Holomorphic function Updated 2025-07-16
Being a complex holomorphic function is an extremely strong condition.
The existence of the first derivative implies the existence of all derivatives.
Another extremely strong consequence is the identity theorem.
"Holos" means "entire" in Greek, so maybe this is a reference to the fact that due to the identity theorem, knowing the function on a small open ball implies knowing the function everywhere.
How computers work? Updated 2025-07-16
A computer is a highly layered system, and so you have to decide which layers you are the most interested in studying.
Although the layer are somewhat independent, they also sometimes interact, and when that happens it usually hurts your brain. E.g., if compilers were perfect, no one optimizing software would have to know anything about microarchitecture. But if you want to go hardcore enough, you might have to learn some lower layer.
It must also be said that like in any industry, certain layers are hidden in commercial secrecy mysteries making it harder to actually learn them. In computing, the lower level you go, the more closed source things tend to become.
But as you climb down into the abyss of low level hardcoreness, don't forget that making usefulness is more important than being hardcore: Figure 1. "xkcd 378: Real Programmers".
Here's a summary from low-level to high-level:
Figure 1.
xkcd 378: Real Programmers
. Source.
Video 1.
How low can you go video by Ciro Santilli (2017)
Source. In this infamous video Ciro has summarized the computer hierarchy.
Infection Updated 2025-07-16
School Updated 2025-07-16
Basically the same remarks as for university, just 10 times more useless, see also: Section "Motivation".

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