In the context of invariant theory, the term "covariant" refers to certain mathematical objects or functions that transform in a specific way under changes of coordinates or transformations. Invariant theory, broadly speaking, deals with questions about which properties of geometric objects remain unchanged (invariant) under group actions or transformations, usually from a linear algebra setting.
Gao Qiu by Ciro Santilli 40 Updated 2025-07-16
The ball game is named cuju.
He is extremely despicable and petty, enjoys only useless things, and is vengeful and disloyal. Rooting for sport teams is stupid.
Surely his family name 俅 is a pun on the same sounding character 求 for ball.
Lin Chong scene by Ciro Santilli 40 Updated 2025-07-16
Lance instructor of the 800,000 Imperial Guards (八十万禁军枪棒教头). TODO understand the "枪棒" part: zhidao.baidu.com/question/206659649.html.
The adopted son of Gao Qiu wanted to fuck his wife, and because of this they frame him of planning to take revenge by killing Go Qiu, even though Lin Chong had decided not to take revenge to avoid harming his wife further.
They just keep trying to kill him, until at one point he just gives up and becomes a fugitive.
His story is well told in The Water Margin.
Usually called by others as 林教头 (lin jiaotou, literally Head Instructor Lin, but usually translated as just Instructor Lin).
Once upon a time, this must have been a nice covered market.
But as of 2020, it is completely surrounded by extremely poor people, to the point that it makes you scared if you stand out in any way by showing any kind of middle/upper class wealth, or being a foreigner.
The market is basically a touristic spot that no person in Sao Paulo will ever go to (unless they are young, single, and can just walk in there by themselves) in the middle of this surreal environment.
In 2020 Ciro was there with his wife on a touristic visit. Living in Europe at the time, he felt even more privileged. So they went to a fruit stand, and the man started giving his wife amazing free samples of very exotic fruit, some of which Ciro had never tasted himself, without saying the price. It did feel like he was giving out too much for free. Then Ciro decided of course to buy some more fruits to pay for the show, which was a nice show. Then while buying, it came out a bit more expensive than would have been reasonable, but Ciro was too dazzled by the speed and noises, and he paid for it. Later on, he told his wife about it, and how he felt that they had added some ultra-expensive bulk fruits that were of a clearly lower level than the gold nuggets of the free samples (especially for Brazil's cost standards). The presenter was an extremely crafty con artist, and Ciro felt like they had specifically preyed on Ciro Santilli's self perceived compassionate personality, because it was apparent that those men were underprivileged and fighting for their living day by day with those over-expensive fruits. This was an extremely valuable lesson, Ciro was glad that it was learnt at a relatively low cost on that occasion.
He used to train the 800,000 imperial guard troops at the Capital, much like Lin Chong. He's not one of the 108 Stars of Destiny.
Mount Liang by Ciro Santilli 40 Updated 2025-07-16
The term "Mount Liang" generally refers to both the mountain and the surrounding marshy areas.
The novel always uses the term "梁山泊' (liang2 shan1 po1) to refer to the place.
Video 1.
How did the Liangshan ponds form? by CCTV (2019)
Source. Chinese only, but still fun to see the real place.
As mentioned at hero108.fandom.com/wiki/The_108_Heroes there are only 3 women amongst the 108:
Another notable reference is in Lost Horse LLC, MacKenzie Bezos's charity instrument.
Breakdown:
  • 塞翁 sai4 weng1: TODO his name?
  • 失马 shi1 ma3: lost horse
  • 焉知 yan1 zhi1: who knows, literary
  • 非福 fei1 fu2: bad (or) good
Video 1.
Zen master and the little boy scene from Charlie Wilson's War
. Source. This is how Ciro Santilli first heard the old man lost his horse! The scene happens after the Americans seem to have had sucess in arming the Taliban in the 1980s to fight the Soviets, and then they decide to stop all monetary help to rebuild the country, which then leads to a terrorism threat many years later.
Video 2.
The Blessing of Bad Luck by Pursuit of Wonder (2022)
Source. A bit too long. But worth it.
Pu Songling by Ciro Santilli 40 Updated 2025-07-16
Sometimes you just know that your existence will be remembered for a singular reason. Better than not being remembered at all perhaps.
Big collection of a bunch of ghost stories. 90% of them involve some dude dating a beautiful ghost woman or animal that can shapeshift as a woman.
Organized into 12 chapeters as seen on the Chinese wiki: zh.wikipedia.org/wiki/聊齋志異#章節

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact