Ciro Santilli @cirosantilli 35

 Incoming links: Binary search tree

 Home  Updated 2025-02-22  +Created 1970-01-01

Check out: OurBigBook.com, the best way to publish your scientific knowledge. It's an open source note taking system that can publish from lightweight markup files in your computer both to a multi-user mind melding dynamic website, or as a static website. It's like Wikipedia + GitHub + Stack Overflow + Obsidian mashed up. Source code: github.com/ourbigbook/ourbigbook.

Sponsor me to work on this project: 100k USD = I quit me job and work on it one year full time. Status: ~144k / 200k USD reached: 1st year locked-in, 2nd year stretch goal open at 200k USD. 1M USD = I retire and do it forever. How to donate: Section "Sponsor Ciro Santilli's work on OurBigBook.com".

I reached 100k USD after a 1000 Monero donation, so I quit my job for 1 year starting 1st June 2024 to solve as many STEM courses as I can from a world leading university to try and kickstart The Higher Education Revolution. If I reach 200k USD, then I'll do it for two years instead. A second year greatly improve chances of success: year one I solve a bunch of courses, year two I come guns blazing with the content and expand further.

Mission: to live in a world where you can learn university-level mathematics, physics, chemistry, biology and engineering from perfect free open source books that anyone can write to get famous. More rationale: Section "OurBigBook.com"

Explaining things is my superpower, e.g. I was top user #39 on Stack Overflow in 2023^[ref]^[ref] and I have a few 1k+ star educational GitHub repositories^[ref]^[ref]^[ref]^[ref]. Now I want to bring that level of awesomeness to masters level Mathematics and Physics. But I can't do it alone! So I created OurBigBook.com to allow everyone to work together towards the perfect book of everything.

My life's goal is to bring hardcore university-level STEM open educational content to all ages. Sponsor me at github.com/sponsors/cirosantilli starting from 1$/month so I can work full time on it. Further information: Section "Sponsor Ciro Santilli's work on OurBigBook.com". Achieving what I call "free gifted education" is my Nirvana.

This website is written in OurBigBook Markup, and it is published on both cirosantilli.com (static website) and outbigbook.om/cirosantilli (multi-user OurBigBook Web instance). Its source code is located at: github.com/cirosantilli/cirosantilli.github.io and also at cirosantilli.com/_dir and it is licensed under CC BY-SA 4.0 unless otherwise noted.

To contact Ciro, see: Section "How to contact Ciro Santilli". He likes to talk with random people of the Internet.

https://raw.githubusercontent.com/cirosantilli/media/master/ID_photo_of_Ciro_Santilli_taken_in_2013.jpg

Besides that, I'm also a freedom of speech slacktivist and recreational cyclist. I like Chinese traditional music and classic Brazilian pop. Opinions are my own, but they could be yours too. Tax the rich.

Let's create an educational system with:

no distinction between university and high school, students just go as fast as they can to what they really want without stupid university entry exams
fully open source learning material
on-demand examinations that anyone can easily take without prerequisites
granular entry selection only for space in specific laboratories or participation in specific novel research projects

I offer:

online private tutoring for:
- any STEM university course
- passionate younger STEM students (any age) who want to learn university level material and beyond. Can your kid be the next Fields Medalist or Nobel Prize winner? I'm here to help, especially if you are filthy rich! I focus moving students forward as fast as they want on and on producing useful novel tutorials and results
Let your child be my Emile, and me be their Adolfo Amidei, and let's see how far they can go! I will help take your child:
- into the best universities
- into the best PhD programs
and achieve their ambitious STEM goals!
educational consulting for institutions looking to improve their STEM courses
- do you know that course or teacher that consistently gets bad reviews every year? I'll work with the teacher to turn the problem around!
- are you looking to create a consistent open educational resources offering to increase your institutions internationally visibility? I can help with that too.

My approach is to:

propose interesting research projects. The starting point is always deciding the end goal: Section "Backward design"
learn what is needed to do the project together with the student(s)
publish any novel results or tutorials/tools produced freely licensed online, and encourage the student to do the same (Section "Let students learn by teaching", digital garden)

For minors, parents are welcome to join video calls, and all interactions with the student will be recorded and made available to parents.

I have a proven track of explaining complex concepts in an interesting and useful way. I work for the learner. Teaching statement at: Section "How to teach". Pricing to be discussed. Contact details at: Section "How to contact Ciro Santilli".

I am particularly excited about pointing people to the potential next big things, my top picks these days are:

I am also generally interested in:

20th century physics, notably AMO and condensed matter
the history of science, and in particular trying to look at seminal papers of a field

Figure 1.

Ciro Santilli's amazing Stack Overflow profile

. Ciro contributes almost exclusively by answering question he Googles into out of his own need, and never by refreshing the newest question of big tags for low hanging fruit! More information at: Section "Ciro Santilli's Stack Overflow contributions".

Figure 2.
Ciro Santilli's Stack Overflow stats
. Further methodology details at: Figure "Ciro Santilli's Stack Overflow stats".

Video 1.

Introduction to the OurBigBook Project

. Source.

Video 2.

OurBigBook Web topics demo

. Source. The OurBigBook topic feature allows users to "merge their minds" in a "sort by upvote"-stack overflow-like manner for each subject. This is the killer feature of OurBigBook Web. More information at: docs.ourbigbook.com/ourbigbook-web-topics.

Video 3.

OurBigBook dynamic article tree demo

. Source. The OurBigBook dynamic tree feature allows any of your headers to be the toplevel h1 header of a page, while still displaying its descendants. SEO loves this, and it also allows users to always get their content on the correct granularity. More information at: docs.ourbigbook.com/ourbigbook-web-dynamic-article-tree.

Video 4.

OurBigBook local editing and publishing demo

. Source. With OurBigBook you can store your content as plaintext files in a Lightweight markup, and then publish that to either OurBigBook.com to get awesome multi-user features, or as a static website where you are in full control. More information at: docs.ourbigbook.com/publish-your-content.

Video 5.

Top Down 2D continuous game with Urho3D C++ SDL and Box2D for Reinforcement learning by Ciro Santilli (2018)

Source. More information: Section "Ciro's 2D reinforcement learning games". This is Ciro's underwhelming stab at the fundamental question: Can AGI be trained in simulations?. This project could be taken much further.

Video 6.

Water Margin tribute to Chinese dissidents by Ciro Santilli (2022)

Source. Part of Ciro Santilli's campaign for freedom of speech in China, see also: cirosantilli.com/china-dictatorship/water-margin.

Figure 3.
Lenovo ThinkPad T430 running a BIOS hello world
. Source code: github.com/cirosantilli/x86-bare-metal-examples. Ciro's Linux Kernel Module Cheat is a closely related and much more important project that covers the Linux kernel and assembly language.

Video 7.

My Bitcoin inscription museum by Ciro Santilli

. Source. Introductory video to Section "Cool data embedded in the Bitcoin blockchain".

 -------------------------------------
|  Force of Will               3 U U  |
|  ---------------------------------  |
| |                  ////////////   | |
| |                ////() ()\////\  | |
| |               ///_\ (--) \///\  | |
| |        )      ////  \_____///\\ | |
| |       ) \      /   /   /    /   | |
| |    ) /   \     |   |  /   _/    | |
| |   ) \  (  (   /   / /   / \     | |
| |  / ) ( )  / (    )/(    )  \    | |
| |  \(_)/(_)/  /UUUU \  \\\/   |   | |
| .---------------------------------. |
| Interrupt                           |
| ,---------------------------------, |
| | You may pay 1 life and remove a | |
| | blue card in your hand from the | |
| | game instead of paying Force of | |
| | Will's casting cost.  Effects   | |
| | that prevent or redirect damage | |
| | cannot be used to counter this  | |
| | loss of life.                   | |
| | Counter target spell.           | |
| `---------------------------------` |
|                                     l
| Illus.  Terese Nelsen               |
 -------------------------------------

Code 1.

ASCII art of a Force of Will Magic: The Gathering card inscribed in the Bitcoin blockchain

Artist unknown, uploaded December 2014. Part of Section "Cool data embedded in the Bitcoin blockchain" where Ciro Santilli maintains a curated list of such interesting inscriptions.

This was a small project done by Ciro for artistic purposes that received some attention due to the incredible hype surrounding cryptocurrencies at the time. Ciro Santilli's views on cryptocurrencies are summarized at: Section "Are cryptocurrencies useful?".

Figure 4.
`YellowRobot.jpg`
. Source.
JPG image fully embedded in the Bitcoin blockchain depicting some kind of cut material art depicting a yellow robot, inscribed on January 29, 2017.
Ciro Santilli found this image and others during his research for Section "Cool data embedded in the Bitcoin blockchain" by searching for image fingerprints on every transaction payload of the blockchain with a script.
The image was uploaded by EMBII, co-creator of the AtomSea & EMBII upload mechanism, which was responsible for a large part of the image inscriptions in the Bitcoin blockchain.
The associated message reads:
Chiharu [EMBII's Japanese wife] and I found this little yellow robot while exploring Chicago. It will be covered by tar or eventually removed but this tribute will remain. N 41.880778 E -87.629210
This is one of Ciro Santilli's favorite AtomSea & EMBII uploads, as it perfectly encapsules the "medium as an art form" approach to blockchain art, where even non-novel works can be recontextualized into something interesting, here depicting an opposition between the ephemeral and the immutable.
At twitter.com/EMBII4U/status/1615389973343268871 EMBII announced that he would be giving off shares of that image on Sup!?, a Bitcoin-backed NFT system he was; making. In December 2023, he gave some shares of the robot to Ciro Santilli.

Figure 5.
2010 Wayback Machine archive of starwarsweb.net
.
This website was used as one of the CIA 2010 covert communication websites, a covert system the CIA used to communicate with its assets. More details at: Section "CIA 2010 covert communication websites".
Ciro Santilli had some naughty OSINT fun finding some of the websites of this defunct network in 2023 after he heard about the 2022 Reuters report on the matter, which for the first time gave away 7 concrete websites out of a claimed 885 total found. As of November 2023, Ciro had found about 350 of them.

Figure 6.
2010 Wayback Machine archive of noticiasmusica.net
.
This is another website that was used as one of the CIA 2010 covert communication websites. This website is written in Brazilian Portuguese, and therefore suggests that the CIA had assets in Brazil at the time, and thus was spying on a "fellow democracy".
Although Snowden's revelations made it extremely obvious to the world that the USA spies upon everyone outside of the Five Eyes, including fellow democracies, it is rare to have such a direct a concrete proof of it visible live right on the Wayback Machine. Other targeted democracies include France, Germany, Italy and Spain. More details at: USA spying on its own allies.

Video 8.

How I found a Star Wars website made by the CIA by Ciro Santilli

. Source. Slightly edited VOD of the talk Aratu Week 2024 Talk by Ciro Santilli: My Best Random Projects about the CIA 2010 covert communication websites.

Figure 7.
Diagram of the fundamental theorem on homomorphisms by Ciro Santilli (2020)

Shows the relationship between group homomorphisms and normal subgroups.
Used in the Stack Exchange answer to What is the intuition behind normal subgroups? One of Section "The best articles by Ciro Santilli".

Figure 8.
Spacetime diagram illustrating how faster-than-light travel implies time travel by Ciro Santilli (2021)
Used in the Stack Exchange ansewr to Does faster than light travel imply travelling back in time?. One of Section "The best articles by Ciro Santilli".

Figure 9.
Average insertion time into heaps, binary search tree and hash maps of the C++ standard library by Ciro Santilli (2015)
Source. Used in the Stack Overflow answer to Heap vs Binary Search Tree (BST). One of Section "The best articles by Ciro Santilli".

Video 9.

Birch and Swinnerton-Dyer conjecture in two minutes by Ciro Santilli

. Source. Quick and direct explanation of the statement of the BSD conjecture for people who know basic university mathematics. This is one of the Millennium Prize Problems, and you will get a million dollars if you can solve it! This therefore falls in the Simple to state but hard to prove of Ciro Santilli's the beauty of mathematics aesthetics.

A quick 2D continuous AI game prototype for reinforcement learning written in Matter.js, you can view it on a separate page at cirosantilli.com/_raw/js/matterjs/examples.html#top-down-asdw-fixed-viewport. This is a for-fun-only prototype for Ciro's 2D reinforcement learning games, C++ or maybe Python (for the deep learning ecosystem) seems inevitable for a serious version of such a project. But it is cute how much you can do with a few lines of Matter.js!

HTML snippet:

<iframe src="_raw/js/matterjs/examples.html#top-down-asdw-fixed-viewport" width="1000" height="850"></iframe>

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The best articles by Ciro Santilli  Updated 2025-02-22  +Created 1970-01-01

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These are the best articles ever authored by Ciro Santilli, most of them in the format of Stack Overflow answers.

Ciro posts update about new articles on his Twitter accounts.

A chronological list of all articles is also kept at: Section "Updates".

Some random generally less technical in-tree essays will be present at: Section "Essays by Ciro Santilli".

Trended on Hacker News:
- CIA 2010 covert communication websites on 2023-06-11. 190 points, a mild success.
- x86 Bare Metal Examples on 2019-03-19. 513 points. The third time something related to that repo trends. Hacker news people really like that repo!
  - again 2020-06-27 (archive). 200 points, repository traffic jumped from 25 daily unique visitors to 4.6k unique visitors on the day
- How to run a program without an operating system? on 2018-11-26 (archive). 394 points. Covers x86 and ARM
- ELF Hello World Tutorial on 2017-05-17 (archive). 334 points.
- x86 Paging Tutorial on 2017-03-02. Number 1 Google search result for "x86 Paging" in 2017-08. 142 points.
  Figure 1.
  BIOS bare metal hello world running on a Lenovo ThinkPad T430
  . Source.
x86 assembly
- What does "multicore" assembly language look like?
- What is the function of the push / pop instructions used on registers in x86 assembly? Going down to memory spills, register allocation and graph coloring.
Linux kernel
QEMU
gcc and Binutils:
- How do linkers and address relocation works?
- What is incremental linking or partial linking?
- GOLD (-fuse-ld=gold) linker vs the traditional GNU ld and LLVM ldd
- What is the -fPIE option for position-independent executables in GCC and ld? Concrete examples by running program through GDB twice, and an assembly hello world with absolute vs PC relative load.
- How many GCC optimization levels are there?
- Why does GCC create a shared object instead of an executable binary according to file?
C/C++: almost all of those fall into "disassemble all the things" category. Ciro also does "standards dissection" and "a new version of the standard is out" answers, but those are boring:
- What does "static" mean in a C program?
- In C++ source, what is the effect of extern "C"?
- Char array vs Char Pointer in C
- How to compile glibc from source and use it?
- When should static_cast, dynamic_cast, const_cast and reinterpret_cast be used?
- What exactly is std::atomic in C++?. This answer was originally more appropriately entitled "Let's disassemble some stuff", and got three downvotes, so Ciro changed it to a more professional title, and it started getting upvotes. People judge books by their covers.
- notmain.o 0000000000000000 0000000000000017 W MyTemplate<int>::f(int) main.o 0000000000000000 0000000000000017 W MyTemplate<int>::f(int)
  Code 1.
  nm outputs showing that objects are redefined multiple times across files if you don't use template instantiation properly
  . From: What is explicit template instantiation in C++ and when to use it?

IEEE 754

What is difference between quiet NaN and signaling NaN?
In Java, what does NaN mean?

Without subnormals:

          +---+---+-------+---------------+-------------------------------+
exponent  | ? | 0 |   1   |       2       |               3               |
          +---+---+-------+---------------+-------------------------------+
          |   |   |       |               |                               |
          v   v   v       v               v                               v
          -----------------------------------------------------------------
floats    *    **** * * * *   *   *   *   *       *       *       *       *
          -----------------------------------------------------------------
          ^   ^   ^       ^               ^                               ^
          |   |   |       |               |                               |
          0   |   2^-126  2^-125          2^-124                          2^-123
              |
              2^-127

With subnormals:

          +-------+-------+---------------+-------------------------------+
exponent  |   0   |   1   |       2       |               3               |
          +-------+-------+---------------+-------------------------------+
          |       |       |               |                               |
          v       v       v               v                               v
          -----------------------------------------------------------------
floats    * * * * * * * * *   *   *   *   *       *       *       *       *
          -----------------------------------------------------------------
          ^   ^   ^       ^               ^                               ^
          |   |   |       |               |                               |
          0   |   2^-126  2^-125          2^-124                          2^-123
              |
              2^-127

Code 2.

Visualization of subnormal floating point numbers vs what IEEE 754 would look like without them

. From: What is a subnormal floating point number?

Computer science
- Algorithms
  - Figure 5.
    Average insertion time into heaps, binary search tree and hash maps of the C++ standard library
    . Source. From: Heap vs Binary Search Tree (BST)
- Is it necessary for NP problems to be decision problems?
- Polynomial time and exponential time. Answered focusing on the definition of "exponential time".
- What is the smallest Turing machine where it is unknown if it halts or not?. Answer focusing on "blank tape" initial condition only. Large parts of it are summarizing the Busy Beaver Challenge, but some additions were made.

Git

  | 0           | 4            | 8           | C              |
  |-------------|--------------|-------------|----------------|
0 | DIRC        | Version      | File count  | ctime       ...| 0
  | ...         | mtime                      | device         |
2 | inode       | mode         | UID         | GID            | 2
  | File size   | Entry SHA-1                              ...|
4 | ...                        | Flags       | Index SHA-1 ...| 4
  | ...                                                       |

Code 3.

ASCII art depicting the binary file format of the Git index file

. From: What does the git index contain EXACTLY?

tree {tree_sha}
{parents}
author {author_name} <{author_email}> {author_date_seconds} {author_date_timezone}
committer {committer_name} <{committer_email}> {committer_date_seconds} {committer_date_timezone}

{commit message}

Code 4.

Description of the Git commit object binary data structure

. From: What is the file format of a git commit object data structure?

How do I clone a subdirectory only of a Git repository?

Python
- What is the difference between old style and new style classes in Python?
- What is a mixin in Python, and why are they useful?
- What are the differences between threads and processes in Python?
  Figure 6.
  Python Threads vs Processes with 8 hyperthreads
  . Source.
Web technology
- What does enctype='multipart/form-data' mean?
- JavaScript
  - How does JavaScript .prototype work?
  - What is the difference between .prop() vs .attr() in JavaScript?
OpenGL
- Figure 7.
  OpenGL rendering output dumped to a GIF file
  . Source. From: How to use GLUT/OpenGL to render to a file?
- Figure 8.
  Example of a texture atlas containing glyphs
  . Source.
  Image by Nicolas P. Rougier, author of Freetype GL.
  Used on Ciro Santilli's answer: How to draw text using only OpenGL methods?
- Figure 9.
  OpenGL glFrustrum vs glOrtho
  . Source. From: How to use glOrtho() in OpenGL?
- What are shaders in OpenGL?
- Why do we use 4x4 matrices to transform things in 3D?
- Figure 10.
  Sinusoidal circular wave heatmap generated with an OpenGL shader at 60 FPS on SDL
  . Source.
  From: Is it possible to build a heatmap from point data at 60 times per second?
  Compared CPU vs GPU shaders.
- Image Processing with GLSL shaders? Compared the CPU and GPU for a simple blur algorithm.
  Figure 11. Source.
  Video 1.
  OpenGL GPU GLSL fragment shader real time v4l2 Linux webcam computer vision box blur vs CPU
  . Source.
Node.js
- What's the difference between dependencies, devDependencies and peerDependencies in npm package.json file?
Ruby on Rails
- What is the difference between +<%+, +<%=+, +<%#+ and +-%>+ in ERB in Rails?
POSIX
- What is POSIX? Huge classified overview of the most important things that POSIX specifies.

Systems programming

What do the terms "CPU bound" and "I/O bound" mean?
Figure 12.
Plot of "real", "user" and "sys" mean times of the output of time for CPU-bound workload with 8 threads
. Source. From: What do 'real', 'user' and 'sys' mean in the output of time?

+--------+                  +------------+       +------+
| device |>---------------->| function 0 |>----->| BAR0 |
|        |                  |            |       +------+
|        |>------------+    |            |
|        |             |    |            |       +------+
   ...        ...      |    |            |>----->| BAR1 |
|        |             |    |            |       +------+
|        |>--------+   |    |            |
+--------+         |   |         ...        ...    ...
                   |   |    |            |
                   |   |    |            |       +------+
                   |   |    |            |>----->| BAR5 |
                   |   |    +------------+       +------+
                   |   |
                   |   |
                   |   |    +------------+       +------+
                   |   +--->| function 1 |>----->| BAR0 |
                   |        |            |       +------+
                   |        |            |
                   |        |            |       +------+
                   |        |            |>----->| BAR1 |
                   |        |            |       +------+
                   |        |            |
                   |             ...        ...    ...
                   |        |            |
                   |        |            |       +------+
                   |        |            |>----->| BAR5 |
                   |        +------------+       +------+
                   |
                   |
                   |             ...
                   |
                   |
                   |        +------------+       +------+
                   +------->| function 7 |>----->| BAR0 |
                            |            |       +------+
                            |            |
                            |            |       +------+
                            |            |>----->| BAR1 |
                            |            |       +------+
                            |            |
                                 ...        ...    ...
                            |            |
                            |            |       +------+
                            |            |>----->| BAR5 |
                            +------------+       +------+

Code 5.

Logical struture PCIe device, functions and BARs

. From: What is the Base Address Register (BAR) in PCIe?

Electronics
- Raspberry Pi
  - Figure 13.
    Raspberry Pi 2 directly connected to a laptop with an Ethernet cable
    . Image from answer to: How to hook up a Raspberry Pi via Ethernet to a laptop without a router?
    Figure 14.
    Raspberry Pi 2 connected to a laptop with an USB UART adapter
    . Image from answer to: How to hook up a Raspberry Pi via Ethernet to a laptop without a router?
    Figure 15.
    Raspberry Pi OS being emulated on QEMU 2.5.0 on Ubuntu 16.04 with a modified kernel
    . Image from answer to: How to emulate the Raspberry Pi 2 on QEMU?
    Figure 16.
    Bare metal LED blinker program running on a Raspberry Pi 2
    . Image from answer to: How to run a C program with no OS on the Raspberry Pi?
Computer security
- Why is the same origin policy so important?
Media
- Video 2.
  Canon in D in C
  . Source.
  From: How is audio represented with numbers in computers?.
  The original question was deleted, lol...: How to programmatically synthesize music?
- How to resize a picture using ffmpeg's sws_scale()?
- Is there any decent speech recognition software for Linux? ran a few examples manually on vosk-api and compared to ground truth.
Eclipse
- How to set up the Eclipse for remote C debugging with gdbserver?
Computer hardware
- Are there good open source standard cell libraries to learn IC synthesis with EDA tools?
Scientific visualization software
- Figure 17.
  VisIt zoom in 10 million straight line plot with some manually marked points
  . Source. From: Section "Survey of open source interactive plotting software with a 10 million point scatter plot benchmark by Ciro Santilli"
Numerical analysis
- Video 3.
  Real-time heat equation OpenGL visualization with interactive mouse cursor using relaxation method by Ciro Santilli (2016)
  Source.
Computational physics
- Figure 18.
  gnuplot plot of the y position of a sphere bouncing on a plane simulated in Bullet Physics
  . Source. From: What is the simplest collision example possible in a Bullet Physics simulation?
Register transfer level languages like Verilog and VHDL
- Verilog:
  Figure 19.
  Interacgive ASDF-controlled demo with core logic written in Verilog using Verilator
  .
  From: Is it possible to do interactive user input and output simulation in VHDL or Verilog?
  See also: Section "Verilator interactive example"
Android
- Figure 20. Source. From: How to compile the Android AOSP kernel and test it with the Android Emulator?
- Video 4.
  Android screen showing live on an Ubuntu laptop through ADB
  . Source. From: How to see the Android screen live on an Ubuntu desktop through ADB?
Debugging
Program optimization
- What is tail call optimization?
- Figure 21.
  gprof2dot image generated from the gprof data of a simple test program
  . Source.
  From: How can I profile C++ code running on Linux?
  The answer compares gprof, valgrind callgrind, perf and gperftools on a single simple executable.
Data
- Figure 22.
  Mathematics dump of Wikipedia CatTree
  . Source.
Mathematics
- Figure 23.
  Diagram of the fundamental theorem on homomorphisms by Ciro Santilli (2020)
  
  Shows the relationship between group homomorphisms and normal subgroups.
  From: What is the intuition behind normal subgroups?
- Section "Formalization of mathematics": some early thoughts that could be expanded. Ciro almost had a stroke when he understood this stuff in his teens.
- Figure 24.
  Simple example of the Discrete Fourier transform
  . Source. That was missing from Wikipedia page: en.wikipedia.org/wiki/Discrete_Fourier_transform!
Network programming
- How to make an HTTP get request in C without libcurl?
Physics
- What is the difference between plutonium and uranium?
- Figure 25.
  Spacetime diagram illustrating how faster-than-light travel implies time travel
  . From: Does faster than light travel imply travelling back in time?
Biology
- Figure 26.
  Top view of an open Oxford Nanopore MinION
  . Source. From: Section "How to use an Oxford Nanopore MinION to extract DNA from river water and determine which bacteria live in it"
- Figure 27.
  Mass fractions in a minimal growth medium vs an amino acid cut in a simulation of the E. Coli Whole Cell Model by Covert Lab
  . Source. From: Section "E. Coli Whole Cell Model by Covert Lab"
Quantum computing
- Section "Quantum computing is just matrix multiplication"
- Figure 28.
  Visualization of the continuous deformation of states as we walk around the Bloch sphere represented as photon polarization arrows
  . From: Understanding the Bloch sphere.
Bitcoin
- Section "Cool data embedded in the Bitcoin blockchain"
GIMP
- Figure 29.
  GIMP screenshot part of how to combine two images side-by-side in GIMP?
  .
Home DIY
- Figure 30.
  Total_Blackout_Cassette_Roller_Blind_With_Curtains.
  Source. From: Section "How to blackout your window without drilling"
China
- What would happen if I walked around Beijing with a t-shirt that said "freedom of speech is pretty great"?

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B-tree  Updated 2025-02-22  +Created 1970-01-01

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Like Binary search tree, but each node can have multiple objects and more than two children.

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Computer science  Updated 2025-02-22  +Created 1970-01-01

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A branch of mathematics that attempts to prove stuff about computers.

Unfortunately, all software engineers already know the answer to the useful theorems though (except perhaps notably for cryptography), e.g. all programmers obviously know that iehter P != NP or that this is unprovable or some other "for all practical purposes practice P != NP", even though they don't have proof.

And 99% of their time, software engineers are not dealing with mathematically formulatable problems anyways, which is sad.

The only useful "computer science" subset every programmer ever needs to know is:

for arrays: dynamic array vs linked list
for associative array: binary search tree vs hash table. See also Heap vs Binary Search Tree (BST). No need to understand the algorithmic details of the hash function, the NSA has already done that for you.
don't use Bubble sort for sorting
you can't parse HTML with regular expressions: stackoverflow.com/questions/1732348/regex-match-open-tags-except-xhtml-self-contained-tags/1732454#1732454 because of formal language theory

Funnily, due to the formalization of mathematics, mathematics can be seen as a branch of computer science, just like computer science can be seen as a branch of Mathematics!

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In-order depth-first search  Updated 2025-02-22  +Created 1970-01-01

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This is the order in which a binary search tree should be traversed for ordered output, i.e.:

everything to the left is smaller than parent
everything to the right is larger than parent

This ordering makes sense for binary trees and not k-ary trees in general because if there are more than two nodes it is not clear what the top node should go in the middle of.

This is unlike pre-order depth-first search and post-order depth-first search which generalize obviously to general trees.

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