Slashdot Mirror
The Longest Straight Path You Could Travel On Water Without Hitting Land (gizmodo.com)
An anonymous reader quotes a report from Gizmodo: Back in 2012, a Reddit user posted a map claiming to show the longest straight line that could be traversed across the ocean without hitting land. Intrigued, a pair of computer scientists have developed an algorithm that corroborates the route, while also demonstrating the longest straight line that can be taken on land. The researchers, Rohan Chabukswar from United Technologies Research Center Ireland, and Kushal Mukherjee from IBM Research India, created the algorithm in response to a map posted by reddit user user kepleronlyknows, who goes by Patrick Anderson in real life. His map showed a long, 20,000 mile route extending from Pakistan through the southern tips of Africa and South America and finally ending in an epic trans-Pacific journey to Siberia. On a traditional 2D map, the path looks nothing like a straight line; but remember, the Earth is a sphere.
Anderson didn't provide any evidence for the map, or an explanation for how the route was calculated. In light of this, Chabukswar and Mukherjee embarked upon a project to figure out if the straight line route was indeed the longest, and to see if it was possible for a computer algorithm to solve the problem, both for straight line passages on water without hitting land or an ice sheet, and for a continuous straight line passage on land without hitting a major body of water. Their ensuing analysis was posted to the pre-print arXiv server earlier this month, and has yet to go through peer review. "There would be 233,280,000 great circles to consider to find the global optimum, and each great circle would have 21,600 individual points to process -- a staggering 5,038,848,000,000 points to verify," the researchers wrote in their study.
Anderson didn't provide any evidence for the map, or an explanation for how the route was calculated. In light of this, Chabukswar and Mukherjee embarked upon a project to figure out if the straight line route was indeed the longest, and to see if it was possible for a computer algorithm to solve the problem, both for straight line passages on water without hitting land or an ice sheet, and for a continuous straight line passage on land without hitting a major body of water. Their ensuing analysis was posted to the pre-print arXiv server earlier this month, and has yet to go through peer review. "There would be 233,280,000 great circles to consider to find the global optimum, and each great circle would have 21,600 individual points to process -- a staggering 5,038,848,000,000 points to verify," the researchers wrote in their study.
Or you could use a nice globe and a piece of string.
If you think I voted for Trump because of this post, you're wrong. I voted for Dr. Jill Stein of the Green Party. Again.
As straight as you can get on a sphere, anyway.
Or, expressed differently: start sailing in a particular direction, and do not deviate left or right from that (locally) straightline path until you hit land again.
% that bitch and BAM! Traveling Salesman Problem solved!
It took me a few seconds to see how the path shown on the map is straight. Sure, straight lines on the Earth will look curved on a map, but that path heads very much South, then turns and heads very much North. How can that possibly be straight?
Then it dawned on me. If you're near the South Pole and you head South, toward the pole, then keep going PAST the South Pole, you'll be headed North - all the while going straight.
Where the path goes South of South America, it's near the pole. What looks like a turn North is actually going straight across Antarctica and up the other side.
It is the longest path along a geodetic line. Not a straight in 3-D space.
Huh? If you look at TFA, the line clearly has an endpoint on the western edge of the Indian subcontinent, and does not approach western Europe at all..
Wouldn't 5 trillion comparisons take only about 2000 seconds on a modern processor, even without multithreading or SIMD optimizations?
Man, some people will do *ANYTHING* to avoid Russia!
I should have said the path goes "straight past Antarctica", rather than "straight across Antarctica".
As you head South, as you pass Antarctica you're suddenly heading North, without ever turning.
The longest great circle route they found on land is like the one Christopher Priest used in his science fiction story Inverted World in 1974. Perhaps it's obviously the longest route when you spend some time poring over a globe.
// DevsVult: The Machines Will It
"The path covers an astounding total angular distance of 2883523, for a distance of 32 089.7 kilometers.
This path is visually the same one as found by kepleronlyknows, thus proving his assertion."
the path looks nothing like a straight line; but remember, the Earth is a sphere.
It's not a sphere. It can be approximated as an oblate spheroid with roughness. The faux editors here have no background in science, and the brash generalizations are rampant.
This type of flagrant error goes over their heads. There is certainly enough "unspheriness" of the earth to potentially throw off the result if the calculation were done with a spherical projection.
Take, for instance, the Kola borehole. It is not the deepest borehole on earth, but it is the closest borehole to the core of the earth.
That 'roughness' still meets the qualifications of a billiard ball.
Irrelevent. You are comparing Euclidean Geometry to Spherical Geometry. Apples to oranges.
putting the 'B' in LGBTQ+
Wow, great job understanding a fucking sphere bro! #There is hope for Republicans?
Dontcha mean "apples to pancakes"?
Table-ized A.I.
Try 13,620 km Sierra Lieone to ZhangZhou I think their program need tweaking. See Google Earth
The memories of a man in his old age are the deeds of a man in his prime - Floyd, Pink
A lot of factors will deviate any ship as it travels on the ocean between point A and B, I remember when a friend of mine who's a nautical engineer showed me how many calculations it takes to adjust course due to deviation from the wind alone.
Now that I have read the actual article, several crucial simplification stand out:
a) All calculations are done assuming a perfectly spherical Earth.
b) The ETOPO1 data set has quite limited resolution, using data from (say) Google Earth or OpenStreetMap would probably give significantly better positioning of the actual coast lines. Having looked at both of them for the starting point in Pakistan it seems like you can at least get to a sub-5 m resolution for that coast.
I strongly recommend trying this in Google Earth, since that model will allow you to tilt and rotate the Earth so that the given path actually becomes a straight line and you can roll the Earth on your screen all the way from start to finish!
However, the algorithm they chose to use is still quite reasonable, i.e. relaxing the coast lines to get a fast way to discard most possible paths very easily, and then doing more exact calculations on the remaining possibilities. Since the errors caused by using a spherical model are well within the coastline relaxation offsets, you should be able to use their approach to get candidate paths and then micro-adjust them using a more accurate geodetic model. At this point you could also use Google Earth to trace a much more accurate coast line for the most important locations, i.e. around the end points and the tangential touches along the African and South American coast.
Terje
"almost all programming can be viewed as an exercise in caching"
Yes - the longest _land_ route, which the article is about, does have one end near Sagres, Portugal, but the quoted text is describing the longest sea route.
rant
If you look at TFA (Figure 9), the longest straight line that can be taken *on land* indeed starts in Portugal. You're both correct.
There is a straight path but it is just a lot shorter. The oceans have a depth so you can travel in a straight line through them but it is going to be a lot shorter than 32,000 km.
I would think that drawing a line on a circle would not be hard. All you now need to do is make weg or of all the land and see if that line hits land or not. Something that has been done in Space Duel and any other duelling game.
You could even show an explosion, like in the games.
Don't fight for your country, if your country does not fight for you.
In spherical geometry:
That last one is the rule you've come across.
Is that because he drives a car and Patrick Anderson walks?
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
Spherical coordinate system, have you heard of it?
Longitude, latitude and altitude gives you a coordinate system where you can have a straight path and it is also the coordinate system commonly used for Earth.
"But that is just an abstraction!!!"
Well, so is any other coordinate system of your choice, it's not like you are going to have a straight line through atoms anyway.
I do the flat earth on-land version all the time in Transport Tycoon, and I don't cheat by ignoring small bodies of water!
No, your children are not the special ones. Nor are your pets.
"There would be 233,280,000 great circles to consider to find the global optimum, and each great circle would have 21,600 individual points to process -- a staggering 5,038,848,000,000 points to verify,"
Yeah, right. Technically there are an infinite number of great circles and of points. Though I suppose to the nearest minute of angle is probably going to get you close (360x60 = 21600, hence that appears to be their unit of measure).
Yes - the longest _land_ route, which the article is about, does have one end near Sagres, Portugal...
Not to be pedantic, but the subject of the article is the algorithm.
...but the quoted text is describing the longest sea route.
Exactly. The original AC is complaining about the summary saying "Pakistan" instead of "Portugal" -- like it's a typo. The subject of that sentence in the summary is the sea route, as you said. So Pakistan is correct, not Portugal.
The AC is complaining about a line in the summary discussing the sea route, though.
I don't think these researchers dug deep enough into the history of this. For those who are interested, here is the reddit post:
https://www.reddit.com/r/MapPorn/comments/15mwai/the_longest_straight_line_you_can_sail_almost/
Here's another reddit thread that he cross-posted to from five years ago; it seems that the researchers didn't dig deep enough:
https://www.reddit.com/r/todayilearned/comments/15mxxp/til_you_can_sail_almost_20000_miles_in_a_straight/
Apparently he learnt it from a Wikipedia article, where it is also reported (without citation) that the longest distance only on land is 13,573 km (8,434 mi).
The edit was added with this revision by Wikipedia user Muh1974 (who doesn't have a Wikipedia user page). The Talk page around that time has unreferenced "I remember reading somewhere" speculation about the longest great circle. My guess is that Muh1974 checked (somehow) that this path was valid, and had a distance at least comparable to the other ones mentioned in the wikipedia article, but that's where the trail goes cold for me.
Ask me about repetitive DNA
This modded insightful?!?! I thought this was a tech site.
If you call curved lines "straight", then you can get very long "straight" lines, who would have thought? LOL.
What it means to be "straight line" (geodesic) on a curved surface such as the Earth's surface is a very well defined concept. No, you can't make up your own definitions of "straight" and thought you are smarter. Or rather, you could do that, it just made you look silly (and you call yourself "the nerd", oh, the irony!)
A geodesic is the shortest path between two points. A constant heading is a longer path. (Exceptions are lines of longitude, and the equator.)
How do you explain latitudinal lines?
I guess you're more correct, then. :)
You are privileging Euclidean geometry. If a straight line is defined as the shortest distance between two points, then on the surface of the Earth, a straight line is the same thing as a great circle.
All I want is a secure system where it's easy to do anything I want. Is that too much to ask ~~ Randall Munroe
Lines of latitude aren't straight.
All I want is a secure system where it's easy to do anything I want. Is that too much to ask ~~ Randall Munroe
I'd have thought the ovoid nature of the ball would have been a greater problem. The earth is a bit chubby around the waist.
const int one = 65536; (Silvermoon, Texture.cs)
SJW, n: "Someone I don't like, and by the way I'm a fuckwit" - AC
Lines of latitude aren't straight.
What'll really bake your noodle is that no line is ever straight due to the curvature of space...
We'll make great pets
If the north pole is clear of ice can you make it through the Bering Straight in a straight line that would go from Antarctica to Antarctica? Up the Pacific and down the Atlantic?
My other solution would be to be a looping straight line between the tip of South America and Antarctica, you would have a shorter run but after a couple of times around the world you might get to more than 20,000 miles.
Calvin:Do you believe in the devil? Hobbes:I'm not sure man needs the help.
I'd love to see that answer. Likewise for atmosphere, longest undisturbed straight line. While we have an approximate equuation for distance to horizon from a height, it varies massively in reality with all the different heights. Actually, more specific, lower atmosphere up to the highest ground object. That bit's important!
Legalized recreational pot will generate more of these questions for us.
(cough) "Oh shit dood.... You know, it like.... I was just thinking..... like....like what if God made a burrito so hot that he couldn't eat it?....I mean, like you know - couldn't he?
"Ahh, shit Boyd, Pass et the fucking Doritos man, I gotta think about this.
The shepherds did so well protecting the flock that the sheep no longer believed that wolves existed.
If you have a submarine, you could go under the north pole.
The term is "geodesic".
All my liberal friends think I'm a conservative, all my conservative friends think I'm a liberal.
The earth is a bit chubby around the waist.
Let's see how *you* look when you're 4.5 billion years old.
I don't look a day over 3.5 billion.
const int one = 65536; (Silvermoon, Texture.cs)
SJW, n: "Someone I don't like, and by the way I'm a fuckwit" - AC
"Pancakes to oranges" would be more on point.
If you think I voted for Trump because of this post, you're wrong. I voted for Dr. Jill Stein of the Green Party. Again.
This modded insightful?!?! I thought this was a tech site.
If you call curved lines "straight",
If you can get a straight line on a curved surface, you've already redefined "straight".
If you think I voted for Trump because of this post, you're wrong. I voted for Dr. Jill Stein of the Green Party. Again.
Can't you just go round and round off the coast of Antarctica and never hit land, making the longest path "how ever long you want it to be?" ?
If that were the definition then you could sail the 60th parallel south and head due west and keep that course infinitely.
I'm not really a space nerd, so no, I don't look at satellite tracks on 2D maps. I'm a computer nerd, a time nerd, and a few other things, but not a space nerd.
It DOES make sense after you think about it for a minute, or if you're uses to seeing that.
Why does it need to be a Great Circle route? A Great Circle route is a route that follows an arc of a circle whose origin is the center of the Earth. But if I plot a course to follow a line of Longitude such that I drive around Antarctica, I've followed a straight path but just not a Great Circle route. There's other non-Great Circle routes that go at an angle, the only key is where the origin is of the circle. On top of that, limiting to just Great Circle routes make the additional fallacious assumption that the Earth is a sphere, when it's actually an oblate spheroid: it bulges at the Equator, so the Great Circle that is the Equator is actually larger than a Great Circle that passes through the poles. (For clarity: it's really really close to a sphere, but they're looking for extremes so it matters.)
Not saying the solution won't be a Great Circle route - It likely will be, since that's the theoretical biggest possible straight line. But there's no reason is *has* to be.
weylin
67.5% Slashdot Pure I guess I need to work on that....
In Mother Russia, globe circles you.
Bob Stein, http://bobste.in
Or so I've heard. Before today, even!
There's no time like the present. Well, the past used to be.
I doubt it makes that much difference for the purpose here. It's not going to make the Irish Sea turn out to be wider than the Pacific.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
Ever been to Wales? Your definition of straight down will vary quite a lot just by walking a mile or two.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
That depends which angle you look at them from, doesn't it?