English (language) by Ciro Santilli 35 Updated +Created
Romance language by Ciro Santilli 35 Updated +Created
Half-precision floating-point format by Ciro Santilli 35 Updated +Created
Give examples by Ciro Santilli 35 Updated +Created
Keep the example/theory ratio high, very, very high.
For natural sciences, add as many reproducible experiment images/videos/descriptions as you can.
It is OK to treat things as black boxes by Ciro Santilli 35 Updated +Created
You don't need to understand the from first principles derivation of every single phenomena.
And most important of all: you should not start learning phenomena by reading the from first principles derivation.
Instead, you should see what happens in experiments, and how matches some known formula (which hopefully has been derived from first principles).
Only open the boxes (understand from first principles derivation) if the need is felt!
E.g.:
  • you don't need to understand everything about why SQUID devices have their specific I-V curve curve. You have to first of all learn what the I-V curve would be in an experiment!
  • you don't need to understand the fine details of how cavity magnetrons work. What you need to understand first is what kind of microwave you get from what kind of input (DC current), and how that compares to other sources of microwaves
  • lasers: same
Physics is all about predicting the future. If you can predict the future with an end result, that's already predicting the future, and valid.
Electric guitar by Ciro Santilli 35 Updated +Created
See also some remarks of Ciro Santilli's thoughts on the instrument Ciro Santilli's musical education.
Group homomorphism by Ciro Santilli 35 Updated +Created
Like isomorphism, but does not have to be one-to-one: multiple different inputs can have the same output.
The image is as for any function smaller or equal in size as the domain of course.
This brings us to the key intuition about group homomorphisms: they are a way to split out a larger group into smaller groups that retains a subset of the original structure.
As shown by the fundamental theorem on homomorphisms, each group homomorphism is fully characterized by a normal subgroup of the domain.
Globalization reduces the power of governments by Ciro Santilli 35 Updated +Created
While Ciro Santilli is a big fan of having "one global country" (and language), which is somewhat approximated by globalization, he has come to believe that there is one serious downside to globalization as it stands in 2020: it allows companies to pressure governments to reduce taxes, and thus reduces the power of government, which in turn increases social inequality. This idea is very well highlighted in Can't get you out of my head by Adam Curtis (2021).
The only solution seems to be for governments to get together, and make deals to have fair taxation across each other. Which might never happen.
Fourier inversion theorem by Ciro Santilli 35 Updated +Created
A set of theorems that prove under different conditions that the Fourier transform has an inverse for a given space, examples:
Calysta by Ciro Santilli 35 Updated +Created
Classification of finite groups by Ciro Santilli 35 Updated +Created
As shown in Video "Simple Groups - Abstract Algebra by Socratica (2018)", this can be split up into two steps:This split is sometimes called the "Jordan-Hölder program" in reference to the authors of the jordan-Holder Theorem.
Good lists to start playing with:
It is generally believed that no such classification is possible in general beyond the simple groups.
Ciro Santilli's film tastes by Ciro Santilli 35 Updated +Created
Ciro Santilli has already watched all the best films in history, and as a result any of those new movies that is full of clichés and has no innovative aspect at all (99.99999% of all modern movies) makes Ciro want to puke and to start Googling TV Tropes to classify as many clichés as possible.
Good movies are those that teach you mechanisms of the real world. Willing suspension of disbelief must be maintained at all costs.
Or of what could happen a world where a single sci-fi element is added and explored to its limits.
Love is not an interesting aspect of the world. You solve your love life at university, Tinder or Tango.
The actually interesting aspects of the world are:
Movies with a lot of action scenes, with exception of some war movies, are shit.
The Sliding scale of idealism vs. cynicism must be close to Cynicism max at all times. Movies with pure good and pure bad are shit.
Knowing spoilers has no effect in the film's enjoyment. The interest of storyline concepts is all that matters, visuals and acting are useless.
In a multi-language film, when two foreign characters speak English to each other when they obviously would have spoken their native language, that is a crime. Original language + subtitles is a must!
Theoretical physics by Ciro Santilli 35 Updated +Created
Natural selection by Ciro Santilli 35 Updated +Created
Natural logarithm by Ciro Santilli 35 Updated +Created
Conservation of energy by Ciro Santilli 35 Updated +Created
Alex Honnold by Ciro Santilli 35 Updated +Created
Current-voltage characteristic by Ciro Santilli 35 Updated +Created

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