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Is the average sinuosity of the world's rivers equal to pi?

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Re: Is the average sinuosity of the world's rivers equal to pi?

#41

Post by eitally »

brittonsmith wrote: post #38
reilly3000 wrote: post #33

Why on earth would the rivers of the world have an average sinuosity of pi? Rivers are super dynamic and are effectively a side effect of localized water cycles and geology. This seems like Music of the Spheres... Aka looking for harmony in a chaotic universe.

An explanation of this is put forth in both the video and paper linked to in the opening paragraph. The principle is that bends in rivers tend to grow as erosion happens on the outside of the bend and soil deposition on the inside. This increases sinuosity until the point at which the bend comes full circle, forms an oxbox lake, and returns the local region of the river to a straight line with sinuosity of 1. The val…

I suspect damming (and other human intervention as you note) in general causes restrictions in sinuosity, artificially either preventing on creating local regions of sinuosity = 1.

Re: Is the average sinuosity of the world's rivers equal to pi?

#42

Post by zamalek »

Osmium wrote: post #40
zamalek wrote: post #39

Earlier quoted context omitted.

The coastline paradox is a matter of accuracy (significant digits). As you "zoom in" on the coast this is what happens to the length: 100km > 120km > 128km > 129.5km > 129.52km > 129.528km > 129.6281km > ... If you have to "zoom in" to see a length feature it means that the length feature is small and therefore the contribution to the overall length that these features provide diminishes. Something like a sigmoid[1],…

> As you "zoom in" on the coast this is what happens to the length: 100km > 120km > 128km > 129.5km > 129.52km > 129.528km > 129.6281km > ... I don't think that's true. In real life this series does not converge unless you specify a minimum feature size, which you hinted at. This isn't just a mathematical curiosity; real life coastlines are fractal and have no well-defined length, as the parent poster's link explains…

> To measure a coastline you have to specify a minimum feature size.

Not coastlines: only fractals. The name of the paradox is really unfortunate because it doesn't apply the coastlines "all the way down." You can't keep subdividing a coastline because eventually you start working with curves meaning that you can use calculus and meaning that you can work out limits.

The actual issue with real-life coastline (and river) length is that it's continuously changing.

[Edit to your edit]: yep. However the important result is that we can actually arrive at a length for a river, regardless of the mathematical thought experiment.

Re: Is the average sinuosity of the world's rivers equal to pi?

#43

Post by Osmium »

zamalek wrote: post #42
Osmium wrote: post #40

Earlier quoted context omitted.

> As you "zoom in" on the coast this is what happens to the length: 100km > 120km > 128km > 129.5km > 129.52km > 129.528km > 129.6281km > ... I don't think that's true. In real life this series does not converge unless you specify a minimum feature size, which you hinted at. This isn't just a mathematical curiosity; real life coastlines are fractal and have no well-defined length, as the parent poster's link explains…

> To measure a coastline you have to specify a minimum feature size. Not coastlines: only fractals. The name of the paradox is really unfortunate because it doesn't apply the coastlines "all the way down." You can't keep subdividing a coastline because eventually you start working with curves meaning that you can use calculus and meaning that you can work out limits. The actual issue with real-life coastline (and riv…

Agreed that the fact it's continuously changing is an additional issue, but I don't see the "eventually you start working with curves" argument. Where are these curves on a typical coastline?

If you're measuring the coastline on a map, that argument holds, but the map is only one representation of the reality, and they've already made decisions regarding minimum feature size implicit in the construction of the map.

But yes, also agreed that measuring rivers should be fine, because you can represent it as a one-dimensional line along the 'centre of mass' of each segment of the river, which should give well-defined values regardless of what the 'edges' of the river look like.

Re: Is the average sinuosity of the world's rivers equal to pi?

#44

Post by zamalek »

Osmium wrote: post #43
zamalek wrote: post #42

Earlier quoted context omitted.

> To measure a coastline you have to specify a minimum feature size. Not coastlines: only fractals. The name of the paradox is really unfortunate because it doesn't apply the coastlines "all the way down." You can't keep subdividing a coastline because eventually you start working with curves meaning that you can use calculus and meaning that you can work out limits. The actual issue with real-life coastline (and riv…

Agreed that the fact it's continuously changing is an additional issue, but I don't see the "eventually you start working with curves" argument. Where are these curves on a typical coastline? If you're measuring the coastline on a map, that argument holds, but the map is only one representation of the reality, and they've already made decisions regarding minimum feature size implicit in the construction of the map. B…

> Where are these curves on a typical coastline?

Between atom nuclei.

Re: Is the average sinuosity of the world's rivers equal to pi?

#45

Post by Osmium »

zamalek wrote: post #44
Osmium wrote: post #43

Earlier quoted context omitted.

Agreed that the fact it's continuously changing is an additional issue, but I don't see the "eventually you start working with curves" argument. Where are these curves on a typical coastline? If you're measuring the coastline on a map, that argument holds, but the map is only one representation of the reality, and they've already made decisions regarding minimum feature size implicit in the construction of the map. B…

> Where are these curves on a typical coastline? Between atom nuclei.

How so? Do you fit the positions of your nuclei to a spline to get your curve? How about quantum uncertainty in its position? How do you assign whether a given nuclei belongs to the 'coast' or to the 'sea', etc. I don't think it holds.

Re: Is the average sinuosity of the world's rivers equal to pi?

#46

Post by zamalek »

Osmium wrote: post #45
zamalek wrote: post #44

Earlier quoted context omitted.

> Where are these curves on a typical coastline? Between atom nuclei.

How so? Do you fit the positions of your nuclei to a spline to get your curve? How about quantum uncertainty in its position? How do you assign whether a given nuclei belongs to the 'coast' or to the 'sea', etc. I don't think it holds.

> How about quantum uncertainty in its position?

Aw crap, really good point. You're right.

Re: Is the average sinuosity of the world's rivers equal to pi?

#47

Post by votingprawn »

gus_massa wrote: post #2

It would be nice if the distribution graphic of the sinuosity has units. Also, there is a clear outlier with sinuosity 7.6. Which river is it?

And also numerous rivers with sinuosity < 1, i.e. the river is shorter than the straight line distance between the source and mouth.

Re: Is the average sinuosity of the world's rivers equal to pi?

#48

Post by lsjroberts »

Author here, feel free to contact me if you're interested in this or a scientist in a related field - lsjroberts [at] outlook {dot} com

Thanks for the feedback, I'm working on expanding the project to import data from a couple of sources, you can follow it at http://github.com/lsjroberts/pi-me-a-river

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