A Ring can be seen as a generalization of a field where:
- multiplication is not necessarily commutative. If this is satisfied, we can call it a commutative ring.
- multiplication may not have inverse elements. If this is satisfied, we can call it a division ring.
The simplest example of a ring which is not a full fledged field and with commutative multiplication are the integers. Notably, no inverses exist except for the identity itself and -1. E.g. the inverse of 2 would be 1/2 which is not in the set. More specifically, the integers are a commutative ring.
The simplest non-commutative, non-division is is the set of all 2x2 matrices of real numbers:Note that is not a ring because you can by addition reach the zero matrix.
- we know that 2x2 matrix multiplication is non-commutative in general
- some 2x2 matrices have a multiplicative inverse, but others don't
These are apparenty an important part of transcriptional regulation given the number of modifications they can undergo! Quite exciting.
Ciro Santilli's bad old event memory by 
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01Ciro Santilli has a bad memory for events that happened a medium time ago, for example in order of months/years. Especially if they are one-off things that have no relation to anything else.
For example, Ciro never remembers which places he travelled to just once, and who was in each trip! He has images of several places he travelled to in his head, and would recognize them, but he just doesn't know where they were!
Another example, Ciro was looking at the carpet at their house, and asked where it came from. His wife replied immeidately: from Bercy shopping quarter in Paris about 10 years ago, and you took it on your back for a long walk until we could find the bus back home because we were concerned it wouldn't fit in the train!
The same goes for scenes from movies and passages from music, which explains why Ciro's art consumption focuses on innovative discrete "what happened" and "general gist" ideas, rather than, analog details such as colors and shapes.
Going back even further in time, Ciro starts to forget the less close friends he had, because the events start to fade away.
Paradoxically however, Ciro believes that this bad memory is one of his greatest strengths and key defining characteristics, because it leads Ciro to want to write down every interesting thing he learns, which motivated OurBigBook.com and his Stack Overflow contributions and his related Ciro Santilli's documentation superpowers.
It also somewhat leads Ciro to like physics and mathematics, because in these fields you "can deduce everything" from very few base principles, so if you forget them, it does not matter that much as you can re-deduce stuff over and over. Which is somewhat where the high flying bird attitude comes from. It is hard to go deep when you have to re-prove everything every time. But the upside is that anything that sticks, does so because it has a broad net to stick to, and therefore allows Ciro to make unusual and unexpected connections that others might not.
Ciro believes that there are two types of people, and most notably software engineers, which are basically data wranglers: those with bad memory and those with good memory.
Those with bad memory, tend to focus on automating and improving their processes a lot. They take much longer to do one-off specific deep knowledge tasks however.
The downside of the good memory ones is that sooner or later they will find tasks that no matter how much memory they have, they cannot solve without automation, and they will fail at those.
This dichotomy also explains why Ciro sucks at code reviews, but is rather the person who runs the interesting patches by himself and finds some critical problems that the more theoretical code reviewers missed.
If Ciro had become a scientist, he would without doubt be an experimentalist, just like in this reality he is a GDB/runtime person rather than a "static source analysis" person. Those who have bad memory prefer to just run experiments over and over and observe system state at runtime.
Other effects of having a bad memory include:
- code duplication, or a constant fear of it at least, because Ciro forgets that some functionality exists already
- meeting aversion, because everything that is not recorded will fade away
- passion for backward design, because by the time a piece of knowledge learnt in school might be useful (and 99.99% won't), it will have been long forgotten
Related: jakobschwichtenberg.com/about/ from Jakob Schwichtenberg:
In some sense, one of the biggest benefits I have over other people in physics is that I'm certainly not the smartest guy! I usually can't grasp complex issues very easily. So I have to break down complex ideas into smaller chunks to understand it myself. This means, whenever I describe something to others, everyone understands, because it's broken down into such simple terms.
On C2 wiki, therefore it cannot be wrong wiki.c2.com/?QuasiGreatTeacher:
Pinned article: ourbigbook/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!
Intro to OurBigBook
. Source. We have two killer features:
- 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-calculusArticles 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/derivativeVideo 2. OurBigBook Web topics demo. Source. - 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.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
Figure 5. . 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. 
- Infinitely deep tables of contents:
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