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Finding the longest straight line you could sail without hitting land
- sanxiyn 9y agoIf you like this sort of things, you absolutely should read "Which lines of longitude and latitude pass through the most countries?". https://nwhyte.livejournal.com/2929721.html https://nwhyte.livejournal.com/2929721.html
- nasredin 9y agoThrough Greece and I didn't read the other one because the author is a terrible writer. Central America (?)
- landtuna 9y agoAnd what better way of showing it than a Mercator map!
- enriquto 9y agoThe maps on the page are not Mercator, but what's the problem with Mercator? It is a perfectly reasonable projection, with some nice properties.
- Freak_NL 9y agoIdeally they'd show a map with a projection based on having the line drawn on it as a straight horizontal or vertical line in the middle of the map. So basically, a Mercator projection with the line being illustrated as its 'equator'. That would require a custom rendering for each line though.
- OscarCunningham 9y agoThey have these illustrations in the paper. https://arxiv.org/abs/1804.07389 https://arxiv.org/abs/1804.07389
- ColinWright 9y agoGiven the length of the line over water, that would be a somewhat bizarre map.
- jsjohnst 9y agoSee page 9/10 of the source paper.
- cookingrobot 9y agoI like this idea, and they're not in the paper. (The paper shows a globe rotated so the paths are straight, but not a flat mercator projected map). It should be possible to make one with this tool: http://mrgris.com/projects/merc-extreme/ http://mrgris.com/projects/merc-extreme/
- landtuna 9y agoA single map using that projection calls a lot of attention to the quirks of projecting a sphere onto a plane. A different projection or multiple maps centered on segments of the line would call attention to the straight path you'd take as you graze landmasses.
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- rwmj 9y agoI don't have a globe handy, but can't you sail indefinitely round and round Antarctica? Or doesn't following a line of lattitude count as a "straight line".
- enriquto 9y agothat would certainly not be a geodesic (the only sensible defintion of "straight line" on a sphere), more like a circle. It would be just like running circles around your house.
- deleted 9y ago[deleted]
- larkeith 9y agoYou would have to keep turning slightly South to maintain a bearing parallel to the lines of latitude - the only one that's "straight" (it curves downward, but not North or South) is the Equator.
- dbatten 9y agoSource? My gut tells me this is not true, but I'm willing to be convinced.
- OscarCunningham 9y agoGet a ball and a piece of string. Put the string on any two points of the ball and pull it tight. You'll observe that the path the string follows is part of an "equator" of the ball.
- mseebach 9y agoThe problem is that the proposed solution doesn't "count" for the purposes of this experiment, which uses a great circle definition of "straight". The easiest way to visualise a great circle, is to place a piece of string over a globe between your origin and destination and pull it tight, that will track a great circle route between the two (and how a flight flying straight between Europe and the US west coast will take off on an pretty northern bearing, and land on a ditto southern, despite not actually going over the north pole and Europe and the US being located east/west of each other). If you tried to place the string around Antarctica and pull it tight, it'd slip off in the southern direction, which represents the parent's explanation that you'd be steering south (from a great circle course) to keep straight along a latitude.
- OscarCunningham 9y agoThey use height data rather than land/water data, and assume that there's just a cutoff at sea level. I think this gives them the correct answer for the water path, but it gets things wrong for the land path because there are a lot of lakes and rivers above sea level and also some dry land below sea level. If you don't allow the path to cross any lakes or rivers at all then I think the land path has to be much shorter, since rivers makes it impossible to make any progress at all in most places. If you trace their path it definitely goes through several lakes. The optimal path is probably across a desert, my guess would be Antarctica. If you do allow the path to cross lakes and rivers then I think there's a longer path than the one they give, starting in Liberia and ending near Fuzhou, China. They probably didn't spot this one because it passes too close to the Dead Sea, which is below sea level (and crosses the Suez canal, which is at sea level).
- arikrak 9y agoIs that a straight line? Maybe they allow crossing rivers but not seas/lakes.
- jfries 9y ago> They probably didn't spot this one because it passes too close to the Dead Sea, which is below sea level This is adressed in the paper. The relevant part of the problem statement: "the longest distance one could drive for on the earth without encountering a major body of water" and about the Dead Sea: "Guy Bruneau of IT/GIS Consulting services calculated [5] a path from Eastern China to Western Liberia as being the longest distance you can travel between two points in straight line without crossing any ocean or any major water bodies. However, the path crosses through the Dead Sea (which can be considered to be a major water body), and hence does not satisfy the constraints originally set out."
- OscarCunningham 9y agoOh, I didn't spot that they had already considered that path. However I don't accept their defence. 1) Depending on environmental conditions, my path can cross the Lisan Peninsula. https://en.wikipedia.org/wiki/Lisan_Peninsula https://en.wikipedia.org/wiki/Lisan_Peninsula (EDIT: In fact there's enough clearance to just go completely south of the Dead Sea) 2) Their path crosses the Volga River, which is much larger in total surface area than the Dead Sea. And at the point at which they cross it, the Volga is just as wide as the Dead Sea.
- votepaunchy 9y agoThe Earth is not a sphere. https://en.m.wikipedia.org/wiki/Figure_of_the_Earth https://en.m.wikipedia.org/wiki/Figure_of_the_Earth
- shawnz 9y agoFrom that page: > the Earth deviates from spherical by only a third of a percent, sufficiently close to treat it as a sphere in many contexts
- wlll 9y agoIt's a sphere in human scale.
- kgwgk 9y agoWhat do you mean by “human scale”? It may be a sphere in much larger scales (~1000km) but I’d say it’s far from being a sphere in human scale (~1m).
- wlll 9y agoIt's based on context. So something like a scale that makes sense when going about your average human business. For instance, the sun is 150 million miles from the sun. It's not, it's slightly less, but for "normal" human activity (eating, sleeping, sailing in straight lines, programming web apps, etc. etc.) it doesn't matter, it's close enough. So for the earth (as someone else pointed out): > the Earth deviates from spherical by only a third of a percent, sufficiently close to treat it as a sphere in many contexts (https://en.m.wikipedia.org/wiki/Figure_of_the_Earth https://en.m.wikipedia.org/wiki/Figure_of_the_Earth) For most of what most of us do with our everyday lives it's good enough, to the extent that pointing out that "the earth is not actually a sphere" just sounds pedantic. It did occur to me that sailing in a straight line could be interpreted as an actual straight line, but the surface of the ocean is spherical(fine, -ish) and so, modulo waves, we might actually be measuring an infinitely small distance on the earth that was sailable (Ah ha, got you all!) but realised that jokes about derivatives, despite the crowd, weren't going to be all that amusing :)
- larkeith 9y ago"A global map with resolution of 1.85 kilometers has over 230 billion great circles. Each of these consists of 21,600 individual points, making a total of over five trillion points to consider." What? Is there something I'm missing here, or did they just decide to include "individual points" as an utterly useless way of inflating the difficulty of a brute-force approach?
- Luc 9y agoThe longest path needs to start and end somewhere along a great circle. So those individual points are needed.
- larkeith 9y agoThe only relevant points are those that make up the coastlines - there is no need to test paths that start and/or end in the middle of sea or land.
- Luc 9y agoOh I see what you mean. Yes, I suppose it is worded that way to impress the reader with the big numbers involved, when many of them can be trivially rejected.
- pbhjpbhj 9y agoCoastlines are close to infinite in length (they grow inversely to the length of the measure used; idealised mathematical 'coastlines' are fractal and infinite), we can limit them by limiting the resolution.
- lifeisstillgood 9y agoat a 1.8 km resolution (without checking my maths) 21,000 points along a great circle is basically every 1.8km so i guess you are checking at each 1.8km if you just drove into water (or vice versa) Your point that you only need to fail once is fair - there is a lot of boundary conditions one can apply quite quickly
- sorokod 9y agoIsn't "straight line" somewhat arbitrary? How about "the longest circle you could sail without hitting land" or some other reasonably smooth shape?
- yitchelle 9y agoI was just thinking this. If it is allow to sail over the same places more than once, they must be a route that is just a circle. Maybe along one of the southern parallels?
- algorithm_dk 9y agoYes, "straight" is misguiding.
- cup-of-tea 9y agoThat's pedantic. Most people will realise that "straight line" means constant bearing.
- sandworm101 9y agoBut, unless you are passing over a pole, a great circle doesn't use a constant bearing.
- mikeash 9y agoFrom the maps they show, it’s pretty clearly a great circle (the obvious meaning for “straight line” on the surface of a sphere), not constant bearing.
- cup-of-tea 9y agoWhoops, turns out I didn't actually understand what "constant bearing" meant. What I actually meant was "no rudder/steering" which is exactly what people would imagine as travelling in a straight line. A constant bearing actually gives a Rhumb line: https://en.wikipedia.org/wiki/Rhumb_line https://en.wikipedia.org/wiki/Rhumb_line
- deleted 9y ago[deleted]
- mcrider 9y agoThis reminds me of a discovery I made while vacationing in the Corn Islands, Nicaragua -- There was a giant cube buried in the middle of nowhere with one corner poking out of the earth. A plaque nearby said it was the 'soul of the world' and I looked it up to find this funny old organization (http://www.souloftheworld.com http://www.souloftheworld.com) had planted the cubes around the planet, saying that their positions were the vertexes of a cube that was positioned in such a way (and only possible in this way) that every corner touched land. Apparently it has a certain spiritual significance, which is funny to me, but I thought it was really interesting that someone went through the trouble to create them.
- 24gttghh 9y agoWow those are going to confuse the hell out of future beings (if there are any left). I wonder if they're all "built" already?
- mcrider 9y agoI don't believe so. I know there is one on the island of Molokai in Hawaii, which I always wanted to visit when I used to live in Honolulu, but otherwise its not a super tourist-friendly place to visit and I opted to visit other islands instead. The Corn Islands, however I highly recommend to anyone!
- ModernMech 9y agoGood call. I've been there. Got attacked by fish. Would not recommend.
- evanb 9y ago"I have cubed the earth, with 4 simultaneous _corner_ days in 1 rotation of Earth!" -- Dr. Gene Ray, Cubic and Wisest Human.
- dgritsko 9y agoHow can you quote him and not link to Time Cube? http://timecube.2enp.com/ http://timecube.2enp.com/
- OrganicMSG 9y agoThis is cool. Though as you take into account more of the detail of the shape of the surface, your straight line can get a lot longer. I would be interested to see one that takes into account the large scale ocean surface topography, to see if that can change it by much.
- mjsweet 9y agoI loved the final question in the article: “The question now is: who will be the first to make these journeys, when, and how?” These have the potential to become quite important journeys... with the potential for many “firsts”... and also much contention; how much did they deviate from the path, how much deviation from the path is acceptable? So many interesting questions to ask.
- NKosmatos 9y agoSame here, that’s what I thought as well :-) I’m sure that the big documentary channels will pick this up and we’ll see both journeys in a few years. Seems to me that the land journey will be harder to complete. When you’re sailing it’s easy to keep a “straight line” without having to consider mountains, rivers, permissions, politics and any other obstacles associated with crossing land.
- kijin 9y agoIt won't be easy to sail in anything resembling a straight line through the Drake Passage unless your ship is very big. Speaking of big ships, you might also want to avoid icebergs.
- mjsweet 9y agoYeah I was thinking about how hard it would be to stay “true” to the path as possible if a race or challenge was by wind power only. Also in competition, points could be given or taken based on the amount of deviation from the line etc.
- nkrisc 9y agoFor the land route a realistic approach would be to plot major checkpoints along the true great circle path and just navigate between those checkpoints in whatever way (preferably on land) is most feasible. That would still be interesting.
- ollybee 9y agoThat final question struck me as odd, the next question for my mind was could the technique be generalised to a map on a torus?
- hokkos 9y agoGoogle maps seems unable to find a route between Jinjiang, Quanzhou, Fujian, China and Sagres, Portugal : https://www.google.com/maps/dir/Jinjiang,+Quanzhou,+Fujian,+Chine/Sagres,+Portugal https://www.google.com/maps/dir/Jinjiang,+Quanzhou,+Fujian,+...
- grkvlt 9y agoFYI, the PDF of the source paper is https://arxiv.org/pdf/1804.07389.pdf https://arxiv.org/pdf/1804.07389.pdf
- ColinWright 9y agoIn case people are wondering: A global map with resolution of 1.85 kilometers ... 1.85 km is roughly one Nautical Mile, which is roughly one arc-minute of a great circle. As such it's a natural unit of measure. The original definition of the meter was 1 ten-millionth of the distance from the North Pole to the Equator via Paris, making the Earth's circumference 40 million meters. Divide by 360 degrees per circle, then by 60 arc-minutes per degree, and you get (40 x 10^6) / (360 x 60) which is about 1852 meters. Just in case people were wondering ...
- gonvaled 9y ago> As such it's a natural unit of measure As natural as the number 360, and 60. I would argue the meter seems more natural, since it is related to 10 fingers ...
- theresistor 9y ago360 and 60 are quite handy, by virtue of having a lot of integer divisors. For a civilization where long division is unknown or limited to a few scribes, being able to divide things by common fractions easily is an important criterion in a system of measure.
- mkagenius 9y ago> since it is related to 10 fingers If your parent comment is correct. 10 finger thing will merely be an afterthought.
- ColinWright 9y agoGiven that you are already using degrees, arc-minutes, and arc-seconds in your specifications of latitude and longitude, it makes sense to use a unit of distances that meshes with them. Using meters makes less sense because it doesn't work well with the size of the Earth. Difficulties with measurements and conversions are like a dead cat under the carpet - no matter how you push it about there's always an inconvenient lump and a bad smell. The Earth is inconveniently shaped, and you simply have to deal with it. The existing system of measurements may offend your sense of taste, but it has evolved over time to be useful to those who have to use it. Attempts to devise systems a priori and without taking into account the extensive experience of those who actually use them have always failed. There's probably a reason for that.
- state_less 9y agoGoing from Pakistan to Russia seems like the wrong way around Cape Horn. Today you've got 30 kt winds gusting up to 50 kts. Who wants to beat into that? https://www.windy.com/-57.136/-71.191?-37.370,-80.244,3,m:3Vaecv https://www.windy.com/-57.136/-71.191?-37.370,-80.244,3,m:3V...
- bufferoverflow 9y agoI windsurf in 30 knot winds at sea. Yeah, it's rough, but it's not hurricane level madness that rips ships apart.
- jacquesm 9y agoThat sounds like a lot of fun :)
- chime 9y agoWind surfing has a surprisingly high fun/expertise ratio. You can start surfing on your own in as little as 2 hours of training. I was chasing dolphins on my second day of surfing. Of course, like any sport/hobby, it can take years to master but even for complete beginners it can a lot of fun.
- bufferoverflow 9y agoCorrect. You can make it easy or tough simply by choosing smaller/bigger sail and applying less/more force. So it can be very relaxing in 20 knots, especially on a lake.
- mindB 9y agoI thought the solution set had to be convex or concave for branch and bound to work as an optimization algorithm, and this one clearly isn't? EDIT: Nope. It's just the objective function that needs to be convex, not the constraints.
- kxyvr 9y agoTechnically, you need neither. Branch and bound works by solving a series of relaxations with fixed integer variables in order to better search the discrete space. Now, imagine we're solving a minimization problem. Finding a feasible solution to the problem may be difficult, but if we were to find one, discrete variables and all, we'd have an upper bound on how good the solution could be. Simply, it's feasible, but not optimal, so the objective value is higher. Now, since integer variables are hard to work with, we can relax them into continuous. For example, instead of a binary variable that's {0,1}, we could relax it into a continuous variable bounded between 0 and 1, [0,1]. If we do this relaxation and find the globally optimal solution, then we have a lower bound as to how good the solution is. In branch and bound, if we can show that the lower bound for one branch is not as good as the upper bound of another branch, we don't have to explore that branch. Now, convexity comes into play because it allows us to correctly determine these lower bounds because we can guarantee a globally optimal solution to the relaxed problem. If we lack convexity, it's hard to find such solutions. Does that mean branch and bound requires convexity? No. You can still perform branch and bound using locally optimal solutions and even though you don't have a guaranteed global bound, there's relatively good information about where we should search next. This can lead to good, but not provably globally optimal solutions.
- mindB 9y agoBut the article was making a strong claim that this was the provably optimal solution. In this case it is, because the objective function (in the way I'm assuming they formulated the problem) is convex.
- xs 9y agoWhy not start at the most southern point of South America and go due east? Maybe even 0.01 degree South. Couldn't you do loops around the Earth before hitting Antarctica?
- bufferoverflow 9y agoGoing east is only straight at the equator.
- snowwolf 9y agoFor the water challenge couldn't you just sail the 60th parallel south forever? https://en.wikipedia.org/wiki/60th_parallel_south https://en.wikipedia.org/wiki/60th_parallel_south Also could we challenge flat earthers to the same challenge and see who travels the furthest?
- murbard2 9y agoStraight line here is taken to mean geodesic, the shortest possible path on the surface between two points. Parallels on the sphere are not geodesics!
- logfromblammo 9y agoIf we're going to split hairs, an actual straight line would be tangent to Earth at the point of the boat, and you could sail forever, so long as you do it at the speed of light and don't hit the land masses on some other celestial body. There is some definition of "straight line" that includes a course of a constant bearing, or a rhumb line. It's straight when plotted on a Mercator projection. By that definition, keeping to a true east or true west bearing would be a straight line.
- andbberger 9y agoMeh, this is the worst kind of pedantry imo. Like, first of all, doesn't matter. But if you must, you're going to have to go with 'as would be defined by mathematicians' - because they spend a lot of time thinking about these things, and thus are by far the most qualified to have an opinion.... And the mathematicians have thought long and hard about how the Euclidean concept of a straight line generalizes to other geometries... and came up with geodesics... aka great circles...
- logfromblammo 9y agoWhy would mathematicians take precedence over people who navigate ships and airplanes for a living? Also, ellipsoidal geodesics aren't always circles. "Thinking long and hard" isn't actually much of a qualification, if you think about it long enough and hard enough. Playing around with the definition of "straight line" is just an amusement, putting different theoretical constraints on the recreational problem. The whole thing is pedantry to begin with, so don't be surprised when someone pops their head in with something unexpected just to show off how clever they think they are. Launching pointless academic arguments is almost the whole point. It shows the audience that everyone involved is very smart, and all possibilities have been duly considered, and therefore the agreed-upon answer must be very significant, reliable, and noteworthy.
- cozzyd 9y agoI wonder if the answer changes if you consider actual geodesics instead of great circles (which are geodesics on a sphere, but the Earth is not a sphere). Even great ellipses (closer in length to actual geodesics) can deviate laterally from the geodesic by kilometers. See e.g. https://geographiclib.sourceforge.io/html/greatellipse.html#gevsgeodesic https://geographiclib.sourceforge.io/html/greatellipse.html#...
- borkt 9y agoThey need to account for currents as well otherwise a straight line wouldn't be straight at all
- hadlock 9y agoAbsolutely. Particularly under sail, where top speed is typically going to be under 15mph (often under 8mph), a 2mph side current can impact course over ground quite a bit over a day or two when you are only doing 200 miles a day.
- cup-of-tea 9y agoWhy are these comments full of people trying to make what is an interesting and easy to understand problem into an insanely complicated problem? This is hacker news. We're not actually going to sail around the world. It's interesting because someone used a computer to find an answer.
- Ranlot 9y agoLooks like another cool app: Click somewhere on the coastline and it'll take you to what's directly on the other side of the sea. Results may be surprising: https://ranlot.shinyapps.io/coastlinetrip/ https://ranlot.shinyapps.io/coastlinetrip/
- jhanschoo 9y agoFurther reading on the branch-and-bound technique: https://en.wikipedia.org/wiki/Branch_and_bound https://en.wikipedia.org/wiki/Branch_and_bound
- GW150914 9y agoWeird, they talk about great circles yet insist on “straight line” rather than geodesic terminology. Still a good read though.
- noetic_techy 9y agoIts always surprised me that you cant get to the farthest eastern reaches of Russia by car. Its such a massive amount of territory they hold in the east, you could easily start another country as large as China or the USA out there.
- cornholio 9y agoIf anyone is interested in a 7000 mile trek, this is the approximate path of the land route: http://www.gcmap.com/mapui?P=prm-JJN http://www.gcmap.com/mapui?P=prm-JJN
- macintux 9y agoThanks. Maybe I'll try that over lunch next week. I was curious one day after reading yet another comment contrasting driving in Europe vs driving in the U.S., distance-wise, and I decided to measure Seattle->Key West and compare that to Europe. Decided that the equivalent would be Paris->China (almost, I think the terminating point was eastern Kazakhstan).
- julienchastang 9y agoI once flew from Chicago to Beijing and the thing that astonished me is that you are over land the entire flight except in the vicinity of the Bering Strait.
- SeoxyS 9y agoIf your plane flies the shortest great-circle path, you'll fly over the arctic sea, which is definitely water, though sometimes solidified. IAH or DFW would be better examples :).
- 205guy 9y agoI love geographic puzzles such as this one. Here are links to some other interesting ones. Longest straight lines of sight, modulo some atmospheric refraction (has been discussed on HN before): https://beyondhorizons.eu/lines-of-sight/ https://beyondhorizons.eu/lines-of-sight/ Furthest points from the sea/land: https://en.wikipedia.org/wiki/Pole_of_inaccessibility https://en.wikipedia.org/wiki/Pole_of_inaccessibility Latitude and longitude integer degree intersections around the world: http://confluence.org/ http://confluence.org/ The integer degrees is arbitrary, but it provides a random sampling of landscapes. I like the idea of going out to find some defined spot, like geocaching without any caches. It also provides a page of antipodes photos, places exactly on the other side of the earth from each other: http://confluence.org/antipodes.php http://confluence.org/antipodes.php Must also mention earth sandwiches: http://www.zefrank.com/sandwich/ http://www.zefrank.com/sandwich/ Fun fact: there are parts of the Pacific ocean that are opposite each other, therefore the Pacific ocean spans (not covers) half the globe.