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Earth Math Software Science

The Longest Straight Path You Could Travel On Water Without Hitting Land (gizmodo.com) 141

Posted by BeauHD from the ring-of-fire dept.
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.
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The Longest Straight Path You Could Travel On Water Without Hitting Land

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  • A staggering 5,038,848,000,000 points (Score:5, Insightful)

    by I'm New Around Here ( 1154723 ) on Wednesday May 02, 2018 @10:39PM (#56545044)

    Or you could use a nice globe and a piece of string.

    • I don't get it, how will that prove that you've found the two points that result in you needing the longest piece of string?

      • A string by itself wouldn't. But a rubber band stretched taught between two points would try to shrink to the shortest possible length between those points along the surface of the globe, which is always a great circle arc. Think of how soap bubbles floating in the air always try to form spheres - the soap tries to pull itself tight, resulting in a structure with the least surface area for the amount of enclosed air. Same idea - a rubber band band tries to pull itself tight, resulting in the shortest dis
        • That would be a demonstration or justification - probably good enough to pas as a "proof" in a court of law. Not good enough to pass as a proof in the court of mathematics. The technique they actually used was a "branch and bounds" relaxation algorithm, which would find a minimum (or maximum) for a continuous function. It's a bit more open to challenge for a (potentially) discontinuous data set though, but that's a wider argument which is amenable to localised "brute force" searching.

          When I read the headl

      • Re:A staggering 5,038,848,000,000 points (Score:5, Funny)

        by thegarbz ( 1787294 ) on Thursday May 03, 2018 @02:48AM (#56545506)

        Repeat your test at 5,038,848,000,000 different points and keep the longest string you used :-)

    • It's been about 50 years, but ISTR that one of the standard map projections has the property that straight lines on the map are great circles when plotted on a globe. Wikipedia says map in question is a Gnomonic Projection. Seems like that might be a good place to start if one needed a quick solution to the problem.

      • Re: (Score:2)

        by armb ( 5151 )

        Except that doesn't preserve (ratios of) lengths, so it's not so helpful finding the longest route. It also shows at most half the surface (and needs an infinite map to do that).
        No projection preserves both lengths and angles; the globe and string is a better suggestion.

        • Ever try plotting a great circle on a globe with a string? Try it. In practice, it's harder than one would think. Good for determining distance. Not good for midpath error. Really difficult if the path is longer than 20000km (half the circumference).

          • Ever try plotting a great circle on a globe with a string?

            Get your globe - I've got one (birthday present from the wife - nice choice!). Measure it's diameter.

            Get a sheet of that "corrugated plastic" popular for storage/ archive boxes and sign boards (it's cheap, available, stiff, and cuttable.

            Mark a circle the same diameter as your globe onto the board, then cut a circular hole in the board.

            Dis-mount the globe from it's spindle.

            Experiment. You'll soon get to the limits of the accuracy of your globe and

      • Gnomonic projections are limited to slightly less then a hemisphere. You'll need at least four of them to cover the globe. May as well just use a globe.

    • 5,038,848,000,000 points is nothing on a modest PC (eg. An i7 with 8 cores at 3GHz is 24,000,000,000 clock cycles per second).

      I can't imagine it took more than a few minutes to run.

      • Re: (Score:2, Informative)

        by Anonymous Coward

        5,038,848,000,000 points is nothing on a modest PC (eg. An i7 with 8 cores at 3GHz is 24,000,000,000 clock cycles per second).

        I can't imagine it took more than a few minutes to run.

        I know this is Slashdot and we don't read the article... but the article has this to say about the subject:
        "Armed with this technique and a regular laptop computer, Chabukswar and Mukherjee calculated the sea route in just 10 minutes."

        • This is Slashdot, I wasn't expecting them to actually provide a link to the article instead of some paywalled, third-hand news source.

      • Then again, this is 2018. They probably did it in Python or something.

    • Re: (Score:2)

      by dohzer ( 867770 )

      Replace 'nice globe' with 'Earth', and I like your idea.

    • Re: (Score:2)

      by gotan ( 60103 )

      A piece of string wouldn't work, since the path is more than half way around the globe.

  • % that bitch and BAM! Traveling Salesman Problem solved!

  • Took me a few seconds to see how that's straight (Score:5, Interesting)

    by raymorris ( 2726007 ) on Wednesday May 02, 2018 @11:07PM (#56545092) Journal

    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.

  • not the "straight" path (Score:1)

    by Anonymous Coward

    It is the longest path along a geodetic line. Not a straight in 3-D space.

    • Re: (Score:2)

      by vux984 ( 928602 )

      It is a perfectly straight line within the coordinate system / topological space being considered.

  • Wouldn't 5 trillion comparisons take only about 2000 seconds on a modern processor, even without multithreading or SIMD optimizations?

    • That's what I thought, too, any reasonable algorithm would bang through that in a managable time on any modern processor.

    • I'd imagine it would take a bit longer than 2000 seconds, because the data has to be fetched from RAM, etc. That said, their map would be far smaller than 5 trillion bits. If it was only a few megs, it would fit in the L1 cache at least.

  • 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.

  • Spoilers (Score:3)

    by jimtheowl ( 4200185 ) on Wednesday May 02, 2018 @11:22PM (#56545130)
    "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."

  • Technically, you cannot travel in a straight line for ANY distance on the surface of a sphere, right?

    At best you can have a single point of tangency.

    I mean, come on, if you're going to be pedantic, let's really be pedantic!

  • Comment removed based on user account deletion
  • Try 13,620 km Sierra Lieone to ZhangZhou I think their program need tweaking. See Google Earth

    • Certainly seems to pass through the bottleneck at Suez and misses the Caspian Sea.

      • Looking more closely, unless Google Earth's model is very far from Earth's oblate spheroid shape (or its ruler widget is broken) then there are a lot of paths from Sierra Leone through Suez to China and with a lot of wiggle room to spare. I wonder if the model TFA used has the Suez Canal marked as a coast-line and so discounted these paths.

  • 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.

    • Re: (Score:2)

      by dcw3 ( 649211 )

      One would hope that any Capt. worth his salt would be steering into the wind to compensate, and still follow a straight line. At least that's what I learned about "crabbing" into the wind when you're landing a Cessna.

  • 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 [slashdot.org] or OpenStreetMap [slashdot.org] 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 Goog

  • Comment removed based on user account deletion

  • Is that because he drives a car and Patrick Anderson walks?

  • "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).

  • That Reddit Post (Score:5, Informative)

    by gringer ( 252588 ) on Thursday May 03, 2018 @03:57AM (#56545628)

    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/ [reddit.com]

    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/ [reddit.com]

    Apparently he learnt it from a Wikipedia article [wikipedia.org], 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 [wikipedia.org] by Wikipedia user Muh1974 (who doesn't have a Wikipedia user page). The Talk page [wikipedia.org] 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.

  • 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.
  • If you have a submarine, you could go under the north pole.
  • 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?" ?

    • No, because that's not a great circle route. Just like sailing round and round Anglesey or Rockall isn't.

  • Why does it need to be a Great Circle [wikipedia.org] 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 [wikipedia.org] 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 assumptio

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