this post was submitted on 25 Aug 2024
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[–] [email protected] 37 points 2 months ago (5 children)

Arnt most borders fractals so can any border be the largest?

[–] [email protected] 37 points 2 months ago* (last edited 2 months ago) (4 children)

No, because borders are made up by humans and humans can't write down or even measure infinitely small

[–] [email protected] 15 points 2 months ago

Some borders drawn as straight lines on maps sure. But we also define borders by rivers and all sorts of other fractal things.

[–] [email protected] 7 points 2 months ago

Borders are just social construct

[–] [email protected] 4 points 2 months ago (1 children)

We can if we make tools to do it for us.

[–] [email protected] 3 points 2 months ago (1 children)
[–] [email protected] 1 points 2 months ago

Actually, in this case, it's easily solved. Trying to measure an infinitely complex curve will never halt, answer found.

[–] [email protected] 2 points 2 months ago (1 children)
[–] [email protected] 1 points 2 months ago

It's kind of subtle how exactly you're using numbers when writing limits. You're either not actually doing infinitesimals, just Cauchy sequences centered around a point, or you are and you get to enjoy the axiomatisation of the hyperreals.

[–] [email protected] 21 points 2 months ago (2 children)

You'll have to represent each border on the same scale, so no. Also, why are you being flagged as a bot?

[–] [email protected] 11 points 2 months ago* (last edited 2 months ago) (2 children)

I was writing a bot and must have accidentally enabled it for my main account. Fuck im retarted.

Even Firefox's coloured containerisation can't fix stupid

[–] [email protected] 7 points 2 months ago

LIES!!! AI IS TRYING TO INFILTRATE US!!! BURN THE BOT WITCH!!!!

[–] [email protected] 2 points 2 months ago (1 children)

Your username is cursed, thanks for bringing that combination of words to life

[–] [email protected] 1 points 2 months ago

Don't thank me, thank chatGPT.

[–] [email protected] 4 points 2 months ago (1 children)

Anyone can just go into their account settings and mark their accout as a bot. Idk why you would though

[–] [email protected] 4 points 2 months ago

You would do that if you were running that account using a bot.

[–] [email protected] 13 points 2 months ago* (last edited 2 months ago)

Yes, but non-coastal borders become nice curves at a certain resolution just because they're legally defined by points.

Coastal borders are legally vague AFAIK, since they're defined as a nautical mile from "the shore" or something like that, but when you're already on the ocean a matter of a few meters tends not to matter.

[–] [email protected] 7 points 2 months ago (2 children)

considers

Well, they aren't fractal, that's for sure.

It is true that we could make borders more-closely-map to physical features, and that would increase the length somewhat.

And we can define borders however we want, so that's up to us.

But ultimately, matter is quantum, not continuous, so if we're going to link the definition of a border to some function of physical reality, I don't think that we can make a border arbitrarily long.

[–] [email protected] 9 points 2 months ago (2 children)

Coastlines are indeed fractals, and a similar argument could be made for any border defined by natural phenomena (so like, not the long straight US/Canada border).

[–] [email protected] 6 points 2 months ago (3 children)

Coastlines are not self repeating and they are fundamentally finite.

[–] [email protected] 6 points 2 months ago (1 children)

I believe they were referring to this, where technically a coast could be seen as similar to fractals

https://en.wikipedia.org/wiki/Coastline_paradox

[–] [email protected] 11 points 2 months ago

Literally from that page

The coastline paradox is often criticized because coastlines are inherently finite, real features in space, and, therefore, there is a quantifiable answer to their length.[17][19] The comparison to fractals, while useful as a metaphor to explain the problem, is criticized as not fully accurate, as coastlines are not self-repeating and are fundamentally finite.[17]

[–] [email protected] 2 points 2 months ago (1 children)

Fractals are not necessarily self repeating, they just contain detail at arbitrarily small scales.

[–] [email protected] 1 points 2 months ago

Which a physical space cannot fulfill

[–] [email protected] 1 points 2 months ago (1 children)

Fractals are not required to be self-repatiing. For example, the Mandelbrot set is a non-self repeating fractal pattern.

And please elaborate on how they are fundamentally finite.

[–] [email protected] 2 points 2 months ago (1 children)

Coastlines exist in the real world, they are by definition finite structures. You can only zoom in to them so far before the structure is no longer a coastline.

[–] [email protected] 0 points 2 months ago (1 children)

Thats making a lot of assumptions about quantum physics

[–] [email protected] 1 points 2 months ago

An atom is not a coastline, even if it is a piece of one

[–] [email protected] 3 points 2 months ago* (last edited 2 months ago) (1 children)

Well, quantum mechanics is continuous, just in a way that often maps to discrete things when measured. I'm sure someone has written a research paper on quantum law, but I wonder if anyone who actually knows quantum mechanics has.

[–] [email protected] 2 points 2 months ago (1 children)

It is only continuous because it is random, so prior to making a measurement, you describe it in terms of a probability distribution called the state vector. The bits 0 and 1 are discrete, but if I said it was random and asked you to describe it, you would assign it a probability between 0 and 1, and thus it suddenly becomes continuous. (Although, in quantum mechanics, probability amplitudes are complex-valued.) The continuous nature of it is really something epistemic and not ontological. We only observe qubits as either 0 or 1, with discrete values, never anything in between the two.

[–] [email protected] 2 points 2 months ago* (last edited 2 months ago)

Sure, but if you measure if a particle is spin up or spin down in a fixed measurement basis, physically rotate the particle, and then measure again the amplitudes change continuously. You could also measure it in another basis, which themselves form a continuous family, and get a similarly logical answer (although not independently of the first one). I don't know much about quantum field theory, but I do know that fields in it are continuous, just like they are in classical theories.

All in all, while quantum logic is part of what makes it continuous, I think I'd still stand by that it is continuous.