Talking about integrals, the fun part is that even with a coastline of indeterminate length, the area of a continent is easy to define to arbitrary precision - you can just define an integral that’s definitely inside the area and one that’s definitely outside the area, and the answer is between those two

Is it?

The main problem with a coastline’s shape isn’t the fractality of it, or the relative size we measure in (the “resolution”).

It’s the fact that a coastline isn’t a static thing. The tides move the shoreline by up to a few meters.

Then there are tectonic movements. These are much slower, but much more powerful: at one point Asia wasn’t even a thing.

As you take the “resolution” up, yes - you’ll see various fractal-like behaviour.

But, and thus is a big but: this will happen even if you take a straight ruler of, say, 1m in length (or, since we have to deal with every little edge case here, the part of it that actually measures out a meter). If you zoom in on it at the molecular and atomic levels, you’ll come across the same problem: a straight line isn’t a straight line! Just by taking an optical microscope, you’ll see the inherent jaggedness (fractality) of our supposedly-straight ruler. It turns out our ruler just appears straight at the human “resolution” (scale).

But does that mean a ruler measuring out 1m isn’t 1m long? While it may not have tectonic or tidal movements, the molecules building up the ruler aren’t straight.

Does this mean the ruler, “zoomed in enough”, will appear to be of infinite length?

Yes.

But does that mean its length is infinite?

No. Its length is clearly 1m, +/- a small rounding error.

The same idea applies to our coastline.

Talking about integrals, the fun part is that even with a coastline of indeterminate length, the area of a continent is easy to define to arbitrary precision - you can just define an integral that’s definitely inside the area and one that’s definitely outside the area, and the answer is between those two.

What is the difference between length and area, other than the one dimension they are apart?

What you’re taking as a common sense assumption for area is equally applicable to the length. Find two extremes, and the answer is somewhere in the middle. The less extreme those extremes become, the more accurate the approximation.

Just as you can integrate the area, there must be an equivalent process to integrate the length.

And besides, any curve used to model the length of a coastline is a bigger assumption than a sufficiently sane “resolution” used to divide the curve into discrete intervals for the purposes of geodesic measurements. As you vary the number of reference points,the length will indeed increase. But after each successive round of refinement, the difference will be less and less, even though it will consistently rise. At one point, it will become insignificant enough.

Why does area get to be especially fun and definite while length, its one-dimension-away sibling doesn’t?

What about volume? Is it an unsolveable enigma like length, or a long-solved problem like area?

It isn’t.

When you look at the number of real numbers, you can always find new ones in both - you’ll never run out.

That being said, imagine (or actually draw) two number lines in the same scale. One [0,1] the other [0,2]. Choose a natural number n, and divide both lines with that many lines. You’ll get n+1 segmets in both lines.

When you let n run off into infinity, the number of segments will be the same in both lines. This is the cardinality of the set.

But for practical purposes of measuring a coastline, this approach is flawed.

Yes, you’ll always see n+1 segments, but we aren’t measuring the number of distinct points on the coastline, but rather its length, i.e. the distance between these points.

If you go back to your two to-scale number lines and divide them into n segments, the segments on one are exactly two times larger than on the other.

This is what we want to measure when we want to measure a coastline. The total length drawn when connecting these n points (and not their number!) as the number of points runs off towards infinity.

The solution to this “paradox” is probably closer to the definition of the integral (used to measure areas “under” math functions) than to that of the cardinality of infinite sets (used to measure the number of distinct elements in a set).

How come?

You can route traffic without Cloudflare.

You can use CDNs other than Cloudflare’s.

You can use tunneling from other providers.

There are providers of DDOS protection and CAPTCHA other than Cloudflare.

Sure, Cloudflare is probably closest to asingle, integrated solution for the full web delivery stack. It’s also not prohibitively expensive, depending on who needs what.

So the true explanation, as always, is lazyness.

With 3d you make the model and it’s “naturally” 3d (obviously). If you want to make a 2d sprite have a different perspective, you need to animate (often times draw) it specifically. As they mentioned it before, it’s mostly useful for animations and movement. It may not even be “reusability” as much as “lack of need to think about perspective” or “scalability”.

Another point is that with a 3d engine under low-storage concerns (like say, the N64) you can do a lot of fuckery like having a total of ~10 textures and just apply various color tints (and maybe a blur here and there) to make it seem like there’s more. While 2d engines do support this nowadays, it’s still hard for artists to “fake” such a wide gamut of sprites, just by the nature of the medium. There’s no model to apply a texture to, so you’re limited to having a base sprite and recoloring it.

You could do a modular approach in 2d. For example, a character is built of the body (arms+face), hair, pants, shirt and shoes and change them individually. Same for houses with roofs, doors, windows and walls, etc.

However, as already said, you’re limited by perspective a lot. Each new perspective requires almost double the sprites.

Isn’t this how the gaming boom and bust cycle always worked?

Indie(ish) games boom, AAA studios buy them and make them bust.

The ban doesn’t need a 100% perfect AI screening protocol to be a success.

Just the fact that AI is banned might appeal to a wide demographic. If the ban is actually enforced, even in just 25% of the most blatant cases, it might be just the push a new platform needs to take off.

There’s four core things you could need for the bathroom:

1. Bleach gel for the toilet bowl. Can also be used on other porcelain surfaces, but not for metal or natural stone (if you don’t want to ruin it).

2. A calc remover to remove calc deposits outside the toilet bowl. Can be substituted with either vinegar or citric acid. Can be used on metal, but do not let it stay on for long - 30 seconds is fine if you clean every 2w to 1mo. Even shorter times if you’re truly regular with your duties.

3. A degreaser for general cleaning (to remove soap residue and other nasty stuff). Can be substituted with dish soap, but is usually a bit more effective so less scrubbing needed.

4. If you get clogged sinks, those declogging solutions are okay. As most people have PVC piping you can just get the cheapest one. If you live in an antique house/apartment with lead piping, you should splurge on the enzyme-based variety, assuming you need it in the first place.

It’s only 2025 and we’re back in the thirties?

Clearly, that will have to wait another four-ish years!

Yeah, that’s not it.

There’s this thing known as consent and purpose. For a GDPR violation, you need to lack either.

When your job has a noticeboard of names, emails and birthdays, they probably got your consent to post it up there. They didn’t get consent to post it onto Facebook.

Yeah, sharing a photo can be a GDPR violation. Because you need to prevent unneccessary processing of data. Like what Facebook does. That’s why most places require you to sign a waiver to allow photos and similar stuff being posted online.

It can be a lot of work. But so is writing a contract. You can’t just do some stuff willy-nilly, and for a good reason.

That being said, the GDPR is mostly unenforced. What it means in practice is “don’t ask, don’t tell”. Meaning, if you keep the info you do have under wraps, you should be fine. Just don’t go whoring your customers’/employees’ info out to your 18 356 “data partners”. Bonus points for having an “Accept All” and “More Options” button, but no “Reject All”.

1st prize for those whose “Reject All” doesn’t encompass “legitimate interest”.

If only.

You are a bunch of mistakes in a trenchcoat.

At least according to the quote.

All so businesses and companies can increase productivity, reduce staff, and then turn around and increase prices to customers.

As if. The only thing AI is to businesses is a lost bet. And they don’t like losing. So they’re betting even more, hoping some shiny “AGI” starts existing if they throw enough money into wasting other resources onto the AI bandwagon.

It’s not a trench coat, it’s a french coat!

Nothing good will come of this.

Playing devil’s advocate here a bit, but

This is a good way to test the water. If they give a nonsense response, then what use would it be to do the same thing for somethijg there’s an even greater problem?

The US is sinking into fascism at an alarming rate, and many other “leaders” are taking inspiration - all over the world, including Europe.

Signing an online petition with your name and ID is a great way of saying “I’m ripe for the disappearing”. Just look at what happened to Charlie Kirk “critics”.

All I can see is two wailords humping eachother. Love is in the air.

Every now and then, I can’t help but wonder

Is me’s AC ready for Summer?

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Israel is trying to whitewash their genocide by “supporting” the conflict that would bring in the most good PR, which happens to be the Russia-Ukraine war.

It says little about Ukraine, a bit more about Israel, but a lot about public conscience - people are rising up against Israeli genocide, and Israel feels the need to do something to shift the media focus.

Honestly, taking arms from Israel, while it kind of helps Israel’s reputation, still means less equipment doing genocide.

A win in my book. Now, if only Ukraine took 50 more, the Flotilla broke through and some sane country got Netanyahu to the ICJ, the world would be a better place.

Don’t forget JRAFIK JINTERJANJE JORMAT!