this post was submitted on 20 Nov 2025
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Mildly Infuriating
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Nah, that's silly. Asia obviously has the longest coastline.
Sure, based on that paradox, the specific measurement of a given coastline will differ. But if you pick a standard (i.e., 1km straight lines), Asia is easily the longest. Doesn't matter what standard you pick.
The only way the paradox matter here is of you pick different standards for different coastlines. Which, os obviously wrong.
Some infinites are larger than other infinites.
It's not a true fractal, so the length has some finite bounding. It's just stupidly large, since you are tracing the atomic structure.
Let F be a geometric object and let C be the set of counterexamples.
F is a True Fractal ⟺ F satisfies all properties P₁, P₂, ..., Pₙ
Where for each counterexample c ∈ C that satisfies P₁...Pₙ: Define Pₙ₊₁ := "is not like c"
The definition recurses infinitely as new counterexamples emerge.
Corollary: Coastlines exhibit fractal properties at every scale... except they don't, because [insert new property], except that's also not quite right because [insert newer property], except actually [insert even newer property]...
□ (no true scotsman continues fractally)
This motherfucker coming correct with subscripts.
That's a fair point. I forgot that some infinites are larger than other infinites.
Did you also forget about Dre?
Did you forget about the game?
Isn't it a bit like saying "there's obviously more real numbers between 0 and 2 than between 0 and 1"? Which, to my knowledge, is a false statement.
If between 0 and 1 are an infinite number of real numbers, then between 0 and 2 are twice infinite real numbers, IIRC my college math. I probably don't.
In math they'd both be equal
Discrete math typically teaches that some infinities are greater than others.
Yes, but those are both the same infinite according to math, so no, they're still equal.
? But they’re not the same infinity according to math.
Here's the proof: for each number between 0 and 1, double it and you get a unique number between 0 and 2. And you can do the reverse by halving. So every number in the first set is matched with every number in the second set, meaning they're the same size.
They are literally both ℵ~1~ though?
Aren’t the number of real numbers and the number of integers also infinite? But they aren’t considered equal. The infinite for real numbers is considered larger.
Yes, the number of Intergers is ℵ~0~, the number of real numbers ℵ~1~, and this is what people generally mean with some infinities are bigger than others. Infinities can also be seem bigger than another, but be mathematically equal. The number of natural, real and rational numbers are all infinite, and might seem different, but they are all proven ℵ~0~.
Claypidgin was talking about the real numbers between [0,1] and [0,2], which are both ℵ~1~ infinite. Some infinities are indeed bigger than others, but those 2 are still the same infinity.
The cardinality of the two intervals [0,1] and [0,2] are equivalent. E.g. for every number in the former you could map it to a unique number in the latter and vice versa. (Multiply or divide by two)
However in statistics, if you have a continuous variable with a uniform distribution on the interval [0, 2] and you want to know what the chances are of that value being between [0,1] then you do what you normally would for a discrete set and divide 1 by 2 because there are twice as many elements in the total than there are in half the range.
In other words, for weird theoretical math the amount of numbers in the reals is equivalent to the amount of any elements in a subset of the reals, but other than those weird cases, you should treat it as though they are different sizes.
Sure, the length of the intervals is easily compared. But saying
is false. They are both aleph 1. In other words, for each unique element you can pick from [0,2], I can pick a unique element from [0,1]. I could even pick two or more. So you can't compare the number of elements in the two in a meaningful way other than saying they both belong to the same category of infinite.
This is the whole crux of the coastline problem, isn't it?
Funny that so many uses of maths depends on measurement, and yet so many pure mathematicians seem to be clueless about how we actually measure things and why its useful. It doesn't even matters about all this bullshit about infinities , were talking about the real world. It's all about the precision of the tape measure. Here's a true story from back in the day:
English Mathematician: You'll need an infinite number of bricks to build a wall around any island's coastline. French guy: come on over and see Mont Saint Michel it's vraiment genial!
English Mathematician: Oh that wall is infinitely far away from the true coastline, those bricks are not regulation infinitesimal length. If they'd started from the other corner they'd have got a different shape, and for sure needed infinite number of infinitesimal bricks to actually build that wall. Sloppy french masons. I can prove it I'll blast them all away with cannon fire until the glorious mathematical truth is revealed underneath.
One year later French inhabitants: fuck off english maths whore!
Ten years more laterer Hi french dudes! I'm back with a greater number of even bigger state of the art truth seeking cannon. I will prove this if its the last thing i do.
One year later . . .