Why You Can’t Measure the Coastline of Britain

how long is the coastline of the United States you might think the answer to that question is as simple as typing it into Google and seeing what comes up or measuring it all out yourself but it's actually a very strangely complicated question it might be impossible for anyone to really answer no when you type the question into Google you'll end up with three completely different answers from three separate trustworthy sources the Congressional Research Institute cites that the length is 29 093 miles while the CIA cites a different number at 19924 Miles while the National Oceanic and Atmospheric Administration or NOAA cites a way higher number at 95 471 miles and the discrepancy between all three of these different organizations answers isn't unique to just the coastline of the United States consider the following question which country has the longest coastline in the world most sources will agree that the answer to that is Canada which might not be too surprising because Canada is a geographically huge country and the second largest in the world where its sheer length of Coastline can be clearly on a map but according to the cia's World Factbook the answer for the country with the world's second longest coastline is a lot more interesting and less expected Norway it's potentially unexpected because Norway isn't really a huge country and at first glance it doesn't really look like Norway's coastline is particularly long either but the thing about Norway is that the closer and closer you zoom in on the Norwegian Coast the more complicated it appears to become the coast is dominated by Jagged fjords that zigzag around in every direction and then there's all this seemingly endless amount of islands to consider as well it turns out that Norway actually has the second highest number of islands of any country in the world there's more than 239 000 of them in fact the top three countries in the world by number of islands were all pretty surprising for me to find out because they're all just next to each other right here in Scandinavia Sweden Norway and Finland these three countries alone possess more than 685 thousand different Islands between them which is rather astonishing because that's more than three times all of the other Islands everywhere else in the world combine it's just that most of the Scandinavian islands are all really really tiny and uninhabited like just look at all these little islands around the coast just outside of Stockholm it'll take you days to count all of these up so when measuring the coastlines of each of these countries the lengths of all these hundreds of thousands of islands must be individually calculated and added to the sum of the country's Mainland Coastline and since Norway's Mainland coastline is also super Jagged pretty much everywhere and there's hundreds of thousands of islands it's not that hard to understand how the CIA came to the conclusion that norways is the second longest coastline in the world their final calculation came out to 51 748 miles for the total length of the Norwegian Coast which is more than two and a half times the length of the entire United States Coastline that they also came up with but also only about out half the length of the United States Coastline that Noah came up with separately essentially everybody you ask how long a certain coastline is will always give you a different answer and this phenomenon is known as the coastline Paradox it's also rather easy to see how this can end up happening when you try and measure the coast of a country yourself let's take the United Kingdom as a rather straightforward example the UK is an irregular shape with many different Islands bays and peninsulas and no matter how close you continue to zoom in on a place like the west coast of Scotland the coastline only gets more and more detailed down to the point where you reach the beach itself and the individual grains of sand that make it up the hardest part about measuring any country's coastline is therefore deciding where to even start and if you want to be completely accurate with your final number you're gonna have to closely analyze every single piece of the coastline with something like an electron microscope and even then it still might not even be enough since that would probably take an infinite amount of time it's far more straightforward to to Simply estimate the total length of the coast instead and the easiest way to do that is by taking a map and placing many equally sized segments or rulers around the country's perimeter and then adding up the lengths of those segments so let's use a ruler that's 200 kilometers long we Place several of these 200 kilometer long rulers around the coast of Burden until we surround the island with 12 of them which when added altogether equals an estimated length of 2400 kilometers all right but then let's replace the size of our rulers with one that's only half the size at 100 kilometers long we do the same thing with these smaller rulers and now find that it takes us 28 of them to surround the coast which when added up gives us a new Total estimated length of 2 800 kilometers 400 more than we had during the initial measurement and then if we have the size of the ruler again to 50 kilometers it'll take us 68 of them to surround the coast and adding them all up gives us another estimated length of 3 400 kilometers which is now 600 kilometers longer than we had during the initial measurement when we were using a larger ruler that was four times longer this is the coastline Paradox in action each time you use a smaller ruler to measure the length of the country's Coastline the answer becomes increasingly larger to the point where eventually you could be using ruler sizes down to the atomic level and the answer would begin approaching infinity and this means that the more complex in areas coastline is the more open its length than span is to personal interpretation which has had fascinating implications on global geopolitics throughout the ages one of the greatest historic examples of this mathematical principle causing diplomatic headaches before it was well understood was back during the late 19th century dispute between the United States and the United Kingdom on where the border between them across Alaska and Canada should actually be set you see everybody back then had a different idea on where this bordering what is today the Alaskan Panhandle should actually be placed the United States insisted that it was here while Canada and the UK government insisted it was here while the British Columbia government further in insisted that it was actually here and much of the differing claims here stemmed from the different ways that every party was measuring the coastline 40 years before the Americans purchased Alaska the territory had belonged to the Russians and they signed an agreement with the UK that partially defined the Border here with a highly ambiguous phrase that read a lion parallel to the winding of the coast of course the coast and the Alaskan Panhandle region looks pretty much just like the coast of Western Norway and it's covered in Jagged fjords and Scattered Islands meaning that the extent of how much the coast winds is sort of open to your own interpretation and the way you measure it which ultimately meant that the Border could also be pretty open to interpretation when measuring out the border that was parallel to the winding of the coast everybody involved used a different way to measure how much the coast winded that happened to benefit their own geopolitical claims and thus everybody came up with wildly different claims on where the Border should actually be placed after Alaska's border was firmly set by arbitration in 1903 and after the territory became a state half a century later in 1959 it easily became the U.S state with the longest coastline by most measurements and that's not really a surprise because Alaska is by far the biggest state in the country by area but of course the issue of how to accurately measure Alaska's Jagged Coastline in many islands has remained a problem in cartography through to the present day using two totally different methods the Congressional research service published a report for the U.S Congress that measured the Alaskan Coastline at 10 960 kilometers while NOAA measured it separately at nearly five times longer than that at 54 563 kilometers which does seem a little absurd because that's longer than the entire circumference of the earth regardless of how they came to these wildly different conclusions both the CRS and Noah agree that Alaska has the longest coastline of the U.S states and they each agree that Florida has the second longest coastline but fascinating they both disagree significantly from then on for the rest of the state's order because of their different yet still equally valid methods of measurement the CRS believes the California and Hawaii possess the third and fourth longest coastlines of the states which kind of makes sense because California has a long coastline and Hawaii is a bunch of islands but Noah conversely insists that the order after Florida is actually Louisiana and Maine for the third and fourth longest coastlines which seems odd because when looking at a big map the Louisiana and Main Coast seats appear much smaller than California but when you zoom in much closer to the California coast and scroll across it you'll notice how smooth of a curve it is almost continuously from the south to the north conversely when you zoom in more closely on either the Louisiana or Maine coasts you can quickly see how insanely Jagged and fragmented both of them are pretty much everywhere and when using smaller units of measurement like I assume Noah was using it's not that hard to see how they came up with the Louisiana coast being more than twice as long as the California coast and how in using longer units of measurements like I assume the CRS used they came up with the opposite result that California's Coast is roughly twice as long as Louisiana's the fascinating thing though is that both of those answers are technically true and it's simply just up to your own perspective and opinion on whether or not California or Louisiana have the longer Coastline saying one is longer than the other is not a definitive fact and is purely subjective this concept of the coastline Paradox was first noticed and written about more than 70 years ago in 1951 by a cartographer named Lewis Richardson he had been studying whether or not the length of borders between countries had any effect on their likelihood to go to war and during his research he noticed a peculiarity between the border of Spain and Portugal this is the longest uninterrupted Border in the modern European union and it is the second oldest border anywhere in the world having been continuously fixed in place for well over 700 years now ever since 129 97 there has been a very long time for each side of that border to understand its length and nonetheless Richardson noticed that the Portuguese and Spanish maintain Different official links for it the Portuguese felt it was 1214 kilometers long while the Spanish fell to a shorter at just 987 kilometers this was of course simply because the Spanish were using a longer ruler to measure the Border than the Portuguese were using an effect that was later dubbed the Richardson effect the sum of the segments used to measure a curved line like a border or a coastline is inversely proportional to the common length of those segments in other words meaning the shorter the segments used to measure the longer the measurement of the curved line becomes and the closer you get to the curved Line's true length now this method of measuring mostly works fine for smooth curves like the coast of California or the coast of Africa but it starts breaking down when you attempt to measure Jagged coastlines like Norway Scotland Alaska or Louisiana the closer you look at these kinds of coasts the more rough edges are revealed so when you use smaller and smaller rulers the length of the coast doesn't ever converge toward any fixed answer that everyone can agree upon it just keeps getting longer and longer as you approach infinity and so an answer has to be given before you get to that point this concept was even better explained a decade later in the 1960s by The Works of the brilliant mathematician Benoit mandelborough who developed the concept of fractals and geometry in his 1967 paper titled how long is the coast of Britain mandelbro explains the concept of fractals applied to measuring the coast of Britain one of the main properties in geometric fractals is their self-similarity meaning that no matter how closely you continue to focus on them the same general shape continues to appear throughout Jagged coastlines in particular like the west coast of Scotland essentially act like fractals because no matter how closely you magnify The View on them a similar pattern of jagged edges appear right down to the very grains of sand and atoms Beyond and down at that Atomic level the coastline is always shifting around round because of erosion caused by constant wind and tidal forces which theoretically could mean that your measurement of the coast could become infinitely long and is thus undefined without an exact satisfying answer in these kinds of environments the best any of us can really ever do is simply estimate the length of the coast as mandelbro is certain in his paper when he wrote Coastline length turns out to be an elusive notion that slips between the fingers of those who want to grasp it therefore any measurement of any Coastline you ever see going forward is not exact and will always be an estimation based on the biases and methods used by the person or organization that did the measuring always take them with a grain of salt and skepticism now you can learn even more about the coastline Paradox and the Beautiful World of geometry through today's sponsor brilliant which heavily inspired this whole video you just watched before making this video I had a basic understanding of geometry from classes I took more than a decade ago in high school but anything much more complicated was just going right over my head I've always struggled with learning math and science and I don't know what I don't know which makes asking the right questions online to Professor Google really tough but then I went through brilliant's course on beautiful geometry which took me through from the very Basics I understood tested my understanding along the way and explained to me the correct answers in detail anytime I got something wrong one of the most difficult parts for me about learning anything new is simply knowing what the right questions are to ask but brilliant removes that barrier for you with curated and guided courses that are designed to steadily level up your knowledge you 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Channel: RealLifeLore

Views: 1,639,318

Keywords: real life lore, real life lore maps, real life lore geography, real life maps, world map, world map is wrong, world map with countries, world map real size, map of the world, world geography, geography, geography (field of study), facts you didn’t know

Id: AD4vPNBSrKY

Length: 14min 20sec (860 seconds)

Published: Fri Dec 16 2022