The length of a coastline is infinity

IIRC Mandelbrot uses the metaphor of the coast of Britain (which does of itself suggest his idea as we now understand it) as being something which can be iterated to arbitrary (cum-infinite) length , or one of his fractals.

For more along these lines OP, simply see about fractals in general. Mandelbrot's "Fractal Geometry of Nature", wiki etc. (upon review, page 53 of the above contains a cute literal "fractal swastika" which has not been called out).

The volume of a tesseract/hypercube is infinite

Fractal dimensions

You're summation helped me understand this phenomenon really well cheers

not in the real world, branlet

IRL, the length does not exist at all

Did you know that like, a number can go on forever if you write it that way? wow amazing

>Planck length at the most extreme anyway.
It's supposed to be a way of introducing the concept of fractals, and doesn't relate to the real world in an absolute way any more than any aspect of geometry does.
You might as well complain pi isn't "real" because you can't draw a perfect circle.

Since it's a real physical thing, it does converge to a definite length at Planck resolution.

Mitochondria is the Powerhouse of the Cell

you didn't contribute positively at all. you should honestly feel ashamed for making such a low quality comment.

What are limits?

>The length of a coastline is infinity
>something finite in quantity
>in universe that does have minimal length
>infinite
"no"

yes in reality numbnuts

>in universe that does have minimal length
Found the brainlet.

But what happens when you get to a plank length?

planck length is the limit of our ability to resolve differences in length. it is not the lower limit of actual lengths in the universe. we do not know whether reality is discretized below a planck length

Fuck off aethiest!!

I'm surprised how many questions and misconceptions were solved ITT this quickly. This never happens here.

>This thing that we made up has infinite volume

I have an imaginary hyperdick that contains infinite dicks and that's still too few for the mouth of anyone who buys into the hypercube meme

>length
stopped reading right there

What usually happens is, question is answered or misconceptions is cleared up in the first post, followed by 200 posts from people that don't understand or didn't care to read the thread.

If you had an infinitely sharp blade and an infinitely subdividable block of pound cake, could you make infinitely many slices, creating infinite surface area while maintaining constant volume?

This seems like an obvious yes but you would need a steady hand so as to not compress the pound cake and maintain the same volume.

Up until the planck length fuck yeah

OP here
Made this thread an yesterday in advance to get autists to give up their dankest fractals
Fuck yall but love yall
T. LSD op

like a fractal =/= a fractal
unless we can measure infintesimal lengths, then there is no finite volume with infinite circumference

(not to mention, reality is quantized so there is no infinitesimal length available that isn't arbitrary as fuck desu)

Yeah, there's a whole definition of dimensionality bases on this

>unless we can measure infintesimal lengths, then there is no finite volume with infinite circumference
Length is infinitely indivisible, ignore these idiots talking about the Planck length

when you are measuring your infinite circumference, how are you measuring the infintesimal lengths? how long does it take you to measure it? where are you storing the information?
inb4 stereographic projection

SORRY! GOT THE MESSAGE LATE! ENJOY!

Thanks man I'mswimming in that

I hate stupid un-intuitive bullshit stuff like this, it's like saying "There's an infinite amount of toothpaste in a tube" because you can't squeeze out every single molecule
it's stupid

>reality is quantized

That's only if you measure it in a plausible manner. To be mathematically correct you would use an incredibly large lasso made of very soft and malleable rubber - rubber that can get infinitely close to any surface it approaches. You throw the lasso over the island, pull at an infinitely durable cord until the rubber touches every crevice of the coastline. Take the lasso off, trace around it and do some math shit to figure out the perimeter of the lasso. Boom. Non-infinite answer.

This shit wouldn't work irl because we don't have the materials for it desu.

>volume

...

Isn't the coastline fractal thing true for any space with features similar to a portion of a coastline? Like trying to measure the surface area of a cave or something?

The solution is to place each side in a sin function and set x to 0.

irrelevant questions

>infinitely close to any surface

the sum of the circumferences of the fundamental particles that make up an object seems like a reasonable (finite) upper bound to the circumference of an object
im just waiting for some kind of evidence that there is an object with finite volume and infinite circumference

sum of circumferences of each fundamental particle and the distances between each pair even

>true
reality doesn't work like a fractal since you can't infinitesimally divide a length/surface/whatever. Up to a certain level it's a good analogy.

Other examples: Surface of a sponge or of the human lung (something like 100m^2) .

What you are all missing in this post is that all measure is relative to something else. Even if you have a ruler, the ruler itself is defined.

This is a Platonic fallacy. There is no ideal form by itself, only the difference between two narrative objects seen from a third.

This is like searching for a monopole. All stories are Ouroboran: the snake vomits itself up from nothing when you define its head that is regurgitating its tail.

Measures are juxtaposed against the problem they are meant to solve, or the story they are trying to tell, and are scaled accordingly...