Why Nobody Knows the World’s Longest River

Instead of breaking the length in smaller parts of 10 KMs, you should have broken down into the lengths of Toyota Corolla

"Honey, I'll go out expedition to measure a river length" "Fine, but don't get too political" "I won't"

Elementary school: The Nile River is the world's longest river! RealLifeLore: Are you sure about that mate?

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.

We all know who found the true source of the Nile: Jeremy Clarkson, James May, and Richard Hammond.

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.

"The length will approach infinity as the measuring units get smaller." frantically goes to measure pp on the molecular level

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

"It's not about how long it is, it's about what's inside that counts" - Pinnochio

We all know, James May is the discoverer of the true source of the Nile.

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)

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.

As an American, I welcome the new measuring unit of "Frances Per river basin."

so they're about equally long within a margin of error, gotcha

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 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.

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.

RLL: "The length will approach infinity as the measuring units get smaller." Integral calculus: "Am I a joke to you?"

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'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. :/