Rock music by Ciro Santilli 40 Updated 2025-07-16
Video 1.
Space Oddity by David Bowie (1969)
Source.
Video 2.
Stairway to Heaven by Led Zeppelin (1971)
Source.
Can be calculated efficiently with the Extended Euclidean algorithm.
The beauty of this algorithm is that because exponentiation grows really fast, there is no hope that we can ever learn all the digits of an exponential, as there is simply not enough time or memory for that. Therefore, a natural sub-question is if we can know some part of that number, and knowing the smallest digits is the most natural version of that question.
Figure 1. Source. This is a microscope, I kid you not. TODO photo of what you can see with it.
Electron microscope by Ciro Santilli 40 Updated 2025-07-16
All of them need a vacuum because you can't shoot elecrons through air, as mentioned at Video "50,000,000x Magnification by AlphaPhoenix (2022)".
Video 1.
Two Photon Microscopy by Nemonic NeuroNex (2019)
Source. Shows a prototype of a two-photon electron microscope on an optical table, and describes it in good detail, well done.
X-ray crystallography by Ciro Santilli 40 Updated 2025-07-16
One of its main applications is to determine the 3D structure of proteins.
Sometimes you are not able to crystallize the proteins however, and the method cannot be used.
Crystallizing is not simple because:
  • you need a considerable amount of the protein
  • sometimes it only crystallizes if you add some extra small chemical that stabilizes it
Cryogenic electron microscopy can sometimes determine the structures of proteins that failed crystallization.
Break the meta by Ciro Santilli 40 Updated 2025-07-16
To break the meta means to find a new strategy that offers a significant advantage over the existing meta.
Video 1.
How One Man Changed the High Jump Forever by Olympics (2018)
Source. Dick Fosbury created and implemented the Fosbury Flop jump style in 1968.
Video 2.
Akiyo Noguchi asks the rules while climbing! | Beta Break Ep.1 by Albert Ok (2020)
Source. Happened at the 2015 IFSC Climbing World Cup during the Haiyang, China, bouldering event. The author has a playlist of such climbing meta breaks. In climbing, the meta is called "the beta". Climbing competitions are perhaps the sport in which the meta is broken the most often, since each stage is unique.
Video 3.
Lukas Hofer's Revolutionary Technique by IBU TV (2019)
Source. Lukas created a new technique to pack up his rifle during biathlon competitions.
It is true that one image is worth a thousand words, but unfortunately it is also true that one image takes up at least as much bytes as a thousand words!
Having one single page to rule them all is of course the ideal setup for a website, as you can Ctrl + F one ToC and quickly find what you want.
And, with Linux Kernel Module Cheat Ciro noticed that it is very hard to write so much intelligent prose that becomes larger than reasonable to load on a single webpage.
He then started using this technique for everything he writes, including this page and Chinese government.
However, if there are too many images on the page, the loading of the last images would take forever in case users want to view the last sections.
There are two solutions to that:
Ciro is still deciding between those two. The traditional approach works for sure but loses the one page to rule them all benefits.
The innovative approach will work for interactive viewing, but archive.org will fail to load the images for example, and there may be other unforseen consequences.
Wikimedia Commons is awesome and automatically converts and serves smaller versions of images, so always choose the smallest images size needed by the output document. Readers can then find the higher resolution versions by following the page source.
This also comes to mind: motherfuckingwebsite.com
zettelkasten.de/posts/overview/ from zettelkasten:
How many Zettelkästen should I have? The answer is, most likely, only one for the duration of your life. But there are exceptions to this rule.
Where to store images by Ciro Santilli 40 Updated 2025-07-16
Since images are large, they bring the following challenges:
  • keeping images in the main Git repository with text content makes the repository huge and slow to clone, and should not be done
  • storing and serving images could cost us, which we want to avoid
To solve those problems, the following alternatives appear to be stable enough and should be used decreasing preference:
The following do have direct links:
3Blue1Brown by Ciro Santilli 40 Updated 2025-07-16
Amazing graphs and formulas.
Python graphics engine open sourced at: github.com/3b1b/manim "Animation engine for explanatory math videos". But for some reason there is a community fork: github.com/ManimCommunity/manim/ "This repository is maintained by the Manim Community, and is not associated with Grant Sanderson or 3Blue1Brown in any way (though we are definitely indebted to him for providing his work to the world). If you want to study how Grant makes his videos, head over to his repository (3b1b/manim). This is a more frequently updated repository than that one, and is recommended if you want to use Manim for your own projects." what a mess.
MathDoctorBob by Ciro Santilli 40 Updated 2025-07-16
He got so old from 2012 to 2021 :-)
This dude did well. If only he had written a hyperlinked wiki rather than making videos! It would allow people to jump in at any point and just click back. It would be Godlike.
mathdoctorbob.org/About.html says:
Robert Donley received his doctorate in Mathematics from Stony Brook University and has over two decades of teaching experience at the high school, undergraduate, and graduate levels.

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 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.
  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