Ciro Santilli @cirosantilli 37

All of them need a vacuum because you can't shoot elecrons through air, as mentioned at Video "50,000,000x Magnification by AlphaPhoenix (2022)".

It is true that one image is worth a thousand words, but unfortunately it is also true that one image takes up at least as much bytes as a thousand words!

Having one single page to rule them all is of course the ideal setup for a website, as you can Ctrl + F one ToC and quickly find what you want.

And, with Linux Kernel Module Cheat Ciro noticed that it is very hard to write so much intelligent prose that becomes larger than reasonable to load on a single webpage.

He then started using this technique for everything he writes, including this page and Chinese government.

However, if there are too many images on the page, the loading of the last images would take forever in case users want to view the last sections.

There are two solutions to that:

Ciro is still deciding between those two. The traditional approach works for sure but loses the one page to rule them all benefits.

The innovative approach will work for interactive viewing, but archive.org will fail to load the images for example, and there may be other unforseen consequences.

Wikimedia Commons is awesome and automatically converts and serves smaller versions of images, so always choose the smallest images size needed by the output document. Readers can then find the higher resolution versions by following the page source.

This also comes to mind: motherfuckingwebsite.com

zettelkasten.de/posts/overview/ from zettelkasten:

Website: www.theoremoftheday.org/

A linear map is a function $f:V_1(F)\to V_2(F)$ where $V_1(F)$ and $V_2(F)$ are two vector spaces over underlying fields $F$ such that:

A common case is $F=\mathbb{R}$, $V_1={\mathbb{R}}_m$ and $V_2={\mathbb{R}}_n$.

One thing that makes such functions particularly simple is that they can be fully specified by specifyin how they act on all possible combinations of input basis vectors: they are therefore specified by only a finite number of elements of $F$.

Every linear map in finite dimension can be represented by a matrix, the points of the domain being represented as vectors.

As such, when we say "linear map", we can think of a generalization of matrix multiplication that makes sense in infinite dimensional spaces like Hilbert spaces, since calling such infinite dimensional maps "matrices" is stretching it a bit, since we would need to specify infinitely many rows and columns.

The prototypical building block of infinite dimensional linear map is the derivative. In that case, the vectors being operated upon are functions, which cannot therefore be specified by a finite number of parameters, e.g.

For example, the left side of the time-independent Schrödinger equation is a linear map. And the time-independent Schrödinger equation can be seen as a eigenvalue problem.

Online forums that lock threads after some time are evil. What else needs to be said?

Ciro Santilli dislikes the fact that they take themselves too seriously. Ciro prefers the jokes and tech approach.

"More complex and general" integral. Matches the Riemann integral for "simple functions", but also works for some "funkier" functions that Riemann does not work for.

Ciro Santilli sometimes wonders how much someone can gain from learning this besides the beauty of mathematics, since we can hand-wave a Lebesgue integral on almost anything that is of practical use. The beauty is good reason enough though.

Grouping by age as done in traditional education as of 2020 is useless.

Rather, we should group students by subject of interest; e.g. natural sciences, social sciences, a sport, etc., just like in any working adult organization!

This way, younger students can actually actively learn from and collaborate with older students about, see notably Jacques Monod's you can learn more from older students than from faculty.

This becomes even more natural when you try to give students must have a flexible choice of what to learn.

This age distinction should be abolished at all stages of the system, not only within K-12, but also across K-12, undergraduate education and postgraduate education.

This idea is part of the ideal that the learning environment should be more like a dojo environment (AKA peer tutoring, see also dojo learning model), rather than an amorphous checkbox ticking exercise in bureaucracy so that "everyone is educated".

Perhaps, even more importantly, is that we should put much more emphasis on grouping students with other students online, where we can select similar interest amongst the entire population and not just on a per-local-neighbourhood basis.

Text materials are generally superior to video because they:

Only produce video material if:

Never create videos of people just speaking hardcore content for long amounts of time.

If you have to use videos, make them as short as possible, and index them with a textual table of contents.

Also consider using sequences of images or GIFs instead of videos, since those are cheaper.