be straight. In special geometry they are, for all intents and purposes, but in higher euclidian geometry they form large circles
It’s more that 2d projections of 3d objects are wonky and unintuitive.
I don’t know… straight, I would assume, means that I could walk or drive a vehicle and not turn at all, ignoring any external influences like waves and currents in this case.
But your vehicle would itself “curve” “downwards” due to gravity, surely a straight line means that you can point a laser, or a hypothetical 0 mass particle beam, uninterrupted from your starting point to your destination.
Depends on your frame of reference. When traversing the surface of a globe, your described concept of a straight line isn’t intuitive.
in ur every day life if u travel in a car without changing direction would u say that u went in a straight line or in an arc. Clearly u are just trying to be a pedantic cunt for no reason.
How can any line that is on the surface of a sphere by straight rather than a curve?
By defining the coordinate system as a sphere.
Basically, there are multiple right answers, but the most correct answer depends on how you define coordinates.
In “simple”, xyz it’s not a line.
In Euclidean geometry, a straight line can follow a curved surface.
In bullshit physics, everything is warped relative to spacetime so anything can or cannot be a line, but we won’t know.
Yup, found the round earther.
Haa, here people, we found a flat earth denier…
GET THE ROUNDIE!
Earth is a lie.
it’s a bit of a “spirit of the law vs letter of the law” kind of thing.
technically speaking, you can’t have a straight line on a sphere. but, a very important property of straight lines is that they serve as the shortest paths between two points. (i.e., the shortest path between
AandBis given by the line fromAtoB.) while it doesn’t make sense to talk about “straight lines” on a sphere, it does make sense to talk about “shortest paths” on a sphere, and that’s the “spirit of the law” approach.the “shortest paths” are called geodesics, and on the sphere, these correspond to the largest circles that can be drawn on the surface of the sphere. (e.g., the equator is a geodesic.)
i’m not really sure if the line in question is a geodesic, though
What is the slope of a straight line, a linear function? Now what is the slope of a nonlinear function, aka a curved line?
A geodesic would only be accurately labeled a “straight line” IF it was on a plane. On a curved or uneven surface it’s a nonlinear function.
i think it depends on what you mean by “accurately”.
from the perspective of someone living on the sphere, a geodesic looks like a straight line, in the sense that if you walk along a geodesic you’ll always be facing the “same direction”. (e.g., if you walk across the equator you’ll end up where you started, facing the exact same direction.)
but you’re right that from the perspective of euclidean geometry, (i.e. if you’re looking at the earth from a satellite), then it’s not a straight line.
one other thing to note is that you can make the “perspective of someone living on the sphere” thing into a rigorous argument. it’s possible to use some advanced tricks to cook up a definition of something that’s basically like “what someone living on the sphere thinks the derivative is”. and from the perspective of someone on the sphere, the “derivative” of a geodesic is 0. so in this sense, the geodesics do have “constant slope”. but there is a ton of hand waving here since the details are super complicated and messy.
this definition of the “derivative” that i mentioned is something that turns out to be very important in things like the theory of general relativity, so it’s not entirely just an arbitrary construction. the relevant concepts are “affine connection” and “parallel transport”, and they’re discussed a little bit on the wikipedia page for geodesics.
Thank you for the informative answer
This whole post is a good illustration to how math is much more creative and flexible than we are lead to believe in school.
The whole concept of “manifolds” is basically that you can take something like a globe, and make atlases out of it. You could look at each map of your town and say that it’s wrong since it shouldn’t be flat. Maps are really useful, though, so why not use math on maps, even if they are “wrong”? Traveling 3 km east and 4 km north will put you 5 km from where you started, even if those aren’t straight lines in a 3d sense.
One way to think about a line being “straight” is if it never has a “turn”. If you are walking in a field, and you don’t ever turn, you’d say you walked in a straight line. A ship following this path would never turn, and if you traced it’s path on an atlas, you would be drawing a straight line on map after map.
Stop making up bullshit to justify it. It’s not a straight line so don’t say that it is. Words have meaning.
You are absolutely correct, but to add on to that even more:
When we talk about space, we usually think about 3D euclidean space. That means that straight lines are the shortest way between two points, parallel lines stay the same distance forever, and a whole bunch of other nice features.
Another way of thinking about objects like the earth is to think of them as 2D spherical manifolds. That means we concern ourself only to the surface of the earth, with no concept of going below the surface or flying up into the sky. In S2 (that’s what you call a 2D spherical manifold), and in spherical geometry in general, parallel straight lines will eventually cross, and further on loop back and form a closed loop. Sounds weird, right? Well, we do it all the time. Look at lines of Longitude, for example.
We call the shortest line connecting two points in curved manifolds geodesics, as you said, and for all intents and purposes, they are straight. Remember, there is no concept of leaving the sphere, these two coordinates is all there is.
What one can do, if one wants to, is embed any manifold into a higher-dimensional euclidean one. Geodesics in the embedded manifold are usually not straight in higher-dimensional euclidean space. Geodesics on a sphere, for example, look like great circles in 3D.
Absolutly fantastic explination of how to conceptualize the complexities of geometry. Such an interesting area of mathematics
Dude that’s awesome. How did you make these images??
I didn’t, it’s from a spiegel.de article
That’s not a straight line, although it is possible to follow without changing direction😊
But following the surface of a sphere causes you to constantly change direction
Would straight plane be as understandable?
Correct! Technically :P
I KNOW IT’S BASICALLY A CIRCLE IN 3D SPACE. There is an exact amount of pedantry at play here, and you’re going over.
Would you say that they… crossed the line?!?! 😏😏😏
In our space time frame of reference, we never change direction, we travel in a straight line. It’s a straight line.
And when Im walking, in my frame of refrence, the houses on the side of the road move behind me.
Low IQ: it’s not a straight line
Medium IQ: it’s a geodesic on a sphere, so it is a straight line
High IQ: it’s not a straight line
He’s right, you know.
About the line?
About everything, damn it!
It’s a straight line through non-euclidean space
unfortunately in reality it is a curved line on a sphere
In actual reality there would be wind and water currents diverting any ship sailing that route from the depicted “line” anyway so the whole argument is pointless
The only straight line paths in the universe are followed by electrostatically uncharged non-accelerating objects in free fall in a vacuum. Or massless particles.
Nuh uh. My fifth grade math teacher told me that if I drew a line with an arrow on graph paper and no other line intersected it, that it would continue on into infinity!
Whole Universe eh? That exists and is bounded on a curved space time.
I’m just joking, but you can really take this to the extreme lol
Spacetime is curved. Inertial paths through spacetime are straight.
Euclidean space is not the only space where straight lines are possible.
What if we assume the ship is actually a spherical cow
Every line is a straight line in one dimension
THAT would be one god damn brutal sail. Both horns, Southern Atlantic crossing followed up by the Indian Ocean.
The range of foulies you would need to bring would be 3/4 of your pack. Foulies underwear and A sock (you’re going to lose one anyways)
I assume you mean “both capes.” While this line does come within a few thousand miles of the Horn of Africa, that’s not known as an especially hard sailing area but maybe for pirates.
Sailing this line in the other direction would be considerably harder.
Lolololol. Bro I’ve been around Africa in a 30 foot sailboat with an 8 foot draft. ‘Not hard sailing’ ? You have obviously never been on a boat at sea, let alone around either horns, capes, or whatever. Look up Shipbreakers, it’s a type of wave, then come tell me its not a hard sailing area.
Lololol GTFO of here with that bullshit.
Cmon man. Yes I’ve been a few places in sailboats. North sea in the winter for one. You clearly were trying to refer to Cape Horn and The Cape of Good Hope (or Cape Agulhas). Just take the L and don’t be a twat.
Ridiculous. This line is clearly gay.
This is bi erasure.
Not even 10 am and I’m being erased.
Never thought I’d get to use “bisectional” outside of JD Vance jokes
Saying that it’s bi erasure is gay erasure.
We claimed it is erasure first, and now here’s our flag.
Hey, you even have the eraser right there is the middle! I suppose that makes it convenient?
Lmao at the admission that the entire identity of being bi is claiming erasure and playing victim.
I really do love convenience!
This whole map is woke.
It’s bi sectional.
Why’d they go that way? They could have gone the other way and the line would have still been technically straight, but the route looks like it would have been shorter.
The picture was about sailing the longest direct line.
It’s not the longest anyway, but that’s what it was about. Technically one could sail infinitely many times around Antarctica in a straight line.
around Antarctica in a straight line
No, that’s not Earth’s great circle, you’ll be turning slightly. It only seems straight on most map projections.
It would, however, seem like a straight line to whoever was on the boat, because they’d be traveling due west the whole time, and the course corrections they’d have to make to keep going west would look the same as course corrections needed to account for wind, ocean currents, etc.
Well, I stand corrected. I guess we’ll need to wait for the ice on the North pole to melt before we can make a more stupid voyage.
Because going in that route would make it touch land which in the twitter post it says straight line without touching land
I’ve always thought Australia was a trouble maker.
What land would it touch?
India. You would have to set off somewhat perpendicular to the Indian coastline to be perfectly straight.
For some reason I don’t think this is true.
A straight line connecting two things does not necessarily have to connect to said things perpendicular to their border.
Not to mention, India’s coastline is very much not straight on a local scale. You’re bound to find a place where it turns perpendicular to the journey close to the theoretical starting point anyway.
Alaska, Canada, Russia, a few on the -stans.
This is the longest straight-line all-water route on earth.
*folds world map in half
*sticks pencil throughYou youngsters with your Einstein Rosen-bridges! Always in too much of a hurry to take the scenic route!
A straight line may be the shortest distance between two points, but it is by no means the most interesting.
-The Third Doctor, Doctor Who
Reminds me of the movie Event Horizon.
I honestly believe that sometimes, my genius, it generates gravity.
HYPERSPACE
Globists will argue that on a globe this is a straight line. Seen these arguments before, don’t work on me
Nice. Be proud.
Dunno what of, but be proud anyway!
Thanks! I’m very proud of seeing the truth. Watch this short video and you will being to understand. But watch it to the end, it’s short enough
Don’t know about other clients, but vger shows a thumbnail of the video
The ending really brings the whole video together. Thanks for sharing!
One of the most compelling arguments I’ve heard. I must say I was a skeptic before but this really opened my eyes
You know, I’d never actually thought of it that way. Very informative video for it’s short length. Thank you for sharing.
You’ve made a believer of me.
I’ve seen that video a hundred times and it never fails to disappoint
Got error: “Sign in to confirm that you’re not a bot”
Hmm, really makes you think…
Your dad and I think you should start looking for a job.
I can’t legally work in my country I’m not old enough
But still, don’t you hunger for the mines?
Toiling in the meme mines.
Edit: I have just finished reading The Neverending Story and this reminds me of the last part where Bastian works in the picture mines until he finds the right picture.
Fuck it
Eats the mines
There was a conversation I read a while ago that showed how a sailboat could travel a straight line over water from Halifax, Nova Scotia in Canada, travel southeast and end up on the west coast of British Columbia.
Basically sailing from the east coast of Canada to the west coast of Canada in a straight line.
The line was published by David Cooke in this YouTube video. It lies on a plane but is not quite a great circle (in practice, you’d be turning slightly) and good luck sailing over the Antarctic ice shelfs this decade.
Hey that’s neat pulled it up in a 3d globe web app and its pretty close to straight
