Is there something like an "average frequency of rivers reaching the sea"?

[Yora]

I am working on a fictional map where all settlements are located on the coast or on navigable rivers. And I realized that I actually have no idea if small rivers reaching the sea are actually a common thing.

Is there any rough ballpark average for how many rivers you will pass while travelling along a coast? I guess it depends very much on the terrain. The landscape that I am using as reference is the coastline from Alaska to California.
If I have 1000 km of coast, is there some kind of number of navigable rivers that would seem plausible?

[snowblizz]

Unfortunately... "it depends".

What's "navigable" e.g. a viking longship, a galley and a cog have fery different draft requirements let alone compared to a modern containership.

A river may only be "navigable" to short extent. Even big rivers may not be navigable by larger craft due to silting and such.

It's going to depend on the topography of the region. And the climate.

If you take the American west coast e.g. most rives are likely to be short and fairly straight affairs, it's not that far from the nearest watershed, ie the Rockies to the ocean. On the other side of the rockies rivers tend to flow down to the 1 big collection point, the Mississippi basin.



So I'm going to have to say no, not really. Just take a punt at it, you are unlikely to find a good "correct" answer anyway.

[Knaight]

Kind of. There has been some research done in terms of absolute number of rivers organized by Strahler order*, and while most of it is paywalled some of it gets through in weird ways. Most notably you have the table below:
http://4.bp.blogspot.com/-ZtFJ7yEqnQM/VJ-Z_RQGVdI/AAAAAAAASeo/Moyfzh1g0Z8/s1600/Mean%2BStream%2BLength%2BWidth.png
It looks pretty self explanatory, but just in case it isn't: The columns are the Strahler order of the stream, the number of streams in that order (estimate), the average length of the streams, the total length of all streams of that order, and the average width of those streams. It's also worth noting that the data gets dominated by small groups and thus randomness starting with order 10, especially given that there is literally just one order 12 stream (the Amazon at its mouth), and one order 11 stream that isn't a tributary of the Amazon (the Nile). Basically, the Amazon is a stupid huge river and it distorts the data for fictional purposes.

So, first things first - what are your biggest streams? I don't know the geography of the coastline you're using in any intricacy, but a quick look at the list on the Main stem (https://en.wikipedia.org/wiki/Main_stem)wikipedia page pulls up some data. It's irritatingly US centric, but the short version is that the Mississippi is order 10, and there are 8 main stems (which can be expected to reach ocean or peter out) at order 9. This explicitly includes the Columbia. I don't know the situation on the coast of Canada, but the Columbia drainage basin extends pretty high into it and judging by global precipitation maps I doubt it's got anything too huge. I did find a map that shows strahler order by line thickness (https://muir-way.com/products/hydrological-map-of-canada), so call it another 3 order 9 streams there. Judging by the Alaskan edge there there's something sizeable in the region, so call it 5 overall.

Now, let's talk smaller streams. There's a definitional requirement that there are at least 2 streams order N-1 feeding each stream N. The table above suggests a maximum of 5ish on average - but plenty of these streams either peter out or hit ocean instead of a larger stream. What streams are viable for vehicles really depends on the vehicle, but judging by the table I'd say small canoes, kayaks, rafts, etc. start looking good around order 4, while the average order 6 stream can probably handle just about any vehicle (I'm assuming a low tech setting; this absolutely doesn't apply to massive ocean liners and the like). There's also the matter of how stream length (which I'm pretty sure is based on the entire length up to the mouth of the stream or where a tributary meets a higher order section) has a correspondence with the chance that any given river is in the area. Looking at the total length column that looks like about 2x on average. So, let's use the 2x figure for streams one might cross.

For your total area there are thus:
5 9th order
10 8th order
20 7th order
40 6th order
80 5th order
160 4th order

Looking at the last 3 that means either 75, 155, or 315 streams big enough for boat travel.

Obviously you'll want to introduce some noise into these numbers instead of having it be that regular, but this should be a start.

*The short version of what that means: A stream fed by no other streams is Strahler order 1. Whenever two streams at order N become one stream they become order N+1. Whenever two streams of orders N and M, N>M meet the order stays N.

[Yora]

This is about rivers in general, correct? It doesn't make a statement about whether each river connects to another river or ends in the sea, right?

[Kato]

Yes, it says nothing about where it ends.

I think the number is too random to be reliable. Different regions have very different geography, similar regions can be different and different regions can be similar. It's unlikely there's no river for a hundred kilometers or two next to each other but overall, nothing is implausible, so.. Do what you want?

[Lord Torath]

Almost all rivers will eventually make it to the sea. Those that don't will almost always be in a basin that doesn't get enough rain to fill up high enough to reach the sea (see the Great Basin in the western US, or the Dead Sea in the western Middle-East). Very, very, few will just peter out and dry up before reaching the sea, like the Colorado river in the US. But that river only ends because we take so much water out of it for drinking, industry, and irrigation. In a medieval society, that is unlikely.

Not all of the rivers that "reach the sea" will do so as a single stream. They may "dissolve" into a massive swamp at the edge of the ocean, with no clear way through. They may form huge deltas with a handful of large channels and a plethora of smaller, shifting ones.

In general, the steeper the slope as you approach the shore, the straighter and more "compact" the river will be as it enters the sea.

[Yora]

The question is, when you travel for 1000 km along a coast, how many rivers will you come across that could take you further inland?

If there is no general rule of thumb and it all depends on specific topography, that's also an answer.

[factotum]

If there is no general rule of thumb and it all depends on specific topography, that's also an answer.

And in fact, that *is* the only answer. If this coastline is like Norway then the rivers tend to exit into the sea via steep-sided canyons (fjords) and so offer much deeper access to the interior than a river going across flat territory would. Also, the form of a rivermouth will determine how popular it is for navigation--a river that exits into a sheltered bay is going to be more used than one that exits into a rock-strewn reef.

[Kato]

If there is no general rule of thumb and it all depends on specific topography, that's also an answer.

Pretty much this, I think. I mean, over a thousand miles I guess you could get anything from 50 to 2000 rivers of varying size. I guess you might get a world average somehow but I don't think that's represantative of anything.

(One problem with finding numbers is... measuring coast length. The obvious solution seems to draw a straight line but of course most people who measure the coast don't care about this but need to include every curve and whatnot, which makes sense for them but is of little help here.
If you want SOME kind of hard numbers, I found Lower Saxony's cost to be about 750 km and has measely 7 rivers of which only three or for would make for good shipping, because they swallow all others. Mecklenburg-Vorpommern has about 13 (or so), mostly very small ones over a length of less than 400 km. So something like a river every 50 km might be a very rough estimate, I guess for the region, with a very varying size.

Also, looking into this made me realize how crazy the Danube is. By all accounts this should be some short thing that probably ends up in Atlantic via the Rhine and nobody would care, because pretty much all German rivers flow north. But nope, not the Danube. That's going to head south, all through south east Europe up to the Black Sea being the most important river in the region by far and probably shaping European history just because it decided to not do what every other German river does.)

[crayzz]

I am working on a fictional map where all settlements are located on the coast or on navigable rivers. And I realized that I actually have no idea if small rivers reaching the sea are actually a common thing.

Is there any rough ballpark average for how many rivers you will pass while travelling along a coast? I guess it depends very much on the terrain. The landscape that I am using as reference is the coastline from Alaska to California.
If I have 1000 km of coast, is there some kind of number of navigable rivers that would seem plausible?

The real answer is going to be varied enough that you could get away with practically anything.

There is this list (https://en.m.wikipedia.org/wiki/List_of_rivers_of_the_Americas_by_coastline) of all the *major* rivers that flow into the various oceans from the Americas. You'll want the north half of the Pacific Ocean list if you're basing your coastline on California to Alaska. That does leave out little rivers, but my guess is that list include the rivers accessible enough for easy entry.

If you just want something plausible and have some half decent programming skills, generating a bunch of random source points and doing a random walk towards the coastline would probably give you a decent river map. A language like Processing would be perfect for this.

[halfeye]

If you just want something plausible and have some half decent programming skills, generating a bunch of random source points and doing a random walk towards the coastline would probably give you a decent river map. A language like Processing would be perfect for this.

It's not about source points, it's about catchment areas. All the rain has to go somewhere. If there's rain there'll be at least a temporary river, the larger the area the more rain is caught for a specific level of rain.

Civ V is very bad on rivers, sometimes there aren't any along a long line of coast (which is probably a reflection of the resources you get from them, but still irritates me).

[Spojaz]

I feel like "average frequency of water body confluence" would actually be a good way of classifying different kinds of terrain. More rainfall, greater slope or less permeable soil could mean a higher WBC. Together with the flow rate, it would give you a pretty good sense of the climate and hydrologic composition of the area. It could even give you an idea of the depth of the water table.

I think the numbers for a given terrain would be the pretty similar whether you were talking about rivers-into-the-sea or tributaries-along-a-river.

In my extremely bad estimation, I would say .5-5 streams big enough for edible fish per mile. For rivers big enough for useful river travel, perhaps there would be one every 2-20 miles.

For a better guess, maybe ask a fluvial geomorphologist?

[crayzz]

It's not about source points, it's about catchment areas. All the rain has to go somewhere. If there's rain there'll be at least a temporary river, the larger the area the more rain is caught for a specific level of rain.

Civ V is very bad on rivers, sometimes there aren't any along a long line of coast (which is probably a reflection of the resources you get from them, but still irritates me).

That's true, but rivers are often mapped as if they had source points. (https://files.prokerala.com/maps/india/map-files/india-river-map.jpg) For the purpose of determining how many rivers actually reach the ocean, simplifying down to source points is probably good enough, at least for generating quasi believable river maps.

[jayem]

I'd expect the number of actually stopped rivers to be so low you can count them (the Jordan, whatever flows in the Aral sea).
It requires a basin that is sufficiently large for the water to evaporate from it as fast as it falls in the correspondingly small catchment area without any holes in it, otherwise it will eventually overflow and carry on.
[Looking it up the technical term is Endorheic]

Regarding indirect reaching, for every tributary a sea entering river has, that's at least one non-sea entering river. Assuming some kind of fractal branching, the total amount as a proportion is going to be tiny.
It will however depend on:
What you count as a river (This is going to dominate by far, by definition the bigger/longer ones are the survivors)
The amount of coast (I'd imagine)
The length and area inland (again I'd imagine)




I think the numbers for a given terrain would be the pretty similar whether you were talking about rivers-into-the-sea or tributaries-along-a-river.

That might be a way for working a rule of thumb.

[Algeh]

I think it's really going to come down to both the geology of the area and what is considered "navigable" for that culture. "Can I get up this river in a canoe if I'm also willing to get out and carry the canoe along the shoreline sometimes?" will generate a different list of navigable rivers than, say, modern container shipping terminals need to be situated on.

Wikipedia has a list of major ports by ocean here: https://en.wikipedia.org/wiki/List_of_ports_and_harbors_of_the_Pacific_Ocean which would help you ballpark it on the low end. For example, there are definitely more than two rivers that make it to the Pacific Ocean in Oregon (Wikipedia has that list here: https://en.wikipedia.org/wiki/List_of_rivers_of_Oregon#Pacific_Ocean ), but only two will be listed among the three ports on that page, since those are the only rivers with major commercial use of that kind.

[halfeye]

I think it's really going to come down to both the geology of the area and what is considered "navigable" for that culture. "Can I get up this river in a canoe if I'm also willing to get out and carry the canoe along the shoreline sometimes?" will generate a different list of navigable rivers than, say, modern container shipping terminals need to be situated on.

Yeah, I came across this thing recently:


The canal route runs 227 kilometers (141 mi), partially along several canalized rivers and Lake Vygozero. As of 2008, the canal carries only light traffic of between ten and forty boats per day. Its economic advantages are limited by its minimal depth of 3.5 m (11.5 ft),[citation needed] inadequate for most sea-going vessels. This depth typically corresponds to river craft with deadweight cargo up to 600 tonnes, while useful sea going vessels of 2,000–3,000 dwt typically have drafts of 4.5–6 m (15–20 ft).[3][4][5] The canal was originally proposed to be 5.4 m (17.7 ft) deep; however, the cost and time constraints of Stalin's First five-year plan forced the much shallower draught

https://en.wikipedia.org/wiki/White_Sea%E2%80%93Baltic_Canal

[Rogar Demonblud]

I'd expect the number of actually stopped rivers to be so low you can count them (the Jordan, whatever flows in the Aral sea).

Higher than that. The Colorado River, as noted, evaporates into the desert because of the amount of water we pull out. Ditto for several rivers in SoCal that get drained to let L.A. drink. Then there's Lake Titicaca in Bolivia. The Caspian Sea swallows the Volga, the Syr Darya and the Amu Darya, three of the major rivers of Central Asia. And there's also the Great Salt Lake.

[DavidSh]

The Syr Darya flows into the northern remnants of the Aral Sea. The Amu Darya is lost in the desert as it approaches the southern remnants of the Aral Sea, although in some centuries part of its flow went to the Caspian. But the main point holds, that neither has ever reached the ocean.

[Imbalance]

Water follows the path of least resistance. What lies under the river often has as much to do with its route as what feeds it. Inundation, saturation, an erosion are among the river's ways of shortening its path, but sometimes it trips the mountain and is blocked for a time. The sea is the biggest river, and it flows into the sky.

In our world, water shapes the land. In yours, let the story do it. I don't watch GOT, but I appreciate Martin's approach (https://bigthink.com/strange-maps/westeros-map?utm_medium=Social&facebook=1&utm_source=Facebook&fbclid=IwAR3JLtv1fxGCFpduEMGYxMfIFFp33uQE4XRiOQurE nMglZeLe5IN_DXXVO8#Echobox=1558128587) (spoiler warning).

[Fat Rooster]

My gut thought would be almost all of them, with large exceptions being noteworthy (and most currently man made). I think that settlements being on navigable rivers is pretty much how civilisation went, (though often because crossing such rivers was hard, and so they were built around bridges).

If you are looking for a river boat based setting, I don't think you actually want them reaching the sea. River boats struggle to get between rivers if they have to deal with sea waves to do so, so you might want to substitute a large river for the sea, and have your settlements on tributaries.

Would you be looking for somewhere like the Mississippi delta (https://en.wikipedia.org/wiki/Mississippi_Delta#/media/File:Mississippi_Delta_SVG_Map.svg)?

If you want rivers that end randomly, there are other ways to do it than evaporation. If the geology has a soft porous rock, and the river flows over a weak spot, it can just divert underground, resulting in a waterfall into a sinkhole and submerged cave system (where a black dragon lives). Bonus points if the flow can back up to the point you get a whirlpool. Unless you have specific geography that prevents it (such as harder rock over a soft layer) any large rivers will just cut themselves a valley though.

[Knaight]

Higher than that. The Colorado River, as noted, evaporates into the desert because of the amount of water we pull out. Ditto for several rivers in SoCal that get drained to let L.A. drink. Then there's Lake Titicaca in Bolivia. The Caspian Sea swallows the Volga, the Syr Darya and the Amu Darya, three of the major rivers of Central Asia. And there's also the Great Salt Lake.
Cases like the Colorado River wouldn't likely apply here - that takes modern agriculture, industry, and settlement to pull of which involves both a fair amount of water per person and a pretty high population density by historical standards.


This is about rivers in general, correct? It doesn't make a statement about whether each river connects to another river or ends in the sea, right?
Strahler order itself doesn't - which is why I dug into the Alaska-California coast region in particular. There's no single piece of convenient information, and you're going to have to synthesize sources one way or another. That post was just one way.

[JCarter426]

One problem with finding numbers is... measuring coast length.
That's an easy one. Coastlines have a fractal dimension, so their length diverges towards infinity as the precision of your measurement increases. Therefore, the most precise answer is that all coastlines have the same length, and that length is infinite.

Given that this distance is greater than the circumference of the Earth, and that rivers on Earth can be found flowing in any direction, the campaign will take place entirely inside a river. There is little need to worry about how many other rivers there are, as we are unlikely to ever leave one.

If you want a less precise answer, you could find a map of a region with similar geography, count the number of rivers that connect with the sea and are big enough to be worth putting on the map for a rough estimate of what is "navigable", and get an average from that. For example, I count about twenty on this map of Sweden (https://upload.wikimedia.org/wikipedia/commons/3/3d/Map_of_Sweden_Cities_%28polar_stereographic%29.png ) and Wikipedia lists the coastline length as 2,000 miles. I'm not sure what metric they're using to measure the coastline, but that would be about 1 river per 100 miles or 160 kilometers of coastline.

[factotum]

Given that this distance is greater than the circumference of the Earth, and that rivers on Earth can be found flowing in any direction, the campaign will take place entirely inside a river. There is little need to worry about how many other rivers there are, as we are unlikely to ever leave one.


Have you read any of Philip Jose Farmer's "Riverworld" books, by any chance? :smallsmile:

[LordEntrails]

That's an easy one. Coastlines have a fractal dimension, so their length diverges towards infinity as the precision of your measurement increases. Therefore, the most precise answer is that all coastlines have the same length, and that length is infinite.
Yea... no.
The coastline does not vary infinitely between the points of a fractal you use to approximate it. Therefore you can not drive the actual length to infinity. Same reason your car does not travel at infinite velocity between points of measurement.

[farothel]

I'll reiterate what others have already said: it depends on a lot of things. Geology, climate, …

For instance in North Africa you have one big one (the Nile) and maybe a couple of small ones on thousands of km of coast. In Western Europe you have a whole bunch of navigable rivers quite close together: Rhine, Maas, Schelde, Seine, Rhone and a couple of smaller ones, which might be navigable with smaller boats. And this coastline is shorter than the one in Africa with only one.

Also a lot depends on where they start out. If for instance the Donau (or what is considered the start of the Donau) had started about 100 metres further West, it would have gone into the Rhine. Of course there would have been a Donau, but it would have started somewhere else (and be shorter).

I would suggest you just create a map which you feel is right.

[Mastikator]

That's true, but rivers are often mapped as if they had source points. (https://files.prokerala.com/maps/india/map-files/india-river-map.jpg) For the purpose of determining how many rivers actually reach the ocean, simplifying down to source points is probably good enough, at least for generating quasi believable river maps.
And sometimes they actually DO have single point source I used google maps to follow the river nile up as far as a I could (https://www.google.com/maps/@7.1044362,30.7828307,13433m/data=!3m1!1e3) (wow that thing goes on forever)
same deal with the daugava river (https://www.google.com/maps/@56.7438162,32.3164246,2378m/data=!3m1!1e3)

[factotum]

And sometimes they actually DO have single point source I used google maps to follow the river nile up as far as a I could (https://www.google.com/maps/@7.1044362,30.7828307,13433m/data=!3m1!1e3) (wow that thing goes on forever)
same deal with the daugava river (https://www.google.com/maps/@56.7438162,32.3164246,2378m/data=!3m1!1e3)

Um, isn't the Nile famously formed of the White Nile and the Blue Nile--e.g. two separate major sources?

[JCarter426]

Have you read any of Philip Jose Farmer's "Riverworld" books, by any chance? :smallsmile:
I have not. :smallconfused:

The coastline does not vary infinitely between the points of a fractal you use to approximate it. Therefore you can not drive the actual length to infinity. Same reason your car does not travel at infinite velocity between points of measurement.
Between finite points of measurement, no. Between an infinite amount of points of measurement (aka fractal dimension), yes.

However, a car is not a recognized SI unit of measurement, so I would advise against its use.

[factotum]

I have not. :smallconfused:

Sorry, didn't mean to confuse you, it's just he has a planet (artificially created, obviously) which consists entirely of a single river valley winding from one pole to the other.

[JCarter426]

Ah, I see. Interesting.

So another possible answer to the question is 1/planet.

[LordEntrails]

And sometimes they actually DO have single point source I used google maps to follow the river nile up as far as a I could (https://www.google.com/maps/@7.1044362,30.7828307,13433m/data=!3m1!1e3) (wow that thing goes on forever)
same deal with the daugava river (https://www.google.com/maps/@56.7438162,32.3164246,2378m/data=!3m1!1e3)

Thunder River in the Grand Canyon is also a single source river. It emerges from a spring in the side of a cliff face. Yes the volume of water classifies it as a river. It is also one of the few rivers that feeds a creek. And it's only 1/2 mile long.
https://en.wikipedia.org/wiki/Thunder_River_(Tapeats_Creek_tributary)

[jayem]

That's an easy one. Coastlines have a fractal dimension, so their length diverges towards infinity as the precision of your measurement increases. Therefore, the most precise answer is that all coastlines have the same length, and that length is infinite.

It's true enough that Spain/Portugal border (measured on a map of Spain) was significantly shorter than the Portuguese/Spanish one (measured on a map of Portugal).

I'm pretty sure there is often a limit, Egypt's (beachy) coast looks to be pretty smooth quickly from the 20km mark. If so the approx will converge to something not far off say 25km.

In Wales however things are pretty much fractal from 2m (and beneath that point you need to chase rivers anyway) to 20km. https://www.google.com/maps/@51.8870226,-5.3106386,163m/data=!3m1!1e3
During this range accounting for each level of bay exponentially increases the length of the coast (although the perimeter has only risen by a factor of less than a million by the time you are using sub-atomic steps.

Functionally I guess you actually want the length of the sailing line (which being at least 100m from any point of the coast will get rid of any of the smaller noise) (and is going to be consistent to about an order of magnitude or two over reasonable scales)

[Knaight]

Um, isn't the Nile famously formed of the White Nile and the Blue Nile--e.g. two separate major sources?

Yes, and that's pretty common. Going back to strahler order from earlier, the Nile is order 11. That means it has, at minimum 1024 little tiny streams feeding into it once you dig back far enough. In practice that number is way higher (it's fed by a rainforest after all).

[factotum]

I'm pretty sure there is often a limit

If nothing else, there is a limit in the real world once you get down to the atomic level, so you could never actually have an infinite coastline.

[halfeye]

If nothing else, there is a limit in the real world once you get down to the atomic level, so you could never actually have an infinite coastline.

Yeah, and the tide goes in and out twice daily. Mandelbrot was overselling it.

[Rogar Demonblud]

Actually, a lot of places only have diurnal (once a day) tides. And the Mediterranean really doesn't have tides at all.

[halfeye]

Actually, a lot of places only have diurnal (once a day) tides.

Don't be daft. Tides take 12.x hours on average, so some days there won't be two high tides in a day, or not two low tides, but there will always be at least three of low tides and high tides, the tides moving in and out will always happen. The tides happen when the Earth and the Sun are aligned, that happens once at noon, and once at midnight, but the Moon though much less massive than the Sun is much closer, so the tides of the Sun and the Moon combine, and the tides we get are due to the combination, and take a variable bit over 12 hours to occur.


And the Mediterranean really doesn't have tides at all.

It has to have tides, the Sun and the Moon still exist, they may be very little different from the tidal movement of the land.

[Rogar Demonblud]

Incorrect. The three tide (https://en.wikipedia.org/wiki/Tide) types are semi-diurnal, diurnal, and mixed. See the chart in the link.

[factotum]

It has to have tides, the Sun and the Moon still exist, they may be very little different from the tidal movement of the land.

Yes, it does have tides, but the tidal range across almost the entire sea is a few centimetres and is thus barely noticeable. If the Earth were perfectly spherical, had no continents and the ocean was the same depth throughout, then yes, everywhere would have the same tide depth, but it isn't like that, and so tidal ranges vary massively from one place to another. (I think the reason the Med has such a tiny tidal range is because there's a fixed volume of water in the basin--the only place it could get extra water from for a proper tide would be from the Atlantic, and the Strait of Gibraltar is too narrow to allow those volumes of water to pass through it on the tidal 12-hour cycle).

[Kato]

Don't be daft. Tides take 12.x hours on average, so some days there won't be two high tides in a day, or not two low tides, but there will always be at least three of low tides and high tides, the tides moving in and out will always happen. The tides happen when the Earth and the Sun are aligned, that happens once at noon, and once at midnight, but the Moon though much less massive than the Sun is much closer, so the tides of the Sun and the Moon combine, and the tides we get are due to the combination, and take a variable bit over 12 hours to occur.

Uhm... No. I mean, a bit yes. But mostly no.
As you say, the tides come mostly from the moon, not the sun. So time of day and tide schedule are only remotely connected which is why tides shift forward each day by about 45 minutes (very roughly). The sun also influences water levels but it's usually negligible compared to the moon, so it's mostly noted if the three bodies align and the effect is emphasized or weakened. Of course in theory you have two overlapping wave functions which are not correlated.
(note: can two bodies align? I mean, I think I know what is meant but an alignment of two just sounds wrong to me)

[Rogar Demonblud]

Yes, two bodies can align. Also, in addition to lunar tides and solar tides, there are also sidereal tides. I don't understand those.

[factotum]

Yes, two bodies can align.

How? Surely they need a third body to be aligning *with*? (e.g. in the case of the Sun and Moon aligning to create bigger tides, it's the Earth that they're aligning with).

[JCarter426]

I'm pretty sure there is often a limit

If nothing else, there is a limit in the real world once you get down to the atomic level, so you could never actually have an infinite coastline.

Yeah, and the tide goes in and out twice daily. Mandelbrot was overselling it.
Typical physics and its "observations" in the "real world" that don't match up to the one, true theoretical reality. I suppose next they'll be claiming that even space isn't continuous and can be quantized.

[Rogar Demonblud]

How? Surely they need a third body to be aligning *with*? (e.g. in the case of the Sun and Moon aligning to create bigger tides, it's the Earth that they're aligning with).

Don't ask me, since I'm not an astrophysicist. But they say it, and I presume they understand their field.

[factotum]

I'm pretty sure whatever you've heard along those lines means there's an implied third body that everyone is assumed to know about--e.g. the Earth in the Sun/Moon tide example.

[Lvl 2 Expert]

Two bodies are always aligned. It's one of the base principles of mathematics: the shortest route between two points is a straight line. So yes, they do mean those two are aligning with the Earth, for a total of three bodies.

As for the primary question of the topic: I have a feeling the answer has pi in it somewhere. I have this feeling because I know the length of a naturally formed river is often about pi times the distance between its origin and its end. (Particularly in places like tge Amazon, with few natural obstacles like mountains.) This happens because a river erodes the ground on its outside bends while leaving material on its inside bends, so any individual bend will over the course of its lifetime erode into pretty much a full circle before the river breaks through the little barrier that's left and the entire circle is left dry. So on average a bend at a random point in its life is half a circle, and a river comprised fully of half circles is pi times the length of a straight line between origin and end.

This same process of forming circles probably helps define the width of a river bassin, and any other river that runs into the bassin stops being a seperate river, so the amount of space between two rivers/streams reaching the coast should be something something pi something radius of a bend something. Or something...

[halfeye]

Two bodies are always aligned. It's one of the base principles of mathematics: the shortest route between two points is a straight line. So yes, they do mean those two are aligning with the Earth, for a total of three bodies.

When I was talking about the Earth and the Sun being aligned, I certaily wasn't implying any third objects. Sure, two spheres are techically always aligned, but points on the surface of one sphere (in particular the Earth) are not necesarily aligned with the sun, the poles never are, and nor are any points outside a certain number of degrees (22 degrees?) from the equator.


As for the primary question of the topic: I have a feeling the answer has pi in it somewhere. I have this feeling because I know the length of a naturally formed river is often about pi times the distance between its origin and its end. (Particularly in places like tge Amazon, with few natural obstacles like mountains.) This happens because a river erodes the ground on its outside bends while leaving material on its inside bends, so any individual bend will over the course of its lifetime erode into pretty much a full circle before the river breaks through the little barrier that's left and the entire circle is left dry. So on average a bend at a random point in its life is half a circle, and a river comprised fully of half circles is pi times the length of a straight line between origin and end.

This same process of forming circles probably helps define the width of a river bassin, and any other river that runs into the bassin stops being a seperate river, so the amount of space between two rivers/streams reaching the coast should be something something pi something radius of a bend something. Or something...

The lengths of rivers may tend to pi, I don't know about that, however, oxbow bends/lakes tend to be separated by straight stretches of water before the river breaks through the neck and makes them lakes.

[Lvl 2 Expert]

When I was talking about the Earth and the Sun being aligned, I certaily wasn't implying any third objects. Sure, two spheres are techically always aligned, but points on the surface of one sphere (in particular the Earth) are not necesarily aligned with the sun, the poles never are, and nor are any points outside a certain number of degrees (22 degrees?) from the equator.

My apologies, I see, you were just using a weird term for the sun being straight overhead or below a certain longitude, which could be considered an alignment of the tree objects earth, sun and a specific spot on the Earths surrface.