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.
TODO clear attribution source:
Some people say, "Give the customers what they want." But that's not my approach. Our job is to figure out what they're going to want before they do. I think Henry Ford once said, "If I'd asked customers what they wanted, they would have told me, 'A faster horse!'" People don't know what they want until you show it to them. That's why I never rely on market research. Our task is to read things that are not yet on the page.
Calculus of variations Updated 2025-07-16
Calculus of variations is the field that searches for maxima and minima of Functionals, rather than the more elementary case of functions from to .
Linting Updated 2025-07-16
Star Trek: The Next Generation Updated 2025-07-16
Ciro Santilli likes this.
He doesn't have the patience to actually watch full episodes with rare exceptions, rather just watching selected scenes from: www.youtube.com/channel/UCdeIGY2DIjpGf0A2m9GSE3g, but still, it is interesting.
What appeals to Ciro in this series is how almost nothing is solved by violence, almost everything is decided in the bridge, at the "cerebral" level of the command structure. This reminds Ciro of a courtroom of law sometimes.
Maybe there's also a bit of 90's nostalgia involved too though, as this is something that would show on some random cable channels a bored young Ciro would have browsed during weekends, never really watching full episodes.
One crime of many episodes is being completely based on some stupid new scientific concept, which any character to back it up.
Another thing that hurt is that due to their obsession with the senior members of the crew, sometimes those senior members are sent in ridiculously risky operations, which is very unrealistic.
Episodes that Ciro watched fully and didn't regret:
Semi worth it:
Not worth it:
  • Cause and effect
TODO
  • s06e11 Chain of command
Mathieu group Updated 2025-07-16
Contains the first sporadic groups discovered by far: 11 and 12 in 1861, and 22, 23 and 24 in 1973. And therefore presumably the simplest! The next sporadic ones discovered were the Janko groups, only in 1965!
Each is a permutation group on elements. There isn't an obvious algorithmic relationship between and the actual group.
TODO initial motivation? Why did Mathieu care about k-transitive groups?
Their; k-transitive group properties seem to be the main characterization, according to Wikipedia:
Looking at the classification of k-transitive groups we see that the Mathieu groups are the only families of 4 and 5 transitive groups other than symmetric groups and alternating groups. 3-transitive is not as nice, so let's just say it is the stabilizer of and be done with it.
Video 1.
Mathieu group section of Why Do Sporadic Groups Exist? by Another Roof (2023)
. Source. Only discusses Mathieu group but is very good at that.
Janko group Updated 2025-07-16
Monster group Updated 2025-07-16
Video 1.
Group theory, abstraction, and the 196,883-dimensional monster by 3Blue1Brown (2020)
Source. Too basic, starts motivating groups themselves, therefore does not give anything new or rare.
Unlike the simple case of a matrix, in infinite dimensional vector spaces, the spectrum may be continuous.
The quintessential example of that is the spectrum of the position operator in quantum mechanics, in which any real number is a possible eigenvalue, since the particle may be found in any position. The associated eigenvectors are the corresponding Dirac delta functions.
Einstein solid Updated 2025-07-16
One important quantum mechanics experiment, which using quantum effects explain the dependency of specific heat capacity on temperature, an effect which is not present in the Dulong-Petit law.
This is the solid-state analogue to the black-body radiation problem. It is also therefore a quantum mechanics-specific phenomenon.
Debye model Updated 2025-07-16
Wikipedia mentions that it is completely analogous to Planck's law.

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