No One Knows How Long the US Coastline Is (discovermagazine.com)

How long is the U.S. coastline? It's a straightforward question, and one that's important for scientists and government agencies alike. From a report: The U.S. Geological Survey could give you an answer, too, but I'm going to tell you right now that it's wrong. In fact, no one could give you the right answer, and if you look around, you'll find a number of estimations that differ by seemingly improbable amounts. One government report lists the number as 12,383 miles. The same report admits that a different government agency says the figure is actually 88,612 miles. That's an almost eight-fold disparity for a fact that seems simple to obtain. We all know how to use a ruler, right?

Well, we all know how to measure a straight line, but what about a curve? And what if that curve has curves? The crux of the problem comes down to geometry, and the fundamentally uneven nature of coastlines. Though the border between land and sea may look fairly straight when seen from far away, they're anything but. Coastlines jut and dip, curve and cut, and each deviation from a straight line adds distance. Some of these features are massive, like bays, while others are miniscule.

Comments

+/- 12,383 miles

[Anonymous Coward]

Do I win or do we need to involve AI?

Re:+/- 12,383 miles

[Shikaku]

https://en.wikipedia.org/wiki/...

The best answer I can give is >0.

Re:+/- 12,383 miles

[Anonymous Coward]

https://en.wikipedia.org/wiki/List_of_U.S._states_by_coastline

method 1 only includes states with ocean coastline and excludes tidal inlets
method 2 includes Great Lake coastline and the extra length from tidal inlets

Method 1 yelds 12,479 mi (20,083 km)
Method 2 yelds 94,122 mi (151,475 km)

Re:+/- 12,383 miles

[Joce640k]

Isn't "coastline" the very first example they give in Fractals 101?

It certainly was back in the 1980s when I was at school but here it is as front page news on Slashdot. FFS.

Now get off my lawn.

Re:+/- 12,383 miles

[Actually, I do RTFA]

No, coastlines are the second example. Snowflakes are the first.

Re:+/- 12,383 miles

[Anonymous Coward]

You indeed might want to use stereo multi-spectral imaging satellites and analyze the images with an AI.

Re: +/- 12,383 miles

[Anonymous Coward]

Wrong.

This whole article and discussion are preposterous.

The coastline is not one distance. It is an ever changing variable.
It is affected in the short term by the tides. And it's affected in the long term by erosion.

And it hasn't been important to know all this time so why now? What makes it important enough to not just estimate?

Re:+/- 12,383 miles

[quadbox]

Yeah, we had an exam problem on this for the Australian coastline when I was doing chaos theory. There's a fairly famous paper where some guy (forget his name) got a spectacularly good estimate of the length of the british coastline using just the usual box-counting method

Re:+/- 12,383 miles

[bugs2squash]

If I had to pick any one value I would have given exactly zero.

If water is described as "water molecules with gaps between them" Then water is essentially everywhere in the USA and there is no natural closed boundary that excludes it, the whole of the USA is an underwater rock formation.

Re:+/- 12,383 miles

[GrpA]

Australia defined a standard about how big a feature had to be to be regarded as "coastline" - same with rivers mouths and the like. Once this was defined, then anything outside of this definition no longer counted, and the coastline was measured quite accurately, in a way that if measured in the future, could identify whether the coastline was shrinking or expanding.

eg: https://ebrary.net/10179/manag...

Re:+/- 12,383 miles

[badboy_tw2002]

Wrong, its pedantic slashdot argument comment threads first, snowflakes second, and THEN coastlines.

Re:+/- 12,383 miles

[Anonymous Coward]

You mean the deeper we go the less funny it gets?

Re: +/- 12,383 miles

[arglebargle_xiv]

It also depends at what resolution you're measuring. If you go down to the atomic level you're going to get (a) a very, very long coastline and (b) no certainty over exactly how long it really is.

Re: +/- 12,383 miles

[Anonymous Coward]

No, deeper is exactly as funny. And so on.

Re:+/- 12,383 miles

[Anonymous Coward]

Aha, here we are! An Alaskan snowflake with an infinite 'coastal' perimeter.

Re:+/- 12,383 miles

[thoughtlover]

And yet, how correct you are... just depends what snowflake you're talking about.

https://youtu.be/HvXbQb57lsE?t...

PBS Nova - Fractals - Hunting the Hidden Dimension

Re:+/- 12,383 miles

[Anonymous Coward]

Isn't "coastline" the very first example they give in Fractals 101?

It is, but as an example it is about as good as pi is for integers between 7 and 8
Coastlines are complex and transient, but not in the sense those words are used in mathematics.

Fractals is this neat mathematical thing that no-one really knows what to use for yet, a hammer looking for a nail.
When some people see something that can't be easily modeled as a simple geometric shape the fractal-hammer gets a mention.

Re:+/- 12,383 miles

[Anonymous Coward]

Well, if no-one can agree on a proper definition as is common in the US, wouldn't measuring the land area be just as usable for that purpose?

Re:+/- 12,383 miles

[Anonymous Coward]

It wasn't in my school. I had to learn about fractals by reading Martin Gardner's column in Scientific American in the library outside of school in the early seventies.

You get off *my* lawn.

Re:+/- 12,383 miles

[michelcolman]

That's a nice estimate for the error bound, but the question is: how much plus or minus 12383 miles.

Re:+/- 12,383 miles

[Anonymous Coward]

this is much more interesting than the third example.

Re: +/- 12,383 miles

[Anonymous Coward]

Yeah, its a fractal

Re:+/- 12,383 miles

[Anonymous Coward]

How wide is the coastline?

It's infinite.

[jd]

Coastlines are fractal and have 1.4 dimensions. This does mean Cthulhu could break out at any moment.

Re:It's infinite.

[Obfuscant]

Coastlines are fractal and have 1.4 dimensions.

And being fractal makes the initial question of "how long" meaningless. To what resolution? If you look at the molecular level, it is nearly infinite. If you look at the sand grain level, less so. If you look at one foot intervals, even less so.

That of course leaves the question of how you define the coastline. It's not just bays and similar features that create issues, but AT WHAT TIDE LEVEL? Do you define the "coast" as being at the mean high high water (MHHW), mean sea level (MSL), high water line, or where? Do you count both sides of the Outer Banks in North Carolina, both sides and the inner edge of the sounds behind them, or just the outer edge?

The question is also meaningless because it changes nothing. Nothing changes if you say that the US coast is 1,000,000km or 200,000km or 1km. If you're estimating how much it will cost to install coastal protection you will measure how long the protection measure is, not how long the coast is behind it.

So, must be a slow news day at /.

Re:It's infinite.

[Anonymous Coward]

It is certainly wrong to say it is 1km. There is a lower bound to the length of a coast line. It can not be shorter than the longest straight line distance between any two points on the coast line.

Re: It's infinite.

[Anonymous Coward]

Thank you!

I RTFA and was wondering what kind of jibberish he was going on about when he left out the simplest issue which was âoein what stateâ

Re:It's infinite.

[Anonymous Coward]

Then you can give a finite measure in units of miles^1.4 and still compare different countries' coastlines.

Re:It's infinite.

[sexconker]

It can not be shorter than the longest straight line distance between any two points on the coast line.

Of course it can.

A: Not all land between points of coastline is coastline. We don't even have a solid definition of coastline to start measuring.

B: In strict 3 space, measuring coastline makes little sense. Lines are 2D, the coast is 3D, and you first need strict rules for tracing the path before you can measure it. How do you handle a cliff on a beach? What if it juts out over the water? When considering 2D projections, it makes a bit more sense. But "the longest straight line distance between any two points on the coast line" in such a projection is infinite. Consider "the longest straight line distance between" your dick and your ass based on a 2D projection (flat map) of Earth. That line would simply wrap around the Earth forever in an infinitely tight spiral. Or consider the simpler scenario of wrapping around Earth once. That's "the longest straight line distance", yet we can show the actual distance is shorter, even if we don't know the true position of either point. Start by drawing a bounding box around each point with whatever accuracy/precision we want / can achieve, then measuring the distance between the outer edges of the bounding boxes. This gives us an upper bound for the actual distance. (You can simply draw a line segment between the points, then draw lines perpendicular to that segment at each point, and find where those lines intersect the bounding boxes to determine the "outer edge" of each bounding box.)

Re:It's infinite.

[ath1901]

Don't forget waves or kids playing on the beach.

I'd argue the length of the coastline is exactly what the surveyors office says it is. It is a matter of definition, not measurement. There is no coastline on the beach, only on maps.

While I'm at it, if a tree falls in the forest, there is a sound. The standard definition of sound does not require a human listener. The sound of one hand clapping? I can clap with one hand. It sounds almost like clapping with two hands.

Fractals are cool. Cooler than coastlines.

Re:It's infinite.

[Anonymous Coward]

Well it is called coastline paradox and it can be found in other fields too. Like how many organic matter exists on a certain area or the like, which makes some calculations very difficult as a slight change will change the outcome significantly.

Re:It's infinite.

[zieroh]

And being fractal makes the initial question of "how long" meaningless. To what resolution? If you look at the molecular level, it is nearly infinite. If you look at the sand grain level, less so. If you look at one foot intervals, even less so.

Agreed. It's a meaningless question, and any answer will be just as meaningless, if not more so.

Re:It's infinite.

[Baloroth]

No real coastline is infinite, because real coastlines are made up of matter which is made up of atoms, not mathematical idealizations. Only mathematically ideal coastlines are infinite. You can, of course, create many different measures for the length of the coastline, some of which will be much much longer than others (but also useless), but all of them will be longer than some number (a strict lower limit would be the size of the "rectangle" that contains the US minus the length of the box that crosses over dry land, but the minimum practical definition would be longer than that) and shorter than some other (much larger) number, which would be the length if you measured the distance between individual atoms along the coastline. Note that the latter definition is not only not practical but also difficult to define except in an instant of time, as what is "sea" and what is "shore" theoretically changes with tides and even waves, but it absolutely is a finite number.

Re:It's infinite.

[Dragonslicer]

It can not be shorter than the longest straight line distance between any two points on the coast line.

Of course it can.

A: Not all land between points of coastline is coastline. We don't even have a solid definition of coastline to start measuring.

Instead of a straight line through three-dimensional space, the shortest possible length would be the length of the shortest line between two points (for the surface of a sphere, I think it's part of a Great Circle). Any way that the coastline deviates from that line must increase the length, since by definition that line is the shortest possible line connecting those two points. You also have to add the requirement (which the GP probably just left unstated) that you measure each contiguous coast separately; obviously Atlantic and Pacific coasts must be separate, maybe also the Gulf of Mexico. For example, the shortest possible length of the Atlantic coast is the "straight" distance from the northern-most point on the coast to the southern-most point.

But "the longest straight line distance between any two points on the coast line" in such a projection is infinite. Consider "the longest straight line distance between" your dick and your ass based on a 2D projection (flat map) of Earth. That line would simply wrap around the Earth forever in an infinitely tight spiral. Or consider the simpler scenario of wrapping around Earth once. That's "the longest straight line distance", yet we can show the actual distance is shorter, even if we don't know the true position of either point. Start by drawing a bounding box around each point with whatever accuracy/precision we want / can achieve, then measuring the distance between the outer edges of the bounding boxes. This gives us an upper bound for the actual distance. (You can simply draw a line segment between the points, then draw lines perpendicular to that segment at each point, and find where those lines intersect the bounding boxes to determine the "outer edge" of each bounding box.)

You're misinterpreting the GP. By "the longest straight line distance between any two points on the coast line", I believe the GP meant the longest of the shortest-length lines between every pair of points. In other words, the shortest line between the two farthest points.

Re:It's infinite.

[Wraithlyn]

Congratulations, you win a gold medal in pedantically overcomplicating things and completely missing the point.

If I say "longest straight line I can draw on the US West Coast", it's pretty obvious I'm talking about a line from the NW tip of Washington to the SW tip of California, in a direct "as the crow flies" path, not spiralling around the fucking planet. The word "LONGEST" in this CONTEXT means "the farthest two points from each other you can find" on the coastline.

Re:It's infinite.

[Anonymous Coward]

That of course leaves the question of how you define the coastline.

This is extra hard in places like Antarctica. Do you count the coast as the extent of the winter sea ice, summer sea ice, multi-year sea ice, meteoric ice, grounded ice or where the coast would be without ice? The last one ignoring that removing the weight of the ice would cause the continent to raise, moving the coast as well.

Re:It's infinite.

[vux984]

"The sound of one hand clapping? I can clap with one hand."

The action you are likely performing is not generally recognized as 'clapping'. So the sound it makes is irrelevant.

"The standard definition of sound does not require a human listener."

What so-called "standard definition of sound" are you using? I just checked two separate dictionaries and both of them defined sound in terms of sensing vibrations on the auditory structures of an ear as their first definition of sound (noun).

"I'd argue the length of the coastline is exactly what the surveyors office says it is. It is a matter of definition, not measurement. "

Clearly there are wrong answers though. 1 mile is clearly wrong. Equally clearly there is no limit to the number of correct answers, but it depends on methodology -- so first you set a methodology, then you make your measurements according to that methodology. The stricter and more well defined the method, the stricter and more restricted the range of values that will satisfy it.

Furthest extent of land, at low tide, on the vernal equinox, 2020, to a resolution of 5 meters. With suitable definitions to decide when and where to leap over water to reach islands, cross stream and river mouths, whether to cross over the opening to a bay or inlet, or to follow it around based on the size of the opening, salinity of the enclosed body, depth at the opening, etc.

Re:It's infinite.

[No Longer an AC]

but AT WHAT TIDE LEVEL?

Next click-bait headline:

Our country expected to lose 20% of its coastline at low tide!

Re:It's infinite.

[Immerman]

Ah, but atoms are composed of quantum particles, which strictly speaking have neither a definite size nor position, but rather a wave-function that extends to the farthest reaches of the universe with non-zero probability. The circumference of even a single electron is thus exactly equal to that of the entire universe, which may or may not be infinite.

Unless you impose some completely arbitrary cut off point (e.g. there's a 99.99999999% chance that the atom will resolve as being within this area when its wavefunction momentarily collapses), *all* truly accurate measurements of size will be infinite.

Re: It's infinite.

[Anonymous Coward]

You must be new here, welcome.

Re: It's infinite.

[Anonymous Coward]

Technically speaking, they do have a definite size location etc. This is a common misconception of QM.

We have to represent them in our mathematical models because they behave like wave functions, but they exist in a definite time and place, even if we don't know what it is for each particle specifically.

Re:It's infinite.

[Anonymous Coward]

It isn't infinite because length ceases to have any meaning below the Planck length, so that is the smallest possible deviation that can measure.

Re:It's infinite.

[thinkwaitfast]

Also depends on the instantaneous tide state.

Re:It's infinite.

[dryeo]

And where is the NW tip of Washington State? Point Roberts? Then you have to consider the coast enters Canada for a while before rejoining Washington (Point Roberts is only accessible by land from Canada). One of the San Juan Islands? Then you have a length of no coast line.

Re:It's infinite.

[jrumney]

The longest point on the west coast would start in Alaska, and the GP's point then becomes very relevant.

Re:It's infinite.

[UnknownSoldier]

> quantum particles, which strictly speaking have neither a definite size nor position,

Did you miss the memo that the wave function collapses when you measure them?

> truly accurate measurements of size will be infinite.

Total nonsense. The Planck Length isn't zero. It is a discrete amount. Furthermore we aren't measuring at the sub-atomic level. Accuracy +/- of some _#_ meters is more then "good enough". i.e. 33,333 km +/- 10 km.

Re: It's infinite.

[I'm New Around Here]

You called, sir?

Re:It's infinite.

[I'm New Around Here]

"The West Coast" typically only includes California, Oregon, and Washington. If you want to include Alaska, it would be more accurate to call it "the US Pacific Coast". But then that may logically include Hawaii as well.

Re:It's infinite.

[Immerman]

But only for the instant of the measurement - as soon as you look away to write your report it'll be infinite again.

What does the plank length have to do with anything? I'm not talking about fractal limits, in which case it would most certainly would put an upper bound on length (though at ~10^25 plank lengths across a hydrogen atom, it's going to be a VERY high bound)

I'm talking about the fact that we know with certainty that every quarticle in a baseball has infinite "size", but you want me to believe the ball itself has a well defined finite size?

Re:It's infinite.

[thoughtlover]

And to that end, so there's no confusion, I say, "As the worm crawls."

Re:It's infinite.

[religionofpeas]

Did you miss the memo that the wave function collapses [wikipedia.org] when you measure them?

Wave function collapse is a feature in some interpretations of quantum mechanics. There are also interpretations that don't require a collapse.

Re:It's infinite.

[Anonymous Coward]

nearly infinite

Idiot.

Re: It's infinite.

[Anonymous Coward]

Maybe the size of an object isn't the point particle size but the size of the space of the electron cloud that repels other matter? :) You know, the rough size of objects as we understand them outside of math. ;)

Re: It's infinite.

[Anonymous Coward]

what changes is the cost of building the wall

Re:It's infinite.

[ath1901]

What so-called "standard definition of sound" are you using? I just checked two separate dictionaries and both of them defined sound in terms of sensing vibrations on the auditory structures of an ear as their first definition of sound (noun).

I was referring to the one used in sentences like "I recorded the weird sound my car makes". It is generally assumed you used a microphone to record vibrations in the air and not electrodes in the brain to record the vibrations there. Also technical measures like sound pressure use non-human-brain based definitions of sound.

Clearly there are wrong answers though. 1 mile is clearly wrong. Equally clearly there is no limit to the number of correct answers, but it depends on methodology -- so first you set a methodology, then you make your measurements according to that methodology. The stricter and more well defined the method, the stricter and more restricted the range of values that will satisfy it.

I believe we are in agreement. The only thing I would add is that a fine grained method would probably have to rely on arbitrary judgement calls. For example, if a kid digs a new 5cm wide canal on the beach, should that be included or ignored with a 1cm resolution? Even with a 5m resolution you will get a similar problem with areas under construction. Probably also dry docks.

Re:It's infinite.

[Wraithlyn]

You're missing the forest for the trees.

The point is that we can easily establish a MINIMUM. Nitpicking over what would exactly would constitute maximums is completely missing the point.

Well shit

[Anonymous Coward]

Well, we all know how to measure a straight line, but what about a curve? And what if that curve has curves?

If only an entire branch of mathematics had this pretty much nailed down for like 400 years now.

Re:Well shit

[Immerman]

They nailed it down the concept, but never provided a useful answer - other than the fact that for any well-formulated fractal the answer is likely "infinity".

Re:Well shit

[unixisc]

Ain't that the beginning of how Differential Calculus was developed? Breaking one variable into small parts, and then integrating all those parts to arrive at a more accurate result?

More than 6

[Anonymous Coward]

I know it's more than 6

Re:More than 6

[Immerman]

Actually, it's exactly 5.72938473829. Determining the units is left as an exercise for the reader.

Where do you draw the line?

[jellomizer]

We have rivers that fan out into the ocean. How far up the river do we go until we are no longer at the coastline. I want to sell my home to be on the coast even though it is hundreds of miles away from the ocean and thousands of feet above sea level, however there is a little stream next to my home, which leads to a creak, that leads to a river, which leads to a larger river then goes into the ocean.

Re:Where do you draw the line?

[Anonymous Coward]

The general rule is that if you can measure a tide, it is on the coast.

Re:Where do you draw the line?

[jrumney]

There's also another area where the line is fuzzy - do you include Puerto Rico? American Samoa? Guam, Wake Island and the Northern Mariana's? The smaller the island, the more it contributes to the coastline in proportion to its land area, so these seemingly insignificant parts of US territory may make a big difference.

Re:Where do you draw the line?

[lenski]

Several years living in Willingboro NJ, near the Rancocas creek... I remember that the river there had a visible tide. (It's been 47 years, but...) I remember its amplitude being far less than the effect at the beach. This is about 4 miles up the creek from the Delaware river, about 40 miles from the mouth of the Delaware.

I'm guessing that doesn't count as "coastline"....

Off-topic: The specific place where I saw the effect was at what is now the end of Bridge Street but at the time had a bridge that had at one time been a gear-driven "draw" bridge, rotating to allow water-borne traffic to pass.

Re:Where do you draw the line?

[Anonymous Coward]

I draw the line at the east coast and the west coast.

Someone just discovered fractals!

[Anonymous Coward]

The coastline problem is literally a textbook example of fractals. The "size" of the object (perimeter, area, etc.) depends on the scale at which it is measured (the size of the "ruler" one uses). A coastline has finer and finer features as one zooms in, so the overall length/perimeter one computes is larger and larger as one uses a finer resolution. For a perfect/mathematical fractal, the coastline could actually be infinite in length.

This is absolutely interesting. But also not new. Everyone with a passing familiarity with measuring coastlines knows about this issue.

Re: Someone just discovered fractals!

[bill_mcgonigle]

Fifth-grade news for nerds.

Re:Someone just discovered fractals!

[dgatwood]

For a perfect/mathematical fractal, the coastline could actually be infinite in length.

Fortunately for us, the dimensions of quarks quantize the possible values somewhat, so it is finite, but large. Still, do you go across one side of each atom, or do you go all the way around each one until the closest point to the next?

Re:Someone just discovered fractals!

[Dast]

And if you go "around" an atom, and at what state of excitement do you measure it in?

Re:Someone just discovered fractals!

[Immerman]

Except quarks, like all quarticles, don't have a well-defined circumference. Instead they have a quantum wave function that extends to infinity with non-zero probability. To make any non-infinite measurement you must first impose an arbitrary cut-off point on that probability.

Re:Someone just discovered fractals!

[John.Banister]

If it's the first atom you measure around, you might be kind of excited, but after a while the excitement wears off and they all start to seem the same.

Re:Someone just discovered fractals!

[Anonymous Coward]

And if you go "around" an atom, and at what state of excitement do you measure it in?

Since we are looking at the extreme end of the resolution we are clearly interested in the upper bound, so the one that gives the largest coastline.

I saw this about a month ago

[Anonymous Coward]

https://www.youtube.com/watch?...

coastline paradox

[Anonymous Coward]

https://en.wikipedia.org/wiki/Coastline_paradox

Re:Coastline Paradox

[Hognoxious]

It was mentioned in Gleick's book "Chaos" - one of the first mainstream books about the subject. I read it when I was an undergrad and I'm, ummmm, not young (though my apparent age varies depending on what size calendar you use).

Re:Coastline Paradox

[SuiteSisterMary]

Neil deGrasse Tyson has a chapter about this, and the coastline paradox, in Death by Black Hole.

Re:Coastline Paradox

[wonkey_monkey]

Now that is exactly the information that should have been put in the summary.

Fractal measurement

[Anonymous Coward]

Coastlines are the best example by far of a measurement that is fractal in nature. The self-similar, irregular, and convoluted nature of coastline ensures that there is an essentially infinite distance to be found if you examine the quantity at a sufficient resolution.

Mandelbrot beat them

[dabadab]

Mandelbrot's* well-known "How Long Is the Coast of Britain?" article (published in 1967) starts with this question - and it goes on to discuss self-similar curves that are a type of fractals.

*: yes, he is the guy who came up with the Mandelbrot fractal

Re:Mandelbrot beat them

[apoc.famine]

Yep. And it's silly to even attempt to find an exact measure for that very reason. The best you can do is set a somewhat arbitrary cut-off, and measure to that standard. Anything else is just a waste of time.

Re:Mandelbrot beat them

[Anonymous Coward]

Use a piece of string to measure it.

A very long one.

Re:Mandelbrot beat them

[Anonymous Coward]

But the width of the piece of string that will affect your answer more.

Re:Mandelbrot beat them

[TeknoHog]

Mandelbrot's ... yes, he is the guy who came up with the Mandelbrot fractal

Not quite! The Mandelbrot set* as the index set for stable/connected Julia sets was known by Fatou and Julia around 1920. It was later named in honour of Benoit Mandelbrot.

*I sat through a three-lecture series by Mandelbrot in 1999 when I was an undergraduate in Cambridge. I distinctly remember him saying "The Mandelbrot set is not a fractal. It's beyond fractals." In simple terms, I think he referred to the fact that it's the edge of the set that is a fractal; like coastlines, the length of the edge depends on how precisely you measure it. But the set itself is "simply" a 2D area. Of course, due to the fractal edge it's hard to define its area exactly, but it doesn't run off into infinity when you increase the precision (as happens with the coastline).

Re:Mandelbrot beat them

[Aighearach]

This is exactly it; the question of how long the coastline "really" is is of no interest to "science" or government or civics or any physical human activity: all that matters is the establishment of a system that gives predictable values that are "good enough" to keep most people from fighting over them. That's all. Make a rule; measure to the rule. It is useful to know generally how much coastline one place has in comparison to another place, but the details don't matter.

Scientifically it is a nonsense question; who cares where you drew the line between the two words? If you wanted to measure the displacement of the continent within the US territories there are various physics models that can do a good job without ever needing to decide that. Instead you'd want to start from a good datum of the Earth's mass, and a detailed 3d surface map. There are lots of things that you would naturally measure or total in doing that, but coastline isn't likely to be one. You'd only worry about that in cartography, and then only in reference to some sort of arbitrary standard.

Re: Mandelbrot beat them

[Anonymous Coward]

Unless you want to build a wall around your country. A nice, beautiful, strong wall.

Re: Mandelbrot beat them

[Anonymous Coward]

donâ(TM)t use a string, use an army of humanoid robots with standard shoulder width, and march them all to the coastline and tell them to stand there shoulder to shoulder until somebody says stop ... donâ(TM)t worry, these robots are completely biodegradable

Re:Mandelbrot beat them

[the phantom]

It all depends on what you mean by "fractal." The term has no precise mathematical meaning.

Re:Mandelbrot beat them

[TeknoHog]

It all depends on what you mean by "fractal." The term has no precise mathematical meaning.

If you're going to dispute something that Mandelbrot himself said about fractals, then please provide some more info. I have merely studied fractal geometry as a part of my advanced math studies. I would say anything with a non-integer dimension is a fractal. Of course, you'll have a bunch of different definitions for dimension, but they generally agree in the sense of defining which objects are fractal. In this case, the edge of the Mandelbrot set has a dimension between 1 and 2.

Re:Mandelbrot beat them

[the phantom]

I'm not disputing anything that Mandelbrot said. He himself walked back from a formal definition of a fractal, and ultimately chose not to give a precise mathematical definition. From the second edition of Mandelbrot's book (on page 459):

...to leave the term "fractal" without a pedantic definition, to use "fractal dimension" as a generic term applicable to all the variants in Chapter 39, and to use in each specific case whichever definition is the most appropriate.

In the first edition of the book, Mandelbrot suggested that a fractal should be any set with Hausdorff dimension strictly larger than its topological dimension (note that this does not mean that the Hausdorff dimension is non-integer; only that it is larger than its topological dimension). However, it was pointed out that there are lots of sets that we intuit as fractals, but which fail to satisfy this property (the Devil's staircase, for example, has both topological and Hausdorff dimension equal to 1 (it is a rectifiable curve)).

Falconer, who (in my opinion) is a much better source for a rigorous mathematical discussion of fractals, also chooses not to give a formal definition. From the introduction Fractal geometry. Mathematical foundations and applications (pp. xx--xxi):

In his original essay, Mandelbrot defined a fractal to be a set with Hausdorff dimension strictly greater than its topological dimension... This definition proved to be unsatisfactory in that it excluded a number of sets that clearly ought to be regarded as fractals. Various other definitions have been proposed, by they all seem to have this same drawback.

My personal feeling is that the definition of 'fractal' should be regarded in the same way as the biologist regards the definition of 'life'. There is no hard and fast definition, but just a list of properties characteristic of a living thing...

When we refer to a set F as a fractal, therefore, we will typically have the following in mind.

1. F has a fine structure, i.e. detail on arbitrarily small scales.
2. F is too irregular to be described in traditional geometric language, both locally and globally.
3. Often F has some form of self-similarity, perhaps approximate or statistical.
4. Usually, the 'fractal dimension' of F (defined in some way) is greater than its topological dimension.
5. In most cases of interest F is defined in a very simple way, perhaps recursively.

Such a load of bullshit.

[Anonymous Coward]

Measuring a curve isn't a problem... as long as it is "well behaved". The problem with the coastline is that it (a) rather behaves a bit like a fractal (of course down to some finite limit distance) and (b) the smaller features (which contribute significantly to length) are variable over time.

Thus, the problem itself is ill-defined. But the blurb is just nonsense (can you say fake science?).

Re:Such a load of bullshit.

[Anonymous Coward]

From the summary,

Though the border between land and sea may look fairly straight when seen from far away, they're anything but.

Invoking the "anything but straight" property, the border is cheerful, anxious, purple, and well behaved.

You said

Measuring a curve isn't a problem... as long as it is "well behaved"

It is well behaved therefore it can be measured.

It seems straightforward, but it's not.

[arcade]

This comes down to the resolution used. Think fractals. What's your minimum measurement unit? 10km? 1km? 100m? 10m? 1m? 10cm? 1cm? 1mm? Smaller?

The smaller the unit of measurement, the larger the coastline, as you can cover smaller and smaller details.

Then it's the question of where to place the coastline. High tide? Low tide? Middle? What about the "type of coastline"? It seems obvious if it's rock .. but what if it's sand? Where do you put the line?

Re:It seems straightforward, but it's not.

[Anonymous Coward]

This probably goes for the surface of any object. Take a ball... at most resolutions you'll get the same answer but as soon as you get down to a microscopic level you'll see the surface is actually pretty rough and the peaks and troughs double the distance compared to the higher resolution.

Re:It seems straightforward, but it's not.

[Anonymous Coward]

This comes down to the resolution used. Think fractals. What's your minimum measurement unit? 10km? 1km? 100m? 10m? 1m? 10cm? 1cm? 1mm? Smaller?
The smaller the unit of measurement, the larger the coastline, as you can cover smaller and smaller details.
Then it's the question of where to place the coastline. High tide? Low tide? Middle? What about the "type of coastline"? It seems obvious if it's rock .. but what if it's sand? Where do you put the line?

So the place to ask this is on StackOverflow. Then the moderators can flame it as "too vague / too general", "has been asked before" and "don't ask us to code your homework". Just like about 96% of the threads there.

Coastline Paradox

[Issildur03]

There's a famous paper by Mandelbrot on the question of coastlines: "How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension".

In short, coastlines are fractal and effectively have infinite length.

https://en.wikipedia.org/wiki/...

Minimum measured feature size

[DRJlaw]

Well, we all know how to measure a straight line, but what about a curve? And what if that curve has curves? The crux of the problem comes down to geometry, and the fundamentally uneven nature of coastlines.

Everyone competent knows how to measure the lengths of curves, and curves that have curves. The issue is that based upon your use case and needs, different people pick what are essentially different resolutions for their mapping and length measurements, which means that you discard the lengths of features or "curves" that are approximately that size or smaller. If you measure the length from a map that has a 1 mile resolution, you'll get a substantially shorter length than from a map that has a 100 ft resolution, which will be a substantially shorter length than from a map with a 1 ft resolution, etc.

There isn't one right answer. There are a range of answers that are all approximations at scales that should be relevant to different types of users.

It's a duck...

[Anonymous Coward]

If it walks like a duck..
Quacks like a duck..
Floats like a duck... .. it means that the coast line is a witch... at which point you must burn her/him!

If one of you mopes would just Wikipedia this you would realize that the two measurements deal with different things:
1) Ocean coasts not including the great lakes nor tidal inlets.
2) Including he great lakes and tidal inlets.

https://en.wikipedia.org/wiki/List_of_U.S._states_by_coastline
Now, get off my lawn and go back to watching Faux News

The Answer is Infinity idiots

[Anonymous Coward]

Yes the coastline is a fractal, fractal means fractional dimension. It would need an infinite length of infinitesimal measuring string to measure, you will get variable answers....

Manifest Destiny

[Anonymous Coward]

How big is the planet again?

Re:Manifest Destiny

[OrangeTide]

You can travel billions of miles on the Earth's surface without revisiting any point.

Re:Manifest Destiny

[slew]

You can travel billions of miles on the Earth's surface without revisiting any point.

It's even worse than that, you can divide the earth's surface into a finite number of pieces and reassemble them to be two different earths each having the same surface area as the original earth..

https://en.wikipedia.org/wiki/...

Then lather, rinse and repeat...

The measurement should fit the purpose.

[Anonymous Coward]

It's like how much water to fill up a swimming pool? You're not going to use a graduated cylinder.

OTOH, you're not going to use a garden hose to do a titration.

Same with measuring coastlines.

Then again, if I had a beachfront home, I think I would love to say that I have a 1,000 mile beach between two other homes that are 50' apart by the tape measure.

Needs another standard of measurement

[FeltLion]

Like the average human stride length, so it would be measured "as if you were walking the entire course on foot" For example: The coastline is 1,000,000,321 "strides" in length.

Re:Needs another standard of measurement

[youngatheart]

I like this answer. The words "practical" and "standard" are underrepresented in these comments, but that's the most practical standard I think I've seen suggested.

When I saw this article pop up, I thought perhaps there would be a discussion about competing standards and how practical each was. I understand the philosophical question that isn't fully resolvable, but I was thinking of ways that you could get consistent answers and was disappointed not to see more posts along that line.

Perhaps you draw a straight line from one extreme point on the coastline to greatest distance opposite point, then expand that by putting points at a determined distance nearest the intersection of water and land at GMT. You'd still be able to alter the answer by varying the distance between points, but it'd give reasonably consistent answers. You could then say the western border of the US coastline of X km at a resolution of 1km. You could get a completely different number by switching to a resolution of 1m or 1cm, but the usefulness of the number for comparisons would be similar to how we weigh things. Sure, it's impossible to know how much a 1cm^2 of water weighs exactly due to quantum and gravity fluctuation, but you can get consistent answers if you define the environment and measurement scale.

Saying "nobody knows exactly" may be technically accurate for all measurements, but that's philosophy when what most people need is a practical answer for the purpose of doing work. I suspect I'm more inclined to an engineering perspective than a philosophical one, but that's what you need if you're estimating how much concrete you'll need for a coastline road.

Re:Needs another standard of measurement

[wonkey_monkey]

Low tide or high tide? What do you do about rivers? Fjords? Streams?

Re:Needs another standard of measurement

[Anonymous Coward]

The average of high and low. Cross streams at a point parallel to the averaged angle of the near/far sides, circumnavigate fjords. "as if one were walking"

Complex questions

[bobstreo]

Islands, salt water, fresh water., rivers, streams...

Do we include Puerto Rico and other US territories?

Re:Complex questions

[Aighearach]

Wait, didn't Debt Island sink? Did it float back up?

/s

How much coastline does Bermuda have during a storm?

The real absurdity of it comes when you consider coastal salt marshes, which is a lot of land. Are brackish swamps land or sea? Do you have to measure how far the water goes up the mangrove trunks at high tide? How many days of the year the dirt is exposed at low tide?

Just use the baseline

[Anonymous Coward]

The baseline has been defined to cope with the fractal nature of coasts.

It varies with the tides

[olsmeister]

Aside from all the other considerations that everyone else has mentioned, the exact length will also vary from high tide to low tide.

What country is U.S. ?

[Anonymous Coward]

Since we are being childishly pedantic, what country is U.S. Geological Survey from? Shouldn't it be the U.S.A. Geological Survey? Or is USA being rounded-off down to US?

Measuring contest

[Anonymous Coward]

Give it up, USA: no matter how many coastline lengthening ads you respond to, yours will never be as long as that of the country next door. Don't worry, coastline size isn't that important.

Non-Scientific Language Question

[holophrastic]

As usual, the question isn't specific enough to have an answer. Therefore, people think it's difficult to answer.

The answer is very simple, ask for what you want.

Maybe it's how far a ship would need to travel to get to any point -- ships take gentle curves. Maybe it's how long would it take to see it all on-foot -- humans take 1-yard-long straight lines.

Another stupid question: which came first, the chicken or the egg? Again, a language question. Define the word "egg" and it's easy.

If "egg" is any egg, then dinosaurs had eggs long before chickens.
If "egg" is "chicken egg", then define "chicken egg".
If "chicken egg" is an egg laid by a chicken, then the chicken came first, by your own definition.
If "chicken egg" is an egg from which a chicken hatches, then the egg came first, by your own definition.

Stupid questions are questions that only exist because of the manner in which you formed the question itself.

As my associate likes to say: "the answer is 6. there. now, what are you going to do with it?"

Decide what you actually want to know -- that means how you're going to use the information. Ask that question. There won't be anything crazy about it.

How long is a shoreline? Tide in or out? At what depth -- does a puddle ruin everything? Footprints? What about waves lapping on the beach?

Hey, what about the birth from a river?
Do we include the entire river?
Where does the river become the ocean?
Right, that's easy, it's where the fresh water changes to salt water.
How do you want me to measure that, given that the river's "fresh" water has dirt in it.
At what level of salinity does your version of "fresh" water become your version of "salt" water?

Arbitrary trivia is arbitrary from the start. Decide what you're doing. Are you designing battleships, or water-ways for salmon? I promise, the navy doesn't agree with the fish, and they don't need to.

Re:Non-Scientific Language Question

[thegarbz]

It isn't as obvious however that this is arbitrary.

Think of the usual "how long is a piece of string" question. That is arbitrary. However when you say "how long is THIS piece of string" it ceases to be arbitrary. Now a string is flexible and can be stretched out then measured end to end to come up with an exact answer.

By logical extension the costline can as well, except it can't due to the fractal problem. And this is where I'm getting to: With this line of thinking the intuitive answer is that there should be an exact solution to the problem. How long is "THIS" coastline, THIS is a thing and things are measurable.

Unlike the string example it's not immediately obvious that the question was arbitrary.

Re:Non-Scientific Language Question

[holophrastic]

You've missed your own mistake.

Substitute your "string" that you said "is flexible and can be stretched out then measured" with a straight piece of elastic band.

You can say "THIS" elastic band as many times as you'd like. But "THIS elastic band" has multiple configurations. An infinite number of configurations. It stretches, it compresses, it collapses, and it breaks.

So, would you measure my elastic band at full extension? Full compression? Zero tension? The tension for which it was designed to be used?

I think you'll find that whenever you custom-order a custom spring or elastic -- commercially I mean -- there are a dozen specifications to choose. You'll find yourself ordering an elastic by four dimensions of length.

Your coastline is exactly the same. It can be measured by multiple dimensions -- right down to the length of the ripples it creates in the water.

I can measure it for you, but it won't be the measurement that you want. Tell which measurement you want, and I'll get it for you, no problem.

The problem of not being to measure it is your problem for not describing "measure" in a repeatable way. That's your fault, not the shoreline's and not mine.

When a client asks me to "build a web-site", it's their fault that I don't build the one that they want. It's not "difficult to build a web-site". It's difficult for them to tell me what they want. Again, that's their problem. And you'd better believe that I charge more for determining what they want than I do for actually building it.

It took me half of my career to learn that one -- that often just "figuring out what the client wants" is the work for which they are hiring me. It's not my lack of ability building web-sites, it's their lack of ability ordering web-sites. It's my skill that lets me walk them through the process. I charge for that. I charge a lot.

Took me ten years to recognize that.

Re:Non-Scientific Language Question

[Aighearach]

It was an interesting thought experiment until the discovery of DNA, but now we understand that the egg clearly comes before the chicken.

Where you draw the line between what you call a "chicken" and what you would consider a proto-chicken is arbitrary, but wherever you draw that line, a proto-chicken laid the first egg that would grow into a chicken.

If you go back far enough, when the egg shell was first invented, the proto-bird and proto-mammal were the same. We came out of the shallow sea together, the mammals and birds, and diverged some time after that. It doesn't really matter where you draw the lines; the Proto-foo gave birth to the Baby-foo, which grew into a Foo. The egg comes before the thing it grows into. At some point you draw the line "not chicken/chicken," and it starts with the egg.

Re:Non-Scientific Language Question

[Anonymous Coward]

I use bacon grease as masturbatory lubrication.

Re:Non-Scientific Language Question

[thegarbz]

I think you just re-enforced what I said with an equal but different example.

Arbitrary involves arbitrary words.
Non-arbitrary involves pointing to something specific: "THIS". Additional knowledge is required to realise that it is in fact arbitrary.

This string can be measured. By extension everything specific we point to should be measurable.
But wait this border can't be measured because there's an additional factor (fractal problem) that affects its length.
But wait this rubber band can't be measured because there's an additional factor (extension) that affects its length.

Neither of those are intuitive to the general public.

Re:Non-Scientific Language Question

[Peter P Peters]

humans take 1-yard-long straight lines.

What is this 1867? How long is that in chains or furlongs?

That's how I measure my dick

[Anonymous Coward]

It's 2.86 miles looooong.

Re:That's how I measure my dick

[Anonymous Coward]

Is that with or without a bowl of hot grits?

Easy, just make a new unit!

[WilliamGeorge]

The length of the US coastline is equal to... 1 US Coastline. Good luck with conversions to metric, though - we hate that here in the States ;)

Re:Easy, just make a new unit!

[thegarbz]

How many laps around the library of congress building is that?

Re:Easy, just make a new unit!

[Aighearach]

How many laps around the library of congress building is that?

Exactly 1, the Library of Congress is already inside the land border!

The Earth is Flat!

[Anonymous Coward]

easy.. just draw a nice straight line!

I volunteer to measure it

[93 Escort Wagon]

I will create a KickStarter to fund my measurement of the US coastline. It will obviously require a significant amount of logistical support, so I will conservatively pick $25 million US as “fully funded”. If we don’t hit that target, I will still use the donations to fund a measurement of a section of the coastline for now - probably part of Oregon, or perhaps one of the Hawaiian Islands.

Also unanswered...

[Anonymous Coward]

How many grains of sand are there along our coasts? How many birds live within 2 miles of the ocean? How many turtles hatch along our coasts each year? How many fish swim within 100 meters of the beach? How many seashells wash up every year? How many bottle caps are littered on our beaches? ....

This is about 40 years old

[OneHundredAndTen]

Mandelbrot brought this up 40 years ago, using the coast of Britain as an example instead.

Re:This is about 40 years old

[Anonymous Coward]

Eventually, an 8 year old little girl got bored and told him to stop. She was "Miss Sweetie Poo", at the annual Ig Nobel awards. There is a collection video of these girls at https://www.youtube.com/watch?... .

1975 called, they want their Fractals back

[Anonymous Coward]

Slashdot is supposed to be news for nerds.

I guess the real "news for nerds" story here is someone from 1975 invented a time machine, came to 2018, discovered slashdot, and submitted a post.

almost eight-fold?

[OrangeTide]

Now slightly more than 7 means almost 8?

7.16x is not closer to 8x than 7x.

Re:almost eight-fold?

[Actually, I do RTFA]

7.16x is closer to 8x than 4x, and what kind of heathen uses non-power-of-two multipliers?

Re:almost eight-fold?

[Anonymous Coward]

E-series is another option, the E6 series gives you a good set of numbers that are within 20% of your target (when raised by a power of 10): 1.0, 1.5, 2.2, 3.3, 4.7, 6.8.

So the answer is that 88,612 miles is almost a 10x difference from 12,383 miles. (1.0 x 10**1)

metric/english confusion strikes again

[Anonymous Coward]

You said miles when you meant millimeters.

Terrible Summary

[Notabadguy]

This summary starts by assuming that the information is important, and that the inability to clearly define that piece of information is bad.

The article does not explain why knowing the precise amount of coastline *is* important.

Because it probably isn't that important.

Re:Terrible Summary

[Immerman]

It's important for all sorts of different reasons, the "problem" (for the article) is that any particular reason comes with a certain level of relevant spatial resolution, which then allows you to determine a definite answer.

If you want to build a coastal barrier 10 feet in from the high water (or 1 mile out from the low-water mark) - the resulting elimination of fine detail makes the measurement comparatively simple. Basically, it's a question whose answer is entirely context dependent - trying to eliminate the context to get "the one true answer" is about as useful as trying to answer "How heavy is red?"

Are Slashdot Editors Legitimate Nerds?

[K. S. Van Horn]

Because if they were, they'd realize that none of this is news to their readers.

Think about the countries with fjords, like Africa

[Anonymous Coward]

As designed by Slartibartfast on Earth 2.0:

https://youtu.be/nGcBmlDTcHo

start with ...

[Hugh Jorgen]

Agreeing upon the definition of "coastline," oceanic, lakes? Mean tide, low tide, high tide? So yes, no surprise the variance is all over.

Uee a boat NOT a rule!

[Anonymous Coward]

How freaking hard is it to drive a boat around the coast & measure the distance traveled? It would take time but it's not rocket science. And if you want more accuracy send out survey teams. The US has only been in existence for >200 years, seems like more than enough time to complete such a project. Hell, this would probably be even easier today now. Just send someone out with GPS equipment, walk the coast line & track the movements. Send the data back & analyze...done.

Same with edges of the roads

[Anonymous Coward]

If you look at edges of the road under microscope, you may see similar issue. You have to define the resolution in order to determine length. Assume resolution is 10 meters, then draw a line from point A to another point B so that the water does not encroach or recede more than 10 meter at any point in between. This is the length of the coast from point A to point B. Continue this exercise to get the length of the whole coast. Larger the resolution, smaller the coastline (resolution should still be much smaller than the lengths, so you can't have resolution in 1000 km) but it will sort of reach some asymptotic value (by about 1-2 km) and this is the minimum coastline.

Ask Slartibartfast

[neoRUR]

He can give you an exact answer...

Its not 42.

Context

[LucasBC]

The "correct" answer will always depend on context. For example, does one need to know the macro distance for the sake of marine travel, or the micro distance for the sake of water-to-land exposure.

Smooth the jaggedness

[Anonymous Coward]

You could consider the region consisting of all points within 1 mile of any point of US land then find the perimeter of this smoothed region.

Norway

[swell]

Pretty sure that Norway's coast is longer. We could ask Slartibartfast if we can just get to Magrathea to find him. Warning: they only cater to the rich and may not want to speak to you.

Ruined maps

[The New Guy 2.0]

Let's not forget that the "weather maps" disagree with what is seen from space...

Re:Ruined maps

[wonkey_monkey]

...what?

WTF is US?

[Anonymous Coward]

Yeah, never heard.

The length of the coastline is, actually, known

[Anonymous Coward]

...because it is defined to be the length measured on a map of a particular resolution. The two very different figures cited in the summary are the length of the coastline and the length of the shoreline, the latter defined by a higher resolution. Not correct, not news, not an appropriate /. submission.

Re:The length of the coastline is, actually, known

[wonkey_monkey]

Neither of those figures are the actual length of the coastline.

Now I have seen it all!

[nospam007]

Now they sell us Geography 101 from last millennium as "news for nerds, stuff that matters."

I even almost RTFA before my brain awoke.

It depends on who is President

[k6mfw]

Trump will claim he has made it the longingnest!

Throw some money at it?

[Anonymous Coward]

I'm sure the federal government will spend hundreds of millions of dollars on this. And thank god, I mean we really need to get to the bottom of this.

How many brain cells does msmash NOT have?

[Anonymous Coward]

...a similarly meaningless and obscure question.

Easier counterexample

[Actually, I do RTFA]

There's a far easier counterexample, that works in 2D even. Imagine a circle that is an island. Choose any two points. The longest, when they are opposite, straight line is a distance - lets call it d or 2r. It's totally less than the coastline, by a ratio of about 7:22.

Re:Easier counterexample

[sexconker]

The clown I replied to stated that the coastline could never be shorter than that distance.
You're doing it backwards.

Re:Easier counterexample

[Anonymous Coward]

How exactly is that a counterexample? You might RTFA, but you don't appear to RTFC

Re:Easier counterexample

[Actually, I do RTFA]

Ah, okay, fine, then the island should look like a "U". Either way, easier choices.

Re:Easier counterexample

[Anonymous Coward]

Holds for U-shaped islands as well.

what about a curve?

[iamhassi]

what about a curve? It's called calculus, not hard to measure a curve, high school students can do it.

Re:what about a curve?

[Actually, I do RTFA]

Coastlines are fractals, not curves. You cannot measure their length with calculus. Their length literally changes at the resolution you choose to measure them at.

Re:what about a curve?

[Bartles]

They aren't really fractals. You could measure a coastline at any given moment down to the atomic level. It's not infinite.

A fractal measurement challenge for you all.

[az-saguaro]

Read the article. It turns out that this is not a scientific journal or communique, not a technical report or abstract, not detailed information written by experts for experts. It is a general interest blog discussing items of scientific interest. It makes no claim to be novel or current. Furthermore, the article is not about the coastline per se. The second half of this very brief article discusses fractals and the relevant concepts about measuring length with respect to scale. While many people on Slashdot know this subject and its implications, many other people out there might not. So, as an informative article for laymen, it is perfectly reasonable for the forum it was published in. Even by those standards, it was still brief and naive, but if you have never encountered the concept before, it was a reasonable enough introduction to the idea. It does make one wonder though why it was posted on Slashdot, being as basic as it is.

However, the post has elicited many comments, and now, a challenge. For those who say the coast length is moot, well no, not really so. True, we can quibble the details, and the coastline is dynamic rather than static, and it all depends on length of your ruler. But that does not invalidate that the measure is important based on context. Examples:

- A boat is tasked to follow the coastline, maintaining a tangent or parallel course at all times, 200 meters of the shoreline. The boat has an aft screw, a certain length (e.g. 60 meters), and a certain rudder turning radius. Assume that the boat is laying cable and furthermore that it must to perform to perfect efficiency so that it can maximize the amount of cable it carries rather than excess fuel. How many kilometers will it ply, how many kilometers of cable are needed, how much fuel in its tanks?

- A coastal highway is being built 100 meters back from the high tide waterline. The road will be 10 meters wide. It will go from town A to town B, 20 kilometers from each other as the crow flies. Concrete and asphalt must be specified. How much of each are needed to complete the project?

- Recent seismic or volcanic activity has altered a coastline, creating a new large rocky mass along the coastline near an urban area. The altered contour creates new wave or current or tidal patterns that threaten erosion to coastline. How much rock, timber, concrete, or whatever will be needed to create a new seawall or jetty to protect human structures? Or, based on the metrics of those waves and tides, what will be the erosion rate along nearby beaches?

In each example, the length of the coastline has a tangible meaning. A rowboat that wants to follow the coast 10 meters away will have a different measure than an oil tanker following 2 kilometers away, but for the problems presented, their relative lengths matter. Based on the physical scales of each problem, the shorter rulers with longer coastlines, and the longer rulers measuring shorter coastlines must all be filtered out to yield the Goldilocks answer. As Obfuscant stated in a response above, "If you're estimating how much it will cost to install coastal protection you will measure how long the protection measure is, not how long the coast is behind it."

So, here is the challenge or invitation. Please respond below with realistic scenarios of a scientific, mathematical, engineering, or commercial nature where the length of the coast does matter for the problem or project at hand. They could be hypothetical or imagined, or they could be real world examples of prior endeavors or ordinary practices.

Post here . . . . . .

there can be a comprehensive answer

[Anonymous Coward]

if one is willing to accept a clever way to measure (or model) the length of a coastline:
the length of the US Coastline is X miles at scale Y with dimensionality Z.

the values of X, Y, and Z need to be determined, of course, but in describing it that way, should you need to have a length at some scale other than Y (call it Y'), you will be able to apply rigorous mathematical principles to calculate X'

Only one possible answer

[LynnwoodRooster]

42.

How much wood could a wood chuck chuck...

[Anonymous Coward]

...if (and only if) a wood chuck could chuck wood?

Take that Slashdot.

Chicken and egg

[Ecuador]

I don't get the "chicken or the egg" dilemma. I haven't tried "researching" it, but it always seemed obvious to me that the answer is "the egg".
We just have to go back to the first chicken. The definition of the "first chicken" is that while it is a "chicken", its parents are not. Sure, it would be hard to actually define at which point back we stop considering the ancestors chickens, down to the specific mutation, but we do have to stop at some point.
So, you have "not chickens", producing an egg which gives a chicken.
Ergo, egg came first.
Don't know, am I missing something?

Re: Chicken and egg

[Anonymous Coward]

Yes. Perhaps the thing the first chicken came from is not really an egg. More of a proto-egg.

Re:Chicken and egg

[Anonymous Coward]

Try thinking "not chickens" lay "not chickens" eggs. From which then a chicken hatches. So the chicken was first. From there the chicken can lay chicken eggs. Ergo the chicken was first. Both my described view and your view can be seen as true individually, but not at the same time.

Re:Chicken and egg

[Anonymous Coward]

It's a more amusing question when you don't bring evolution or theology into it.

• 1. All eggs come from chickens, therefore the chicken came first.
• 2. All chickens come from eggs, therefore the egg came first.

Which one wins? From a more childish point of view it's difficult to know which one to go with. It's a common kind of problem though. Lots of programming projects, for example, have the following problem:

• 1. You can't get the specs without a quote.
• 2. You can't get a quote without the specs.

So we generally refer to it as a chicken-and-egg problem.

Spelling nitpick

[Opyros]

It's "minuscule", not "miniscule".

It Doesn't Matter

[Anonymous Coward]

It doesn't matter. Only a bunch of eggheads would get their panties in a twist over something so stupid. You just order the roughly correct amount of wall construction materials with options for another 10% and start building. Git 'Er Done!

Discover Magazine!?

[Anonymous Coward]

Now we've taken to citing random "reports" from Discover Magazine, a pop culture/ pop science magazine geared towards the average layman? Seriously? The only news to report here is that the report shows that the government report upon which it is reportedly based is a poor one, I'm sad to report.

Differs by the resolution

[Anonymous Coward]

It's a fractal property.

Roughness

[Waccoon]

Benoit Mandelbrot himself declared that the "roughness" of the coastline was a more important metric than the interpretation of its length.

Coastline Paradox

[Anonymous Coward]

Jesus Fucking Christ... how is the Coastline Paradox news?

Does it include all the territories and islands?

[X!0mbarg]

As the title suggests, there are a lot of little places (Porto Rico, Hawaii, etc) that also add to the total, too.

Then, how far into a river do you track the coastline before it becomes riverbank?

Lots to consider. Little wonder there's differing opinions on it all.

Length of our coast? That can be determined!

[Anonymous Coward]

There is a simple and easy scientific test we can perform to measure the length of the American coast.

1. Pick 1-mile long straight line somewhere along the coast, and straighten the coast out along this line. This is our control segment.
2. Obtain and set aside about 300 billion barrels of oil.
3. Stop all ocean and wind currents. Alternatively, if that is considered infeasible, completely wall off and cover the entire coast.
4. Evenly distribute the oil within the stilled coastal waters (Even distribution by surface area).
5. Once the oil settles, extract and measure the amount of oil recovered from the entire coast.
6. Divide the amount of oil recovered from the entire coastline by the amount of oil recovered from the mile-long control segment.

The result should be a close and objective approximation of the length of our beautiful American coast in miles.

I just don't get why they don't rasterize

[Anonymous Coward]

You could use Earth latitude / longitude rasterization to a particular resolution good enough in any region of the Earth (except for the pole regions, maybe), and measure the coast lines by measuring the lengths of the areas they go through.

Or you could line circles of fixed radius along the coast line, e.g. such that the coast line goes right through their centers and measure how many such objects there are.

The results would be within a very finite margin of error, and even universally applicable on Earth.

To get somewhat consistent results even for different countries, you would need to start from several satellite images from high and low tides and average out over maybe a year.
Even then, the length may change over time though.

It's not about "real" length, e.g. as in how many atoms you need to build the coast line (as there is no such thing that could be measurable - the tides are changing that values significantly)... hm, but thinking again, maybe, you could rasterize with atomic resolution and determine the number of atoms within that huge margin of error.

Always changing

[Tony Isaac]

In addition to the coastline being a fractal pattern, there is the fact that the coastline is constantly changing, at many levels. The tides go in and out, erosion deposits silt at the mouths of rivers, hurricanes wipe away beaches. Not only are coastlines un-measurable because of their complex shape, but because it's a moving target.

It's actually a stupendously large number...

[Bartles]

...and if you take the time to measure, the length of the coastline increases almost infinitely as you increase the resolution of the measurement system. What is the perimeter of a fractal?

What is a coastline

[Anonymous Coward]

Am I the only one who thinks that the "coastline" is not a well-defined object? Apart from the issue with rivers, which has been mentioned, the sea and the land do not meet at a precise, static line, but it is changing at all kinds of timescales. Go to a beach and try to measure a short stretch of "coastline" with a ruler. What is the coastline here https://www.youtube.com/watch?v=cO_IFJaWmhA https://www.youtube.com/watch?v=MD0tXdSsnBA ?

Low tide

[Anonymous Coward]

High tide or ow tide.

How long is the US coastline?

[leed_25]

"The US coastline is X miles long at a resolution of Y centimeters". There. FTFY.

Definition of coastline (Re:It's infinite.)

[Anonymous Coward]

Take the area between the highest high tide and the lowest low tide. Find the length of the shortest curve in this area that goes from border to border. Ignore overhangs.

Quick!

[prisoner-of-enigma]

Quick, somebody spend an absurd amount of taxpayer dollars to answer a question that nobody cares about! And the answer will very constantly because the coastline is always changing due to erosion, deposition, etc.

But hey! I'm sure somebody somewhere will get a billion-dollar grant to study this "problem" and provide a 6,000-page report to Congress that will never be read by anyone.

Mine is bigger than yours?

[ebvwfbw]

It's in the name - coastLINE. It's a LINE. No curves, etc. I have a feeling someone had a bet and they tried to re-define what a coastline is. Here we are.

Not hard.

If only we could take pictures from space...

[Anonymous Coward]

If only there were some way to take pictures from space...
maybe we could compile a database of high resolution pictures from space, from a bunch of artificial cameras orbiting the earth somehow, and have it cover the entire u.s.

the we could just make some kind of program that detects the edges -- call it, hmm... -- an edge detection algorithm. that sounds like a good name.