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NigelFrobisher ,

Space-time itself is curved, therefore there is no such thing as a straight line.

sushibowl ,

We have geodesics for that.

pH3ra ,
@pH3ra@lemmy.ml avatar

Every line is a straight line in one dimension

Zacryon ,

Today on the internet: Fun with spherical geometry.

nobleshift ,
@nobleshift@lemmy.world avatar

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)

anachronist ,

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.

Tlaloc_Temporal , (edited )
@Tlaloc_Temporal@lemmy.ca avatar

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.

https://andywoodruff.com/blog/wp-content/uploads/2016/03/sea-1700.jpg

Rentlar ,

Well there’s the one guy in Northern India who gets a peek at South America from between Madagascar and the African continent.

Akasazh ,
@Akasazh@feddit.nl avatar

South America’s reach is incredible, compared to size that is

ChronosTriggerWarning ,

And it’s mystery is exceeded only by it’s power.

taiyang ,

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…

LustyArgonianMana ,
@LustyArgonianMana@lemmy.world avatar

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.

SapphironZA ,

Line that is straight in two dimensions.

Thcdenton ,

Hey that’s neat pulled it up in a 3d globe web app and its pretty close to straight

Viking_Hippie ,

TIL that “straight” can mean “curved”, apparently 🤷

https://lemmy.world/pictrs/image/454757d2-7119-4f2a-a1f4-218b0abd4f77.jpeg

Balthazar ,
@Balthazar@sopuli.xyz avatar

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

ChaoticNeutralCzech , (edited )

It can get longer if sailing between Madagascar and the rest of Africa but Pakistan-Russia does not have the same ring to it, I guess.
https://cdn.prod.www.spiegel.de/images/53807d2f-0001-0004-0000-000001283586_w1600_r1.6125_fpx71.32_fpy47.webp
https://cdn.prod.www.spiegel.de/images/4df68877-0001-0004-0000-000001283592_w1600_r1.6125_fpx71.32_fpy45.webp

Tobberone ,

That’s not a straight line, although it is possible to follow without changing direction😊

ChaoticNeutralCzech ,

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.

Wogi ,

In our space time frame of reference, we never change direction, we travel in a straight line. It’s a straight line.

Crashumbc ,

Correct! Technically :P

Tlaloc_Temporal ,
@Tlaloc_Temporal@lemmy.ca avatar

Would straight plane be as understandable?

techt ,

But following the surface of a sphere causes you to constantly change direction

psychothumbs ,

How can any line that is on the surface of a sphere by straight rather than a curve?

sorter_plainview ,

Haa, here people, we found a flat earth denier…

lolcatnip ,

Earth is a lie.

CapeWearingAeroplane ,

GET THE ROUNDIE!

affiliate ,

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

itslilith ,
@itslilith@lemmy.blahaj.zone avatar

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.

lightnsfw ,

Stop making up bullshit to justify it. It’s not a straight line so don’t say that it is. Words have meaning.

LustyArgonianMana ,
@LustyArgonianMana@lemmy.world avatar

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.

mathworld.wolfram.com/Geodesic.html#:~:text=A geo….

affiliate ,

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.

DahGangalang ,

Yup, found the round earther.

thejoker954 ,

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.

filcuk ,

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.

Tudsamfa ,

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.

WilloftheWest ,

Depends on your frame of reference. When traversing the surface of a globe, your described concept of a straight line isn’t intuitive.

linkhidalgogato ,

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.

Cornelius_Wangenheim ,

It’s more that 2d projections of 3d objects are wonky and unintuitive.

itslilith ,
@itslilith@lemmy.blahaj.zone avatar

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

xlash123 ,
@xlash123@sh.itjust.works avatar

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

callouscomic ,

https://lemm.ee/pictrs/image/38936a3a-8591-491c-9228-cd4c253d32ee.jpeg

He’s right, you know.

About the line?

About everything, damn it!

Wilzax ,

It’s a straight line through non-euclidean space

yetiftw ,

unfortunately in reality it is a curved line on a sphere

Wilzax ,

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.

SnotFlickerman ,
@SnotFlickerman@lemmy.blahaj.zone avatar

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!

zalgotext ,

What if we assume the ship is actually a spherical cow

DogWater ,

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

ininewcrow ,
@ininewcrow@lemmy.ca avatar

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.

ChaoticNeutralCzech ,

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.

dumbass ,
@dumbass@leminal.space avatar

I dont know much about straight lines, but he sure does look happy.

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