xitter

The only good way to spell that platform’s name. Love it!

I like to take an evening stroll down Murder to do some mordor.

Clearly “grrr”

Geese decry aerial restitution.

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).

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.

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.

No, a female cockroach is clearly a cockroachie.

Nothing good will come of this.

Clearly it’s nodes.

Well, NFTs just might be just useless enough.

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”.

So odday, then?

It isn’t lazy to have a mastered skill and use it. It’s lazy not taking the time to master it.

That being said, the biggest lazies of them all are the curriculum writers which don’t make teaching future working adults how to use a clock a priority in grade school.

Or should we get rid of spoons or hammers?

I have to say, I’m quite fond of my pneumatic hammer. When will my pneumatic silverware become a thing?

I just can’t be bothered to expend any energy while I’m eating! It’s supposed to give me energy, after all!

I agree.

That being said, there’s a difference between having a disability and just not having had enough practice.

Just having an analogue clock in all rooms and halls of a school is a way to give people the opportunity to get the practice.

In higher grades you can have an analogue clock in front and a digital “cheat” one in the back. If they’re not sure, they can glance at that. And if that cheat clock is only in every other room. Most will learn because it’s easier that way.

When reading the clock comes as a topic of the curriculum in 1st or 2nd grade, having the teacher ask a student to read the time periodically from the classroom clock for a few months will make sure everyone has had at least some opportunities to practice.

Of course, if someone does have a problem bordering on disability, accomodate them. Regardless of whether their parents took the time and money to have it diagnosed or not. But a quarter of a class having it is either bad luck or just bad methodology.

Edit: all this applies to elementary school.

I feel that learning cursive is important.

First you learn how to write ordinary letters. That trains your fine motor skills so you can write them reliably (try writing with your non-dominant yourself hand to see).

What cursive teaches you is how to write quickly. Of course, no one will write in pure, perfect cursive. Most people settle for a style somewhere in between. It teaches you the concept of “you can combine letters together to make you write faster” and “here are a bunch of ways to combine them”. It’s a good thing, Especially if they end up going to college.

Giving them a few more weeks of practice in reading and writing is a great way to avoid them being partially illiterate.

You can also just ask the staff to change the room numbers and send everyone an update. That way you get a room, no one is disturbed and people running the hotel have an infinite amount of work to do!