Big O notation by Ciro Santilli 40 Updated 2025-07-16
Module bound above, possibly multiplied by a constant:
is defined as:
E.g.:
  • . For , is enough. Otherwise, any will do, the bottom line will always catch up to the top one eventually.
The Sims by Ciro Santilli 40 Updated 2025-07-16
A young Ciro Santilli really liked this game, the way it makes you feel.
RSA (cryptosystem) by Ciro Santilli 40 Updated 2025-07-16
Based on the fact that we don't have a P algorithm for integer factorization as of 2020. But nor proof that one does not exist!
The private key is made of two randomly generated prime numbers: and . How such large primes are found: how large primes are found for RSA.
The public key is made of:
Given a plaintext message m, the encrypted ciphertext version is:
c = m^e mod n
This operation is called modular exponentiation can be calculated efficiently with the Extended Euclidean algorithm.
The inverse operation of finding the private m from the public c, e and is however believed to be a hard problem without knowing the factors of n.
However, if we know the private p and q, we can solve the problem. As follows.
First we calculate the modular multiplicative inverse. TODO continue.
This is one of the most canonical examples of "Cult leader Jesus tries to divert faith from an old religion into his own".
Trinity (nuclear test) by Ciro Santilli 40 Updated 2025-07-16
Plutonium-based.
Its plutonium was produced at Hanford site.
Video 1.
Trinity Test Preparations by AtomicHeritage (2016)
Source. Appears to be a compilation of several videos, presumably each with their own separate LA-UR, though these are not noted. Credited: "Video courtesy of the Los Alamos National Laboratory Archives", TODO how to search that archive online?
Video 2.
Trinity: Getting The Job Done
. Source. Good video, clarifies several interesting technical points:
Turing machine by Ciro Santilli 40 Updated 2025-07-16
The dominating model of a computer.
The model is extremely simple, but has been proven to be able to solve all the problems that any reasonable computer model can solve, thus its adoption as the "default model".
The smallest known Turing machine that cannot be proven to halt or not as of 2019 is 7,918-states: www.scottaaronson.com/blog/?p=2725. Shtetl-Optimized by Scott Aaronson is just the best website.
A bunch of non-reasonable-looking computers have also been proven to be Turing complete for fun, e.g. Magic: The Gathering.

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