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Coastline paradox
- bigyikes 3y agoStep 1: Acquire small beachfront property Step 2: Put property on the market, listed as having a mile of beach Step 3: ??? Step 4: Profit There's no way this could backfire, unless the buyer asks how big your ruler is. But a true gentleman never questions the size of another's ruler, so you should be in the clear.
- dmoy 3y ago> There's no way this could backfire, unless the buyer asks how big your ruler is. Or it goes through a real world court system where judges take very dim views to that level of pedantry...
- deleted 3y ago[deleted]
- __blockcipher__ 3y agoYes, the GP was clearly serious in their advice to exploit the coastline paradox in order to mislead would-be buyers! (/s)
- thih9 3y agoListings already have these and worse things. E.g.: properties are routinely described as “X minutes away from beach”, where in reality it’s impossible without teleportation.
- em-bee 3y agoas the crow flies at the speed of a bullet
- Aachen 3y agoDo bullets fly for minutes? (Edit: to be clear, that's a genuine question. I would imagine they drop to the ground before the "three minutes from the beach" have passed no matter the firing angle, but I don't know.)
- rootusrootus 3y ago> Do bullets fly for minutes? Effectively no. MythBusters said a 30-06 shot straight up could hit 10K feet and would take just under 1 minute to hit the ground. I'd be comfortable asserting that a 30-06 is about the largest 'normal' cartridge. Bigger ones definitely exist, but they're a niche. Handgun rounds are generally a lot slower and lighter than a 30-06, so they'll all be even quicker to reach the ground. Plus, to hit the beach, you'd shoot at about a 45 degree angle instead of straight up, which would reduce the height reached.
- deleted 3y ago[deleted]
- m4rtink 3y agoDepends on gravity of the body and its atmospheric pressure and related variables (wind speed, temperature, composition - lead bullet could meld on Venus, etc.). Low gravity & no atmosphere- bullet reaches escape velocity and wanders off to space. Very high atmosphere & fired high up above ground (if any - eq. gas giant) and bullet might take quite a while to fall.
- ClassyJacket 3y agoBullets take the same amount of time to fall as if you dropped it!
- defrost 3y agoNot exactly: https://en.wikipedia.org/wiki/Magnus_effect#In_external_ballistics https://en.wikipedia.org/wiki/Magnus_effect#In_external_ball... can make ULR bullets drop faster or slower depending on crosswind direction and strength.
- deleted 3y ago[deleted]
- throwbabyaway 3y agoWhere I'm from realtors solve this problem by declaring the length of the sea-opening (not sure of the English word, not a native speaker), the length of the straight line between two ends of the coast access. Well, this could be a problem, of course, if you are selling an island.
- rdlw 3y agoEspecially if you're selling the whole island except for the place where a two-meter-wide footbridge connects to it. The sea-opening would be two meters no matter the size of the island
- dmonitor 3y agowould be especially misleading if it’s a cove a U shaped beach would be listed with half its effective beach area
- deleted 3y ago[deleted]
- dang 3y agoRelated: Coastline Paradox - https://news.ycombinator.com/item?id=24437749 https://news.ycombinator.com/item?id=24437749 - Sept 2020 (32 comments) Coastline Paradox - https://news.ycombinator.com/item?id=21214958 https://news.ycombinator.com/item?id=21214958 - Oct 2019 (1 comment)
- justinl33 3y agoNext time you go to measure your waistline, just remember: have you really put on weight, or is it just the coastline paradox?
- margalabargala 3y agoThis unfortunately doesn't quite work, because while there's no well defined upper bound, there is a lower bound.
- justinl33 3y agotrue, but you could just argue that any increase was just a result of over-estimating the last time you measured
- margalabargala 3y agoThe lower bound is generally very easy to measure precisely. So a change in that would be immediately noticed. For example, how long is the North Carolina coastline? No idea. But we can measure the precise distance between the point where that state's border with South Carolina meets the ocean, and the point where the border with Virginia meets the ocean. The coastline must be at least this long. And if you measure your waistline, you can draw a cord around your midsection with some known amount of force. Your true waistline may be larger, but it is at least that large. And if that number increases...well, we're in a period of relatively high inflation already, what's one more thing?
- TylerE 3y agoMuch more complcated problem than you're implying as NC has no unbroken coast. It's all shoals and barrier islands - and when you're inside that, swampland.
- dotancohen 3y agoThat does not affect the lower bound as described.
- n_plus_1_acc 3y agoIt also imples that any border between countries that is defined by a natural border, eg a river is infinitely long, right?
- tukajo 3y agoNo since water boundaries like rivers are defined as the middle of the river, not as the shifting coast of either side of the river.
- alistairSH 3y agoNot always. The boundary between VA and MD (states in the USA) is the Virginia shoreline of the Potomac River. Which has caused oddities over the years… At one time, gambling and liquor were illegal in VA, so casinos set up boats at the low tide line. Customers parked in VA and walked onto the casino barges from the Va side, but they were technically in MD. You need to follow MD fishing regulations even from VA shore (though a VA license is ok).
- macintux 3y agoMy uncle once argued a case in the U.S. Supreme Court regarding Indiana & Kentucky's border, which was initially established in the middle of the river. The Ohio River has gradually shifted south since the border was established, so some parts of Kentucky are now on the "wrong" side of the river.
- cozzyd 3y agoThe former capital of Illinois is on the wrong side of the Mississippi nowadays
- n_plus_1_acc 3y agogenuine question: how is the middle defined when both shores are fractals?
- School-Cotton 3y agoThe coastline paradox relies on the assumption that the coast is equally “jagged” at all levels. Is this actually true? I mean, if I go to the beach and look at the line where the water meets the land it doesn’t really seem like a fractal to me. The outer boundary of land masses gets smoothed out by erosion from the water, right?
- groestl 3y ago> it doesn’t really seem like a fractal to me. That's because you don't look close enough.
- infradig 3y agoThe Wikipedia article states it's not really fractal.
- ravi-delia 3y agoIt actually bottoms out pretty low though. The apparent fractal dimension changes over scales, but is sufficient that ruler length really does make a huge distance in coastline length
- meheleventyone 3y agoSure but the quantity that’s important is your sampling accuracy. Even on a visually smooth beach there is enough variation for that to significantly impact the results. This closely relates to numerical integration where often you’re dealing with fixed sized steps and for example can simulate significantly stiffer materials with a smaller timestep.
- paulddraper 3y agoIf the coast is a sandy beach, then it is usually pretty smooth. But in other cases ... https://www.nps.gov/articles/images/acad-ship-harbor-rocky-coast_web.jpg https://www.nps.gov/articles/images/acad-ship-harbor-rocky-c...
- HarHarVeryFunny 3y agoAre there any definitions of length, or specifically perimeter length, that are more intuitive for comparison purposes, and practical, and actually used, perhaps separating smoothed path length from path roughness?
- EnigmaFlare 3y agoThere's convex hull which is how you measure your body with a measuring tape. The tape straightens itself over any recesses like where your belly button is.
- OskarS 3y agoI’ve always found this argument very cool (and obviously true in a mathematical sense) but not really ”practically” relevant. Like, the only reason you would be interested to know the length of a coastline is because you want to know how far a ship would need to travel, and that is pretty well-defined. Or, like, if you wanted to do a naval blockade, you would need to know how many ships you’d need to cover the entire coast, given that a single ship can only cover so much. Still a cool argument though.
- Gravityloss 3y agoThat's similar to what Robert L. Forward responded at school. He was transferred from mathematics to physics (to good effect!). He had a hilarious autobiography online but can't find it anymore...
- em-bee 3y agowhat if you want to take a hike along the beach and you want to estimate how long it will take to walk?
- OscarCunningham 3y agoThe interesting thing is that while there is a 'practical' length, it varies depending on the application. So if you want to put a wind turbine every 1km along the coast, and a lamp post every 100m along the coast, the number of lamp posts you need won't be 10 times the number of wind turbines. It will be more.
- strogonoff 3y agoThe coastline paradox is useful as an illustration of how any measurement or observation is performed against an abbreviated version of reality that corresponds to a specific practical purpose, whereas the underlying complete reality is never phenomenologically accessible. (Measuring the coastline to arbitrarily high precision would require an arbitrarily high amount of energy and time, all the while the coastline is undergoing natural processes that change the result of the measurement.) Just how there can never be a complete map, there can never be a complete and provably correct model of reality. A sufficiently detailed map becomes the territory, and if you with your measuring apparatus are part of the territory then you’d need to recurse infinitely. The fact that there can never be a complete map (complete and provably correct model of reality) is irrelevant to natural science itself, but it’s relevant to how we think about natural science and its limitations when it comes to explanatory capabilities.
- ilaksh 3y agoI think I've heard this in reference to the difficulty of software estimation. The project details and potential problems are unknowns until you get to that specific part of the project. Even though theoretically you can see the "shape" and rough size of the project when zoomed out.
- valyagolev 3y agoyou also should, and inevitably will, cut corners smaller than your "step" when actually following the "coastline" in development. the more fixated one on the smallest details, the longer it will end up
- chrisweekly 3y agoYes, there's a classic blig post (sorry, no bookmark handy) about an analogous trip from SF to LA.... Also, (maybe counterintuitively), in software estimation the more fine-grained the estimates, the more likely they are to _underestimate_ project scope. For areas that are better-understood, the estimate will be (properly) limited in scope (reducing the overall buffer) -- which leaves less margin for error in the areas with more unknowns, where the biggest scope bloat is hiding. As a rule, software estimates should use a very broad brush. (This also helps mitigate the tendency of PHBs and product owners to mistake precision for accuracy.)
- kqr2 3y agohttps://techcrunch.com/2016/04/30/estimate-thrice-develop-once/ https://techcrunch.com/2016/04/30/estimate-thrice-develop-on...
- skrebbel 3y agoWoa, from way back when a traffic sign with the word “Estimate” was considered helpful imagery
- chrisweekly 3y agoThanks, yes - that's the one. (Too late for me to correct "blig" -> "blog", whoops.)
- irrational 3y agoI’ve never taken calculus (the last math class I took was an algebra class in high school in the late 1980s). But I read a description of calculus once that used the example of trying to figure out the length of a coastline and described how one could use smaller and smaller sections to estimate the length and this is what calculus is all about. But, this article doesn’t mention calculus at all, so now I’m wondering if my impression of what calculus is used for is all wrong.
- HL33tibCe7 3y agoCalculus and why it doesn’t help here are mentioned in the “mathematical aspects” section of the article
- Remnant44 3y agoCalculus deals with things that are sufficiently smooth on a small scale, and thus converges. For example, approximating a circle with smoother and smoother polygons. The length of those polygons will converge to the circumference of the circle. The coastline paradox is the classic example of a fractal; the dimension of a fractal is actually greater than that of the space it lives within!
- Solvency 3y agoThe word converge always confused me here when learning English. It's not like the edges of a circular polygon "converge" even in a hypothetically perfect circle. They more....blend together, or lose their edge. Either way maybe I've never properly understood the term.
- yuriks 3y agoWhat converges is the resulting value of the calculation. As you add more lines the approximate result (of the circumference) gets closer and closer to the true answer. It's not necessarily referring to the geometric shape of the polygon. (Though you can also see it as, if you take any given point on the circumference of the polygon, as you add more segments, that point will get closer and closer to the true edge of a circle.)
- nyc111 3y agoAll surfaces are definitional. A surface exists when you define it.
- tedunangst 3y agoCan you get a decent approximation by measuring displacement? Dump a bucket of water in the ocean, observe the level of sea rise, that tells you the volume of the island, and indirectly the area of the edge.
- ClassyJacket 3y agoNope. Edges do not work that way. Mathematically a fractal outline can have infinite length but finite area.
- rdlw 3y agoDo this with Gabriel's horn and you'll observe that it has an area of pi, which does not reflect the fact that its perimeter is infinite.
- tedunangst 3y agoYeah, I'm not sure how I concluded you could go from volume to area.
- ClassyJacket 3y agoIt does seem intuitive that you'd be able to, I can certainly understand how you'd think that. But no!
- paulddraper 3y ago> the area of the edge No, it will give you the area of the island (more precisely, the area of the sea-level cross section of the island).
- cozzyd 3y agoConsider a short portion of shoreline in Fourier space. By keeping the "DC" term constant (i.e. the integral), you have complete freedom to change all other terms. By increasing high frequency terms the length of shoreline can tend to infinity without changing the area of the island.
- arp242 3y agoAnother fairly counter-intuitive map-related thing is that Edinburgh is further west than Bristol, and roughly on the same longitude as Cardiff. There's no real advanced math or optical illusion going on here, it's pretty obvious when you look at the map. It's just that our minds just make a simplistic "it's on the east coast, and therefore further east than things on the west coast"-shortcut. It works most of the time, except when it doesn't.
- chungy 3y agoReno, Nevada is further west than Los Angeles, California. Same effect, US perspective :) Heck, Spokane, Washington is nearly the same longitude as Los Angeles.
- naikrovek 3y agoI understand why the measurement of a coastline changes depending on how you measure it. I do not understand why it is important to measure coastlines. ¯\_(ツ)_/¯
- ravi-delia 3y agoIt isn't
- thih9 3y agoNote that it can apply to borders too. > the Portuguese reported their measured border with Spain to be 987 km, but the Spanish reported it as 1214 km.
- naikrovek 3y agook so why does it matter for borders? the location of the border seems important, but not the length.
- deleted 3y ago[deleted]
- Animats 3y agoA simple way to think about this is this: draw circles along the coastline, all of radius R, such that the entire coastline is within some circle, with the circles centers are spaced R apart. For a given R, there is some minimum number of circles N which will cover the coastline. Smaller values of R require more circles. The length of the coastline for a value of R is RN. Plot RN vs. R. Trying to use a ruler on an irregular edge is ill-defined. If you formulate the problem as a chain of circles, there's a well defined result.
- OscarCunningham 3y agoWhat you will find is that in the plot the length doesn't level off as R gets smaller. It will just get larger without bound.
- heads 3y agoI was surprised to see that the real world example really does go up and up as the resolution of measurement increases: https://en.m.wikipedia.org/wiki/File:Great-britain-coastline-paradox.gif https://en.m.wikipedia.org/wiki/File:Great-britain-coastline... If stops at ~50m resolution. I imagine it could go even further.
- deleted 3y ago[deleted]
- SirMaster 3y agoWhy don’t the people in charge of measuring just agree on some unit of resolution?