# Is the coastline paradox only applicable to physical coastlines? **URL:** \ **Category:** Factual Questions\ **Created:** [June 22, 2021, 4:27pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844 "2021-06-22T16:27:12Z")\ **Posts on this page:** 20\ **Page:** 9
**Author:** ![Whack-a-Mole](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whack-a-mole/32/141_2.png) [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)\ **Post date:** [June 26, 2021, 4:31pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/161 "2021-06-26T16:31:36Z")
Yet you can’t do it. ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [June 26, 2021, 4:33pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/162 "2021-06-26T16:33:51Z")
> [@Whack-a-Mole](#): > > @Francis_Vaughan and I are on the same page on this point. Yes and no. I stand corrected on some points, some of which I embarrassingly had forgotten. Line filling areas are mathematically sensible. Then there are things like the Smith–Volterra–Cantor set, which I had forgotten about, but had come across. But, even mathematically, an infinite coast does not, _by definition_ fill the universe. It is perfectly possible for the infinite cost to be bounded in extent and area. In mathematics reasoning about infinity is not trivial, and there are lots of pitfalls and interesting and unexpected things. But this is within the scope of mathematical definition. Not physical world. I don’t think anyone is actually in dispute with anyone else, but there is some element of talking about different things. In the physical world the only issue is that the length of the cost is ill defined, and can vary, generally increasing in length as it is measured at smaller scales, until it becomes nonsensical to make the scale smaller. In the physical world, invoking a proper mathematical infinity is a very dubious thing to do. The moment you try to it isn’t clear anything that is stated after has any sensible foundation to reason about. Any idea that “by definition” any property involving infinity is true is already likely wrong. Invoking infinity in a discussion of physical length of a coastline can’t involve discussion of any “defined” properties of the line, because the entire idea is ill defined in the first place. ---
**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\ **Post date:** [June 26, 2021, 4:36pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/163 "2021-06-26T16:36:18Z")
You are not. ---
**Author:** ![Whack-a-Mole](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whack-a-mole/32/141_2.png) [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)\ **Post date:** [June 26, 2021, 4:37pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/164 "2021-06-26T16:37:11Z")
He said “yes and no” so we’re both right and wrong. It remains, there is NO physical line you (or anyone) can draw that is infinite and will fit in this universe for reasons that really should be abundantly obvious. It only works as equations and abstract concepts. ---
**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\ **Post date:** [June 26, 2021, 4:38pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/165 "2021-06-26T16:38:28Z")
He also said. > [@Francis\_Vaughan](#): > > But, even mathematically, an infinite coast does not, _by definition_ fill the universe. This is the first, of possibly many, barriers to your understanding. ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [June 26, 2021, 4:40pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/166 "2021-06-26T16:40:40Z")
> [@Lance\_Turbo](#): > > This is the first, of possibly many, barriers to your understanding. So by definition any fractal coast does fill the universe? I suspect you missed the intention of the italics, they were quoting, not emphasising. ---
**Author:** ![leahcim](https://avatars.discourse-cdn.com/v4/letter/l/b4bc9f/32.png) [@leahcim](https://boards.straightdope.com/u/leahcim)\ **Post date:** [June 26, 2021, 4:41pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/167 "2021-06-26T16:41:39Z")
> [@Whack-a-Mole](#): > > The OP asked about “physical coastlines”. A real thing. Just to nitpick even further, a “physical coastline” is an abstraction, at least at scales of less than a few metres. Informally it’s “where the water meets the shore”, but is that at high tide or low tide or some average of the two (and if so, average over what time scale). Do individual waves move the coast line when then come in and out or is there some kind of short-term time average being applied there, too? The ambiguity in the definition certainly comes into play long before we get to the “how to we account for the space between atoms” level of precision. To the extent that a precise definition of “coastline” is required for civil and legal purposes, it is basically just an abstract curve in space, loosely correlated with the position of water and land at any time. ---
**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\ **Post date:** [June 26, 2021, 4:45pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/168 "2021-06-26T16:45:20Z")
Are you asking me? My answer is no. A one dimensional object can be infinitely long and not fill the enitre universe. An infinitely long one dimensional object could fit in a shoebox. @Whack-a-Mole, is the poster that doesn’t grasp this. ---
**Author:** ![Whack-a-Mole](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whack-a-mole/32/141_2.png) [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)\ **Post date:** [June 26, 2021, 4:46pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/169 "2021-06-26T16:46:09Z")
I get it just fine. Your problem is thinking a real world anything can be one dimensional. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [June 26, 2021, 4:49pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/170 "2021-06-26T16:49:18Z")
At least no one is asking yet if the Banach–Tarski paradox is applicable to physical balls… ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [June 26, 2021, 4:49pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/171 "2021-06-26T16:49:29Z")
> [@Lance\_Turbo](#): > > @Whack-a-Mole, is the poster that doesn’t grasp this. > [@Lance\_Turbo](#): > > This is the first, of possibly many, barriers to your understanding. I was responding to this, which was apparently directed at me, so yes I was asking you. I do assume you misread the intent of my earlier post. This entire conversation is getting slightly surreal. ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [June 26, 2021, 4:50pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/172 "2021-06-26T16:50:37Z")
> [@DPRK](#): > > At least no one is asking yet if the Banach–Tarski paradox is applicable to physical balls… What, you suggest it isn’t? 🤪 ---
**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\ **Post date:** [June 26, 2021, 4:52pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/173 "2021-06-26T16:52:19Z")
The board software doesn’t mark who you’re replying to if it is the post immediately above. I hit reply on @Whack-a-Mole 's post and the, “Your,” in “This is the first, of possibly many, barriers to your understanding,” refers to @Whack-a-Mole and not @Francis_Vaughan. My mistake. I should have been clearer. ---
**Author:** ![Whack-a-Mole](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whack-a-mole/32/141_2.png) [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)\ **Post date:** [June 26, 2021, 4:53pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/174 "2021-06-26T16:53:39Z")
_“I thought it was one of the prime numbers of the Zenith series.”_ ~Hans Zarkov ---
**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\ **Post date:** [June 26, 2021, 5:03pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/175 "2021-06-26T17:03:57Z")
> [@Whack-a-Mole](#): > > Your problem is thinking a real world anything can be one dimensional. Your problem is thinking there can’t be. ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [June 27, 2021, 12:10am UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/176 "2021-06-27T00:10:25Z")
> [@Little\_Nemo](#): > > > [@Senegoid](#): > > > > The discussion here is strongly related to the not-quite-but-almost infinite threads we’ve had in the past asking if 0.999=1. Sorrowfully, the really major such thread seems to have gotten lost in the transition, as I can’t find it. > > [Is it this one?](https://boards.straightdope.com/t/is-0-999-1/10990) Sorry, not. Your link is a thread of a scant 72 posts, none of them by me. The BIG one went on and on for many hundreds of posts, including many by me. The point I wanted to make (and did at length in the lost thread) is that many people are confused about infinite series and infinite decimals, and further don’t have a clear notion of limits. OTOH, the math-heads who do have a clear notion don’t usually explain things well for the less-initiated. I’ll cite the following as just one example: > [@Chronos](#): > > An infinite straight line is one possible thing of infinite length. But it’s not the only one, and there are plenty of others that do fit just fine inside (let’s say) a rectangle of small, finite dimensions. To a non-mathematician who isn’t familiar with such things, the above is simply incomprehensible, and sheds no light whatever. (I think the question dealt further with the idea that a one-dimensional figure can be sufficiently convoluted that it actually fills a two-dimensional space, or that a closed curve of infinite length can enclose a finite area, which the above cite doesn’t address at all.) This thread is full of posts like that, as are all those threads about 0.99999, as are just about all threads about advanced topics. And how is this thread related to the 0.999… question? Because it has to do with infinite series, and sums thereof, and the notion that such sums may or may not converge to a limit, either of which cases requires at least a basic concept of infinite series and limits. In the lost thread (maybe it’s still around if only I can find it?), I tried to give a detailed beginner-level tutorial. And yes, it does require “playing with definitions”, as it is necessary to carefully define infinite sums in a way that works and that is also consistent with our traditional notion of sums. ---
**Author:** ![Whack-a-Mole](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whack-a-mole/32/141_2.png) [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)\ **Post date:** [June 27, 2021, 12:15am UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/177 "2021-06-27T00:15:30Z")
> [@Lance\_Turbo](#): > > Your problem is thinking there can’t be. If you can produce a 1-dimensional object take it to Stockholm and collect your Nobel Prize. ---
**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\ **Post date:** [June 27, 2021, 12:31am UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/178 "2021-06-27T00:31:27Z")
How am I supposed to bring the coastline of Norway to Stockholm? Think. 😉 ---
**Author:** ![Whack-a-Mole](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whack-a-mole/32/141_2.png) [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)\ **Post date:** [June 27, 2021, 12:39am UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/179 "2021-06-27T00:39:44Z")
I am thinking: You are suggesting you can put an infinite line in a finite space. If so, that space does not need to be as big as Norway. You could fit it on a sheet of paper. Surely you can get that piece of paper to Stockholm. That’s the easy part. ---
**Author:** ![MrDibble](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mrdibble/32/114_2.png) [@MrDibble](https://boards.straightdope.com/u/MrDibble)\ **Post date:** [June 27, 2021, 10:48am UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/180 "2021-06-27T10:48:15Z")
Is the Norwegian coastline not a real-world thing? It’s certainly one-dimensional (or, possibly, two-dimensional - lots of cliffs in Norway, but I’d argue coastline is the land-sea-air interface hence one-dimensional - but the same arguments hold for surfaces filling spaces as for lines filling areas), but is it a real world thing to you? [Previous page](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844.md?page=8) [Next page](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844.md?page=10)