As a Brazilian, I will accept any measurement that shows that the Amazon is longer than the Nile, even if you have to count Pedro's toilet pipes that dump into the river to increase its length.
Coastline paradox arises mostly from lines heavily zig-zagging in tiny scales. But rivers are not one-dimensional lines, they have widths, so I believe the paradox can easily be avoided with carefully chosen definitions. For example: given two points A and B on the river, the distance between A and B is the shortest distance one would have to travel while remaining on the river surface. That should smooth out any zig-zags. Now all you have to do is choose such A and B that would maximise the distance (B obviously should be adjacent to a sea or ocean). That should not only bypass the coastline paradox but also prevent such "tricks" like adding the lake coastline instead of a shorter path across the lake.
The lake shouldn't even be included either because it's a lake and therefore not the river. It's merely the source of it but not where it starts. It should be measured from the mouth and triviaries don't make sense to include either if we refer to them as entirely differently named rivers. I don't get why this is complex either lol
@@lunaloveless7234 The fact that a part of the river has a different name doesn't mean its not the same river. That is a horrible argument. There are streets in my city that change names randomly, but the street still goes in the same directions and has the same number of lanes. It doesn't become a different street just because the name changes. Excluding a portion of a river just because some people decided to call it something else makes no sense. You pretty much just displayed why it's complex in your own inability to see the flaws in your own statement.
@@bh_quicksilver251 lets say your streetruns thru a park and is a diff name on the other side, diff # on houses. It would not be the same street. U cant take a tributary river that runs into lake victoria and make it count as the Nile. The nile starts at the mouth of the lake. The lake is lake victoria not the nile river. Anyway u calculate it: the Amazon wins.
The ONLY thing that makes sence is to add the longest tributary rivers to it. Why are you comparing rivers to streets, its not the same. The whole point of measuring river lengths is to know the distance the water travels across the land. It's RETARDED to cut the measurement short just because certain parts of the river were discovered by different people at different time and therefore are named differently. Naming has nothing to do with actual geography of earth, naming different parts of a water stream differently doesn't fucking change it's length.
Thank you, this is exactly what I thought as well. Going in the middle results in theoretical infinity, but going with practical route (it has practical use because it's what you'd want to approach with a boat if you wanted to travel the shortest possible distance) results in a non-arbitrary, finite length.
3:57 This statement is misleading. Infinite chunks of infinitely small size don’t necessarily add up to infinity (see also: Zeno’s Dichotomy Paradox). It is well within the realm of possibility that as you approach infinitely small measuring steps, you also approach a fixed value. This is also true for coastlines. The number approached will be very much higher than a more useful value, but the value “increasing to infinity” is kinda a thing people just say that they assume is correct. Fractals have an infinite scope, whereas the world has a fundamental smallest length.
Just a guess off the top of my head, but I'd say linear algebra could help you find the equation of the line the river makes in slope intercept form, and then you could use good ole fashioned calculus to find the length of the curve.
*Decreasing the fractal size increases the length of the river logarithmicly, not to infinity. Once you reduce your measuring size to "continuous", using euler's number will find the true maximum size.* The reason why countries dont have continuous measurement of their coastline is that it's impossible to achieve practically.
Elementary school: The Nile River is the world's longest river! RealLifeLore: Are you sure about that mate? Me: Yeah....since I'm not currently in a mental institution....I'm sure. ¬_¬
sure what I learned in middle school Nile is longest and Amazon is largest even when a nerd ask about Amazon tributary and say Amazon look longer geography teacher discuss same things that real life lore mentioned where want to start and end and the funny thing that was 25 years ago for me and still no one agrees
I think there's some problems with what's being described here. Definitions of rivers aside (which _is_ a big issue; like whether lake Victoria counts as part of the river), there's no fractical problem and not much other measurement problem. You just need to measure the shortest distance possible. No running along the edge of land, and hence no fractal problem. When it does encounter land it only hits the "pointiest" tips, so it doesn't get much worse the more you zoom in. Sure there's still the issue of water levels changing the measurement distance, but that can be dealt with in it's own way (like measuring at max an min)
But there is. Did you not pay attention? Using centimeters allows you to follow the river and always be centered in the river, using kilometers sometimes allows you to be in the river, sometimes jumping over land because it can only be so curved and still measured accurately. Using a different scale greatly changes how long a river is as well as makes way for the country border paradox the narrator also mentioned. Theoretically this problem becomes more and more of an issue the smaller your scale is / despite a smaller scale being more closely accurate.
@@TJ-im5kp, plus, where is the center. Do you measure it down to 100 meters, 50, 10, 1? What is 1 meter is too much? Let's try a centimeter, a millimeter, or a nanometer
The only problem with this is that for practical purposes, measuring the shortest distance possible would be misleading for boats that have to travel the river and want to know the distance they have to travel.
@@Doublemonk0506 What? That doesn't matter because meters are universally defined as the length of the path travelled by light in a vacuum in 1/299 792 458 of a second. A centimeter, milimeter, or nanometer's definitions are derived from the definition of a meter. You will get the same result regardless of metric.
That part annoyed me as well. All that using a shorter measurement does is increase the accuracy of the measurement. It’s basic calculus. As you use an infinitesimally small unit of measurement, the length of the river absolutely does NOT go to infinity. It goes toward a limit, which would be the distance of the river. That part of this video was incredibly inaccurate. The longest river is very easy to calculate. Just use the longest path from source to delta. It doesn’t matter the nomenclature of the river. If the river split and rejoins, use the longest of the splits.
My geography teacher gave us once a similar task to measure length of a river, but we had to do it with a string instead, so we could bend it to the shape of that river
It can be also tricky, as large rivers are quite wide. You can go with your string always in the middle, try to follow one side or try to follow the biggest flow. I am pretty sure the results would not be identical
I think you were not right when you said rivers don’t have a finite length to which they converge. While coastlines are fractals and therefore they tend to infinity, rivers are not necessarily fractals and don’t necessarily tend to infinity.
I was thinking the same thing. If a little peninsula of land sticks out two feet on the coast, and you had to follow the coast, you would walk right two feet and then left two feet. But if you're cruising down the center of the river, you just float past it. I would think a realistic measurement is just go in a boat that stays more or less centered between coastlines.
If you measure a river by going exactly in the middle (which can also be wildly subjective), it's basically just taking a position based on two shorelines, which actually ends up being infinite just like the two shorelines are. "More or less centered" is not a valid option, because then you'd be arbitrarily deciding what is centered enough and what is not. However, there is a much more sensible way of measuring a river. Just ignore where the middle would be, and instead imagine that you are driving a boat that's infinitely small and has an infinitely small turning radius. Then just take the shortest possible route with that boat along what you think is the longest possible version of the river, and you get a finite distance that would IMO be a fair way to measure a river. Yeah, it would cut some corners a bit compared to just going in the middle, but it's actually a non-arbitrary way of getting a finite length, and it's even realistic, being based on what you'd want to realistically do if you wanted to go along the river as fast as possible. You of course can't do this to a shoreline without arbitrary measurement choices.
I always thought it was silly they included Lake Victoria into the measurement. Lake Victoria is, well a lake, and while the source, does not constitute the river. It's measurement should be at the mouth of the where the two meet. I did some quick measurements on google maps, and according to that same logic, the Great Lakes system and the St. Lawrence seaway would make a 2500 kilometer "river".
There's nothing that prevents Lake Victoria from not being counted as a part of a river... There's a justifiable it is just an unusually broad part of the Nile river.
@@shambhav9534 Then why not count the grest lakes as part of the St Lawrence ? Edit : thanks to BeingTheHunt for pointing out that the great lakes are included in the technical lenght if the St Lawrence. Also I personnally still find it an odd practice
@@meneither3834 mainly because "rivers" are a human concept which has no bearing on reallity. If most people believe that the great lakes are part of the st.lawrence river then they will become that. I agree that there should be a consistent way of measuring lakes and rivers but at the end of the day its all semantics and no one cares that much about what the lenght of rivers are
I aswell don't really buy the fractal argument either. The problem is that the definition of length for rivers is way too vague for any actual measurement to have a precision of more than around, I don't know, say, 10^1-10^2 meters even if some idealized models of rivers were fractals. But if you do have a mathematical fractal, calculus is not going to help you. That was my point.
I took a double take at that and watched it again to see if I misunderstood, was so confused. Edit: On a second thought, I believe it might be just explained very poorly in the video and there might be some merit to the point. But it is confusing, and don't know why he really mentioned it so narrowly Edit: The fractal thing only makes sense if you are going to measure length of river coast. I don't think that is very applicable here, as you would want to measure length along some points on the river even if you do 'hacks' like the River Victoria one. So, one a 3rd thought, yeah, not suitable here imho
Yeah, that seems pretty easy, but which tributary do I start first? For an instance, take the Nile, do I follow the While Nile or the Blue Nile? Or, or, or, do I start from Alexandria (mouth of the Nile) and then reach Khartoum (where the Nile divides into Blue and White) and then add both the White Nile and Blue Nile distances to the distance from Alexandria to Khartoum??? Huh, pretty sick.
@@mk_57 I think OP is more pointing out that a simple river with curves and no tributaries can still be accurately measured without measuring with small straight lines, which makes the infinity argument in this video factually incorrect.
It be great if there was such a thing as an odometer that worked on a boat. Some boats may have a speedometer and possibly an instrument to measure hours of engine use, but I've never seen an odometer that worked on water. These days we use a GPS to measure distance travelled on water; before - in the olden days before GPS was readily available - we used maps and made our best guess. I'd love to have a mechanical way to measure boating distance 🙂
As a human, whose ability to conceptualize comes from my experience as a human, I think the standard unit should be a small vessel, say 4m, riding centered between banks (in cases where the water splits and comes back together, it should be whichever channel is larger). This, to me, would give the lengths meaning. This doesn't happen with road lengths, or the distances between cities. Also, I chose 4m for the length of the vessel/resolution, because I had a 12 foot long alumicraft and it was the perfect size for a couple friends and a case of beer.
Yes! And as a matter of fact the length difference as a function of resolution doesn't really explode with the river problem like it does with the coastline problem. It makes more sense to count the path's length than to wave it away-a water molecule has to travel that distance after all.
yeah, and I'm not sure but I feel like the fractal effect wouldn't be as strong in this situation, rivers generally flow in lazy curves so I would imagine you wouldn't have huge differences in distance using a 1-10 m range of step sizes. To me the intuitive way to measure a river would be the shortest (length) path a water molecule could take from a source to the ocean maybe modelled by some kind of smooth curve rather than discreet steps.
Minnesotan here, it was cool to hear Lake Itasca mentioned! Although I should point out it's pronounced "Eye-tass-ka". There's also some controversy as to if it's the real source of the Mississippi. Many people consider it to actually be Lake Nicolet, which is connected to the opposite end of Itasca by a small creek.
I'm from Colorado and I've hiked the tallest mountain in Colorado. The highest mountain and second highest mountains in Colorado are neighbors and there is only a difference of 10 feet between them. The two mountains are Mt Elbert (14,439 feet) and Mount Massive (14,429 feet). Here, it is tradition for many hikers to take a rock from the base of one of the mountains and carry it all the way to the top of their respective favorite and deposit it at the top. My rock is on the top of one of the mountains. I can't tell you which other than the fact that it is the tallest. I am suggest that surveyors of the respective Amazon and Nile rivers bring shovels with them next time. When they get to the source of their river... start digging.
I don’t think the limit of the river’s length as you reduce the unit to 0 is actually infinite. It will just approach the true path length of the river, which is kind of like a line integral over that curve. Rivers aren’t infinitely nested repeating fractals, contrary to the analogous image you showed lol.
Yeah. That bugged me. Coasts do have that problem, somewhat. It still doesn't get to infinity, but it does get kind of fractal (does the surface of a fjord count? If so do the inlets in the rock of the fjord, the holes in those, the cracks, the ridges in the rock?). River length is a vaguely similar problem, but it doesn't reduce that much since it is a fluid that is a ultimately all the same
Because from a seafaring viewpoint this is where you enter the river...and despite some of the "actresses " named here, most people have stuff enter in the mouth. Lmao
Because that’s where it opens up to the ocean? The rivers and continents are the bodies. Plus, throughout history sailors would travel the seas and enter rivers from the mouth. You can’t have a rectum and no mouth!
A river's length changes throughout centuries. This is because silicate and other minerals erode on one side of a river than the other. This erosion leads to a concave side, the side with harder, more stable minerals; and a convex side, the side with more erosion. This leads to a curve or bend in the river which increases throughout the ages, thus increasing the river's length. When the curve reaches a point where the two ends of the curve meet, they form an oxbow or horseshoe lake which is independent from the river. The river then returns to a straight line, thus its original length. New channels and merging rivers could also be formed by erosion, though this is rare due to the variation in thickness and hardness of soils and minerals surrounding the river. In theory, the Nile is longer in length than the Amazon, which leads to more curves therefore longer. Overtime though, this varies and the length of the river also varies. It depends when the lengths of the rivers were recorded and how precise the measurements are.
I love rivers man. They're like natural magical roads through the wilderness where you can float and explore until you are fatigued and eventually drown surrounded by piranhas... Sorry, just felt funny to write it like that :D
length doesn't have the same fractally unbounded problem as the shoreline perimeter problem. Let there be a river of arbitrary length and shape with a defined starting point and a defined ending point. There is a minimum length path that can be drawn between the points, staying within the bounds of the riverbanks, such that no other path can be shorter than it, even with an infinitesimal rule. Up your math game bruh!
Well thought. That adjusts to the definition of distance, which independently of the ruler of measurement, states that it's the minimum path between two points.
I'd measure it by shortest travel distance (as if by boat). This would jump edge to edge of the river, but would at least be consistent for all rivers, and take into account any amount of bending. It also has a reasonable reason for measuring this way; if you wanted to travel the river by boat or kayak, this is the minimum distance you would have to travel. It doesn't entirely eliminate the "make the segments shorter and the river gets longer" problem, as you still have to travel the inside curves of river bends. :/
Personally, I think you should measure the length of a river by measuring how long a semi-sized boat would have to travel to get from one end to the other, and if it branches you should follow the biggest branch. Still, it doesn't really matter as you should always state precisely what you are measuring and what branches you have used
Even though the last research was done by the Brazilian geographic society, but it looks reasonable enough to me. Unless the Egyptian geographic society could find a hidden small tributary for the Nile River which beats that measurement, I will accept the fact that the Amazon River is the longest river in the world.
@@guppy719 I mean, if they're gonna measure the Nile down the shoreline of the Lake Victoria instead of directly down the center point, measuring the Amazon to its farthest mouth is fair game to me.
@@tiovon8209 same, like, the exact same shoreline fractal paradox is going to apply if you measure it like that, therefore approaching infinity with small enough units. like why would you do that
egypt: we have the longest river in the world! brazil: NO we have the longest river in the world! the rest of the countries that the nile and the amazon flows through: *are we a joke to you?*
@@sohopedeco I'm not so sure about that. Especially given the dispute between Egypt and Ethiopia, which in a way used to also involve the British, on the Nile river.
@@aes1373 The dispute STILL involves the British considering that the true mouth of the nile could very well be near Gibralter where the Mediterranean meets the Atlantic. James May made a very valid statement with the Nile.
This paradox is real, but practicality should prevail in a case like this. The measurement should be done by counting how long it takes to sail the river at a constant speed, that would give it a human scale, which is the most relevant scale to us.
The Orinoco River empties into the Amazon through the Casiquiare Canal which is a natural canal that connects the Amazon to the Orinoco River. The direction of the flow in the canal depends upon how the ocean tides effect the canal but whether one flows into the other does not make either river the winner since they are both interconnected. The addition of the Orinoco River adds many miles to the length of the Amazon River, which means that you can put the Orinoco River at the top of the list, since it really does include the Amazon headwaters.
4:00 "...approaches infinity..." No, that's incorrect. Unlike the famous "Coast of Great Britain" paradox, a river has a macroscopically smooth centerline, and that centerline does not get endlessly fractal like the sand on the coast. So a 1 m scale ruler is plenty small-enough to very accurately follow the centerline of any river, and switching to a 1 mm scale ruler would not lead towards infinity. Only the last few meters at the source would you have any opportunity for the infinite fractal growth that you assume. In conclusion, a 1 m scale ruler is small enough for any river.
What you're saying seems to contradict itself. The banks of the river are a fractal just like a coastline. Therefore, it follows that the centerline, which is the centerpoint between the banks, would also be a fractal. The centerline of the river is inextricably tied to the geometry of the river's banks.
@@LimitedWard by that logic everything is a fractal and there would be no way to actually measure anything, if u wanna measure a river its a lot easier than the lunacy in this video
@@LimitedWard the center-line is not based on the lenght of the bank but on two points from each bank and even if the bank were to be fractal (which is nor really th case) the bank is still a mostly continuous line and so is the center line for all but at most a finite set of point. hence there is a finit lenght of the centerline Beside if the length was infinite, what about the flow ? what about the volume of water in the system ? is there infinite amount of water in each river flowing at infinite speed ? Or does a drop joining the river never make it to the ocean (finite speed + inifinite length)
Rivers are not infinitely long, even if you use infinitely small measurements. In mathematic, there is a concept known as limits. I can understand the issue with measuring some rivers, like the Amazon, because they have so many tributaries. But the curves would only cause the river to reach a limit of so long.
Not all sequences have well defined limits at infinity. For example, the Koch snowflake has an infinite perimeter (but a finite area), and that informs the issues with country borders. That being said however, the fractal justification is also insufficient to claim that a river is infinitely long.
@@neerajkrishnang3916 if by country borders you mean coastlines, then yes they are truly much worse than rivers to measure unlike the rivers here, what he said about their lengths extending to infinity if you go down small enough actually turns into reality thanks to nature It follows a concept similar to how long all your blood vessels are. If you put them all together in a line you would get a distance longer than the earth to the moon (or several times that?).
Honestly I feel like the tributaries of rivers should all count as part of the main river's total length. Due to this, I've always considered the Amazon the longer of the two even before this video; far more lengthy tributaries.
Apparently they haven't watched Season 19 Episode 6 and 7, where it's revealed that James May found the source of the nile (despite his car breaking down)
RLL is incorrectly applying the shoreline problem to the river length. A river does, indeed, have a definable minimum length with an infinitesimal rule.
How would the length of a river ( and a coastline) approach infinity? shouldn't it approach a constant number because the amount of length gain would be small if we have small initial units.
because the shoreline, like fractals, become more defined as the unit decreases. If it's small enough you'll be measuring the distance between atom to atom on the shoreline, which for mathematics sake, we can say the L does go towards infinity.
Think about it like this...if you divide into atomic scale units to cover the size of a river, you would have an "infinite" number of atoms covering the length... Since the atomic scale is very small, but it is still a feasible number, you would get very small number x infinite = infinite... That was the ELI5 of the thing, I'm pretty sure Fractal Theory and Limit theory can give you a more precise explanation but I don't really remember my Calculus classes hahahahha
@@ImTHECarlos98 But there aren't infinite atoms in the world. Wouldn't it be like that problem of 1/2 + 1/4 + 1/8 + 1/16 and so on where it eventually approaches one, and the river coastline approaches a concrete number?
Interesting that you mentioned adding the Missouri to the Mississippi. However, you failed to mention that the Missouri is presently longer than the Mississippi. Every time an ox-bow curve cuts through or flood waters change the delta, they flip-flop. They are that close in length.
Btw, Itasca is pronounced eye-tas-cuh, with the first “a” sound being short as in “cat”, and the second “a” being a short “u” as in “tug”. I live a couple hours away, and have been to the source of the Mississippi a few times. Pretty cool little park.
@@enriquegarcia2790 Besides saying that I heard it pronounced the other way and admitting that whoever pronounced it that way initially probably said it wrong, this is not a corruption of a Native word. As per Wikipedia: "The Ojibwe name for "Lake Itasca" is Omashkoozo-zaaga'igan (Elk Lake); this was changed by Henry Schoolcraft to "Itasca", coined from a combination of the Latin words veritas caput ("true head [of the Mississippi]"). It is one of several examples of pseudo-Indian place names created by Schoolcraft."
4:00 no, it's not going to approach infinity. You were talking about the coastline paradox, which doesn't work in this case. Even with infinitely small divisions, length of the river would still be finite.
You use the phrase "nearing infinity" to say that a number is so big, that there's no way for a human to really understand just how big it is. It is mathematically wrong to say that, that is true, but it wasn't meant to be mathematical, just a phrase to help a bit visualising. An example would be to say that there are "infinite" ways to mix a game of cards, although the number of possible ways is 10^52 and thus finite. And I don't get what you mean by "doesn't work in this case" since it does. You can go into molecular measures and have a "nearly infinite" length, both in measuring the lengths of a river and a coastline. And what you also talked about: If you use infinetly small measures, meaning infinitely smaller than molecular measures although that would be physically impossible from our current knowledge, it would be, in fact, infinetly long. Without wanting to offend you, not really anything you said made sense.
@@drbruley8045 the point is that a coastline has an edge, which can be fractal-like, because it doesn't have to be a smooth function (might be getting the terminology wrong, I am used to saying that in a different language). On the other hand, when we measure a river, we use a smooth function, which has natural parametrization, aka well-defined length, that doesn't depend on resolution.
@@ВикторФирсов-е9ф I don't see how the video is wrong for pointing out that some people have said we could measure rivers the same way. Eventually the video does cover a lot of different ways we have measured the world's longest rivers. If anything, the video is more informative for including more info.
I would say the most fair way to measure is the following: imagine you have a really long measuring tape. Put it in de water, as long as you can continue rolling it out in the water, *as long as it stays stretched*, that measurement is the legal. The longest possible road can be taken. That way al branched are considered and no stupid bends are legal.
Issue 1: I disagree that the smaller your measuring unit is, the closer you get to infinity. In fact, the smaller your unit, the closer you get to the real value. The smaller the value, the more curved the path is without taking shortcuts that subtract from the true length. This is analogous to how PI was measured at first. The radius is known and fixed, so to know PI we need to know the circumference. The early methods to mathematically calculate this was through polygons inside and outside the circle, and the more sides it has, the greater the precision giving an upper and lower bounding limit. But Veritasium explains it better in the video called "The Discovery That Transformed Pi". The bottom line is... the smaller your unit, the lower the error, and the closer you get to the real value. If you were to go down to the atomic scale, you could presumably get the true length. But the law of diminishing returns applies, so the real question is how small does our measuring unit need to become so that the margin of error is "good enough", though depending on the purpose of this measurement, we first need to define how good is "good enough" while also being large enough to make measuring feasible. Issue 2: It seems that the controversy of which is the longest river comes from the fact that everyone sets their own rules on how to measure. Naturally, that will give different results. It's like measuring how tall we are, but are we wearing shoes? high heels? tall hair? slouching? without clarifying those variables, of course, you can get wildly different results. In my personal opinion (emphasis on opinion, not fact), the best way is to consider that the "main" river at each "intersection", is the one with the greater debit of water. So yes, a narrower but faster-moving flow could could be considered the main rover, over a wider but much slower-moving flow. This would apply both for joining, and for splitting. Additionally, the measured path for length should be the middle between the 2 banks. Thus, for example in the case of the Nile through a lake, the path of the measured Nile, would be through the mathematical middle of the lake which can be considered as just a widening of the river. I'm sure there are other details that I haven't thought of, but if brighter minds would come together to a consensus, everything could be ironed out.
THIS!! I see a great value in popular science channels like this one, BUT only when they themselves are not propagating conceptually incorrect facts or views...
Not quite right. This would only be true of a mathematically perfect entity. With a river, you need to measures parts of the curve either in the center, or along the banks. In both cases "what counts as the center/banks" depends on how precisely you measure. Because the river is a real world entity that can be measured with arbitrary precision, you run into the exact same issue as what's know as the "Coastline Paradox", give it a Google. The only thing close to a resolution to the Coastline Paradox would be to use a Planck length as your unit of measurement, but that's also not practical at all. Imagine sailing down the Amazon trying to measure the banks of the river within a Planck of accuracy.
Yup. I came here to check for a discussion of how an infinite number of things gets asymptotic, not infinite if their increase a factor in the range (1,2). Oh, infinite sums!
@@jackalope2281 What he's said is right. YOU CANNOT go to infinity just by choosing a smaller unit of measure when measuring the river. That's not how it works. The smaller the unit, the lower the error. True, you cannot have an error of 0. But it can be small enough that the error simply doesn't matter. Square root of 2 technically can be represented as a number with a 2 digit precision. It just has such a high error margin you need to get a higher precision. At a 10 digit precision, most calculations will be practically with a small enough error margin that you can perfectly use it. So the video is wrong. So are you.
@@liviuganea4108 Are you sure the formula for calculating the coastline length as the precision approaches infinity has the same growth rate as that of root 2? There are plenty of limits that approach infinity. The tricky part with the coastline paradox is that there isn't one distinct formula to track the growth rate, it would depend on the specific contours of the coastline being measured. But one can imagine a part of the coastline that spirals down into infinity (like a fractal), meaning infinite precision can in fact lead to an infinite length measurement. But any detailed contour even besides a fractal pattern would function much the same as the fractal for this purpose, thus allowing any coastline to approach infinite length as the precision approaches infinity. Again, you are right in that an infinite series (or limit) doesn't always have to approach infinity. But in this case, the growth rate can be arbitrarily large, since there is no discernable end to how much detail we can choose to include in our measurement. This is not a purely mathematical problem to work through, it necessarily involves some interpretive pragmatics due to it's nature as a real-world measurement question. e.g. A circle in real life is not a perfect circle. So how many sides does it have? Similar issue.
If you reduce the length of measurement, you wouldn’t approach infinity. You would eventually get closer and closer to the rivers actual length. You’re approaching a finite limit. This is high school calculus.
My rules for river measurements: 1, Take the longest continuous waterway that exists in the same river system. (Despite what name it is called) 2, Measure the length of the actual riverflow, like you were on a ship following it. So yes, every curve counts, and not just the distance that the river bridges across. 3, Always use the river's center line for determining the river's length. 4, Always take the longer rout around islands, and at the river's mouth.
The problem with river's centre line is, there isn't always the same water level. Once you will get some curve as the centre line and a month later, this curve will change drastically (especially with the Amazon) :/
I think he meant to say North America. Either that or he doesn’t know that the Missouri is longer because it’s constantly overshadowed by the Mississippi.
Never inu 27 years of life have I heard that Amazon river is the longest one. I always learned that Nile is the single longest river. But Missouri-mississipi river is even longer, but for some reason, it's divided into 2 different rivers
At 11:57 you say that the Amazon is 6992km long and the Nile is 6953km long and conclude that there is a 140km difference. But it's only 39km. Or you got one of the lengths wrong and it's actually 140km. Sooooo, which one is it? Otherwise great video, as usual.
The problem is that they don't have clear rules to measure the rivers length because I think when measuring the length they should take the widest tributary for example not just the one that will make the river longer
"The answer will end up approaching infinity". "Depending on what you use, the answer could end up on a range from 300km up to infinity". With all due respect, what is this guy even talking about here, what is his point, you could literally make this argument for absolutely everything that has a length and can be measured. Also, sure let's totally ignore the concept of convergence right?
The point is that the shoreline paradox makes measuring rivers hard to quantitate, which in turn makes them hard to compare. It's really not that hard to understand.
@@mechanomics2649 Found this paragraph on wikipedia on the coastline paradox: The problem is fundamentally different from the measurement of other, simpler edges. It is possible, for example, to accurately measure the length of a straight, idealized metal bar by using a measurement device to determine that the length is less than a certain amount and greater than another amount-that is, to measure it within a certain degree of uncertainty. The more accurate the measurement device, the closer results will be to the true length of the edge. When measuring a coastline, however, the closer measurement does not result in an increase in accuracy-the measurement only increases in length; unlike with the metal bar, there is no way to obtain a maximum value for the length of the coastline. I didn't realize that convergence was not a thing when dealing with fractals, and since coastlines behave like fractals, a more precise measurement device will not actually lead to a more accurate measure of it's true length.
why can't they just use a boat that measures how much km they have moved ( like a normal car i mean ) and try to sail as close to the middle as possible....
I hate to pick on kids for my example, but since I have a young child, I know where I'm coming from: Step 1: Ask a five-year old to draw a rectangle. No rulers, straight-edges, etc., just draw it. Perfect lines--no, of course not. Even most adults not in art/architecture/engineering professions would have SOME deviation in the sides of a rectangle. Fair enough, though, you could still reasonably measure it around through simple mathematics of some of the curvature of the lines. Step 2: Ask a two-year-old to trace his/her hand on a piece of paper. At the end just have him/her connect across the points where you stop tracing at the wrist bones. THAT'S how the Earth REALLY is! Try measuring the length around of THAT! That's where deviation comes into play in measurement.
@@thetrainmon use a gps map with a scale of 1mm=10km or something, put a rope and try to always follow the middle of the river. The length of the rope is the length or the river. No deviation, maybe 0.01% longer or shorter :)
I love how he said that the Amazon measurement was a bit of a stretch but the people counting not only Lake Victoria, but also measuring its coast line, making it significantly longer is all fine, hahaha
@@TinyLordCthulhu The Atlantic doesn't have a mouth, the Mediterranean does (at Gibralter). As such the nile & any other river flowing into the Mediterranean is longer than the shAmazon.
Well at the end the longest was the actual Amazon after BOTH rivers used the longest possible measurements they could. And honestly considering the fact the Amazon holds over 20% of the non salt water in the world. Ummm I'd just go with the much larger river. It doesn't matter what Ocean/Sea the river is connected to.
measuring the lenght of a river shouldnt be dependent on the shoreline whatsoever... its a line down the aproximate center point... which might still make measuring a true lenght nearly impossible, however its not nearly infinite.
How do you find the approximate center point though? I think you're vastly oversimplifying how that would work. Not to mention the center line of a river would still be infinite if you decrease your unit of measurement.
@@LimitedWard the deepest point in that cross section... sure that is approximate, but these approximation still yield a finite and convergent measurement... with an error bar if you want, but that error bar does not 'explode' and is manageable. in anycase it IS a finite length and the scale of the stick you use to measure has an convergent effect.... as you can see with the number the author mentioned: as the stick get smaller the effect of the change in size of the sitck get smaller even faster. first order of magnitude got hs length double (aka 100%).. the second order of magnitude got the lenght up by 12% of so.... this converge fairly quickly
@@listen1st267, but do you measure that once or for the entire course of a river? How far apart are these new centerlines? Should it account for the changing of the river?
4:08 I’m pretty sure that the length of the river does not go to infinite, it converges. The problem is that we can’t measure it in infinitesimal units. BTW you are actually approaching to an integral (the arclength to be exact).
Except atoms do not actually touch each other, and are made up of constantly moving particles. So, yes, it is does get infinite if you get to a molecular level and beyond.
If you plot the measured length against the length of the measuring ruler (for reasonable cases) and end up roughly with an exponential curve, then you've got a fractal. Fractals are everywhere in nature: surfaces of clouds or bodys of water, shorelines and rivers, many types of plants, etc.
@@vitorboldrini6337even if they don’t touch they are at a scale of nanometers, so you are measuring that small lengths of empty space that may not even count. The “real result” may be a huge number but not infinity. Remember that the infinity is just a concept not a number.
@@pierrestober3423 Yes actually the coastlines are fractals, well they approach enough to be considered one of them, since fractals is a limit process.
@@vitorboldrini6337 Except we're not measuring rivers according to their shoreline but rather their center, which is simply described by curves, which do not go to infinity when measured but converge on a finite number.
I think it's possible to get an exact number. Overlay a piece of string over a map program that you can straighten out and keep the string at the same zoom as the map so the string is an accurate distance reference. You can apply this to both sides of a river or border or even river border, lake border, etc. and average out the numbers. Assuming the map's distance reference is accurate all you have to do is measure. From there you have to apply elevation changes, in a less complicated and slightly less accurate example, If you apply this to the Mississippi River it starts at 1,475 feet in elevation and ends at 725 feet of elevation, this increases the length you get from the string. To get the exact measurement you'd have to calculate the exact elevation changes along the whole river or border. If you are trying to decide where it begins and it has multiple points to choose from, you choose the furthest from the end or calculate all variables.
The fractalness of water is easy to see. Just realize that every stream of water is in itself just like a river, feeding into an ever bigger river. They're all the same, but just at different sizes. Which explains why you can't truly measure the longest river, as you'd never be able to stop with each infinitisemaly small stream, which are always changing in lengths, sizes, and paths.
They also flow different directions hence making them different rivers. Also having different start points and the same end point are 2 different rivers. At the meeting point you can argue they are arbitrary.
As a Minnesotan it is my sworn duty to correct your pronunciation of Itasca- you said it-is-ka when it’s actually i-tas-ca- it should rhyme with Alaska.
OOFTA THANK YOU!!!! I'm gonna leave my own comment anyway, but that was an instant pause on the video for me. The poor Texas guy is just trying his hardest here.
Fun fact about the Mississippi River. Depending on how you define "uphill" and "downhill", the Mississippi River actually flows "uphill". Lake Itasca is 5.9 km closer to the center of Earth than New Orleans and the Mississippi Delta. It is not gravity that drives the Mississippi River to flow. It is the centrifugal effect that causes the water to move against true gravity, as the water tries travel in an inertial straight line, away from the Earth's axis of rotation. It feels like gravity from our point of view, and it feels like a downhill journey from Minnesota to Louisiana for this reason. It is ultimately getting closer to sea level, because sea level and the overall shape of our planet settles on an oblate spheroid shape based on hydrostatic equilibrium at its surface to adapt to balancing the centrifugal effect and gravity.
3:57 Breaking down length into infinitely small differential length will help us in getting the correct value of the length and will not result in infinite length. This is what we do in integral calculus. Integrating the differential parts.
I think you might be correct for the river, but not for the shoreline problem. They are separate, not analogous, as presented in the video. People have presented other issues, such as where you draw the course. The most navigable channel where the most water flows might be on the outside of bends, but most certainly not along the shorelines of the “lakes”.
@@Markle2k Right. However as for rivers, RLL really shouldn't have been talking about shorelines since surveyors use the centerline to determine rivers
@@listen1st267 The problem is how you calculate the centerline is based on how you measure the banks, which is what leads to discrepancies between measurements.
@@heliogen5959 yeah it can lead to discrepancies but I was bringing this up because other comment threads were buying into RLL's idea that the length of a river could be calculated to be infinity, which just isn't reasonable. Using the centerline would lead to approaching a finite value (or range)
4:10 Infinity, really? For very little measuring stripe lengths, you of course have to give those stripes somewhat the direction of the river instead of going from left to right to the left and so on.If you can tell the direction of the line properly, you should come to the fact that a sequence of river lines getting more and more accurate will converge. (At least I hope so.) But if it converges, then you'll get a line of infinite accuracy (Always the middle of the river). This line is the image of a continous function from [0,1] to something three-dimensional. It should be basic analysis to realize: The length of that perfect line - let it be huge, but it will not be infinite.
4:00 Wait, if you decrease your measuring increment, the river length wouldn't approach infinity. It would approach but never reach the actual river's length
The solution to measuring irregular shapes isn't "fractals," it's calculus. And there is a definite answer to the circumferences of irregular shapes...
Saying that the Nile starts on the other side of lake Victoria is like saying that it ends on the other side of the Mediterranean sea. It makes no sense
I live in MN, we probably say it wrong since it's an indigenous word but I have never heard Itasca said that way and I kind of prefer it haha. We always heard it as It-Ah-sca and I just loved that it was even referenced in this video. I love you work, great job!
@@chito5954 It's not even really Latin. It's arguably more accurate to call it an English neologism, because it was intentionally created (albeit by joining parts of two different Latin words) for use as a single word in the English language.
I remember doing a in-class activity based on this weirdness; we were divided up into 9 groups; 3 groups used a string, some pins, and the map on a corkboard to measure a few different rivers. 3 using broken up segments and the last 3 groups used a ruler to measure it out as the crow flys. all the groups used the same three rivers but even between the groups that used the same method, our answers varied; our teacher then explained that the reason why it varied was due to our different views on where a river starts and ends. In the end it was not only a lesson on geography but also how different views on the same subject can both be right and wrong.
0:53 It’s what I like to call the Google Effect. Everyone disagrees with each other and it makes it very confusing for some average Joe like me to know who’s right and who’s wrong. It’s not limited to just geography. It’s just all over Google.
There's a creek in Wyoming that flows into both the Snake and Mississippi rivers. If you were an ambitious fish you could swim from the Pacific Ocean to the Gulf of Mexico through American rivers.
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Instead of breaking the length in smaller parts of 10 KMs, you should have broken down into the lengths of Toyota Corolla
The three types of measurement: The Metric, The Imperial, *and the Toyota Corolla*
I don’t think RLL has done Toyota Corolla references for a while now but should bring them back
@@Chrono_topher lol
how about football fields
"2,176 Toyota Corollas, in fact..."
As a Brazilian, I will accept any measurement that shows that the Amazon is longer than the Nile, even if you have to count Pedro's toilet pipes that dump into the river to increase its length.
Ngl the Brits use Lake Victoria coastline as part of Nile River is pure cheating
😂
lol
Things are heating up in the Potamology community
Me too
Coastline paradox arises mostly from lines heavily zig-zagging in tiny scales. But rivers are not one-dimensional lines, they have widths, so I believe the paradox can easily be avoided with carefully chosen definitions. For example: given two points A and B on the river, the distance between A and B is the shortest distance one would have to travel while remaining on the river surface. That should smooth out any zig-zags. Now all you have to do is choose such A and B that would maximise the distance (B obviously should be adjacent to a sea or ocean). That should not only bypass the coastline paradox but also prevent such "tricks" like adding the lake coastline instead of a shorter path across the lake.
The lake shouldn't even be included either because it's a lake and therefore not the river. It's merely the source of it but not where it starts. It should be measured from the mouth and triviaries don't make sense to include either if we refer to them as entirely differently named rivers. I don't get why this is complex either lol
@@lunaloveless7234 The fact that a part of the river has a different name doesn't mean its not the same river. That is a horrible argument. There are streets in my city that change names randomly, but the street still goes in the same directions and has the same number of lanes. It doesn't become a different street just because the name changes. Excluding a portion of a river just because some people decided to call it something else makes no sense. You pretty much just displayed why it's complex in your own inability to see the flaws in your own statement.
@@bh_quicksilver251 lets say your streetruns thru a park and is a diff name on the other side, diff # on houses. It would not be the same street. U cant take a tributary river that runs into lake victoria and make it count as the Nile. The nile starts at the mouth of the lake. The lake is lake victoria not the nile river.
Anyway u calculate it: the Amazon wins.
The ONLY thing that makes sence is to add the longest tributary rivers to it. Why are you comparing rivers to streets, its not the same. The whole point of measuring river lengths is to know the distance the water travels across the land. It's RETARDED to cut the measurement short just because certain parts of the river were discovered by different people at different time and therefore are named differently. Naming has nothing to do with actual geography of earth, naming different parts of a water stream differently doesn't fucking change it's length.
Thank you, this is exactly what I thought as well. Going in the middle results in theoretical infinity, but going with practical route (it has practical use because it's what you'd want to approach with a boat if you wanted to travel the shortest possible distance) results in a non-arbitrary, finite length.
"Honey, I'll go out expedition to measure a river length"
"Fine, but don't get too political"
"I won't"
Lol
Tr
he literally made the same exact video 3 years ago
Why couldn’t the Africans living there find the source? Why did Europeans have to do it?
@@grandtheftavocado Was there a motivation for them to do so?
3:57 This statement is misleading. Infinite chunks of infinitely small size don’t necessarily add up to infinity (see also: Zeno’s Dichotomy Paradox). It is well within the realm of possibility that as you approach infinitely small measuring steps, you also approach a fixed value.
This is also true for coastlines. The number approached will be very much higher than a more useful value, but the value “increasing to infinity” is kinda a thing people just say that they assume is correct. Fractals have an infinite scope, whereas the world has a fundamental smallest length.
Yeah this video loses a lot of credit for this argument. The measurement will converge to a specific value, aka, the correct value.
Just a guess off the top of my head, but I'd say linear algebra could help you find the equation of the line the river makes in slope intercept form, and then you could use good ole fashioned calculus to find the length of the curve.
What he said is the literal description of a line integral too
I looked in the comments specifically to see if anybody else picked up on this
*Decreasing the fractal size increases the length of the river logarithmicly, not to infinity. Once you reduce your measuring size to "continuous", using euler's number will find the true maximum size.*
The reason why countries dont have continuous measurement of their coastline is that it's impossible to achieve practically.
Elementary school: The Nile River is the world's longest river!
RealLifeLore: Are you sure about that mate?
Aussie mate
Elementary school: The Nile River is the world's longest river!
RealLifeLore: Are you sure about that mate?
Me: Yeah....since I'm not currently in a mental institution....I'm sure. ¬_¬
@@West_Kagle
sure what I learned in middle school Nile is longest and Amazon is largest even when a nerd ask about Amazon tributary and say Amazon look longer geography teacher discuss same things that real life lore mentioned where want to start and end and the funny thing that was 25 years ago for me and still no one agrees
US elementary school* the world is way bigger than just one country's school system :P
We all know who found the true source of the Nile: Jeremy Clarkson, James May, and Richard Hammond.
It says here that... Experts couldn't find the true source of the Nile.
Hah, classic Hammond
Real question is which one of them was the first to claim it..
The comment I was always looking for
@@lukesheffield1378 May, he dipped his finger in it first. Although Clarkson might have been the first to dip something else.
You forgot the "Dr." title
"It's not about how long it is, it's about what's inside that counts" - Pinnochio
Giggity
Such a wise words man
Perfectly going to implement it in my life
I’m just a mexican stoner trying to make it out the hood by doing storytimes & reaction videos
Its not about how long it is, its about how prosperous is that civilization on its banks
HAAHHAHAHA
I think there's some problems with what's being described here. Definitions of rivers aside (which _is_ a big issue; like whether lake Victoria counts as part of the river), there's no fractical problem and not much other measurement problem. You just need to measure the shortest distance possible. No running along the edge of land, and hence no fractal problem. When it does encounter land it only hits the "pointiest" tips, so it doesn't get much worse the more you zoom in. Sure there's still the issue of water levels changing the measurement distance, but that can be dealt with in it's own way (like measuring at max an min)
But there is. Did you not pay attention? Using centimeters allows you to follow the river and always be centered in the river, using kilometers sometimes allows you to be in the river, sometimes jumping over land because it can only be so curved and still measured accurately. Using a different scale greatly changes how long a river is as well as makes way for the country border paradox the narrator also mentioned. Theoretically this problem becomes more and more of an issue the smaller your scale is / despite a smaller scale being more closely accurate.
@@TJ-im5kp, plus, where is the center. Do you measure it down to 100 meters, 50, 10, 1? What is 1 meter is too much? Let's try a centimeter, a millimeter, or a nanometer
The only problem with this is that for practical purposes, measuring the shortest distance possible would be misleading for boats that have to travel the river and want to know the distance they have to travel.
@@Doublemonk0506 What? That doesn't matter because meters are universally defined as the length of the path travelled by light in a vacuum in 1/299 792 458 of a second. A centimeter, milimeter, or nanometer's definitions are derived from the definition of a meter. You will get the same result regardless of metric.
That part annoyed me as well. All that using a shorter measurement does is increase the accuracy of the measurement. It’s basic calculus. As you use an infinitesimally small unit of measurement, the length of the river absolutely does NOT go to infinity. It goes toward a limit, which would be the distance of the river. That part of this video was incredibly inaccurate.
The longest river is very easy to calculate. Just use the longest path from source to delta. It doesn’t matter the nomenclature of the river. If the river split and rejoins, use the longest of the splits.
We all know, James May is the discoverer of the true source of the Nile.
😀😀😀....
Only by a couple of seconds but yes. Captain Slow managed to outpace the feeble Orangutan and the Midget
ah, a man of Culture! Great to see you here
A true man of science
he literally made the same exact video 3 years ago
As an American, I welcome the new measuring unit of "Frances Per river basin."
😂😂😂
As long as it isn't the metric system
"How many Texas's does it take to measure a cell margin of the sun?"
Or you could use Texas
Also what’s the plural form of Texas?
@@therealspeedwagon1451 my guess would be Texes
"The length will approach infinity as the measuring units get smaller."
*frantically goes to measure pp on the molecular level*
. LMMFAO 😂
My geography teacher gave us once a similar task to measure length of a river, but we had to do it with a string instead, so we could bend it to the shape of that river
Must have been a damned long piece of string, or a really short river.
And that's why no one wanted to become a geologist.
It can be also tricky, as large rivers are quite wide. You can go with your string always in the middle, try to follow one side or try to follow the biggest flow. I am pretty sure the results would not be identical
I’m pretty sure he meant a string on a map and cut off the excess
@@paragn667 you would still need an infinitely long string to measure the river with complete accuracy.
If people are going to count the curve around Lake Victoria, why wouldn't the Amazon River count the southern route?
Exactly. Like fuck, apparently all they have to do to make the Nile longer is have it swerve back and forth around a lake for 1000km 🤷♂️
I wouldn't count the curve. Just draw the straight line.
Measure the average flow of water. There.
Lol
@@The360MlgNoscoper but average across what? If you deposit into an ocean, there’s still water flow
I think you were not right when you said rivers don’t have a finite length to which they converge. While coastlines are fractals and therefore they tend to infinity, rivers are not necessarily fractals and don’t necessarily tend to infinity.
I was thinking the same thing. If a little peninsula of land sticks out two feet on the coast, and you had to follow the coast, you would walk right two feet and then left two feet. But if you're cruising down the center of the river, you just float past it. I would think a realistic measurement is just go in a boat that stays more or less centered between coastlines.
If you measure a river by going exactly in the middle (which can also be wildly subjective), it's basically just taking a position based on two shorelines, which actually ends up being infinite just like the two shorelines are. "More or less centered" is not a valid option, because then you'd be arbitrarily deciding what is centered enough and what is not.
However, there is a much more sensible way of measuring a river. Just ignore where the middle would be, and instead imagine that you are driving a boat that's infinitely small and has an infinitely small turning radius. Then just take the shortest possible route with that boat along what you think is the longest possible version of the river, and you get a finite distance that would IMO be a fair way to measure a river. Yeah, it would cut some corners a bit compared to just going in the middle, but it's actually a non-arbitrary way of getting a finite length, and it's even realistic, being based on what you'd want to realistically do if you wanted to go along the river as fast as possible. You of course can't do this to a shoreline without arbitrary measurement choices.
I always thought it was silly they included Lake Victoria into the measurement. Lake Victoria is, well a lake, and while the source, does not constitute the river. It's measurement should be at the mouth of the where the two meet.
I did some quick measurements on google maps, and according to that same logic, the Great Lakes system and the St. Lawrence seaway would make a 2500 kilometer "river".
Yeah... I find it dumb to just count Lake Victoria as "part" of the Nile.
There's nothing that prevents Lake Victoria from not being counted as a part of a river... There's a justifiable it is just an unusually broad part of the Nile river.
@@shambhav9534 Then why not count the grest lakes as part of the St Lawrence ?
Edit : thanks to BeingTheHunt for pointing out that the great lakes are included in the technical lenght if the St Lawrence.
Also I personnally still find it an odd practice
@@meneither3834 Good idea.
@@meneither3834 mainly because "rivers" are a human concept which has no bearing on reallity. If most people believe that the great lakes are part of the st.lawrence river then they will become that.
I agree that there should be a consistent way of measuring lakes and rivers but at the end of the day its all semantics and no one cares that much about what the lenght of rivers are
RLL: "The length will approach infinity as the measuring units get smaller."
Integral calculus: "Am I a joke to you?"
The problem is that the length series does not converge for fractals.
@@jolez_4869 Rivers are not actually fractals tho despite what this video implies.
That statement by RLL was infinitely stupid.
Just because something is measured using infinitesimally small units does not make it infinitely long.
I aswell don't really buy the fractal argument either. The problem is that the definition of length for rivers is way too vague for any actual measurement to have a precision of more than around, I don't know, say, 10^1-10^2 meters even if some idealized models of rivers were fractals. But if you do have a mathematical fractal, calculus is not going to help you. That was my point.
I took a double take at that and watched it again to see if I misunderstood, was so confused.
Edit: On a second thought, I believe it might be just explained very poorly in the video and there might be some merit to the point. But it is confusing, and don't know why he really mentioned it so narrowly
Edit: The fractal thing only makes sense if you are going to measure length of river coast. I don't think that is very applicable here, as you would want to measure length along some points on the river even if you do 'hacks' like the River Victoria one. So, one a 3rd thought, yeah, not suitable here imho
I have an idea of how to measure River length:
Step 1: get boat
Step 2: get odometer
Step 3: drive boat with odometer from start to end of the River
Yeah, that seems pretty easy, but which tributary do I start first? For an instance, take the Nile, do I follow the While Nile or the Blue Nile? Or, or, or, do I start from Alexandria (mouth of the Nile) and then reach Khartoum (where the Nile divides into Blue and White) and then add both the White Nile and Blue Nile distances to the distance from Alexandria to Khartoum???
Huh, pretty sick.
@@mk_57 I think OP is more pointing out that a simple river with curves and no tributaries can still be accurately measured without measuring with small straight lines, which makes the infinity argument in this video factually incorrect.
what about the waterfalls?
Step 4: Pay the boat owner by the hour.
It be great if there was such a thing as an odometer that worked on a boat. Some boats may have a speedometer and possibly an instrument to measure hours of engine use, but I've never seen an odometer that worked on water. These days we use a GPS to measure distance travelled on water; before - in the olden days before GPS was readily available - we used maps and made our best guess. I'd love to have a mechanical way to measure boating distance 🙂
As a human, whose ability to conceptualize comes from my experience as a human, I think the standard unit should be a small vessel, say 4m, riding centered between banks (in cases where the water splits and comes back together, it should be whichever channel is larger). This, to me, would give the lengths meaning. This doesn't happen with road lengths, or the distances between cities. Also, I chose 4m for the length of the vessel/resolution, because I had a 12 foot long alumicraft and it was the perfect size for a couple friends and a case of beer.
Yes! And as a matter of fact the length difference as a function of resolution doesn't really explode with the river problem like it does with the coastline problem. It makes more sense to count the path's length than to wave it away-a water molecule has to travel that distance after all.
while that’s fair I also think using that measurement makes numbers too large for a human to intuitively grasp how large the number is
yeah, and I'm not sure but I feel like the fractal effect wouldn't be as strong in this situation, rivers generally flow in lazy curves so I would imagine you wouldn't have huge differences in distance using a 1-10 m range of step sizes. To me the intuitive way to measure a river would be the shortest (length) path a water molecule could take from a source to the ocean maybe modelled by some kind of smooth curve rather than discreet steps.
This is what I was thinking. I don't believe the fractal bullshit has anything to do with this. Just measure it from the center.
That's as solid a piece of logic as I've recently seen on the internet. Cheers!
As a Minnesota native, the way he pronounced "Itasca" broke my soul.
It should be, “Eye-Task-Ah”
Instant rage.
Fellow Minnesotan here looking for this comment. We share the pain.
sameeee
SAME.
Minnesotan here, it was cool to hear Lake Itasca mentioned! Although I should point out it's pronounced "Eye-tass-ka". There's also some controversy as to if it's the real source of the Mississippi. Many people consider it to actually be Lake Nicolet, which is connected to the opposite end of Itasca by a small creek.
Yeah, the pronunciation of Itasca made me cringe a bit.
Fellow Minnesotan! I was about to comment the same thing here!
nobody cares
AI bots can’t read
I'm from Colorado and I've hiked the tallest mountain in Colorado. The highest mountain and second highest mountains in Colorado are neighbors and there is only a difference of 10 feet between them. The two mountains are Mt Elbert (14,439 feet) and Mount Massive (14,429 feet). Here, it is tradition for many hikers to take a rock from the base of one of the mountains and carry it all the way to the top of their respective favorite and deposit it at the top. My rock is on the top of one of the mountains. I can't tell you which other than the fact that it is the tallest. I am suggest that surveyors of the respective Amazon and Nile rivers bring shovels with them next time. When they get to the source of their river... start digging.
Well, they'll end up cutting the South American continent in two if they keep digging the amazon
@@kiambotebbonikay Fuck it. Southern South America
@@exciton9861 hell yeah
@@exciton9861 northern south america aproves
Tldr
so they're about equally long within a margin of error, gotcha
no. For any finite measuring unit, the more fractally bent the river is, the longer it will be.
I don’t think the limit of the river’s length as you reduce the unit to 0 is actually infinite. It will just approach the true path length of the river, which is kind of like a line integral over that curve. Rivers aren’t infinitely nested repeating fractals, contrary to the analogous image you showed lol.
Yeah. That bugged me. Coasts do have that problem, somewhat. It still doesn't get to infinity, but it does get kind of fractal (does the surface of a fjord count? If so do the inlets in the rock of the fjord, the holes in those, the cracks, the ridges in the rock?). River length is a vaguely similar problem, but it doesn't reduce that much since it is a fluid that is a ultimately all the same
Why is the endpoint of the river referred to as the “mouth.” Shouldn’t it be the river’s “rectum”?
Well there's a viral video of a conservative lady, complaining about an*l being taught to kids or something like that, maybe that why.
Funny question, but there is a serious answer.
Because from a seafaring viewpoint this is where you enter the river...and despite some of the "actresses " named here, most people have stuff enter in the mouth. Lmao
Because that’s where it opens up to the ocean? The rivers and continents are the bodies. Plus, throughout history sailors would travel the seas and enter rivers from the mouth. You can’t have a rectum and no mouth!
@@geoffreygriffin3015
Exactly!
A river's length changes throughout centuries. This is because silicate and other minerals erode on one side of a river than the other. This erosion leads to a concave side, the side with harder, more stable minerals; and a convex side, the side with more erosion. This leads to a curve or bend in the river which increases throughout the ages, thus increasing the river's length. When the curve reaches a point where the two ends of the curve meet, they form an oxbow or horseshoe lake which is independent from the river. The river then returns to a straight line, thus its original length. New channels and merging rivers could also be formed by erosion, though this is rare due to the variation in thickness and hardness of soils and minerals surrounding the river.
In theory, the Nile is longer in length than the Amazon, which leads to more curves therefore longer. Overtime though, this varies and the length of the river also varies. It depends when the lengths of the rivers were recorded and how precise the measurements are.
Perfectly said!
It's just geopolitics penis measurement contest.
@@FiredAndIced Yeah, you can just say the Nile is the longest river and that's it, it ends there.
I love rivers man. They're like natural magical roads through the wilderness where you can float and explore until the end of time.
I love rivers man. They're like natural magical roads through the wilderness where you can float and explore until you are fatigued and eventually drown surrounded by piranhas... Sorry, just felt funny to write it like that :D
I love artificial rivers in particular
@@ValkyRiver Where is there an artificial river? Thunder River at Six Flags? lol
@@ChristelVinot There are many around the world if you search for them
(Unfortunately Libya’s got destroyed)
@@ValkyRiver oh, you're talking about canals. yeah... canals are ok I guess... if that's your thing.
length doesn't have the same fractally unbounded problem as the shoreline perimeter problem.
Let there be a river of arbitrary length and shape with a defined starting point and a defined ending point.
There is a minimum length path that can be drawn between the points, staying within the bounds of the riverbanks, such that no other path can be shorter than it, even with an infinitesimal rule.
Up your math game bruh!
I was about to mention the same thing, can't wait for the all mistakes we made video lmao
|-O-| |-o-| |-o-|
Thank you!!! I thought this was the case.
Yea like a fish swimming around in the water. Stupid.
Well thought. That adjusts to the definition of distance, which independently of the ruler of measurement, states that it's the minimum path between two points.
"My river is longer than your river" is a new form of bullying
Also, none of the two actually lies on a single country
@Wurfenkopf It's weird how the countries at the end of each river claim it
I'd measure it by shortest travel distance (as if by boat). This would jump edge to edge of the river, but would at least be consistent for all rivers, and take into account any amount of bending. It also has a reasonable reason for measuring this way; if you wanted to travel the river by boat or kayak, this is the minimum distance you would have to travel.
It doesn't entirely eliminate the "make the segments shorter and the river gets longer" problem, as you still have to travel the inside curves of river bends. :/
Personally, I think you should measure the length of a river by measuring how long a semi-sized boat would have to travel to get from one end to the other, and if it branches you should follow the biggest branch. Still, it doesn't really matter as you should always state precisely what you are measuring and what branches you have used
waterfalls
@@mysheetz8964 lmao
And also stronger current will speed it up or slow it down
Yeah but where on the river? if you do it on one side of the river, the result would be wastly different from the other
well boat can get stuck so.
Even though the last research was done by the Brazilian geographic society, but it looks reasonable enough to me. Unless the Egyptian geographic society could find a hidden small tributary for the Nile River which beats that measurement, I will accept the fact that the Amazon River is the longest river in the world.
Adding the tributary made sense not the part where they changed the traditional mouth.
@@guppy719 I mean, if they're gonna measure the Nile down the shoreline of the Lake Victoria instead of directly down the center point, measuring the Amazon to its farthest mouth is fair game to me.
The Brazilian team was very biased
The nile is undisputedly the longest
@@Desfighter1 did you watch the video...?
@@tiovon8209 same, like, the exact same shoreline fractal paradox is going to apply if you measure it like that, therefore approaching infinity with small enough units. like why would you do that
At 2:51 I could not contain myself when he said “Imagine I’m a CRUEL GEOGRAPHY TEACHER” 😂😂😂
Something : *exists slightly bigger than France
RealLifeLore: *laughs in evil
Fun fact: France is the size of New Mexico
@@NunyaMcBusiness RealLifeLore : *laughs in more evil
The narration, the hard work done by the team, and especially the editing is just extremely good.
Great video as usual! Minnesotan here - just for the record, the local pronunciation for Itasca is eye-TAS-ka!
"Brazil declare a win in a length-measuring contest against Egypt."
egypt: we have the longest river in the world!
brazil: NO we have the longest river in the world!
the rest of the countries that the nile and the amazon flows through: *are we a joke to you?*
Rule's clear: own the mouth, own the river. hahahaha
@@sohopedeco I'm not so sure about that. Especially given the dispute between Egypt and Ethiopia, which in a way used to also involve the British, on the Nile river.
@@aes1373 The dispute STILL involves the British considering that the true mouth of the nile could very well be near Gibralter where the Mediterranean meets the Atlantic. James May made a very valid statement with the Nile.
@@chdreturns But why is the british even involved in African disputes?
@@nutte24 is this even a question? lol
This paradox is real, but practicality should prevail in a case like this. The measurement should be done by counting how long it takes to sail the river at a constant speed, that would give it a human scale, which is the most relevant scale to us.
Great video. Love this channel
I just took a look at my notications and this showed up before youtube notifies me.
Usually how it works
I got a notification for a video like 3 days after it got released
Don't read my name,,,,,-,,,,, /_
The Orinoco River empties into the Amazon through the Casiquiare Canal which is a natural canal that connects the Amazon to the Orinoco River. The direction of the flow in the canal depends upon how the ocean tides effect the canal but whether one flows into the other does not make either river the winner since they are both interconnected. The addition of the Orinoco River adds many miles to the length of the Amazon River, which means that you can put the Orinoco River at the top of the list, since it really does include the Amazon headwaters.
4:00 "...approaches infinity..." No, that's incorrect. Unlike the famous "Coast of Great Britain" paradox, a river has a macroscopically smooth centerline, and that centerline does not get endlessly fractal like the sand on the coast. So a 1 m scale ruler is plenty small-enough to very accurately follow the centerline of any river, and switching to a 1 mm scale ruler would not lead towards infinity. Only the last few meters at the source would you have any opportunity for the infinite fractal growth that you assume. In conclusion, a 1 m scale ruler is small enough for any river.
thank you for putting it into words, this video is just clickbait.
What you're saying seems to contradict itself. The banks of the river are a fractal just like a coastline. Therefore, it follows that the centerline, which is the centerpoint between the banks, would also be a fractal. The centerline of the river is inextricably tied to the geometry of the river's banks.
@@LimitedWard by that logic everything is a fractal and there would be no way to actually measure anything, if u wanna measure a river its a lot easier than the lunacy in this video
@@LimitedWard the center-line is not based on the lenght of the bank but on two points from each bank and even if the bank were to be fractal (which is nor really th case) the bank is still a mostly continuous line and so is the center line for all but at most a finite set of point. hence there is a finit lenght of the centerline
Beside if the length was infinite, what about the flow ? what about the volume of water in the system ? is there infinite amount of water in each river flowing at infinite speed ?
Or does a drop joining the river never make it to the ocean (finite speed + inifinite length)
@@rainman1242 Exactly. When you have arbitrary points, you would need an infinite amount of points to measure the centerline.
Rivers are not infinitely long, even if you use infinitely small measurements. In mathematic, there is a concept known as limits. I can understand the issue with measuring some rivers, like the Amazon, because they have so many tributaries. But the curves would only cause the river to reach a limit of so long.
Exactly, .. and I never understood the problem with measuring country borders. I figured they'd converge to some length eventually.
Pulling a string from one end to the other end should be a perhaps hard but true measure of the length…
Not all sequences have well defined limits at infinity. For example, the Koch snowflake has an infinite perimeter (but a finite area), and that informs the issues with country borders.
That being said however, the fractal justification is also insufficient to claim that a river is infinitely long.
@@neerajkrishnang3916 if by country borders you mean coastlines, then yes they are truly much worse than rivers to measure
unlike the rivers here, what he said about their lengths extending to infinity if you go down small enough actually turns into reality thanks to nature
It follows a concept similar to how long all your blood vessels are. If you put them all together in a line you would get a distance longer than the earth to the moon (or several times that?).
It’s called countable infinities. No matter how small of a unit of measurement the length still slightly changes, even by the billionth of an inch.
Honestly I feel like the tributaries of rivers should all count as part of the main river's total length. Due to this, I've always considered the Amazon the longer of the two even before this video; far more lengthy tributaries.
Same
if measured by tributaries i wonder how big is the missipi river
I'm sure The History Channel also says something about Aliens creating the Nile River
Apparently they haven't watched Season 19 Episode 6 and 7, where it's revealed that James May found the source of the nile (despite his car breaking down)
Only cultured people know why his car is important to this
Let’s take the moment to appreciate how much effort RealLifeLore puts into his content for us. Great job
No
2:48 This reminds me of when we learned about "fractals" in mathematics, but we were challenged with measuring the length of a very curvy shoreline.
RLL is incorrectly applying the shoreline problem to the river length. A river does, indeed, have a definable minimum length with an infinitesimal rule.
@@twinprimeable glad someone pointed that out.
Aw man, as a Minnesotan, the pronunciation of "Itasca" here made me sad. It's pronounced "eye-task-uh", not "it-uh-skuh".
I know. The dot for the Lake was also on the border with Canada.
I 100% did a spit take
It was nails on a chalk board when I heard. I commented as well.
Minnesotans unite!
Jk I'm from Fargo but close enough
Is no one gonna talk about how je made a clean transition from measuring rivers to some sort of knife sponsor
Virgin “longest River fan” vs Chad “largest watershed by annual rain volume”
the THAD "largest desert enjoyer"
"Bro even though its cold, the antarctic is the largest desert on earth"
How would the length of a river ( and a coastline) approach infinity? shouldn't it approach a constant number because the amount of length gain would be small if we have small initial units.
because the shoreline, like fractals, become more defined as the unit decreases. If it's small enough you'll be measuring the distance between atom to atom on the shoreline, which for mathematics sake, we can say the L does go towards infinity.
Think about it like this...if you divide into atomic scale units to cover the size of a river, you would have an "infinite" number of atoms covering the length... Since the atomic scale is very small, but it is still a feasible number, you would get very small number x infinite = infinite... That was the ELI5 of the thing, I'm pretty sure Fractal Theory and Limit theory can give you a more precise explanation but I don't really remember my Calculus classes hahahahha
@@fabioapd Wrong. It's finite. You'd rather eat your cheeseburger than find it out though.
Read the Gleick and Mandelbrot books for the shoreline problem. But that doesn’t really apply here.
@@ImTHECarlos98 But there aren't infinite atoms in the world. Wouldn't it be like that problem of 1/2 + 1/4 + 1/8 + 1/16 and so on where it eventually approaches one, and the river coastline approaches a concrete number?
Interesting that you mentioned adding the Missouri to the Mississippi. However, you failed to mention that the Missouri is presently longer than the Mississippi. Every time an ox-bow curve cuts through or flood waters change the delta, they flip-flop. They are that close in length.
Btw, Itasca is pronounced eye-tas-cuh, with the first “a” sound being short as in “cat”, and the second “a” being a short “u” as in “tug”. I live a couple hours away, and have been to the source of the Mississippi a few times. Pretty cool little park.
Can also be a short "i" sound, like the i in him. The second syllable is stressed.
pretty sure that pronunciation is highly anglicized already
@@TCharlieA I’ve heard it said the other way but I suppose there could be another Itasca or that person was pronouncing it incorrectly too.
None of that Matters as the names are anglicized corruptions of the proper native indigenous names.
@@enriquegarcia2790 Besides saying that I heard it pronounced the other way and admitting that whoever pronounced it that way initially probably said it wrong, this is not a corruption of a Native word. As per Wikipedia: "The Ojibwe name for "Lake Itasca" is Omashkoozo-zaaga'igan (Elk Lake); this was changed by Henry Schoolcraft to "Itasca", coined from a combination of the Latin words veritas caput ("true head [of the Mississippi]"). It is one of several examples of pseudo-Indian place names created by Schoolcraft."
4:00 no, it's not going to approach infinity. You were talking about the coastline paradox, which doesn't work in this case. Even with infinitely small divisions, length of the river would still be finite.
Why not? Are we not still applying the same basic idea of fractal dimensions? That idea has been applied to something as small as a snowflake.
You use the phrase "nearing infinity" to say that a number is so big, that there's no way for a human to really understand just how big it is. It is mathematically wrong to say that, that is true, but it wasn't meant to be mathematical, just a phrase to help a bit visualising. An example would be to say that there are "infinite" ways to mix a game of cards, although the number of possible ways is 10^52 and thus finite.
And I don't get what you mean by "doesn't work in this case" since it does. You can go into molecular measures and have a "nearly infinite" length, both in measuring the lengths of a river and a coastline.
And what you also talked about: If you use infinetly small measures, meaning infinitely smaller than molecular measures although that would be physically impossible from our current knowledge, it would be, in fact, infinetly long. Without wanting to offend you, not really anything you said made sense.
Have you heard about rivers? They have 2 coast lines
@@drbruley8045 the point is that a coastline has an edge, which can be fractal-like, because it doesn't have to be a smooth function (might be getting the terminology wrong, I am used to saying that in a different language).
On the other hand, when we measure a river, we use a smooth function, which has natural parametrization, aka well-defined length, that doesn't depend on resolution.
@@ВикторФирсов-е9ф I don't see how the video is wrong for pointing out that some people have said we could measure rivers the same way. Eventually the video does cover a lot of different ways we have measured the world's longest rivers. If anything, the video is more informative for including more info.
I would say the most fair way to measure is the following: imagine you have a really long measuring tape. Put it in de water, as long as you can continue rolling it out in the water, *as long as it stays stretched*, that measurement is the legal. The longest possible road can be taken.
That way al branched are considered and no stupid bends are legal.
I just have to say that the Amazon River is so beautiful, its like a paradise. Amazon rainforest is a truly beautiful place, protect it!
burn it
jk, it is all in Brazil hands...
@@enasosa1612 f
@@enasosa1612 yeah thats why we are fucked
The Brazillian government just abandoned the amazon rainforest
How about the mosquito?
@@thevoidwalkerbr that's not entirely true.
well using the coastline of a lake and pushing it past another river is more of a cheat than choosing the route i'd still give it to the Amazon
Well, with the amount of water in Amazon, at least we can all agree that the Amazon is the biggest river on earth. Nile needs more girth.
lol real life lore is tricking me into learning more school geography with his entertaining videos
Issue 1: I disagree that the smaller your measuring unit is, the closer you get to infinity. In fact, the smaller your unit, the closer you get to the real value. The smaller the value, the more curved the path is without taking shortcuts that subtract from the true length. This is analogous to how PI was measured at first. The radius is known and fixed, so to know PI we need to know the circumference. The early methods to mathematically calculate this was through polygons inside and outside the circle, and the more sides it has, the greater the precision giving an upper and lower bounding limit. But Veritasium explains it better in the video called "The Discovery That Transformed Pi". The bottom line is... the smaller your unit, the lower the error, and the closer you get to the real value. If you were to go down to the atomic scale, you could presumably get the true length. But the law of diminishing returns applies, so the real question is how small does our measuring unit need to become so that the margin of error is "good enough", though depending on the purpose of this measurement, we first need to define how good is "good enough" while also being large enough to make measuring feasible.
Issue 2: It seems that the controversy of which is the longest river comes from the fact that everyone sets their own rules on how to measure. Naturally, that will give different results. It's like measuring how tall we are, but are we wearing shoes? high heels? tall hair? slouching? without clarifying those variables, of course, you can get wildly different results. In my personal opinion (emphasis on opinion, not fact), the best way is to consider that the "main" river at each "intersection", is the one with the greater debit of water. So yes, a narrower but faster-moving flow could could be considered the main rover, over a wider but much slower-moving flow. This would apply both for joining, and for splitting. Additionally, the measured path for length should be the middle between the 2 banks. Thus, for example in the case of the Nile through a lake, the path of the measured Nile, would be through the mathematical middle of the lake which can be considered as just a widening of the river. I'm sure there are other details that I haven't thought of, but if brighter minds would come together to a consensus, everything could be ironed out.
THIS!! I see a great value in popular science channels like this one, BUT only when they themselves are not propagating conceptually incorrect facts or views...
Not quite right. This would only be true of a mathematically perfect entity. With a river, you need to measures parts of the curve either in the center, or along the banks. In both cases "what counts as the center/banks" depends on how precisely you measure. Because the river is a real world entity that can be measured with arbitrary precision, you run into the exact same issue as what's know as the "Coastline Paradox", give it a Google.
The only thing close to a resolution to the Coastline Paradox would be to use a Planck length as your unit of measurement, but that's also not practical at all. Imagine sailing down the Amazon trying to measure the banks of the river within a Planck of accuracy.
Yup. I came here to check for a discussion of how an infinite number of things gets asymptotic, not infinite if their increase a factor in the range (1,2). Oh, infinite sums!
@@jackalope2281 What he's said is right. YOU CANNOT go to infinity just by choosing a smaller unit of measure when measuring the river. That's not how it works. The smaller the unit, the lower the error. True, you cannot have an error of 0. But it can be small enough that the error simply doesn't matter. Square root of 2 technically can be represented as a number with a 2 digit precision. It just has such a high error margin you need to get a higher precision. At a 10 digit precision, most calculations will be practically with a small enough error margin that you can perfectly use it. So the video is wrong. So are you.
@@liviuganea4108 Are you sure the formula for calculating the coastline length as the precision approaches infinity has the same growth rate as that of root 2? There are plenty of limits that approach infinity.
The tricky part with the coastline paradox is that there isn't one distinct formula to track the growth rate, it would depend on the specific contours of the coastline being measured. But one can imagine a part of the coastline that spirals down into infinity (like a fractal), meaning infinite precision can in fact lead to an infinite length measurement. But any detailed contour even besides a fractal pattern would function much the same as the fractal for this purpose, thus allowing any coastline to approach infinite length as the precision approaches infinity.
Again, you are right in that an infinite series (or limit) doesn't always have to approach infinity. But in this case, the growth rate can be arbitrarily large, since there is no discernable end to how much detail we can choose to include in our measurement. This is not a purely mathematical problem to work through, it necessarily involves some interpretive pragmatics due to it's nature as a real-world measurement question.
e.g. A circle in real life is not a perfect circle. So how many sides does it have? Similar issue.
If you reduce the length of measurement, you wouldn’t approach infinity. You would eventually get closer and closer to the rivers actual length. You’re approaching a finite limit. This is high school calculus.
My rules for river measurements:
1, Take the longest continuous waterway that exists in the same river system. (Despite what name it is called)
2, Measure the length of the actual riverflow, like you were on a ship following it. So yes, every curve counts, and not just the distance that the river bridges across.
3, Always use the river's center line for determining the river's length.
4, Always take the longer rout around islands, and at the river's mouth.
The problem with river's centre line is, there isn't always the same water level. Once you will get some curve as the centre line and a month later, this curve will change drastically (especially with the Amazon) :/
"Mississippi is the second longest river in America"
Missouri: wait a minute
Outro Tuga? Outro João!? Acho que já sabes o que tem de ser dito...
PORTUGAL CARALHO
@@joaosantos5503 eu sou do Brasil
@@varella4255 😢😭😢
Não faz mal hahaha Abraço dos teus irmãos portugueses 💪💙💪
I think he meant to say North America. Either that or he doesn’t know that the Missouri is longer because it’s constantly overshadowed by the Mississippi.
Amazon: i'm literally down here
“Mouth” has always felt like the wrong term for where a river dumps out..
Talking about measurements. As a long-time subscriber of this channel, I can sniff when transitioning to sponsored stuff begins from miles away.
That was a god-tier transition from information to advertisement. Standing Ovation 👏🏾👏🏾👏🏾👏🏾
Never inu 27 years of life have I heard that Amazon river is the longest one.
I always learned that Nile is the single longest river. But Missouri-mississipi river is even longer, but for some reason, it's divided into 2 different rivers
At 11:57 you say that the Amazon is 6992km long and the Nile is 6953km long and conclude that there is a 140km difference.
But it's only 39km.
Or you got one of the lengths wrong and it's actually 140km.
Sooooo, which one is it?
Otherwise great video, as usual.
The problem is that they don't have clear rules to measure the rivers length because I think when measuring the length they should take the widest tributary for example not just the one that will make the river longer
Widest at what point? The branch point, the midpoint of the branches, or some fixed distance from origin or branch point?
Everyone knows that the longest river in the world is the random drunk pissing on the streets at 2am
"The answer will end up approaching infinity". "Depending on what you use, the answer could end up on a range from 300km up to infinity".
With all due respect, what is this guy even talking about here, what is his point, you could literally make this argument for absolutely everything that has a length and can be measured. Also, sure let's totally ignore the concept of convergence right?
The point is that the shoreline paradox makes measuring rivers hard to quantitate, which in turn makes them hard to compare.
It's really not that hard to understand.
@@mechanomics2649 Found this paragraph on wikipedia on the coastline paradox:
The problem is fundamentally different from the measurement of other, simpler edges. It is possible, for example, to accurately measure the length of a straight, idealized metal bar by using a measurement device to determine that the length is less than a certain amount and greater than another amount-that is, to measure it within a certain degree of uncertainty. The more accurate the measurement device, the closer results will be to the true length of the edge. When measuring a coastline, however, the closer measurement does not result in an increase in accuracy-the measurement only increases in length; unlike with the metal bar, there is no way to obtain a maximum value for the length of the coastline.
I didn't realize that convergence was not a thing when dealing with fractals, and since coastlines behave like fractals, a more precise measurement device will not actually lead to a more accurate measure of it's true length.
why can't they just use a boat that measures how much km they have moved ( like a normal car i mean ) and try to sail as close to the middle as possible....
I hate to pick on kids for my example, but since I have a young child, I know where I'm coming from:
Step 1: Ask a five-year old to draw a rectangle. No rulers, straight-edges, etc., just draw it. Perfect lines--no, of course not. Even most adults not in art/architecture/engineering professions would have SOME deviation in the sides of a rectangle. Fair enough, though, you could still reasonably measure it around through simple mathematics of some of the curvature of the lines.
Step 2: Ask a two-year-old to trace his/her hand on a piece of paper. At the end just have him/her connect across the points where you stop tracing at the wrist bones. THAT'S how the Earth REALLY is! Try measuring the length around of THAT! That's where deviation comes into play in measurement.
@@thetrainmon use a gps map with a scale of 1mm=10km or something, put a rope and try to always follow the middle of the river. The length of the rope is the length or the river. No deviation, maybe 0.01% longer or shorter :)
I love how he said that the Amazon measurement was a bit of a stretch but the people counting not only Lake Victoria, but also measuring its coast line, making it significantly longer is all fine, hahaha
I know right? lol
Amazon not only the longest, but the biggest and the most abundant mass of water.
Nile is the longest because the Mediterranean sea is part of it. They said it on Top Gear, so it's correct by default.
And the Amazon is connected to the Atlantic Ocean I still don't think either should count
@@TinyLordCthulhu Well they didn't mention anything about that so I wouldn't put my money on it.
@@TinyLordCthulhu The Atlantic doesn't have a mouth, the Mediterranean does (at Gibralter). As such the nile & any other river flowing into the Mediterranean is longer than the shAmazon.
@@chdreturns Legit nobody count seas as part of a river but ok
Well at the end the longest was the actual Amazon after BOTH rivers used the longest possible measurements they could. And honestly considering the fact the Amazon holds over 20% of the non salt water in the world. Ummm I'd just go with the much larger river. It doesn't matter what Ocean/Sea the river is connected to.
measuring the lenght of a river shouldnt be dependent on the shoreline whatsoever... its a line down the aproximate center point... which might still make measuring a true lenght nearly impossible, however its not nearly infinite.
How do you find the approximate center point though? I think you're vastly oversimplifying how that would work. Not to mention the center line of a river would still be infinite if you decrease your unit of measurement.
@@LimitedWard measure it in metres and then convert it in km. Simple. Metre is the SI unit of length.
@@LimitedWard the deepest point in that cross section... sure that is approximate, but these approximation still yield a finite and convergent measurement... with an error bar if you want, but that error bar does not 'explode' and is manageable. in anycase it IS a finite length and the scale of the stick you use to measure has an convergent effect.... as you can see with the number the author mentioned: as the stick get smaller the effect of the change in size of the sitck get smaller even faster. first order of magnitude got hs length double (aka 100%).. the second order of magnitude got the lenght up by 12% of so.... this converge fairly quickly
@@LimitedWard no it wouldn't. It would approach an actual value. Plus, it's not that hard to find the centerline of the river
@@listen1st267, but do you measure that once or for the entire course of a river? How far apart are these new centerlines? Should it account for the changing of the river?
As a Minnesotan I laughed when he butchered “Itasca”.
4:08 I’m pretty sure that the length of the river does not go to infinite, it converges. The problem is that we can’t measure it in infinitesimal units.
BTW you are actually approaching to an integral (the arclength to be exact).
Except atoms do not actually touch each other, and are made up of constantly moving particles. So, yes, it is does get infinite if you get to a molecular level and beyond.
If you plot the measured length against the length of the measuring ruler (for reasonable cases) and end up roughly with an exponential curve, then you've got a fractal. Fractals are everywhere in nature: surfaces of clouds or bodys of water, shorelines and rivers, many types of plants, etc.
@@vitorboldrini6337even if they don’t touch they are at a scale of nanometers, so you are measuring that small lengths of empty space that may not even count.
The “real result” may be a huge number but not infinity. Remember that the infinity is just a concept not a number.
@@pierrestober3423 Yes actually the coastlines are fractals, well they approach enough to be considered one of them, since fractals is a limit process.
@@vitorboldrini6337 Except we're not measuring rivers according to their shoreline but rather their center, which is simply described by curves, which do not go to infinity when measured but converge on a finite number.
The longest river title is basically a huge 1000's year old argument
I think it's possible to get an exact number. Overlay a piece of string over a map program that you can straighten out and keep the string at the same zoom as the map so the string is an accurate distance reference. You can apply this to both sides of a river or border or even river border, lake border, etc. and average out the numbers. Assuming the map's distance reference is accurate all you have to do is measure. From there you have to apply elevation changes, in a less complicated and slightly less accurate example, If you apply this to the Mississippi River it starts at 1,475 feet in elevation and ends at 725 feet of elevation, this increases the length you get from the string. To get the exact measurement you'd have to calculate the exact elevation changes along the whole river or border. If you are trying to decide where it begins and it has multiple points to choose from, you choose the furthest from the end or calculate all variables.
The fractalness of water is easy to see. Just realize that every stream of water is in itself just like a river, feeding into an ever bigger river. They're all the same, but just at different sizes. Which explains why you can't truly measure the longest river, as you'd never be able to stop with each infinitisemaly small stream, which are always changing in lengths, sizes, and paths.
Right, the names of the rivers are arbitrary. So we renames parts the same name.
Ok then, fair enough. Let us instead paint scaled down replicas of each river and see which required more pigment.
BAM, easy, y'all welcome
@@yoremothra9838 by your definition, a short and wide river can be longer than a narrow and long river
@@TasX Nay lass, I just want us all to create river art, and stop quarreling over which has more droplets. :)
They also flow different directions hence making them different rivers. Also having different start points and the same end point are 2 different rivers. At the meeting point you can argue they are arbitrary.
Was anyone else binging RLL videos when this new one popped up?
As a Minnesotan, the way you pronounced Itasca entertaining
Top Gear found the true source of The Nile 😜
I'm from Minnesota, and to hear him pronounce Itasca in such manner saddens me. But dont mind me I'll get back to my tator tot hotdish and lutefisk.
You're pronunciation of "I-task-uh" made me chuckle
As a Minnesotan it is my sworn duty to correct your pronunciation of Itasca- you said it-is-ka when it’s actually i-tas-ca- it should rhyme with Alaska.
OOFTA THANK YOU!!!! I'm gonna leave my own comment anyway, but that was an instant pause on the video for me. The poor Texas guy is just trying his hardest here.
Fun fact about the Mississippi River. Depending on how you define "uphill" and "downhill", the Mississippi River actually flows "uphill".
Lake Itasca is 5.9 km closer to the center of Earth than New Orleans and the Mississippi Delta. It is not gravity that drives the Mississippi River to flow. It is the centrifugal effect that causes the water to move against true gravity, as the water tries travel in an inertial straight line, away from the Earth's axis of rotation. It feels like gravity from our point of view, and it feels like a downhill journey from Minnesota to Louisiana for this reason. It is ultimately getting closer to sea level, because sea level and the overall shape of our planet settles on an oblate spheroid shape based on hydrostatic equilibrium at its surface to adapt to balancing the centrifugal effect and gravity.
As a Minnesotan, the way you pronounced Lake I-Task-Uh and the positioning on the map got to me, good work overall though!
Basically this is just a game of “what can we add to make our river the longest”
3:57 Breaking down length into infinitely small differential length will help us in getting the correct value of the length and will not result in infinite length.
This is what we do in integral calculus. Integrating the differential parts.
I think you might be correct for the river, but not for the shoreline problem. They are separate, not analogous, as presented in the video. People have presented other issues, such as where you draw the course. The most navigable channel where the most water flows might be on the outside of bends, but most certainly not along the shorelines of the “lakes”.
@@Markle2k Right. However as for rivers, RLL really shouldn't have been talking about shorelines since surveyors use the centerline to determine rivers
@@listen1st267 The problem is how you calculate the centerline is based on how you measure the banks, which is what leads to discrepancies between measurements.
@@heliogen5959 yeah it can lead to discrepancies but I was bringing this up because other comment threads were buying into RLL's idea that the length of a river could be calculated to be infinity, which just isn't reasonable. Using the centerline would lead to approaching a finite value (or range)
@@listen1st267 There’s some calculus involved it that I haven’t gotten up to yet, but I’m pretty sure you’re right.
4:10 Infinity, really? For very little measuring stripe lengths, you of course have to give those stripes somewhat the direction of the river instead of going from left to right to the left and so on.If you can tell the direction of the line properly, you should come to the fact that a sequence of river lines getting more and more accurate will converge. (At least I hope so.) But if it converges, then you'll get a line of infinite accuracy (Always the middle of the river). This line is the image of a continous function from [0,1] to something three-dimensional. It should be basic analysis to realize: The length of that perfect line - let it be huge, but it will not be infinite.
Exactly, it would converge eventually. I mean the length of the river surely wouldn't exceed the diameter of the observable universe, haha.
I love the smooth transition to the sponsor info, well done 👍
4:00 Wait, if you decrease your measuring increment, the river length wouldn't approach infinity. It would approach but never reach the actual river's length
The solution to measuring irregular shapes isn't "fractals," it's calculus. And there is a definite answer to the circumferences of irregular shapes...
it's called the coastline paradox.
@@peepeetrain8755 Integrals
The problem is that the river's shape doesn't have a defined length. It's a type of fractal.
Thanks for this video. This was the topic I was liked in school geography classes
Why do you have a VW avatar for the name Ford?
Saying that the Nile starts on the other side of lake Victoria is like saying that it ends on the other side of the Mediterranean sea. It makes no sense
I live in MN, we probably say it wrong since it's an indigenous word but I have never heard Itasca said that way and I kind of prefer it haha. We always heard it as It-Ah-sca and I just loved that it was even referenced in this video. I love you work, great job!
It's actually latin
@@chito5954 It's not even really Latin. It's arguably more accurate to call it an English neologism, because it was intentionally created (albeit by joining parts of two different Latin words) for use as a single word in the English language.
I remember doing a in-class activity based on this weirdness; we were divided up into 9 groups;
3 groups used a string, some pins, and the map on a corkboard to measure a few different rivers.
3 using broken up segments
and the last 3 groups used a ruler to measure it out as the crow flys.
all the groups used the same three rivers but even between the groups that used the same method, our answers varied; our teacher then explained that the reason why it varied was due to our different views on where a river starts and ends. In the end it was not only a lesson on geography but also how different views on the same subject can both be right and wrong.
I was in the tenth group. The 'who gives a f**k' group.
@@two-sense 😳
0:53 It’s what I like to call the Google Effect. Everyone disagrees with each other and it makes it very confusing for some average Joe like me to know who’s right and who’s wrong. It’s not limited to just geography. It’s just all over Google.
There's a creek in Wyoming that flows into both the Snake and Mississippi rivers. If you were an ambitious fish you could swim from the Pacific Ocean to the Gulf of Mexico through American rivers.
Or U can be smart and use Panama