GIMP by Ciro Santilli 40 Updated 2025-07-16
It's not super easy to use at first.
And it sometimes says that the basic drawing thing you want to do is off the project's scope.
But as you learn more about it and further generalize the concepts, there are often reasonable reasons for those design choices.
And the UI looks good :-)
Examples:
Covariance by Ciro Santilli 40 Updated 2025-07-16
Generally means that he form of the equation does not change if we transform .
This is generally what we want from the laws of physics.
E.g. a Galilean transformation generally changes the exact values of coordinates, but not the form of the laws of physics themselves.
Lorentz covariance is the main context under which the word "covariant" appears, because we really don't want the form of the equations to change under Lorentz transforms, and "covariance" is often used as a synonym of "Lorentz covariance".
TODO some sources distinguish "invariant" from "covariant": invariant vs covariant.
Invariant vs covariant by Ciro Santilli 40 Updated 2025-07-16
Some sources distinguish "invariant" from "covariant" such that under some transformation (typically Lie group):
  • invariant: the value of does not change if we transform
  • covariant: the form of the equation does not change if we transform .
TODO examples.
Lorentz group by Ciro Santilli 40 Updated 2025-07-16
Subgroup of the Poincaré group without translations. Therefore, in those, the spacetime origin is always fixed.
Or in other words, it is as if two observers had their space and time origins at the exact same place. However, their space axes may be rotated, and one may be at a relative speed to the other to create a Lorentz boost. Note however that if they are at relative speeds to one another, then their axes will immediately stop being at the same location in the next moment of time, so things are only valid infinitesimally in that case.
This group is made up of matrix multiplication alone, no need to add the offset vector: space rotations and Lorentz boost only spin around and bend things around the origin.
One definition: set of all 4x4 matrices that keep the Minkowski inner product, mentioned at Physics from Symmetry by Jakob Schwichtenberg (2015) page 63. This then implies:
Inkscape by Ciro Santilli 40 Updated 2025-11-05
Inkscape is a a good software for editing/creating SVG files.
Its functionality is fundamental for as a software for drawing geometry diagrams, as it is a good middle ground between algorithmic generation, and raster graphics.
At 1.0.2, its UI is a bit terrible:
  • the way the menus open on the right with title below the window...
  • several defaults are atrocious, e.g. export drawing rather than page
And it crashes from time to time on Ubuntu 21.04. And it has some glaring bugs, e.g.:
But still, it is a very good initiative.
Kdenlive by Ciro Santilli 40 Updated 2025-07-16
This seems like a decent option, although it has bugs coming in and out all the time! Also it is quite hard to learn to use.
To get started:
  • import a clip
  • drag it onto the track area
Shortucts:
To set the video length, search for "set outpoint" on "monitor".
Add subtitles:
  • Effects
  • Dynamic text
then drag on top of the video track. To add only to part of the video, cut it up first.
Preview has no sound on Ubuntu 20.10. Fixed as of Ubuntu 22.04.
Sound worked on Ubuntu 21.04 though, but it then soon crashed with:
 = = SET EFFECT PARAM:  "rect"  =  0=1188 0 732 242
MUTEX LOCK!!!!!!!!!!!! slotactivateeffect:  1
// // // RESULTING REQUIRED SCENE:  1
Object 0x557293592da0 destroyed while one of its QML signal handlers is in progress.
Most likely the object was deleted synchronously (use QObject::deleteLater() instead), or the application is running a nested event loop.
This behavior is NOT supported!
qrc:/qml/EffectToolBar.qml:80: function() { [native code] }
Killed
amazing.
On Ubuntu 22.04 haven't crashed yet.
ShotCut by Ciro Santilli 40 Updated 2025-07-16
Worked on Ubuntu 20.10.
The UI is a bit too buggy to bear.
How to unsplit, can't find on shotcut 21.05.01: forum.shotcut.org/t/is-it-possible-to-unsplit/1466/2
OpenShot by Ciro Santilli 40 Updated 2025-07-16
Ubuntu 20.10 crash...:
  exceptions:ERROR Unhandled Exception
Traceback (most recent call last):
  File "/usr/bin/openshot-qt", line 11, in <module>
    load_entry_point('openshot-qt==2.5.1', 'gui_scripts', 'openshot-qt')()
  File "/usr/lib/python3/dist-packages/openshot_qt/launch.py", line 97, in main
    app = OpenShotApp(argv)
  File "/usr/lib/python3/dist-packages/openshot_qt/classes/app.py", line 218, in __init__
    from windows.main_window import MainWindow
  File "/usr/lib/python3/dist-packages/openshot_qt/windows/main_window.py", line 45, in <module>
    from windows.views.timeline_webview import TimelineWebView
  File "/usr/lib/python3/dist-packages/openshot_qt/windows/views/timeline_webview.py", line 42, in <module>
    from PyQt5.QtWebKitWidgets import QWebView
ImportError: /usr/lib/x86_64-linux-gnu/libQt5Quick.so.5: undefined symbol: _ZN4QRhi10newSamplerEN11QRhiSampler6FilterES1_S1_NS0_11AddressModeES2_, version Qt_5_PRIVATE_API
On Ubuntu 20.10, just:
ffmpeg -i input.mp4 -vf "subtitles=subtitle.srt" output.mp4
To change font size: stackoverflow.com/questions/21363334/how-to-add-font-size-in-subtitles-in-ffmpeg-video-filter
ffmpeg -i input.mp4 -vf "subtitles=subtitle.srt:force_style='Fontsize=64'" output.mp4
The default appears to be 24, so just multiply that by whatever seems like a reasonable factor.
Note howver that .ass subtitle files can contain style information, which ffmpeg respects. Aegisub can produce and preview such styles, making .ass one of the best options.

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