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SmoothOperator@lemmy.worldto
Mildly Infuriating@lemmy.world•Jeopardy wall calendar pretending that the coastline paradox doesn't existEnglish
1·22 days agoWhy does area get to be especially fun and definite while length, its one-dimension-away sibling doesn’t?
Excellent question, and as you yourself allude to, it’s a question of bounds. If you can establish and upper and lower bound on a quantity and make them approach eachother, you can measure it.
On a finite 2d surface you can make absolute lower and upper bounds on any area - lower is zero, upper is the full surface. All areas are measurable. But on the same surface you can make a line infinitely squiggly and detailed, essentially drawing a fractal. So the upper bound on the length of a line is infinite. Which means not all lines have a measurable length. And that comparing two line lengths might become the same problem as comparing to infinities of the same type, which is not well defined.
This extends naturally to higher dimensions - in a finite 3d space, volumes must be finite, but both lines and areas can be fractally complex and infinite. And so on.
SmoothOperator@lemmy.worldto
Mildly Infuriating@lemmy.world•Jeopardy wall calendar pretending that the coastline paradox doesn't existEnglish
11·24 days agoBut isn’t the issue that coastlines have a fractal nature? That depending on your resolution, you could have a finite or infinite length of a coastline? In which case measurement is hard to define.
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.
SmoothOperator@lemmy.worldto
Mildly Infuriating@lemmy.world•Jeopardy wall calendar pretending that the coastline paradox doesn't existEnglish
11·24 days agoSure, the length of the intervals is easily compared. But saying
there are twice as many elements in the total than there are in half the range
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?
SmoothOperator@lemmy.worldto
Mildly Infuriating@lemmy.world•Jeopardy wall calendar pretending that the coastline paradox doesn't existEnglish
51·24 days agoIsn’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.
SmoothOperator@lemmy.worldto
Games@lemmy.world•Years later, Arkane’s Dishonored is still a modern stealth classicEnglish
2·29 days agoTo me it feels more about consistency. The world aligns with your expressed ideology.
If you’re using the sneaking and non-lethal tools the world becomes a place that believes in the value of life, if you murder indiscriminately the world becomes a place of punishment, where nobody is innocent and the only way forward is to let a plague descend on the land.
Plus, arguably, the parts that get harder when you go lethal are balanced by the inherently more difficult nature of the non-lethal approach.
SmoothOperator@lemmy.worldto
Games@lemmy.world•Years later, Arkane’s Dishonored is still a modern stealth classicEnglish
4·30 days agoInteresting, I’ve never considered choices and gameplay as separate things. Isn’t it more, I don’t know, immersive if gameplay and story are unified?
SmoothOperator@lemmy.worldto
Games@lemmy.world•Years later, Arkane’s Dishonored is still a modern stealth classicEnglish
9·30 days agoNon-lethal also means avoidance rather than conflict. But ultimately, “bad ending” is subjective. You still save the princess, it’s just a more murdery vibe.
Also you get to kill the baddies yourself, it’s the good ending where most are killed for you right?
SmoothOperator@lemmy.worldto
Gaming@lemmy.world•Me and my buddy on our Steam Decks on WW3 while waiting for the artillery barrage to finishEnglish
3·2 months ago“Made for playing games like Halo”, interesting description of the deck
SmoothOperator@lemmy.worldto
Technology@lemmy.world•kurzgesagt – AI Slop Is Killing Our Channel / Destroying the InternetEnglish
1·2 months agoCareful research.
SmoothOperator@lemmy.worldto
Technology@lemmy.world•kurzgesagt – AI Slop Is Killing Our Channel / Destroying the InternetEnglish
384·2 months agoYou can’t really call it slop just because you disagree with their views and representations of things.
Their stuff is carefully researched and sourced, human crafted and open to critique. Whether they’re correct in their assessments or not is of course up for debate, but it’s good craftsmanship and they show their work.
SmoothOperator@lemmy.worldto
Mildly Interesting@lemmy.world•The internet provider on my dorm explicitly allows legal torrents
13·2 months agoIsn’t it harder to find direct downloads? Or am I just stuck in the past on the bay?
SmoothOperator@lemmy.worldto
No Stupid Questions@lemmy.world•What is a good source to read about thought experiments?
11·3 months agoAlso double slit experiment is not so much a thought experiment as it’s an experimental phenomenon that is hard to explain. Also Einsteins thought experiments are actual science, based on reality with actual results…
The double slit experiment was first invented as a thought experiment, and later was built as an actual experiment. It’s the same with relativity, first it was thought up, now it’s experimentally verified. So the examples from relativity you bring up are also more experimental phenomena than a thought experiments at this point.
SmoothOperator@lemmy.worldto
No Stupid Questions@lemmy.world•What is a good source to read about thought experiments?
1·3 months agoI have, I studied these ideas at university. I’m just curious what makes these thought experiments harder than e.g. the double slit experiment, Plato’s cave analogy or Rawls’ veil of ignorance?
SmoothOperator@lemmy.worldto
No Stupid Questions@lemmy.world•What is a good source to read about thought experiments?
2·3 months agoWhat makes relativity the hardest thought experiment?
SmoothOperator@lemmy.worldto
World News@lemmy.world•Gaza Is Burning, and We Are Living ItEnglish
2·3 months agoFor sure, but it’s yet to be seen if the bad outweighs the good. For the last several centuries it’s been going the right way, so there is good reason to hope that a century from now, things are even better than they are today.
Doesn’t mean we shouldn’t fight for the good causes, naturally.
SmoothOperator@lemmy.worldto
World News@lemmy.world•Gaza Is Burning, and We Are Living ItEnglish
1·3 months agoDo the technological and social advances not show that we are also at heart a progressive people with a need to care for eachother and create a better future?
SmoothOperator@lemmy.worldto
World News@lemmy.world•Gaza Is Burning, and We Are Living ItEnglish
3·3 months agoBy most measures, such as number of humans killed in war or child mortality, human suffering in the modern era is less than it’s ever been. In the grand scheme of things, we have made the world a place with much more room for joy and love over the course of human civilisation.
Cool! What’s your take on the empirical method then, considering the relationship between reality and the subject?
The text indicates that it’s only on inheritances greater than 62 million dollars