Ciro Santilli @cirosantilli 37

One of the first formal proof systems. This is actually understandable!

This is Ciro Santilli-2020 definition of the foundation of mathematics (and the only one he had any patience to study at all).

TODO what are its limitations? Why were other systems created?

God, Ciro Santilli respects this guy.

Watching www.youtube.com/watch?v=-SbZZPX-y9g in 2022, who was one of his inspirations, made Ciro miss his guitar so much... one day, maybe, one day.

Like Reddit (option to allow it per community added in late 2021) and support.google.com/.

And of course, 4chan just takes that to a whole new level, usually closing on the same day, and then getting deleted within a week. Why would anyone contribute non-illegal content to that king of system?!

Ridiculous, so when new information comes out, we just duplicate all the old comments on a new thread again?

Remember, Ciro Santilli is the Necromancer God.

Dan Dascalescu agrees for Reddit specifically: www.reddit.com/r/TheoryOfReddit/comments/9oujwf/why_archiving_old_threads_is_a_bigger_problem/

They do seem to have been very innovative, and have had a very good work culture. They also had a huge impact on the Silicon Valley startup scene.

Some products they are known for:

Main implementations: the same as electronic switches: vacuum tubes in the past, and transistors in the second half of the 20th century.

This technique has managed to determine protein 3D structures for proteins that people were not able to crystallize for X-ray crystallography.

It is said however that cryoEM is even fiddlier than X-ray crystallography, so it is mostly attempted if crystallization attempts fail.

By looking at Figure 1. "A cryoEM image", you can easily understand the basics of cryoEM.

We just put a gazillion copies of our molecule of interest in a solution, and then image all of them in the frozen water.

Each one of them appears in the image in a random rotated view, so given enough of those point of view images, we can deduce the entire 3D structure of the molecule.

Ciro Santilli once watched a talk by Richard Henderson about cryoEM circa 2020, where he mentioned that he witnessed some students in the 1980's going to Germany, and coming into contact with early cryoEM. And when they came back, they just told their principal investigator: "I'm going to drop my PhD theme and focus exclusively on cryoEM". That's how hot the cryo thing was! So cool.

Basically the same remarks as for university, just 10 times more useless, see also: Section "Motivation".

Vs: image: the codomain is the set that the function might reach.

The image is the exact set that it actually reaches.

E.g. the function:could have:

Note that the definition of the codomain is somewhat arbitrary, e.g. $x^2$ could as well technically have codomain:even though it will obviously never reach any value in ${\mathbb{R}}^2$.

The exact image is in general therefore harder to characterize.