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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?

#11

Post by mistercow »

IsaacL wrote: post #9

What's the reasoning behind why this should be the case? Something to do with the curvature of the Earth?

There's a link to a video that explains it.

tl;dw: when rivers are very sinuous, the kinks turn into oxbow lakes and separate from the river, so that limits how sinuous they can get. On the other hand, rivers' bends are constantly amplified by erosion. Researchers modeling these phenomena showed that under certain assumptions, these forces are in equilibrium at a sinuosity of ᴨ.

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

#12

Post by pmalynin »

unholiness wrote: post #8
oofabz wrote: post #5

Do rivers actually have a well-defined length? I know coastlines do not, and rivers seem similar. https://en.wikipedia.org/wiki/Coastline_paradox

Yes. With a coastline, the closer you measure, the more length-increasing features you observe, causing the measured length to diverge. Rivers have a finite width, so once the distance between your measurements is smaller than the width of the river, the measured length will converge to the true length.

Indeed, one would reach the plank length -- and hence the distance simply cannot be infinite.

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

#14

Post by thedufer »

pmalynin wrote: post #12
unholiness wrote: post #8

Earlier quoted context omitted.

Yes. With a coastline, the closer you measure, the more length-increasing features you observe, causing the measured length to diverge. Rivers have a finite width, so once the distance between your measurements is smaller than the width of the river, the measured length will converge to the true length.

Indeed, one would reach the plank length -- and hence the distance simply cannot be infinite.

The planck length is simply the base length when you set up your units such that c, G, and h are all 1. There's currently no reason to believe it has any sort of physical meaning beyond that.

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

#15

Post by PhasmaFelis »

What's going on with the HN title font? That square-with-the-bottom-missing character seems to be the proper codepoint for lowercase-pi, but it's definitely a not a recognizable rendering of lowercase-pi. Even in sans serif, the top bar should extend past the corners on the left and right.

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

#16

Post by matt_kantor »

This is somewhat pedantic, but the average anything of anything can never be equal to π; it's an irrational number, and averages (arithmetic means) are ratios.

What should be said is that the average might approach π.

EDIT: I'm wrong, read the replies.

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

#17

Post by IvyMike »

matt_kantor wrote: post #16

This is somewhat pedantic, but the average anything of anything can never be equal to π; it's an irrational number, and averages (arithmetic means) are ratios. What should be said is that the average might approach π. EDIT: I'm wrong, read the replies.

What's the average of 0 and 2pi?

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

#18

Post by StefanKarpinski »

matt_kantor wrote: post #16

This is somewhat pedantic, but the average anything of anything can never be equal to π; it's an irrational number, and averages (arithmetic means) are ratios. What should be said is that the average might approach π. EDIT: I'm wrong, read the replies.

If you're going to be pedantic, do it right.

The average of 0 and 2π is π, so an average can certainly be π. Yes, the average of a finite number of rational numbers cannot be π since π is irrational. But why would the sinuosity of any river be rational? The sinuosity of a circle is exactly π, for example. The true sinuosity of any given river is almost certainly irrational as well, since irrational numbers vastly outnumber rational ones in a very relevant sense: if you pick a real number uniformly at random between 0 and 1, there is literally zero chance that you will pick a rational number. Similarly, there is zero chance that the sinuosity of any river will be π or that the average of any finite number of rivers will be π. However, what they mean when they say this is this more precise fact: if there were an infinite number of rivers formed like those on Earth, the average sinuosity of that infinite collection of rivers would be exactly π.

There. That's how to be pedantic.

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

#19

Post by matt_kantor »

StefanKarpinski wrote: post #18
matt_kantor wrote: post #16

This is somewhat pedantic, but the average anything of anything can never be equal to π; it's an irrational number, and averages (arithmetic means) are ratios. What should be said is that the average might approach π. EDIT: I'm wrong, read the replies.

If you're going to be pedantic, do it right. The average of 0 and 2π is π, so an average can certainly be π. Yes, the average of a finite number of rational numbers cannot be π since π is irrational. But why would the sinuosity of any river be rational? The sinuosity of a circle is exactly π, for example. The true sinuosity of any given river is almost certainly irrational as well, since irrational numbers vastly out…

Good call, I'm not sure why I hadn't considered that. I blame the whiskey!

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

#20

Post by StefanKarpinski »

matt_kantor wrote: post #19
StefanKarpinski wrote: post #18

Earlier quoted context omitted.

If you're going to be pedantic, do it right. The average of 0 and 2π is π, so an average can certainly be π. Yes, the average of a finite number of rational numbers cannot be π since π is irrational. But why would the sinuosity of any river be rational? The sinuosity of a circle is exactly π, for example. The true sinuosity of any given river is almost certainly irrational as well, since irrational numbers vastly out…

Good call, I'm not sure why I hadn't considered that. I blame the whiskey!

No worries. You gave me an excellent excuse to exercise my pedantry in a way that I usually try to avoid so as not to be a social pariah :-)
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