# 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:** 5
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [June 24, 2021, 9:45pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/81 "2021-06-24T21:45:46Z")
> [@Whack-a-Mole](#): > > Does it? Yes it does. The length of Norway’s coastline is only limited by our ability to measure at small scales. It doesn’t approach some figure, it just keeps getting bigger. It is not like 1.0 + 1.1 + 1.01 +1.001 … , it’s like 1 + 2 + 3 + 4 … ---
**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 24, 2021, 9:48pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/82 "2021-06-24T21:48:12Z")
Well…we know for sure that Norway’s coast is not infinitely long. If you go down the road you are suggesting then the dimensions of your keyboard in front of you now is infinitely long. Also not likely. I’m pretty sure you have something wrong. ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [June 24, 2021, 9:48pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/83 "2021-06-24T21:48:42Z")
It’s probably easiest to look at the initial couple of steps and then just understand that the same thing keeps happening with each step. ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [June 24, 2021, 9:49pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/84 "2021-06-24T21:49:46Z")
> [@Whack-a-Mole](#): > > Well…we know for sure that Norway’s coast is not infinitely long. Do we? How long is it? ---
**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 24, 2021, 9:50pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/85 "2021-06-24T21:50:22Z")
Explain how Norway, a place of finite size on a planet of finite size has an infinite coast which, by definition, would fill the universe. ---
**Author:** ![k9bfriender](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/k9bfriender/32/3283_2.png) [@k9bfriender](https://boards.straightdope.com/u/k9bfriender)\ **Post date:** [June 24, 2021, 9:50pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/86 "2021-06-24T21:50:23Z")
First iteration, say you have a permiter of 1. Then the next, you have a peremiter of 1.33…, then 1.77, then 2.37, 3.16, 4.2, 5.6, 7.49, 9.99, 13.3. See how the numbers are increasing faster in each iteration. Take a calculator, and type in 1 \* 1.33333333 and start just hitting the equals key. Your calculator will, before long, decide tha tthe number is infinite enough for _it_. ---
**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 24, 2021, 9:51pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/87 "2021-06-24T21:51:39Z")
So, infinitely approaching something. Like Pi. But never quite getting there. 1.33333333… goes on forever but it never reaches 1.34. ---
**Author:** ![k9bfriender](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/k9bfriender/32/3283_2.png) [@k9bfriender](https://boards.straightdope.com/u/k9bfriender)\ **Post date:** [June 24, 2021, 9:55pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/88 "2021-06-24T21:55:32Z")
No, not like Pi. it is an increasing number without bound. These are entirely different concepts. Nothing like Pi, nothing at all. What number do you think that 2^n is approaching? ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [June 24, 2021, 9:56pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/89 "2021-06-24T21:56:36Z")
No, because the difference between each number is getting bigger, it is not approaching anything. If I write out the difference between each number I get: 0.44, 0.6, 0.79, etc. It just gets bigger, without end, not approaching anything. ---
**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 24, 2021, 9:56pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/90 "2021-06-24T21:56:57Z")
Tell me how Norway has an infinitely long coast. If it does then tell me why your desk is not infinitely long in dimensions. I think you are playing with definitions. ---
**Author:** ![k9bfriender](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/k9bfriender/32/3283_2.png) [@k9bfriender](https://boards.straightdope.com/u/k9bfriender)\ **Post date:** [June 24, 2021, 10:00pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/91 "2021-06-24T22:00:37Z")
> [@Whack-a-Mole](#): > > Tell me how Norway has an infinitely long coast. Norway as a physical object does not. We’ve been over that. Norway as a mathematical ideal does. That’s why we keep going back to mathematical models, like the snowflake or the Mandelbrot set. > [@Whack-a-Mole](#): > > If it does then tell me why your desk is not infinitely long in dimensions. An ideal desk that you can zoom in infinitely is infinitely long in dimensions as well. > [@Whack-a-Mole](#): > > I think you are playing with definitions. No, I _was_ trying to explain the definitions as they are defined and accepted by mathematicians to you. It’s one thing if you are having a hard time understanding them. It’s quite another if you refuse to accept them. Before I even bother to continue this, tell me what number you think that 2^n is approaching. I really don’t think that I have any interest in answering any more of your questions any further unless you can answer me that. ---
**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 24, 2021, 10:02pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/92 "2021-06-24T22:02:38Z")
Yes, you are playing with definitions. Norway and your desk are finite objects in this universe. Then you try to apply a mathematical abstraction to a real world object and pretend you can zoom in infinitely. But you cannot do that in reality. That’s fine as a math exercise but do not pretend it bears any relation to reality. ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [June 24, 2021, 10:04pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/93 "2021-06-24T22:04:36Z")
> [@Whack-a-Mole](#): > > Tell me how Norway has an infinitely long coast. The difference between Norway (or any other coastline, Norway isn’t special) and say a desk, is that a desk has an obvious scale for measuring its dimensions. There is a scale at which it looks like a rectangular shape and it makes sense to use that scale to measure it. A coastline has no such obvious scale. Any scale you choose to use will look very similar. And so any scale is entirely arbitrary and so there can be no obvious length of a coastline. ---
**Author:** ![naita](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/naita/32/5862_2.png) [@naita](https://boards.straightdope.com/u/naita)\ **Post date:** [June 24, 2021, 10:04pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/94 "2021-06-24T22:04:45Z")
> [@Whack-a-Mole](#): > > That’s fine as a math exercise but do not pretend it bears any relation to reality. As long as you keep showing you can’t grasp the math exercise you have no business making determinations about whether it applies to reality or 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 24, 2021, 10:05pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/95 "2021-06-24T22:05:29Z")
Ok…how is Norway infinite? ---
**Author:** ![k9bfriender](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/k9bfriender/32/3283_2.png) [@k9bfriender](https://boards.straightdope.com/u/k9bfriender)\ **Post date:** [June 24, 2021, 10:05pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/96 "2021-06-24T22:05:50Z")
> [@Whack-a-Mole](#): > > Yes, you are playing with definitions. No, I am not. Please do not assert this again as it is not true. > [@Whack-a-Mole](#): > > Norway and your desk are finite objects in this universe. Yes, we’ve been over that. > [@Whack-a-Mole](#): > > Then you try to apply a mathematical abstraction to a real world object and pretend you can zoom in infinitely. But you cannot do that in reality. We’ve been over that as well. Still not sure of your point here. > [@Whack-a-Mole](#): > > That’s fine as a math exercise but do not pretend it bears any relation to reality. No one did. Everyone accepted that this is a mathematical exercise. Well, _almost_ everyone. It doesn’t really matter on the Norway front, as you have refused to accept that the mathematical model of the snowflake has an infinite perimeter. ---
**Author:** ![naita](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/naita/32/5862_2.png) [@naita](https://boards.straightdope.com/u/naita)\ **Post date:** [June 24, 2021, 10:08pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/97 "2021-06-24T22:08:11Z")
> [@Whack-a-Mole](#): > > Ok…how is Norway infinite? The smaller the ruler the longer the coastline. Now I personally don’t think “Norway has an infinite coastline” is correct, but neither is “it will approach a finite number”. If you want to stick with reality coastlines will differ in length depending on your chosen method of measurement. ---
**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 24, 2021, 10:10pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/98 "2021-06-24T22:10:37Z")
You are absolutely, 100% playing with definitions here. Telling me not to do it changes anything. You are applying a mathematical abstraction about fractals to a real world object. It is abundantly obvious that Norway is not infinite. We discussed above about how small you can make your ruler and no matter how small you make it you NEVER get to infinity. Sure you can do that with fractals. Norway is not that. Eventually, in this universe, you have to stop. ---
**Author:** ![k9bfriender](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/k9bfriender/32/3283_2.png) [@k9bfriender](https://boards.straightdope.com/u/k9bfriender)\ **Post date:** [June 24, 2021, 10:14pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/99 "2021-06-24T22:14:51Z")
> [@Whack-a-Mole](#): > > You are absolutely, 100% playing with definitions here. No telling me not to do it makes it different. Cite what definition and how I am playing with it. If your gonna make the assertion, then back it up. > [@Whack-a-Mole](#): > > You are applying a mathematical abstraction about fractals to a real world object. Yes, that is what we said that we were doing. > [@Whack-a-Mole](#): > > It is abundantly obvious that Norway is not infinite. That’s not the point, at all, in this. That you feel the need to keep “reminding” people of that indicates that for some reason, you have not followed what it is that people are talking about here. > [@Whack-a-Mole](#): > > We discussed above about how small you can make your ruler and no matter how small you make it you NEVER get to infinity. What number does 2^n approach? > [@Whack-a-Mole](#): > > Sure you can do that with fractals. Norway is not that. No one has said that it is. Now, that’s a hard one, what’s the perimeter of the man of straw that you have built? > [@Whack-a-Mole](#): > > Eventually, in this universe, you have to stop. I think this is where I will. Good day, sir. ---
**Author:** ![naita](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/naita/32/5862_2.png) [@naita](https://boards.straightdope.com/u/naita)\ **Post date:** [June 24, 2021, 10:23pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/100 "2021-06-24T22:23:16Z")
> [@k9bfriender](#): > > Take a calculator, and type in 1 \* 1.33333333 and start just hitting the equals key. Your calculator will, before long, decide tha tthe number is infinite enough for _it_ . > [@Whack-a-Mole](#): > > So, infinitely approaching something. Like Pi. But never quite getting there. > > 1.33333333… goes on forever but it never reaches 1.34. The suggestion wasn’t about the infinite digits of 1.3333…, it was about repeatedly multiplying by one and one third. That’s how you get the perimeter of the next iteration of the snowflake, and that approaches infinity. If you round one and one third down to 1.333 the increasingly inaccurate estimate underestimates the perimeter length, but still approaches infinity. [Previous page](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844.md?page=4) [Next page](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844.md?page=6)