This video is made possible by brilliant.org. The first 755 people to sign up with "Brilliant", will get 20% off their premium subscription. So, here's the problem that this video is going to be talking about. If you look at any map and see America, you might think that it's easy Just measure the outline of the country and you have your answer. Several people and organisations have already tried this though. Like the Congressional Research Institute, that calculated it to be A second study from them that changed it to The CIA puts it at and a study from "NOAA" calculated the shoreline to be You may have noticed that all of these numbers are different. Which is weird, because they're all just measuring the same coastline. So, what's going on? Well, let's move over to a smaller country like, the United Kingdom and measure the coastline of Great Britain to get a clearer picture. Obviously, the coast of Britain isn't straight Every time you look closer at a line that looks straight you'll see more curves & bends So, how do you measure the length of the coast if, every time you look more closely, it never actually becomes straight You end up using the smallest measurement unit feasible. So, if you were to measure the British coast, using length of 100km you'd end up using 28 of them and get an answer of but if you shortend your measuring units down to 50km's you'd end up using 68 of them and get an answer of which is, 600 kms longer than your first measurement was! This is called and anybody's answer to how long a coastline is depends on what size of measurement they're using first observed by a guy named Lewis Fry Richardson back in 1951, as a way to explain how Portugal and Spain had come up with totally different answers to their mutual border length. The coastline paradox has been annoying cartographers ever since Basicaly, the smaller a unit measurement you use to measure a coastline the longer your answer will become You could, theoretically, go all the way down to the molecular level for your measurement unit but if you do that, the length of the coast seems to approach infinity it doesn't seem to make any sense that you can have a defined space with a finite area, like Great Britain be surrounded by an infinitely long perimeter but there is a similar concept that can be found in mathematics called A "Koch Snowflake", is probably the easiest way to visualise this concept So, imagine a triangle, with equal sides of one put another triangle of each side with equal lengths of one third you can keep repeating this process forever and if you zoom into a snowflake it essentially goes on forever. when you zoom back out to the original starting point you're left with a shape that has a finite area but an infinitely long perimeter A lot of coastlines across the world has similar properties to this so, you can keep zooming in and zooming in on the coast of Britain and the coastline will continue to look roughly the same No matter how far down the rabbit hole you go as mentioned previously, you'll eventually hit the molecular level, if you zoom in far enough and you'll be measuring a beach by counting atoms if you did this forever, you'd find the coast of Britain to be probably millions of km's in length which, just isn't very practical or easy to understand There's also the minor problem, that coastlines tend to change all the time, with erosion every time a wave crashes on a beach, it's shape it changed by a little and that is really hard to accurately pin down on top of this, sea levels are rising around the world which can drastically alter the way a coastline looks in extreme case, like what might happen to the maldives in a few decades entire land masses may become completely swallowed on the other hand, there's the dutch who have been adding land to their coastline now for over 700 years. The point is, Earth is constantly evolving. So good luck going out to a coast with a microscope and measuring the length that way. Every number you see online or in a book for how long a coastline is, is basically just a The true value is impossible to know, and that is the Just take a look at this list from the CIA world factbook on the countries with the longest coastline for a few surprises According to them, Canada is first, which kind of makes sense but the really surprising one is Norway, in second place at a first glance Norway's coast doesn't seem too long especially when compared with countries such as Russia or The United States but when you zoom in closer, Norway's coast get's pretty wild Just look at all these nooks and crannies and islands and fjords The CIA puts the total length of this coast at which, if you stretch that out all in a vertical line would circle the entire Earth at the equator almost one and a half times if you want to kill your entire weekend and see the coastline paradox in action try measuring the Norwegian coast from the south all the way to the border with Russia and put a comment down below comparing your answer with everyone else's of course if you want to do this, or any other coastal measurement. You'll need an understanding of Geometry, Algebra and Fractals Numbers and concepts like these are confusing for a lot of people including myself It was confusing for me, at least, until I tried Brilliant.org rather than telling you how to do algebra problems by memorising things they start by teaching the intuitive ideas behind algebra by playing through their puzzles, you get to understand, how algebra works Brilliant also has tons of other really interesting courses on topics like astronomy. Solar energy Computer memory and special relativity, which similarly, guide you along as you build your core knowledge You can take as many of these incredibly designed courses as you want with their premium subscription which, by being one of the first 755 to click on the link in the description you can get for 20% off [End Screen]
Not as click baity as the rest of his videos.
While I certainly see that measuring with large lengths will produce smaller totals, I'm really not seeing how measuring at the molecular level approaches infinity, unless you chose an intentionally over-convoluted path.
Surely the International society of cartographers or whatever simply need to set a defined unit to which coastlines are measured? Say, 100 meters? Are we agreed? Great! Prob solved lets get a pint.
This isn’t a paradox, it’s just the way fractal geometry works
So you’re saying if I measure my dick at the molecular level...
On another note, the scene of the UK coast at 3:08 is Dawlish in Devon, lovely place!