Talk:Coastline paradox

message: The last paragraph could, I suppose, be made precise, but as it stands it contradicts the first.  Coastlines have no defined length, but this one is longer than that one? Tom Permutt (talk) 21:39, 10 November 2008 (UTC)
thread_title:  Last paragraph contradicts the first 

message: "Since a landmass has features at all scales, from hundreds of kilometers in size to tiny fractions of a millimeter and below" 
Tides negate the need to measure a coastline down to millimeter and below precision.  The variability is so high between tides, that we don't need to go below the meter resolution.  —Preceding unsigned comment added by 65.44.114.33 (talk) 01:49, 30 January 2010 (UTC)
replies: text: The paradox is not one of necessity (how closely do we need to measure), but one of possibility (how closely can we measure). catsmoke (talk) 02:55, 21 June 2019 (UTC)
replies: text: The "paradox" relies on going way beyond what we can reliably and meaningfully measure. Real measurements of coastline lengths are by no means guaranteed to continue growing with further shrinking of rulers. Tides, waves, work effort requirements, measurement uncertainties, and eventually, perhaps, the quantization of space itself, will make further increases of resolution pointless. That is, while the problem does have real practical consequences, the paradox is more of a theoretical exercise. I wish the article shed some  more light on how (and why) to solve the practical problem too. Elias (talk) 12:30, 23 March 2023 (UTC)
thread_title: Tides

message: First, the article states that the coastline of a landmass does not have a well-defined length (which seems correct to me). And then, at the end, there appear coastline lengths in miles and km again (which seems useless if the lenght of the approximation steps is not declared). Even a relationship (percentage) is useless, and even if the same (unknown) step length is used to measure both of them. Can't we delete all those coastline lengths all over Wikipedia...?--Panda17 (talk) 08:33, 30 August 2011 (UTC)
thread_title:  Contradiction 

message: The map images on this article currently have a line on the bottom which is alternately colored black and grey. (What's the word for that line?) Presumably, each black and grey line represents a length, but the maps don't say what. They should either provide units for those lengths, or simply remove that particular line and label the remaining yellow line with its length. The second option seems preferable for its simplicity; the yellow line means that no other units of scale are really needed, and that line is more what this article is about. ± Lenoxus (" *** ") 23:10, 20 September 2011 (UTC)
thread_title:  Images need units clarification/simplification 

message: I have nagging problem with this paradox. Coastlines are not really like this. The East Coast of the United States is dominated by barrier islands and peninsulas. These features are fairly consistent in width, so they are not self-similar. The beaches of southern Long Island are quite straight (except for the occasional inlet). In addition, coastline becomes a meaningless concept in the zone of wave and tidal action.  — Preceding unsigned comment added by Roger J Cooper (talk • contribs) 00:30, 16 September 2013 (UTC)
replies: text: they may appear straight at a certain scale, but as you zoom in that can change. That's the whole point about the fractal aspect of it all. The overall appearance might be straight, but in reality there are countless little serpentines and zigzags. And when you get down to grain-of-sand level, nothing is straight. PurpleChez (talk) 13:15, 10 June 2019 (UTC)
thread_title:  Does the Coastline Paradox Apply to Coastlines? 

message: > More concretely, the length of the coastline depends on the method used to measure it.
That is not true. Coastlines are easily and precisely MEASURED by having a guy roll an odometer equipped unicycle all along the shore, recording the revolutions. Regrettably, most countries are too mean or lazy to do that and they try to GUESS the lenght instead, based on mere teodolite points. Anyhow, the whole issue is rather moot in the era of 0.5 meter resolution public satellite imagery available on the Google Earth Maps site. 82.144.172.66 (talk) 23:05, 5 April 2014 (UTC)
replies: text: An "odometer equipped unicycle" will not measure in the "fractions of a millimeter and below" mentioned in the lead. HiLo48 (talk) 23:13, 5 April 2014 (UTC)
thread_title:  Not precisely worded and quite irrelevant. 

message: "More concretely, the length of the coastline depends on the method used to measure it. Since a landmass has features at all scales, from hundreds of kilometers in size to tiny fractions of a millimeter and below, there is no obvious size of the smallest feature that should be measured around, and hence no single well-defined perimeter to the landmass."
:These same troubles apply to every endeavor of measuring perimeter in the "real world"! Ariel C.M.K. (talk) 13:24, 3 June 2014 (UTC)
thread_title:  Not only for coastlines! 

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thread_title:  External links modified 

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thread_title:  External links modified (January 2018) 

message: The Practicality section feels a lot like someone who came up with their own "solution" to the Coastline Paradox; it has no sources at all.
In addition, it says:
"[...] the problem of measuring the boundary of an atom—which ultimately does not have a defined boundary—arises."
This problem would apply to any measurements, directly contradicting the statement in Mathematical Aspects section that's says:
"[...] unlike with the metal bar, there is no way to obtain a maximum value for the length [...]"
I think this entire section should be removed because it doesn't feel like it contributes to the article, it's more like someone's opinion.
JollyTurbo1 (talk) 05:00, 23 March 2019 (UTC)
replies: text: I think you're absolutely right. I'm removing. -- St.nerol (talk) 15:50, 9 May 2019 (UTC)
thread_title:  Practicality section contradicts rest of article 

message: "When measuring a coastline, however, the issue is that the result does not increase in accuracy for an increase in measurement —it only increases;"
It doesn't increase... it only increases. I suspect something has been lost in translation. PurpleChez (talk) 13:19, 10 June 2019 (UTC)
replies: text: something seems amiss, what it means to say is: The result of measuring the metal bar converges toward a  number with an increase in accuracy, a little more or less, but the results of measuring coastlines will always increase with any increase in accuracy [because fractals and disorder]. cygnis insignis 18:08, 10 June 2019 (UTC)
replies: text:  I've rewritten the sentence. catsmoke (talk) 02:56, 21 June 2019 (UTC)
thread_title:  unclear... to me at least 

message: True coastlines are ever-changing due to tides, waves, erosion, and more. To measure it, there must be some rule defining what line is to be measured. The definition of what is being measured is never given in the article. It just remains as the ambiguous coastline. The only option then is to use another source for the definition. A coastline is defined by Merriam-Webster as "a line that forms the boundary between the land and the ocean or a lake" which will work as a start. This changes over time, so it must be further defined. A specific moment in time could be used, or the average over a specific span of time could be used. The last pieces of the puzzle are the method and scale of measurement. Once these definitions are in place, the specific length can be measured. The coastline paradox, the idea that the perimeter of a land mass is infinite, appears to arise from certain assumptions in the article and incomplete data.
The first external link on the page seems to be the source of the article's problems. I'll refer to it as the source for the rest of this section. Most of the assumptions are made there, and very little information is provided. This source seems to be based on a book from 1961, but no details on the extent of the information in said book are given. Only a few scant examples are provided in the source. The Richardson section only shows six data points, which is where the apparent rapidly expanding length comes from. Unfortunately for the source, six data points can't actually tell much of anything. While it may be true that, over those six data points, the length of a coastline appears to increase faster and faster as the scale decreases, it doesn't show what happens at the extremes of scale, either large or small. A conclusion of any merit cannot be drawn from that, aside from the need for more data. Other examples of scale are given in other sections, but all of these are still in the realm of approximations. None of them actually go down to the smallest scales to see if the supposed paradox holds up. The smallest example labeled in the Examples section is 250m. The data points shown in the Richardson section don't label any of the points. They are just shown on a graph. 
There is a true maximum measurable length to any coastline. It is determined by the coastline's smallest feature. If the measurement scale is larger than this smallest feature, the measurement will be an approximation that will get larger if the scale is reduced and more features are revealed. This growth of length will continue until the scale of the smallest feature is reached. If the measurement scale is smaller than this, it will result in a measurement that will be very close to the true length of the coastline, and it will stop rapidly growing as the scale is reduced further. At this point it will behave like simple curve approximations. There are no more features to expand below this scale, and thus coastlines are not truly fractals. They resemble fractals at some scales, but true fractals have no limits on how small their scales can get. This is a problem in the source. It assumes coastlines to be infinite fractals, but they are not. There is a limit to the smallest size of features to expand. That can delve into quantum mechanics, though, which is way beyond the scope of the article. A brief trip down that rabbit hole reveals that subatomic particles don't actually touch, though, which means there actually is no coastline below a certain scale. There must be a lower limit for what defines a coastline which is larger than subatomic particles, and there must be a smallest scale for features on that coastline.
Approximation can lead to other interesting false conclusions as well, such as the idea that pi = 4. This YouTube video, Rhapsody on the Proof of Pi = 4 by Vi Hart, goes into detail about how this idea works and how it's wrong. It shows that, while there is a specific perimeter length to a given shape, approximations can be very misleading when trying to get the exact measurements. This is a problem with the source as well. It assumes that a few approximations, the six data points, somehow represent the full truth of the situation.
All in all, the coastline paradox does not exist. It only appears to exist in a small data set. Closer examination reveals the flaws in the original arguments as well as the need for more data. This article really needs to be flagged in some way to show that it's not accurate. I do not know how to do that.
This last part is related, but it's about preventing the coastline paradox or others like it from arising. It tackles the very first point. How the coastline is defined determines everything about the measurement results. The only reason there is even room to argue about the accuracy of coastline measurements is that the coastline itself is not defined accurately enough. Is it the border between molecules? Is it larger than that? Perhaps it's best defined as the path a string follows when laid down along the water's edge, which would be quite usable for most people. The supposed paradox isn't a product of measurement scale. It's a product of poor definitions. Science has gotten quite a bit better at rigorous data collection since 1961 though. Maybe there will be a new data set to extrapolate from in the future. Caelen Tigris (talk) 05:03, 1 July 2019 (UTC)
thread_title:  Fallacious Article: Incomplete Data and Jumping to Conclusions 

message: This article claims to be about a paradox, but the content of the article seems to be just a jumbled presentation of various factoids and various discussions, leading to nothing but "Measuring coastlines is actually pretty hard". 
I suggest either deleting the article outright, or doing a complete rewrite that contains only the following: a clear and definitive statement of the paradox, followed by explanations of each proof for it, each method of resolving it (if there are any), and each common objection to it (if there are any). If the article is going to fail to define its own paradox, and fail to show any proofs for it or ways of resolving it, why even bother trying to write any other parts? TooManyFingers (talk) 23:36, 29 August 2021 (UTC)
thread_title:  Article misses its own point 

message: it assume that coastlines are fractal to get the paradox part... and they are not fractal they are baryonic matter, so can be measured in discreet intervals.  
so the basis of this is flawed, ergo the supposition is incorrect.
coastlines are 100% definable in a number of measuring ways, none of which involve fractals.
this is all just nonsense and should be deleted.
82.9.90.69 (talk) 14:29, 31 August 2023 (UTC)
replies: text: The coastline paradox applies to cartography and attempts at modeling the physical world. When doing this, the unit used to define the boundary of the coastline will impact its final length. While you can, in theory, get to the subatomic level to measure a coastline, erosion and tides are going to create enough variation that your efforts will be meaningless. When two countries survey their coastline or boarder, they will come up with different values if they use different spatial resolutions and chosen discreet interval. The paradox is for cartographers trying to give a "correct" measurement.  The paradox exists in cartographic peer-reviewed literature, and if you think it is non-sense I suggest you publish a paper in a cartographic journal, not try and get it deleted from Wikipedia.  GeogSage  (⚔Chat?⚔)  18:17, 2 October 2023 (UTC)
thread_title:  this is not a paradox... 

message: The Wikipedia article How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension covers one peer reviewed journal on a topic. This paper is fantastic, and could easily serve as a section on the page Coastline paradox. However, I don't believe single peer reviewed journals generally need to have their own dedicated Wikipedia page, as they are primary sources that stand alone. Thus, I propose moving the contents of that page into the coastline paradox page as a subsection and made into a redirect. I'm placing relevant tags on each page. Please discuss here, and we can see if we can reach a consensus. 
I'll wait at least two weeks, so until October 1st 2023, for discussion until I make the move permanent.  
GeogSage  (⚔Chat?⚔)  18:35, 17 September 2023 (UTC)
replies: text: That seems fine to merge, yeah. Elli (talk | contribs) 03:30, 24 November 2023 (UTC)
replies: text: Thanks for the feedback! This is one I'm trying to figure out how to approach. Not sure how much content to pull from the journal article. GeogSage  (⚔Chat?⚔)  04:39, 25 November 2023 (UTC)
replies: text: ; I've move most it over, into the Measuring a coastline section. Feel free to refine it in situ. Klbrain (talk) 18:33, 4 January 2024 (UTC)
replies: text: Thank you! I have been meaning to get to this and have been putting it off. Awesome job! GeogSage  (⚔Chat?⚔)  18:35, 4 January 2024 (UTC)
thread_title:  Merge page [[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension]] with this one.