Eigenvalues and eigenvectors Updated +Created
Ł Updated +Created
Video 1.
Exploring! the Special Letters of the Polish Alphabet: L by Polish Girl Next Door (2021)
Source.
Synthetic geometry of the real projective plane Updated +Created
It good to think about how Euclid's postulates look like in the real projective plane:
Unlike the real projective line which is homotopic to the circle, the real projective plane is not homotopic to the sphere.
The topological difference bewteen the sphere and the real projective space is that for the sphere all those points in the x-y circle are identified to a single point.
One more generalized argument of this is the classification of closed surfaces, in which the real projective plane is a sphere with a hole cut and one Möbius strip glued in.
Telephone-based system Updated +Created
This section is about telecommunication systems that are based on top of telephone lines.
Telephone lines were ubiquitous from early on, and many technologies used them to send data, including much after regular phone calls became obsolete with VoIP.
These market forces tended to eventually crush non-telephone-based systems such as telex. Maybe in that case it was just that the name sounded like a thing of the 50's. But still. Dead.
Video 1.
Long Distance by AT&T (1941)
Source. youtu.be/aRvFA1uqzVQ?t=219 is perhaps the best moment, which attempts to correlate the exploration of the United States with the founding of the U.S. states.
Television series that Ciro Santilli watched all episodes of Updated +Created
The best way to watch a television series is: wait for the thing to end. Then watch the first and last episodes of each season. The rest is fluff. And then pick up any missing interesting clips from YouTube. If a series holds you more than those episodes, it is one of the few amazing ones!
Ten ancient famous songs of China Updated +Created
This is a good place to start your journey, though it misses a lot, and some songs are not as memorable as others, there is huge variability in that list.
Video 1.
The Ten Most Famous Melodies in Ancient China
. Source. A single video with a collage of all ten songs.
Zebrafish Updated +Created
Brexit Updated +Created
There are valid reasons to be pro-Brexit, given the uselessness of the European Union.
The problem was how the campaign was conducted, in a purely nationalistic, populist and fake news manner, and largely supported by business leaders who immediately after still wanted to hire cheap foreign labour, use tax havens and move headquarters to other countries, e.g.:
British politician Updated +Created
Eight Chinese Cuisines Updated +Created
This classification is too restrictive, and too South-centered. But if is worth knowing.
eLearning provider Updated +Created
Video 1.
Infomercial: For-Profit Online University by Adult Swim
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Electromagnetic four-potential Updated +Created
A different and more elegant way to express Maxwell's equations by using the:instead of the:
The old man lost his horse Updated +Created
Another notable reference is in Lost Horse LLC, MacKenzie Bezos's charity instrument.
Breakdown:
  • 塞翁 sai4 weng1: TODO his name?
  • 失马 shi1 ma3: lost horse
  • 焉知 yan1 zhi1: who knows, literary
  • 非福 fei1 fu2: bad (or) good
Video 1.
Zen master and the little boy scene from Charlie Wilson's War
. Source. This is how Ciro Santilli first heard the old man lost his horse! The scene happens after the Americans seem to have had sucess in arming the Taliban in the 1980s to fight the Soviets, and then they decide to stop all monetary help to rebuild the country, which then leads to a terrorism threat many years later.
Video 2.
The Blessing of Bad Luck by Pursuit of Wonder (2022)
Source. A bit too long. But worth it.
LeetCode Updated +Created
Their system is quite good actually. Not as good as a GitHub repo with all the tests made explicit. But still pretty good.
BIOS Updated +Created
Carleson's theorem Updated +Created
The Fourier series of an function (i.e. the function generated from the infinite sum of weighted sines) converges to the function pointwise almost everywhere.
The theorem also seems to hold (maybe trivially given the transform result) for the Fourier series (TODO if trivially, why trivially).
Only proved in 1966, and known to be a hard result without any known simple proof.
This theorem of course implies that Fourier basis is complete for , as it explicitly constructs a decomposition into the Fourier basis for every single function.
TODO vs Riesz-Fischer theorem. Is this just a stronger pointwise result, while Riesz-Fischer is about norms only?

There are unlisted articles, also show them or only show them.