The line war has begun
The line war has begun
The line war has begun
It can get a few percent longer if sailing between Madagascar and the rest of Africa but Pakistan-Russia does not have the same ring to it, I guess.
That's not a straight line, although it is possible to follow without changing direction😊
Dude that's awesome. How did you make these images??
I didn't, it's from a spiegel.de article
Today on the internet: Fun with spherical geometry.
This reminds me of some maps by Andy Woodruff.
They weren't made to find long lines, and picking out a single line can be a tad difficult, but it's very interesting nonetheless.
South America's reach is incredible, compared to size that is
And it's mystery is exceeded only by it's power.
Well there's the one guy in Northern India who gets a peek at South America from between Madagascar and the African continent.
There is also just the one straight path from the US east coast (Florida) to Asia.
How can any line that is on the surface of a sphere be straight rather than a curve?
Haa, here people, we found a flat earth denier...
Earth is a lie.
GET THE ROUNDIE!
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 A
and B
is given by the line from A
to B
.) 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
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.
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.
Stop making up bullshit to justify it. It's not a straight line so don't say that it is. Words have meaning.
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.
Space-time itself is curved, therefore there is no such thing as a straight line.
Not true, as when space bends, it bends the rulers and compasses too. We experience no spatial distortion.
A person traveling near the speed of light doesn't feel like time is slower for them (but it is and we can measure it)
The principle is equivalent.
That said, it's not a straight line in any topology standard I am aware of.
Sure you could CREATE a topology framework where this would be considered a straight line, but there is no real world model that could come even close without so much mass being concentrated in static relative areas, and EVEN THEN it would only be straight for a predetermined instant before the mass deforming spacetime began interacting with each other.
That's the problem with spacetime deformations, almost no layman takes into account the ridiculous amounts of static mass to make those strange topologies.
Space-time itself is curved, therefore everything is moving in a straight line, it only appears to be curved to the outside observer
We have geodesics for that.
If anyone wants to grasp the basics: here is some fun reading (leading on to some beautiful math). Changing the idea of parallelity leads to hyperbolic geometry and other fun stuff. :)
Please correct my layman understanding if I'm wring here. But isn't everything traveling in a straight line until an external force is applied. For example the earth orbiting the sun is traveling in a straight line in a curved apacetime. Also if you jump, the moment you leave the ground until you touch it again coming back down you were traveling in a straight line.
I dunno lol
Also if you jump, the moment you leave the ground until you touch it again coming back down you were traveling in a straight line.
relative to the body of earth, including its rotation it would be an arc path, and including it's tilt it would be 3d, if we also include the travel around the sun in orbit, that elongates it around the orbit, so uh.
In my understanding, since gravity is acting on us, an external force is applied when we jump. That's why a jump is a parabola. "Gravity's Rainbow"
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
Every line is a straight line in one dimension
Would clarifying words have helped? "If you only sailed with forward force..." or "Following along the surface of the earth..." or... what?
Obviously they mean that you don't need to make any turns and that straight means an arc around the earth and not through the Earth, unless someone has a very different idea what sailing means...
Depends on what you mean by help. Yes, it would communicate the point better, but it's engagement bait, so the ambiguity is a feature rather than a bug.
Yes I think they mean it's a continuous line, not a "straight" line. As in the line is uninterrupted (continuous). It's also possible they mean the line qualifies as a nonlinear function since it also doesn't double back over itself (A function is a relationship where each input value (X) will create only one output value (Y)).
Math is hard. Describing lines like this is math - calculus actually due to the curve, and actually not just basic calculus but vector calculus because it involves an x,y, and z axis. Most laypeople will struggle to describe a line with the correct jargon.
Line that is straight in two dimensions.
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)
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
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
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.
It's more that 2d projections of 3d objects are wonky and unintuitive.
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 because they want latitudes to be horizontal.
I dont know much about straight lines, but he sure does look happy.
To clarify, as youve not understood the joke, nor read the comments. As far as I understand it, were you to start sailing at the first point, you never have to turn to arrive at the second. That's why it's "straight". On the 2d plane you are completely correct however.
For proper and better informed explanations read the other comments :D
*folds world map in half
*sticks pencil through
I honestly believe that sometimes, my genius, it generates gravity.
You youngsters with your Einstein Rosen-bridges! Always in too much of a hurry to take the scenic route!
HYPERSPACE
Reminds me of the movie Event Horizon.
And like 5 million other movies