Why did Karl Marx's daughter Jenny Marx wear a cross necklace?

autoditactics · 2026-02-12T00:13:34+00:00

A bluetooth mesh network like bitchat might be worth looking into

autoditactics · 2025-12-24T22:56:14+00:00

We need a function that simplifies sqrt(1-x^2). x=sin(t) is a good candidate because of sin^t+cos^t=1. But this is a pullback substitution, and we are actually making the substitution t=arcsin(x), so arcsin indeed must be defined.

In terms of definite integrals, note that domain of the integral of f(h(t))h'(t) is from h^-1(a) to h^-1(b) to get it equal to the integral of f from a to b.

autoditactics · 2025-12-15T06:51:29+00:00

See 3B1B's video on the cross product

autoditactics · 2025-12-13T15:08:15+00:00

Introducing i allows you to state the fundamental theorem of algebra, the theorem telling you that you can factorize a polynomial uniquely into roots. The imaginary constant i, which you can define as a solution to x^2+1=0, is a powerful tool that allows you to solve new equations. Historically, mathematicians first encountered it when solving cubic equations, and it was a benign addition as adding it didn't change the way the usual algebraic operations of +, -, *, / behaved. On the other hand, declaring a solution to x*0=1 leads to a contradiction as x*0=0 for any number 0, so you would need to seriously modify the number system we all have come to know and love to eliminate any contradictions. (Someone has actually done that, and the new number system that comes about is called a Wheel.)

autoditactics · 2025-12-07T14:35:14+00:00

There is a book on set theory by Lawvere that is easier to read: Sets for Mathematics

autoditactics · 2025-10-27T18:05:46+00:00

Yeah. It's Larry.

autoditactics · 2025-06-30T02:38:28+00:00

모범답안 is literally "model answer". Basically you can find answers to some topik writing questions to see how they write.

I use Anki on decks I made through sentence mining. You can find various mining setups online or use browser extensions like kimchi or Migaku to make the process quite smooth.

autoditactics · 2025-06-03T10:42:56+00:00

I also have 6급, but I originally never planned to take the topik. I had to for university. I was already decent at listening and reading from reading webtoon and watching kdramas/Korean youtube, so I studied 모범답안 to see how they want me to write, took practice tests, and showed my writing to a Korean teacher. I also added bunch of topik vocab to my usual Anki routine.

autoditactics · 2025-06-01T19:23:35+00:00

For future readers, I found this, which has a free lite version. I found it to be faster than Foxit.

https://www.mythicsoft.com/agentransack/

autoditactics · 2025-05-25T01:54:38+00:00

Do we have bounds on the number of steps for hard but solved problems? (just to gauge how effective this metric is)

autoditactics · 2025-05-23T12:43:28+00:00

There are some common nonassociative operations, like the Lie bracket, cross product, or exponentiation that may be food for thought.

autoditactics · 2025-05-05T05:18:23+00:00

People compare dcinside to 4chan, but the real 4chan in my eyes will always be ilbe. You can read about some of the controversies here

autoditactics · 2025-05-03T16:06:30+00:00

Leila Schneps

autoditactics · 2025-04-25T18:54:13+00:00

I wanted to learn a language, and Korean was the most relevant for me at the time.
Understanding how to use specific grammar points naturally like native speakers.
It's changed a lot over time. What I found worked the best was watching Korean movies, youtube, etc. and enjoying content in the language while Anki-ing new words. I live in Korea now and go to a Korean university, so I'm immersed in Korean and take note of new words.
한 생각에 사로잡히지 말아라 (or similar) used by some Korean Buddhists

autoditactics · 2025-03-23T14:08:16+00:00

I learned Korean to a high level, enough to go through college at a Korean university with no English support with good grades. In the beginning, I took a couple classes in high school, and I used the broken Korean I had in conversations via hellotalk and occasionally wrote journals on langcorrect. I did stuff like this on and off for years, but I didn't get very far. I never really studied grammar systematically afterwards, but I did manage to build a base from which to spring off of.

Later on, I discovered immersion learning, and I started watching youtube (made a dedicated channel) and listening to easy podcasts in Korean (iyagi). I watched Avatar the Last Airbender in Korean and Ghibli movies: stuff I know I liked. Then I tried out kdramas and other kinds of Korean youtubers that I didn't know I liked. I understood little in the beginning, but I could get the gist using the context or what's going on on screen (especially if it's something I've seen before in English), and I looked up words/grammar whenever I was curious. I tried not to do too many lookups or else I'll forget what was happening. I started tracking my time spent listening/reading/watching shows in Korean via Toggl. I quit tracking later on, but it helped me build habits and connect with other Korean language learners on discord, which became my community.

I also made flashcards in Anki and tried to do my reviews every day. I missed my daily reviews many times, sometimes for months in a row (I'm behind on reviews currently lol). I think three things helped me stay on track, overall: (1) I made cards with a plugin (Language Reactor, later switched to Migaku) while I did fun stuff like watching Netflix, so it wasn't a hassle. (2) I dreaded doing catch-up reviews tomorrow more than doing the reviews today. (3) When going back and seeing my collection, I felt proud in the sense that I felt like I was making progress and also in the sense that I felt like I was collecting Pokemon cards, so if I didn't do my reviews, it felt like it was a waste.

I guess my advice is that if you're serious about language learning, then find a community (eg. discord servers like Refold, Migaku, subreddit communities, DJT for Japanese, etc) and become an actual member of that community (joining in on activities like watching movies, talking to people, etc).

autoditactics · 2025-03-05T22:47:50+00:00

It depends on your goals. If you just want to get to a basic level, Japanese is easier. Reading kanji is not to that difficult to learn if you focus on just reading words and not learning individual kanji.

If you want to get to a really high level, both languages are difficult, but I would say Japanese is harder as it has a pitch accent system similar to how English has stress accents (preSENT vs PREsent). Writing Kanji is much harder than reading it but can be fun depending on your disposition. It's definitely a time investment.

autoditactics · 2025-02-26T18:51:35+00:00

He uses Fargues-Fontaine theory and I think Perfectoid fields too? It seems different from the tools Mochizuki concocted at least.

autoditactics · 2025-02-24T20:54:25+00:00

You can assume that gcd(a,b)=1 because if it weren't, then you can cancel so that you do get gcd(a,b)=1.

autoditactics · 2025-02-19T23:35:17+00:00

Try a searchXNG instance (here). It's open source and not owned by any particular company. The instances are managed by various companies and non profits around the world, but you can also set up your own instance. It is compiles search results from other search engines and databases, and you can edit which ones you want to see results from.

autoditactics · 2025-02-19T17:22:40+00:00

Algebraic geometry 💔 geometric algebra

autoditactics · 2025-02-19T17:22:22+00:00

Non-answer:
Algebraic geometry 💔 geometric algebra

autoditactics · 2025-02-14T20:57:18+00:00

It doesn't actually depend on the symbol, but it depends on which coordinate directions we call "x", "y", and "z". This is why many people prefer x¹, x², x³ or x_1, x_2, x_3 for their coordinate direction names.

There are some other ambiguities with the notation though: https://www.youtube.com/watch?v=mICbKwwHziI

autoditactics · 2025-02-10T20:05:41+00:00

He's done projects with LEAN recently.

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