The Coastline Paradox Explained

  • Published on Mar 2, 2018
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Comments • 12 051

  • Pikalika
    Pikalika 10 months ago +6692

    If only we had some unit of measurement between 1km to molecule sizes

  • shark
    shark 3 months ago +307

    Instead of approaching infinity, wouldn't the coastline perimeter form a sort of exponential curve towards a definite amount as the unit got smaller and more precise?

    • Neo
      Neo 19 days ago

      @Alexa D Yes but it is still have connection to the geometry, because with a single line we would not get bigger perimeter with smaller step distances.
      In this case the perimeter is proportional with the minus log of the distance. - log 0 is inf, but as the disance is never zero, it is not inf.

    • Alexa D
      Alexa D 26 days ago

      @Neo "But the distance can't be 0, so no infinity." That's the point I'm trying to make. This isn't like a series or a fractal because those concepts both involve infinity when this situation does not. There comes a point when you can't zoom in anymore (unlike the way you can infinitely zoom into a fractal) and, assuming it's true that there exists a shortest distance, the measurement of a coastline will always converge to a finite value. It has nothing to do with the geometry of it. And, if you did measure the entire thing in Planck lengths and added those up to get the true value, it wouldn't just be *like* a finite sum, that's exactly what a finite sum *is.* So I think I'm a little confused when you say it's a bit different from what I'm saying, if you could elaborate on that 😊
      I enjoy the conversation too!

    • Neo
      Neo 27 days ago

      @Alexa D i see what you say, but this is a bit different. Smaller distanced means more precision in the coast line, which means bigger curves, more zigzagging, and less truction of the coastline. Its like a fractal, for example a triangle which has smaller similar triangles on its side, and those triangles has smaller triangles, and so on. This fractals perimeter is infinite (similar to why sum of 1/n is infinite).
      Well the coastline is similar. The distance represent the size of triangles. Smaller distances means smaller triangles, and if the distance is 0 then the sum is infinite. But the distance can't be zero, so no infinity.
      It is a quite interesting topic, and i enjoy the discussion.

    • Alexa D
      Alexa D 27 days ago

      @Neo Ooh interesting thought. The only thing is that it's a finite sum, not an infinite series, so it will always approach a finite value. The measurement we use doesn't approach 0, it approaches a constant that is believed to be the smallest unit of measurement. 1.6x10^-35 ish. No matter the distance, there is always a finite number of times you can fit that length in there, even if it's an unfathomably large number of times. So we may end up summing something a disgusting number of times, but still never an infinite number. Sorry if I'm being annoying, I just got a random notification for this thread and clearly I could talk about math all day 😅

    • Alexa D
      Alexa D 27 days ago +1

      @Jer Not quite. Germs & Spices misspoke a little bit there. There IS a standardized x-value we can use - the Planck Length which is believed to be the smallest meaningful measurement in the universe. Now, can we actually measure a coastline that way with current technology? I doubt it. It's something like a billionth of a billionth of a millimeter. But it's not accurate to say that the length of the coast approaches infinity, it's getting closer and closer to a finite value. In fact, as your measurements get smaller and smaller, the change in the answer you get will also get smaller and smaller and, at a certain point, it starts becoming very accurate. That's relevant because that's usually the *opposite* of the behavior of something that approaches infinity.
      For example, let's say we measure using kilometers and get 10,000 km. Then you measure using meters and maybe the length increases to 15,000 km. Then you use centimeters and get 17,000 km. Then millimeters and get 17,500 km. By the time you get down to Planck lengths, the true coast may end up being 17,650 km. I'm completely making these numbers up, but the point I'm trying to illustrate is that you get diminishing returns the smaller a measurement you use.
      Also, there's no such thing as an "infinite asymptote." An asymptote is a line a relation gets close to but never touches. A relation is just any sort of relationship between two variables. y = 1/x is a relation that takes numbers (called x) and produces the reciprocal of that number by putting it under one. So like if x = 2, then y = 1/2. There are two ways to describe asymptotes - their orientation (horizontal or vertical) and location (at what value do they occur). y = 1/x has both a horizontal and vertical asymptote and they both occur at 0 (y = 0 and x = 0 respectively). If you type that equation into google, you may see what I'm talking about. As you move further to the left and right, it's approaching that horizontal asymptote of 0, meaning the curve keeps getting closer and closer to where y = 0 (or the x axis, or the horizontal middle of the graph). As you move further up and down, it also gets closer and closer to where x = 0 (or the y axis). There can be infinitely many asymptotes, y = tan(x) is an example, or a finite number like in 1/x which has two. Anyways, part of why I'm talking about this is because you can see that diminishing returns effect when you look at a graph, or use an equation, that has an asymptote. When x = 1, y = 1 (1/1 is 1), when x = 2, y = 1/2 so that's a 1/2 difference (1 - 1/2 = 1/2) in the y values. Then, when x = 3, y = 1/3 which is only a difference of 1/2 - 1/3 = 1/6. So even though I'm still going up by one in x, I'm moving less in terms of y. (1/6 instead of 1/2) The next value would be 1/4, which is only 1/12 less than 1/3. By the time you get to x = 1000+, many calculators are just going to start rounding your answer to 0 since it's so close (1/1000 = 0.001), even though technically the relation never truly equals 0. That's what measuring the coastline is like. Once our units of measurement get small enough, we are so close to the true value of the coastline that our measurements will start being almost exactly the same.
      Sorry if this is more info than you bargained for, I just saw the comment of the person you replied to who chose to use large vocabulary in uh, creative and new ways let's say (maybe English isn't their first language? In which case, kudos to them I've been learning spanish for a decade and can still barely understand it, let alone technical jargon), and I HAD to say something 😅

  • ShelbZzZ
    ShelbZzZ 2 months ago +42

    or you could get a reasonable estimation by measuring in 1 meter long segments, also you would notice a convergence to an actual number as your unit of measurement approaches 0m . Its basically a limit problem.

    • Louis
      Louis Month ago +1

      No, you can see the coastline as a fractal. If you increase the unit of measurement the length of the coastline would diverge since you would always have to measure around a new curve you discovered by zooming in. To get an exact answer you would have to measure in Planck lengths.

  • It'sGood
    It'sGood 10 months ago +48

    Technically - if you're measuring at the subatomic level then it's impossible to measure as quantum mechanics tells us that the particles do not have a definable length or position.
    Also - good work on getting the difference between the UK and GB right.

  • Barry Wever
    Barry Wever Year ago +4901

    U.S.A.: we don't really know the size of our coast, how do you do it?
    The Netherlands: simple, it's the size we want it to be.

    • Luka Seldenrust
      Luka Seldenrust 2 months ago

      @Itzik Ashemtov actually the opposite, the Dutch engineers who helped create the systems are helping other countries that have water issues as well, it’s not our fault we got the solutions first because our people were drowning from the smallest rainfall

    • Tigerclaw5355
      Tigerclaw5355 3 months ago

      Us Brits be like "actually, our coastline it exactly 25,099.735km and we can make it how we want"

    • Sprinkle Man
      Sprinkle Man Year ago +4

      @Itzik Ashemtov
      It just sounds like you are angry that another country that isnt your country is doing something big brain

    • Alexander Brand
      Alexander Brand Year ago +2

      @Itzik Ashemtov why?

    • Noobmaster69
      Noobmaster69 Year ago

      As a dutch guy i can confirm

  • Funtastrophe
    Funtastrophe 8 months ago +235

    This “paradox” also applies to the surface area of your lungs. That’s why we can never agree on how many football fields your lungs can cover.
    Also, nobody pronounces it the “cotch” snowflake. It’s always either “coke” or that other way that could be flagged by profanity filters.

    • JZ's Best Friend
      JZ's Best Friend 2 months ago +1

      There's no paradox; it's just a matter of accuracy of the measurement.

    • Visassess
      Visassess 2 months ago +1

      @Dark Nebula Ouch, pretty edgy there dude.

  • Văn Minh Lê
    Văn Minh Lê 2 months ago +36

    It may resemble fractals. However, "real" fractals are infinite in nature while coastlines are not, so the only problem is the scale of measurement (as mentioned in the videos and a few others). You can find the exact length of the coastline by measure the distance between each molecule, which is not practice and of little good. You must decide the scale by determining your need, defining how long is "meaningful".
    For example, if NATO wants to measure the coastline to know how many fleets the Russians can have at their harbour, 10m is a reasonable number. OTOH, the Malaysians wants to know how much land they can use for harvesting sea salt, 20-30m probably makes more sense.

    • boldimor84
      boldimor84 2 months ago

      @Văn Minh Lê yes, absolutely. the whole world seems kinda "fractal-ish". who knows how many "smaller parts" we might find at some points below quarks and stuff xD. Everywhere there seems to be more and more details, the more you look :D.
      All of course anyways under the premise of or current physical models. because at the end, all of those things are anyways quite below what a normal human mind can see and comprehend. But i'm getting too far off the actual topic xD

    • Văn Minh Lê
      Văn Minh Lê 2 months ago

      ​@boldimor84 I agree. Like you said, the "direction" where things were going is the point of bringing up fractals. I just wanted to point out that the lower-constraint was what distinguish the theoretical and the physical one.
      Beside, don't you think the surface of the table is fractals-ish? Since the closer you look the rougher it would be, albeit much less obvious than snowflake of course. That way you can just magnify anything and shit'd go weird anyway.
      I'm no scientist so I'm not sure how things look like below the Planck length, but I'm sure it would not be as straightforward as mathematician has in their system.

    • boldimor84
      boldimor84 2 months ago +1

      The idea/concept of fractals might be infinite, but any "real world example" like a snow flake has at the end of the day the same "constraint" of e.g molecules.
      Beside of that, why stop at molecules. Let's get on quantum level (theoretically). Maybe at some point we "find" something smaller than that.
      So while it is ofc not per se "Infinity", it kinda grows quite in this direction, the closer you look.
      So I still find it an appropriate comparison/figure to get the kind of idea

    • South of South Records
      South of South Records 2 months ago +2

      This is the best comment describing this phenomenon tbh

  • Comfy Wizard
    Comfy Wizard 2 months ago +12

    Lewis seems like the kind of dude who would be fascinated by mundane things and end up wasting everyone's time, including his own. The true value isn't impossible to know, the issue is our definition of "coastline". You can calculate coastline with how much water is displaced, rather than using length measurements for the land.

  • Tobias Hagström
    Tobias Hagström 2 months ago +4

    So, how you measure the coast depends on what you need your measurements for. If you need to patrol your coast with ships for defense or surveillance or whatever, you only need to have enough ships for their patrol routs to enclose the landmass, only accounting for the major features and drawing straight lines in the water between them. If you wanna calculate how much beachfront property you can build you, gotta determine what the minimal size is to make an worthwhile lot or neighborhood on, and then measure it with that resolution in mind. If you wanna know how many boats can be docked up against the land, you use another approach, and so on.

  • Thor God of Thunder
    Thor God of Thunder 2 years ago +21866

    Me coming out of Area 51 knowing the exact measurement of the coastline of Great Britain

    • Thom Cat
      Thom Cat 2 months ago

      Top ten comments of all time

      CROW GANG RECORDS 2 months ago +3

      @Krisjin Stark your comment is eerily spooky considering the fact russia has invaded ukraine and the fear of ww3

    • Sal M
      Sal M 3 months ago

      I Laughed SO hard at this comment… THANK YOU

    • VitaminGummies
      VitaminGummies 3 months ago

      Me coming out of the Bermuda triangle knowing the exact measurement of the coastline of Norway:
      _"I am better than you"_

  • Kini
    Kini 10 months ago +72

    2:08 If you add an infinite number of numbers that are getting smaller and smaller, you don't get infinity, per se. Pi or the Eulerian number is also an infinite series of numbers added, but its value converges to a specific number. So the coast of England would do the same thing. The exact extent of a coastline depends more on the definition of the edge and not on the chosen resolution.

    • Ned Peters
      Ned Peters 3 months ago

      smart boi right here

    • Willsk
      Willsk 5 months ago +9

      You are wrong you can add up numbers that get infinitely smaller that go to infinity just look up the harmonic series.

  • Adrian Garcia
    Adrian Garcia 2 months ago +3

    I think the best way to measure it would be by using a drone with AI to follow the coast within the dry area of the beach then measure how far it went.

  • John Counts
    John Counts 10 months ago +72

    Wouldn’t it be easier to just chose a point in the water and measure in a straighter line? And why would you include river inlets into the calculation?

    • Skunk Ape
      Skunk Ape 3 months ago +7

      One, that point in the water you propose already exists. It's called the Continental Shelf. Problem is, measuring the shoreline only works ON THE SHORE! Two, inlets, bays, and coves are features of said coastline. Excluding them would only serve to deliver inaccurate results. Asking why inlets are included is like asking why the cost of tires is included in the sale of an automobile. One is quite literally a part of the other.

    • Jayyy Zeee
      Jayyy Zeee 3 months ago

      Wouldn't it be easier if you would just get with the program?

    • Elm
      Elm 9 months ago +13

      You clearly don’t get the paradox

    • bryce york
      bryce york 10 months ago +5

      To get a more accurate number of land available.

  • Species1571
    Species1571 10 months ago +1

    Do you measure when the tide is fully in or fully out, or halfway between? Then it becomes impossible, because one end of the country will be at a different tide from the other end. And you would also have to count both sides of every single river that leads out to sea, and then both sides of every smaller river that branches off from those.

  • Ryan Wallentine
    Ryan Wallentine Year ago +1409

    3 years ago, I started the grueling task of counting the distance of the Finnish coast at the atomic level, and I can confirm that the Finnish coast is exactly one infinity kilometers long.

    • DrunkPauloCosta
      DrunkPauloCosta Month ago

      @Naþan Ø yeah he must have actually been measuring in infinity miles not infinity kilometres

    • SilasDAgamer
      SilasDAgamer 2 months ago

      @Darth Wiizius same, but you pun-upped me this time

    • Darth Wiizius
      Darth Wiizius 2 months ago

      😁. I'm a pundamentalist y'know.

    • SilasDAgamer
      SilasDAgamer 2 months ago +1

      @Darth Wiizius haha good one

  • Stupid the Fish
    Stupid the Fish 10 months ago +40

    This reminds me of the VSauce episode where he says if we were to get the smallest measurement and mark a sphere in every direction combination possible without winding up in the same spot twice, split the sphere, take half of those points and make them into their own sphere, we’d have two complete spheres, even though each has half of the original sphere.

    • Skunk Ape
      Skunk Ape Month ago

      @⚠︎︎mugwump⚠︎︎ that's a gross oversimplification. The "cells" created aren't solid, and are merely a scattering of particles. As such, neither resulting "cell" is actually a physical construct.

    • ⚠︎︎mugwump⚠︎︎
      ⚠︎︎mugwump⚠︎︎ Month ago

      @Skunk Ape Cell division produces two cells that are smaller than the original cell.
      Banach-Tarski paradox produces two spheres that are the same size as the original sphere.

    • Skunk Ape
      Skunk Ape 2 months ago

      @coolnecromancer1 You might want to do a little more research into cellular division then.

    • coolnecromancer1
      coolnecromancer1 2 months ago +2

      @Skunk Ape I'm fairly certain OP was talking about the Banach-Tarski paradox, which has nothing to do with cell divison.

  • Amdo Brantal
    Amdo Brantal 2 months ago +4

    I'd say measure it like this: how long does it take to walk around the coast? Combine that with the walking speed of your walk and you have a human-sized length.

  • Khrene Cleaver
    Khrene Cleaver 10 months ago +1

    The coast line should be measured by a boat of a constant size coasting around the shore, not where sand meets water.
    The shoreline can stay in paradox.

  • Adam Ellison
    Adam Ellison 10 months ago +2

    You could try measuring where the ocean meats the sand and getting a mean value of when the tide comes in and out, obviously that doesn't factor erosion over time but its an accurate way of getting a coastline measurement for that moment in time

  • Aghate Wahedi
    Aghate Wahedi 5 days ago

    While you can basically turn anything infinite with fractals, i feel like two separate measurements would be great. Give your coastline in 1m intervals so everybody knows how many steps it would take to walk the beach/coastline, and them also in 100m to 1km intervals so that we get a rough geograpic estimate that matches our understanding of basic geometry and maps.

  • Victor Meng
    Victor Meng 5 months ago

    I just remember someone introduced a "puzzle" with a circle inscribed in a square . They tried to draw approximation of the circle's perimeter by "rearranging" the square's border.

  • Nicholas Hernandez
    Nicholas Hernandez 10 months ago

    Imagine measuring a coastline in real time and the tide messes with your measurements. There’s a bay in America that has a change of sea level around 40 feet or so twice a day. That would be amazing to measure in person…and infuriating.

  • Mister Sirius
    Mister Sirius 2 months ago

    This paradox can also be applied to rivers when seeking to establish the longest river in the world.

  • DrDestrukt
    DrDestrukt 2 years ago +3488

    "Let's move over to a smaller Country."
    UK starts sobbing... "not that long ago..."

    • Elliyana
      Elliyana 3 months ago

      @Jeff Willsea viva la vida and fallen kingdom

    • Bon Bonne Bonjour!
      Bon Bonne Bonjour! 8 months ago

      “Moving to a smaller country…”
      And if he pointed to the British empire, that’d be a wild move.

    • Nick Malachai
      Nick Malachai 10 months ago

      @Bup 64 - キノピオ England, Scotland, Aruba, etc, I'd argue don't have independent sovereignty and thus aren't countries, but are sections of a single country (The UK for the first two, the Netherlands for the last, although I don't know how thoroughly Aruba is intigrated with the rest of the Netherlands, considering the distance, so they might be different). Otherwise... What's the distinction between Scotland or England and, say, Texas, which has a functioning government underneath the US federal government?

    • Bup 64 - キノピオ
      Bup 64 - キノピオ 10 months ago

      @Khet The UK is a country, just like the Kingdom of the Netherlands, just they both have other countries inside of them. (England, Scotland, Wales, Sint Maarten, Aruba, Curaçao)

    • Reah Thorolund
      Reah Thorolund 10 months ago

      @KhY_17 Yeah, our country size is like that scene on Men in Black where Will Smith gets that pathetic tiny gun, we look at our country on a map and are like ''Ya tellin me that shitty little glorified life raft did fuckin what? Huh, weird''.
      To others, Great Britain is the island on the right specifically which the video got right, it's 3 countries, but pretty much one big country practically so both descriptions are acceptable imo given the complications involved, not just with EU.

  • Ilodibe uchechukwu David
    Ilodibe uchechukwu David 10 months ago

    I actually did an investigation into fractals and used similar methods to measure the coastline of the uk for my math class

  • zeph0shade
    zeph0shade 2 months ago

    I feel that this is like assigning a digital measurement to an analog world. Sure, there are equivalences, but in the end the most accurate "real world" measurement will come from a "real world" unit that has no fundamental restrictions.

  • AzraelThanatos
    AzraelThanatos 10 months ago +1

    For coastlines, you also have the issue of tides with high and low water levels

    GK SWARM 10 months ago +3

    I have thought of the solution!!! You measure in straight lines in whichever unit your measuring. E.g. if you are calculating in 10km, then you place straight lines of 10km down along the coast. It just depends on the UNIT. You basically create polygons out of the selected unit size. It’s far easier. Its all about relativity to other countries landmasses, so if you set up a universal / shared coastline measurement unit, everyone can use the same one

  • ValkyRiver
    ValkyRiver 2 years ago +741

    I measured the coast of Norway 5 times (using Google Earth):
    Attempt 1: 4000km (2500 miles)
    Attempt 2: 77300km (48000 miles)
    Attempt 3: 2600km (1600 miles)
    Attempt 4: 11200km (7000 miles)
    Attempt 5: 124000km (77000 miles)
    I also got a ridiculously large answer for Greenland, probably because I was using really small measurements.

    • ValkyRiver
      ValkyRiver Month ago

      @Bvarium Exactly right. But each time I used a different zoom/scale for measurement.

    • ValkyRiver
      ValkyRiver Month ago

      @норвежский парень I was measuring on a globe (Google Earth), but used really small measurements.

    • норвежский парень
      норвежский парень Month ago

      Greenland is not nearly as big as on Maps tho

    • Jean-Michel Devereux
      Jean-Michel Devereux Year ago

      @Some dude that rips planet in half right click and several options should show up

    • Jean-Michel Devereux
      Jean-Michel Devereux Year ago +1

      @Some dude that rips planet in half google maps has a feature where u can measure distance

  • Chili Corrigan
    Chili Corrigan 9 months ago

    Previously I understood coastline measurements to be as accurate as driving distances between cities. Having watched this video, I can now appreciate how naive that was!..

  • Jordan Costello
    Jordan Costello 2 months ago +1

    Yeah... I would just put a limit on the scale of features that I would count as coastline, then just plank together those units and add them all up. I might be cutting off bits of land and ocean, but in the end we might give travelers an adequate idea of how far they can travel along the specific region. But the video itself and the idea of natural fractals is super cool, mind blowing really.

  • Plasmagon
    Plasmagon 10 months ago

    Just count at the molecular level and use the WORLDO! (or a longer lasting time freezing ability) to stop time while you count.
    Then the coast line change can't happen until you stop using the time stopping ability.

  • ThatSmartIdiot
    ThatSmartIdiot 3 months ago +4

    I'll have you know I know EXACTLY how long Bolivia and Liechtenstein's coastlines are!

  • Ethanos
    Ethanos 3 years ago +18776

    Why doesn’t somebody just walk around Britain with a trundle wheel

    • Morgan Wheeler Year 11
      Morgan Wheeler Year 11 2 months ago

      @Blue I’m from London and I don’t hate you at all. Neither do I feel superior to you in any way. I love all people from the UK and don’t see you as any different than any Brit.

    • Craig Randle
      Craig Randle 3 months ago

      I’d imagine elevation would make a big impact. Which is interesting because I always considered coastline as linear but I guess it doesn’t have to be

    • Skunk Ape
      Skunk Ape 3 months ago

      @Jcat2224 you measure at the Mean High Water Line, which is a fixed point along the coastline, established by actual Land Surveyors.

  • CurvingFyre
    CurvingFyre 10 months ago +1

    I feel like theres some kind of weighted average you could achieve using a high detail measurement, and several lower detail measurements, to find a number that's accurate and practical.

  • KOBUN40
    KOBUN40 10 months ago

    At a macro level I imagine that this will play a part in the impossibility of determining the actual perimeter of the universe.

  • ClockworkGearhead
    ClockworkGearhead 11 months ago +1

    I mean, the whole point of cartography is to create practical, useful information for travel and building, right? So, if we make a standard based on travel time around the coastline, we can make a standardized measuring distance.

  • Daddy Nunya
    Daddy Nunya 2 months ago +1

    Not weird at all. The shore line changes by many, many miles with just the rise and fall of the tides. 4 times a day on the southeast coast.

  • Kev
    Kev 3 years ago +2740

    Can't a international organisation like U.N just agree that cost line is measured for all countries by, lets say 10 m?

    • ferrous719
      ferrous719 Year ago +1

      How far back from the water do you start? Do you only measure at low tide, or go thru high tide when it's shorter?

    • Himanshu Shekhar Das
      Himanshu Shekhar Das Year ago

      10m is very small to measure

    • Jeke San
      Jeke San Year ago

      @christopher draper Nah,America is clearly beta with all its military bases around the world fearing for some people with ak47 in mountains lmao

  • Andrew Boundy
    Andrew Boundy 10 months ago +1

    Measuring to the molecular level, the measurement would be accurate to one molecule, it would not be infinite - that assumes all measurements are infinite, which is silly. This paradox is essentially just "rounding the corners" - the more corners, the greater the accuracy variation. Not much of a paradox - "straight lines can be measured more accurately" - uhhh, OK.

    • Tom B
      Tom B 10 months ago +2

      Yea pretty won't get an infinitely big measurement by measuring small. It's just the smaller you go the more infinitely "accurate" you get, it's infinite because it can increase infinitely but it increases at an infinitely smaller rate the smaller you go, so essentially the "real" measurement would be like pi where the less you round the "bigger" it is, but it will never be 3.15.

  • Da Sledger
    Da Sledger 7 months ago

    As a Norwegian, I can confirm that Norway is absolutely an archipelago of an archipelago

  • Bitterleaf Castle
    Bitterleaf Castle 10 months ago +1

    Basically the same problem I have when mapping a hiking route into my phone map

  • Chris C
    Chris C 10 months ago

    I have a potential solution-
    Travel from a starting point at constant speed around any given coastline until you come back to the starting point. The absolute length (including length that results from changes in height of the ground from the sea level) is the time you spent (unit time) * your speed (unit length/ unit time)

  • Cara Furry
    Cara Furry 10 months ago +1

    How about this, we all agree on a middle ground measurement to use, and just make that the official way to measure coasts

  • Shift
    Shift 7 months ago +1

    I feel like this paradox can be solved with distance measuring wheels.

  • Elias Binde
    Elias Binde 2 months ago

    I’d say it depends on the purpose of the measurement. For military purposes I’d say using a unit of measurement around the scale of people walking, military camps, blockades etc. so when troops want to move along the coast the distance given is accurate within acceptable margins.
    I’d even say that can be generalized: the length of the shore should include the details a footpath or small road should be reasonably able to follow them. I’d say that’s how we’d get the most relevant measurements for any real purpose.

  • DGtv - Daemon Gaming TV
    DGtv - Daemon Gaming TV 10 months ago +2

    Reminds me of Zeno's paradox of the arrow in motion. Take an arrow in flight towards a destination. The arrow flies halfway there. Then the arrow flies half of the remaining distance, and again half of that distance, and again, and so on... how many halvings until it arrives?

    • Spectral Wiitch
      Spectral Wiitch 10 months ago

      Technically, never. If we have the destination set as 0, no matter how many times we halve 1, we will never get to zero. 0.5, 0.25, 0.125, 0.0625, 0.03125, 0.015625 ...
      We keep getting closer, but we will never reach zero.

  • Leo Baratin
    Leo Baratin 2 years ago +4353

    **Normal people** : Desperately try to measure Norway's coastline.
    **Me, with a lot of IQ points** : measure swiss coastline.

    • Minecraftfan5610
      Minecraftfan5610 Year ago

      @Leo Baratin Global warming was created by Switzerland because they actaully have the strongest military ever but its just a navy so they're waiting untill the oceans rise so much it lifts up their ships and then the swiss navy will rule the world.

    • Joshua pere
      Joshua pere Year ago

      @Gamer du Québec pls don't say Goddamn

    • Leo Baratin
      Leo Baratin Year ago

      @MrRedsjack I mean, mongolia has a fleet too... Yet I don't give a fuck 'cos I'm talking about coastlines my boy.

    • MrRedsjack
      MrRedsjack Year ago

      @Leo Baratin jokes on you as the largest merchant marine company in the world is Maersk which is Swiss.
      Also Switzerland has a sea port that links it to the ocean sailing along the Rhine. Google port of Switzerland.

    • Todd Blevins
      Todd Blevins Year ago

      @SKILLUBER Two guys in a rowboat with a bb gun?

  • F V
    F V 2 months ago

    Since the answer seems to be abstract and dynamic, the the solution will need to be abstract and dynamic as well. Use longitude and latitude to plot points and measure the distance between them using calculus. With at least one constant (gps) remaining the same, a “standard” can be set. Think measuring the perimeter of an odd sized swimming pool.

  • Cyr1lbibi
    Cyr1lbibi Year ago

    very well explained, I love this paradox

    • Jan Il
      Jan Il 3 months ago

      The thing is it’s not really a paradox. It’s just different distances depending on what you measure and how you measure it

  • qwert yuiop
    qwert yuiop 10 months ago

    You just have to use the length scale that makes the most sense for the application. For human perception of the landscape I think it doesn't make much sense to go below a meter or above a few hundred meters. For chemical purposes you'd go to micrometer scale and for weather phenomena you'd go to several kilometers.

  • Legionaru Emanuel
    Legionaru Emanuel 8 months ago +1

    I mean measuring a perfect circle can range all the way from a square to a hexagon or any other polygon untill it makes a circle at the subatomic level
    But I mean you could just measure with phisical means also...

  • Blue_Leader_
    Blue_Leader_ 2 years ago +767

    Actually, while it appears that the length increases indefinitely, it increases less and less with each new unit, so in fact the total length will approach a single value the more resolution you have. So in reality, there is a definite answer to how long any coastline is, it just depends on how accurate you want the measurement to be.

    • Ian
      Ian 8 months ago

      Great answer. It might appear to be exponential but isn't .

    • Michael John Little
      Michael John Little Year ago

      The smallest ruler in the Universe is the Planck length.... that should do it!! Just count the number of Planck lengths... including the distance between the atoms... around the coast and you cannot go wrong!!

    • Akmil
      Akmil Year ago

      Only thing is that that isn't practical at all.

    • Norman
      Norman Year ago

      So a limit

    • Franz Pattison
      Franz Pattison Year ago +1

      Replying to OP: That's only sensible. No finite line or circumference can be indefinite. In a similar but inverted model dividing by half can have infinite results because halving an existing number will never reach zero, but eventually you have so many zeroes after the decimal that it's meaningless to continue and functional zero is assumed.
      This coastline issue is similar except the number really is finite down to whatever the smallest unit of measurement is used, ie one electron. However using the smallest measure of distance isn't practical or necessary, so when using a common measure of distance like miles, eventually the integer would stay the same and the decimals would extend to hundreds or thousands of places. So at that point just use the integer. When it comes to a coastline even half a mile is inconsequential so 45,065 miles for example is functionally identical to one decimal place of 45,065.5, so just round to the lower (or nearest) integer.

  • CoolXG
    CoolXG 10 months ago

    You could just divide your answer to fit the equal value of measurement (e.g 1km = 1000m, so in turn say your measuring 60km of coast, and you get say 60000m because your measuring in meters, all you need to do is divide it by 1000 which equals 60km)

  • Huz7 Edits
    Huz7 Edits 5 months ago

    Wouldn't you driving on a beach from one end to another be enough to determine the coastline?

  • Jarkko Kainulainen
    Jarkko Kainulainen 10 months ago

    You can easily measure the length of the coastline of certain countries.. like Switzerland. No matter what unit you’re using.

  • Vercil Juan
    Vercil Juan 10 months ago

    I think we should just all standardize our unit of measurement of the coast to 1 meter, so we get a fine resolution without getting too small. If everyone agrees on it, it might be feasible to do it just like that and no more mismatch of problems will occur

  • Deven Hull
    Deven Hull 2 years ago +805

    The length of the coast of Great Britain is 1. As I failed to specify the unit, that could be one anything and is therefore technically correct (1 coastline of Great Britain)

  • iφhi
    iφhi 10 months ago +4

    if you've ever heard the saying "good enough for government work" you know how to solve this problem...

  • Setteduetto
    Setteduetto 10 months ago

    I already know this paradox but I clicked the video because I love seeing this illustrated.

  • Max Ferraro
    Max Ferraro 3 months ago

    Couldn't one come up with a system of functions which accurately describes portions of the coastline and use that to calculate the actual length of the coast?

  • Joey
    Joey 3 months ago

    I’ve never known what the coastline paradox is, nor have I ever had any interest in it. This has all change after watching this video

  • BoW Skittlez
    BoW Skittlez Year ago +781

    Simple solution: standardize the base unit for measure. A one line segment cannot be shorter than 10 meters and must not bend more than 45 degrees related to the previous line direction.
    It eliminates the paradox and standardizes how to measure the coastline

    • Naþan Ø
      Naþan Ø 2 months ago

      @Dukjin Im It's a Veridical Paradox

    • Naþan Ø
      Naþan Ø 2 months ago +2

      Law of Social Media #29: If you post a paradox, no matter how old and intractable, some idiot in the comments will act like the answer is obvious.

    • emerillon
      emerillon 2 months ago

      @Oskar Jung don't skip classes too much or your name will be known for a different reason than you wish.

    • DaHolyCanadian
      DaHolyCanadian 2 months ago

      @Nicholas Miller Except the paradox is just a mind game. It has no reason to be even considered if a standardized system is made except to entertain you in a video like this.

    • Skunk Ape
      Skunk Ape 2 months ago

      @Scottie Lowe except that's nowhere near "right". Otherwise Land Surveyors would have switched to that method centuries ago. You can't standardize a measurement and expect to retain accuracy. OP's "simple" solution would only serve to further extrapolate error, therefore further reinforcing the paradox. Land Surveyors already have a near perfect process of measuring land by way of the Pythagorean Theorum and the concept of least squares. Angle and distance is literally the best and only way to accurately measure land.

  • Richard Bread
    Richard Bread 10 months ago

    The tide changes the coastline constantly, so there is a limit on the level of precision. If you want a non-arbitrary unit of measurement, why not measure the average distance between high and low tide?

  • Kevin zheng
    Kevin zheng Year ago +2

    Its all relative, just use the same assumption/standards of measurement with respect to time. Different initial assumptions leads to meaningless comparisons.

  • Sean J
    Sean J 10 months ago +1

    If you’re measuring other lengths, e.g. a border between two countries, in kilometres, then use that same unit to measure the coastline. Why would you create a problem by continuing to subdivide the units just for the coastline measurement? It’s asinine.

  • karanis_jr
    karanis_jr 9 months ago +1

    There is 1 way, I guess... You could add all the answers, and then divide the answer by the number of the guesses.
    e.x. 1, 2, 3. 1+2+3=6 6/3 (because 1, 2, 3, are three guesses)=2. The averege is 2.

  • Octoria Gaming
    Octoria Gaming Year ago +3619

    "Let's move on to a smaller country"
    Great Britain: I used to rule the world

    • e30kitty
      e30kitty 10 months ago

      @Marie-Pier Edwards But you are right about the population. The USA has 2x the population of russia while china has 4x the population of the USA xD

    • Marie-Pier Edwards
      Marie-Pier Edwards 10 months ago

      @e30kitty ok

    • e30kitty
      e30kitty 10 months ago

      @Marie-Pier Edwards I'm not russian i'm german haha XD

    • Andreas Kvisler
      Andreas Kvisler 10 months ago

      * *Viva la vida intensifies* *

    • Marie-Pier Edwards
      Marie-Pier Edwards 10 months ago

      @e30kitty usa: but I’m more populated than you haha

  • AM Games
    AM Games 10 months ago

    I mean, say you had a car that could hover and account for any bumps and cliffs in the geography. If you just drove it along the coast, including the coast of all the islands, wouldn't the odometer give you the true answer?

  • Phox Games
    Phox Games 2 months ago

    What if, instead of measuring a map, we walk the coastline with a measuring wheel and then record the total length. Math is theory and thus why you can come up with a million different answers.

  • Gabifuertes
    Gabifuertes 9 months ago

    How about this: measure the coast in the number of that can be built around it. This way, you measure with area. If the land is thin, you can't build anything, so you just consider it part of the sea.

  • Desert Foxchild
    Desert Foxchild 10 months ago

    I measured Norway but then created a new measurement system that makes everything simple. The answer is 1Nw or 1 Norway. It will always remain a constant of 1 because the measurement is based on the current length of Norway's coast.
    It's impossible to measure anything else by this measurement system though.

  • Pigman Rocker
    Pigman Rocker Year ago +3598

    "and then there is the Dutch".
    Yes, your arguments are invalid. There is no such thing as sea, only unclaimed land.

    • Alejandro Aguirre
      Alejandro Aguirre 2 months ago

      It actually wouldn't get to be infinite, you would get closer and closer to the real number, actually infinitely closer, but It wouldn't grow at some point, it's just logic

    • Jayyy Zeee
      Jayyy Zeee 3 months ago


    • Matthijs Calje
      Matthijs Calje 3 months ago

      Hahaha gekoloniseerd geinig

  • Dukjin Im
    Dukjin Im 3 months ago

    They should have a standard “polygonal measurement for coastline, based on a standard minimal distance of 1 meter or something like that. And use a computer with standardized process on an image of standard resolution/meter, under standard conditions. Just to have a standard.

  • Pikachu Prime
    Pikachu Prime 11 months ago +107

    Math teacher: aw come on the homework is easy
    The homework:

  • JamieTheDinosaur
    JamieTheDinosaur 7 months ago +3

    That’s one benefit of living in Colorado, Wyoming, New Mexico, or Utah: You can know exactly what the perimeter of your state is without having to estimate!

  • Brandon Alsop
    Brandon Alsop 2 months ago

    I made my measurement unit to be 1 Norwegian coast line and found that the Norwegian coast line is 1 Norwegian coastline in length.

  • GRBTutorials
    GRBTutorials 3 years ago +1141

    There is a finite amount of molecules in the coastline, and a finite separation between them, so the total perimeter measured with molecules is still finite. And it’s much closer to 0 than to infinity (though that’s true of every number).

    • playaaaLV
      playaaaLV Year ago

      @Xedoc Culinaris depends on how close you are looking - following the same dumb idea from the video it does.

    • Xedoc Culinaris
      Xedoc Culinaris Year ago

      I don't get your analogy wiith iso 216 . The paper is defined by hight and width. Paper hight or width is not systematically increasing when measuring more accurately.

    • Xedoc Culinaris
      Xedoc Culinaris Year ago

      I don't really understand what you mean. The string, the more accurate you measure will always be smaller than X meter and bigger than X meter. It is not a fractal. The geometry is defined. You can't measure/ calculate a definite maximal length of the coastline. If you can, I believe you.

    • Jeff Willsea
      Jeff Willsea Year ago

      @: 3 the foot!!! XD

    • Максим Глоба
      Максим Глоба 2 years ago +1

      Infinity isn't a number

  • The Raccoonasaur
    The Raccoonasaur 8 months ago

    I figured it out. If you have a 6 foot bendable tube and you bend it, it will still be 6 feet. Just use meters or kilometers and bend them so that they fit the coastline.

  • ObieTriceratops
    ObieTriceratops 2 months ago +1

    This is more an issue with language than anything else. The question "what is the true length of a country's coastline" is not meaningful to ask and has no definite answer because coastlines are arbitrary and abstract divisions of quantum fields that we've perceived.

  • Nicolas Derome
    Nicolas Derome 3 months ago

    I think a measurement unit of 10m makes sense because that's the size of a large wave, and can be measured easily with satellite imagery. Yes, that will result in Norway having a massive coastline, but I think that's valid. If you don't want to include the fjords, you can measure the length of their territorial waters or something instead.

  • Blookbug IV
    Blookbug IV 10 months ago

    I kind of grew up with the idea that coasts were fractal, doesn’t strike me as much of a paradox. Seems obvious the number depends on the scale of the squiggles you measure along. I can imagine this issue was more surprising to people before fractals were popularised and became part of all our collective understanding of nature.

  • PsyintZ
    PsyintZ Year ago +454

    Now we just need someone to walk the Norwegian coastline counting their steps with a fitbit.

    • Micah
      Micah 3 months ago +3

      ok i got 76082mi what about yall

    • Susanne Moseid Bryhni
      Susanne Moseid Bryhni 10 months ago +6

      @Bakerguttenjust gotta walk it different directions
      Whiiiiiiiii splash

    • ShardTheDDon
      ShardTheDDon 10 months ago +31

      @Bakergutten “It builds character”
      -Your Boomer Father

    • Bakergutten
      Bakergutten 11 months ago +30

      ive seen fjords go from sea level to 1000 meters above the sea in like 5 steps, gl walking that coastline

    ABH ABH 10 months ago

    Cant you use a tape and thus avoid the problem of being limited to straight lines?
    This method should give the best answer.

  • Louise Franks Art
    Louise Franks Art 8 months ago

    Norway's coastline is absolutely me, I've seen most of it. It's just full of fjords and little coves and tiny little so many islands. it really is very large coast-wise.

  • jbb
    jbb 3 months ago

    The problem is that they’re counting the coast lines that curve inward (towards land)

  • Paul Kocyla
    Paul Kocyla 2 months ago

    Is there a standard for this?
    Intuitively, I´d take the measurements with the highest resolution possible and apply a low-pass filter to the path integral.
    The filter coefficients that make practical sense could be defined as a standard.
    With "practical sense" I mean resulting in a path length similar to a boat trip along the coast.
    Any high resolution measurement would then render the same values. I wonder how the function F(resolution)=path_length looks like?? Is there a region that is kind of stable (doesn´t grow fast over time), or does it run up strongly monotonously?

    • Ron Geurts van Kessel
      Ron Geurts van Kessel 2 months ago

      Judging from the video there is no standard. I agree, my suggesting would be to use some kind of "common sense" approach, and come to some kind of consensus what "coastline" means to most people, which obviously isn't "infinity". I imagine if you ask a hundred people you'd end up with what is a rough outline of a coast (as if you were to pass by on a small boat), in 50 or 100km increments or something like that, using a filter if necessary as you suggest. You'd end up with, what, 1.300 miles or so for the US west coast, 3.000 or so for the east coast?

  • Art hur
    Art hur 2 months ago

    I also had this problem when i was a kid. (I still am)
    I was into racing. And each track has different length.
    I was wondering how do they measure the length of the track. Do the measure using the racing lines? Do they average the outer circuit and the inner ?
    Do they use tape measure? If the do it wouldn't be accurate due to tape measure width...
    Back then i thought i was stupid because i cant came up with a definitive answer

    • evil993
      evil993 2 months ago

      @Art hur I have no construction experience and definitely no experience building race tracks specifically, but I'd image that for the purposes of racing that you'd only really need to get a close enough measurement. You could do something like using one of those distance measurement wheel on a stick things, draw the course, and then expand that line you drew out to full sized track roads, and then that would be close enough. Or like you mentioned I'm sure an odometer mounted on a car would get you close enough for most racing purposes.

    • Art hur
      Art hur 2 months ago

      @evil993 ohh yeaa
      Youre right.. Measure the materials needed for the track.
      But is that how they do it though?
      Or is it something more simplistic by just letting a racer drive around the track, set the odo meter to 0. and see the result

    • evil993
      evil993 2 months ago

      You could, in theory, measure the total amount of material that went into it's construction, create a smallish "sample section" that has uniform measurements equating to the rest of the track, record the amount of material that goes into it, and then extrapolate that out to the amount of material you have in the total construction of the track. I wonder just how much of a difference in distance there is total if you did a lap in the center of the track vs a lap on either outer edge of the track. Obviously the center one would be longer, but I wonder by how much.

  • swami dude
    swami dude 3 months ago

    I guess we just have to build a sattelite that fires a laser and can determine if it hit land or water. Then have it do multiple runs at different tides and average it out.

  • kitghost1
    kitghost1 2 months ago

    If I'm understanding this correctly, wouldn't just making a standardized coastline measurement unit fix this? Yes it would be hard to decide how long the unit was and it would cause some inaccuracies but atleast then the numbers could be compared equally

  • Dukjin Im
    Dukjin Im 3 months ago +1

    As for the “paradox”, why is it called a paradox at all? It’s just a meaningless question. You only have a paradox when there are two ways of looking at something that are both valid but contradict. In this case, there is just one way of looking at it: the question is wrong. The concept of polygon or shapes or borders only loosely apply to reality, and don’t accurately describe real world objects. Nobody in the word owns a solid “cube” or a “triangle” shaped anything. Because matter is mostly empty space, and countries are a collection of particles, non-continuous.

  • Jack Pada
    Jack Pada Year ago +4480

    heres my solution:
    - get a standard unit for measurement of coasts (say 1 meter)
    - wait for the us to not abide by the standard unit

    • kingkidtmgaming
      kingkidtmgaming 5 months ago

      yes The communist unit of measurement!
      Just to let you know what I said was a joke

    • God of Squirrels
      God of Squirrels 8 months ago

      @Astoroidea screw Celsius for everything but cooking and science. 0 is super cold and 100 is super hot. No decimal points needed

    • The Tavern
      The Tavern 8 months ago

      - profit

    • Dynamic Solution
      Dynamic Solution 8 months ago

      Americans don't need their fingers and toes to count...our base 12 is more accurate.

    • david rickard
      david rickard 9 months ago

      Here's my solution get over 100 colonies lose them all by 1970

  • shay campbell
    shay campbell 2 months ago

    if you know what limits are you'll know that there's np way you can get a perimeter of infinite for a coastline since the coastline is finite. even if you break it down an infinite amount of times you still will approach a finite value.

  • Frank Lombardo
    Frank Lombardo 3 months ago

    All of this assumes that you measure a coastline in qusntized boxes chosen to follow the path of the coast. Essentially using larger boxes ( measurements) means you ignore some level of variance.
    But suppose in stead you took a string and mapped the coastline with it. Then remove the string to get the length. By that method don’t you reach the upper limit of your measurements.

  • Patrick Evans
    Patrick Evans 8 months ago +1

    it would be simple, but labor intensive, to measure. Just get on of those wheels on a stick they use to measure distance with, and walk all the coastlines on earth.

  • Steve The Duck
    Steve The Duck 2 months ago

    Have been to a beach and a river estuary, tidal, that creates new streams and rivulets every time the tide goes out.
    I have seen that the little rivulets become smaller and smaller, branching out, and stop at the size of about the tip of a pencil.
    I expect sand / mud of smaller grain size might go a little smaller.
    Like the people who used Aristotle to decide how many teeth a horse has, it's possible to go to the edge of the water and pull that horses' mouth open and count.
    Give it a try, folks. I don't need to deny the evidence of my own eyes.

  • Jera
    Jera 3 years ago +1872

    Just use the Planck Length for measuring for the most accurate answer.

    • ferrous719
      ferrous719 Year ago

      How far back from the water do you start?

    • Excaliber
      Excaliber Year ago

      @Diogo Rodrigues couldn't you texhniqualky measure it if you put it into a massive vacumme and blasted it with electrons

    • wall
      wall Year ago

      Big brain

    • Statalyzer
      Statalyzer Year ago

      But you'd have to remeasure constantly as the water moves.

    • deg1studios
      deg1studios Year ago +1

      @chair get a computer to do it man. have a lowflying airplane take superzoomed pictures of the coastline with high contrast, and have the computer (with machine learning) divide the coast into water and land. then have it estimate the length of the coast in planck lengths. the plane can use a laser measurer that records the distance from the ground at any one time. the computer will use that distance in a formula to determine how many planck lengths a pixel from the camera footage represents.
      have 50 airplanes do this, each taking off from the same location with a 30 minute delay. the computer computes all of the planes's footage (after the fact, not in real-time), and divides each of the planes's footage into small segments that correspond geographically to the other planes's footage. the computer takes the average result of the 50 versions of each segment, which makes irregularities in any one plane footage less crucial. since the last plane takes off 25 hours after the first, we'll get the average result of high tide, low tide, and everything inbetween.

  • Charlye'Charleston
    Charlye'Charleston 11 months ago

    Essentially there isn't actually such a thing as a coast"line" as a natural phenomenon. It is only ever an abstract concept, conceptualized as a rule of thumb.
    There is only ever coastal area with no clearly defined beginnings nor endings, transitioning into mainland somewhere in some directions and into the sea or ocean in other directions.

  • Stefan Cristian
    Stefan Cristian 3 months ago

    can't you just measure it my walking around the whole coast?
    It would be time consuming, but would it work

  • DrScopeify
    DrScopeify 7 months ago

    You can just use the length of territorial waters which is a straight line along the international maritime boundary. Easy straight line removes all of the costal curves