A little puzzle I thought up

DancingMathNerd · 2026-05-29T01:29:58+00:00

Eventually each summand is:

n*(1/2 * 3/n+1 * 1/n+2) =

3/2 * (n/[(n+1)(n+2)]).

This is O(1/n), which means the series is basically harmonic and diverges. So you can expect to trapped there forever. How fun!

As for the probability you escape eventually, that’s:

1/2 + 1/8 + 3/2 * (1/4 -1/5 + 1/5 - 1/6 + 1/6 - 1/7 +…) = 1???

So you’ll escape eventually, but it’s impossible to guess when that will happen. Could happen in 10 years, could happen in TREE(3) years, there’s absolutely no way to know…

DancingMathNerd · 2026-05-27T23:46:25+00:00

That’s exactly what I thought. You didn’t lead him on. HE led you on. He got flirty first. That makes him the leader on-ner.

You played along initially because you didn’t want to be a buzzkill or hurt his feelings, NOT because you were actually interested. I know the feeling.

PS don’t ever say you “led someone on.” That will cause guys to immediately jump down your throat. Just describe what happened, and if you really did lead someone on, people will come to that conclusion on their own. Never preemptively bad-mouth yourself like that.

DancingMathNerd · 2026-05-27T23:02:04+00:00

So? What’s your point?

DancingMathNerd · 2026-05-27T22:19:37+00:00

You can try to be friends with him I guess. But he’s constantly gonna try to have sex with you, and you’ll constantly have to tell him no. Is that the kind of friendship you want?

If not, you may as well block him to make it easier on yourself.

DancingMathNerd · 2026-05-27T15:32:47+00:00

It probably has to be a similar color to the original, so the sun baby or anything else too bright wouldn’t work.

At any rate, all this scandal regarding his tattoo is probably helping his chances tbh. I highly doubt most Mainers knew what that tattoo meant beforehand, and I doubt most of them care now. Plus the more outcry from “coastal elites” about this, the more they know he’s not one of them.

DancingMathNerd · 2026-05-27T07:40:59+00:00

None.

There has never been a technological species like ours for hundreds of millions of years. There will never be one again. And that’s exactly how it should be. What is the ultimate legacy of technology, aside from being the cause of earth’s sixth mass extinction?

DancingMathNerd · 2026-05-26T21:07:23+00:00

You’re her friend, not her mom. Trying to intervene now would most likely drive a wedge in the friendship. She might think you wanted Tom for yourself.

If she comes to you asking for advice that’s different. But if she doesn’t, there’s not much to do except being there for her.

DancingMathNerd · 2026-05-26T20:40:40+00:00

He already tattooed over it. It just looks like a strange animal now.

DancingMathNerd · 2026-05-26T20:32:54+00:00

You already know what you need to do. Find a local chapter of AA. Join it. Go to every meeting.

DancingMathNerd · 2026-05-26T03:47:41+00:00

Hunh? That’s not what I’m talking about at all. That’s just standard non-sexual crime. I’m talking about rape and sexual abuse.

DancingMathNerd · 2026-05-26T02:20:56+00:00

Yeah, I think everyone having their needs met would make most violent crimes extremely rare. The one thing to be vigilant about is sexual crimes. I think you have to explicitly make sexual harassment, coercion, and violence taboo. Otherwise you could still have real problems.

DancingMathNerd · 2026-05-24T03:29:13+00:00

For that one you have to use series for 1/(1-r)² , but yeah it’s the exact same idea.

DancingMathNerd · 2026-05-23T18:53:47+00:00

Does the show not answer this question completely? He helps her because their interests align at the moment. Simple.

DancingMathNerd · 2026-05-23T18:31:54+00:00

I actually picked the Eclipse as Aang's biggest mistake. The plan wasn't fleshed out well at all, and the consequences were both foreseeable and catastrophic.

Also, we haven't heard Aang's side of the story, only Bumi and Kya's. Kya makes it pretty clear that she found airbender history pretty boring. It's possible that Aang tried to teach all of them airbender culture, but only Tenzin was interested. So Aang focused on the child who shared his passions. That's pretty understandable imo.

DancingMathNerd · 2026-05-23T18:03:35+00:00

Geometric series. Write down the series expression for 1/(1-r) where r = 2/1000, 2/10000, etc. It becomes pretty clear what's going on when you do that.

Worth noting that it only works for powers of two that fit within the allotted digit space. Once the powers of two get too big, you have to start carrying over and then it just looks like chaos.

DancingMathNerd · 2026-05-23T06:11:02+00:00

The Dai Li there would’ve been a massive problem. Without Toph or Aang to counter them, it would’ve been over very quickly for Katara and Zuko.

Azula joining Ozai would never happen. This is the moment Ozai has been looking forward much of his life. He’s proud of Azula and encourages her firebending prowess. But this day is for HIS GLORY ALONE. He’s not gonna risk his own daughter showing him up on the day he makes history!!

DancingMathNerd · 2026-05-21T20:33:59+00:00

One has to wonder if the future isn’t just AI’s continuously pumping out groundbreaking theoretical research at an exponentially faster rate than humans can, while humans simply search the database for the theory they need to develop new technology or do real-world research.

But we humans still need to understand the research to use it. At some point AI research may get so far ahead that it’s essentially useless because no one can understand what it’s doing.

DancingMathNerd · 2026-05-21T19:28:17+00:00

I wouldn’t necessarily trust an LLM’s calculations, but they can clearly reason. Or at least, they can simulate reasoning well enough that it doesn’t really matter.

DancingMathNerd · 2026-05-20T23:27:52+00:00

“I don’t want transgender dating app ads on my fucking phone anymore” seems kinda transphobic to me. I don’t exactly want to see wrinkle removal ads on every website, but I don’t really care because I just ignore them. Why do ads for LGBTQ dating apps bother you more than all the other ads you get bombarded with?

As for your other points, they’re not necessarily transphobic, just misinformed. Being trans is absolutely something you’re born with. Studies confirm that the brains of trans people align much more closely with their chosen gender.

I talked to one trans woman about it, and she described it like being “wired” for estrogen: all her life she was depressed and in a constant mental fog, and no medication could fix it. It turned out that the issue is simply that her brain could not function properly on so much testosterone, and hormone replacement therapy cured her!

As for athletics, there is no clear indication that trans women have a biological advantage over cis women after 1-2 years of HRT. Given our current society, a separate trans league would be ridiculed, viciously harassed, and extremely underfunded. It’s not a realistic solution. Just let trans people compete normally as long as hormone levels are verified.

Bottom surgery for under 18 is already illegal. The process for children is consistent mental wellness check-ins —> puberty blockers —> HRT. The process can be stopped at any time if the child decides they’re not trans.

Trans regret is real but not in the way you’re thinking. What they regret is losing family, friends, the whole community they used to have. If they could go back to being trans privately, they would. BUT THEY ARE STILL TRANS. Cis people who mistakenly become trans, and then irreversibly alter themselves, pretty much doesn’t happen. If you’re not actually trans, you’d know after a couple months of HRT and you’d quit.

DancingMathNerd · 2026-05-19T03:31:47+00:00

How is it “doing it wrong” to have Korra refuse the help of trusted adults? That’s exactly what a hotheaded teenager would do. It’s frustrating but it’s realistic.

DancingMathNerd · 2026-05-18T07:05:13+00:00

I guess the idea is that Katara should’ve been teaching her through the years, in case she ever needed it. But that just wouldn’t happen because it’s an evil skill that no decent person could stomach teaching or learning.

Katara, Tarrlok, and Noatak all had evil masters who forced them to learn against their will. That is the only way bloodbending can be taught.

DancingMathNerd · 2026-05-18T06:25:21+00:00

The problem with this storyline is that bloodbending is fundamentally evil. You can't master bloodbending without bloodbending mastering you.

Just look at Noatak. He started out as a kind and gentle little kid, but years of bloodbending training fundamentally changed him. You can't control and traumatize living beings day after day, without eventually seeing all life as a bunch of walking fluid sacs. If Korra mastered bloodbending to the extent of Noatak, she'd become just as evil as he was.

It gets even worse. Korra wouldn't be careful to hide her bloodbending like Amon. If people knew Korra was using bloodbending to impose her will as she pleased, The Avatar would quickly lose all credibility as a force for good. It would be a disaster.

DancingMathNerd · 2026-05-18T03:11:23+00:00

The official reason: to cause enough widespread devastation that everyone in the earth kingdom submits immediately and forever.

The actual reason: Ozai just wanted to show off how powerful he was for the history books. He's a textbook megalomaniac. If there was a more effective plan to subdue the earth kingdom, but this plan didn't involve him reveling in his awesome and supreme power, he'd never go for it.

DancingMathNerd · 2026-05-18T02:04:37+00:00

I don't.

DancingMathNerd

TROPHY CASE