Ciro Santilli @cirosantilli  40

An inner product $x\cdot y$ induces a norm with:

In a vector space, a metric may be induced from a norm by using subtraction:

The partial differential equation of non-relativistic quantum mechanics.

Experiments explained:

Experiments not explained: those that the Dirac equation explains like:

To get some intuition on the equation on the consequences of the equation, have a look at:

The easiest to understand case of the equation which you must have in mind initially that of the Schrödinger equation for a free one dimensional particle.

Then, with that in mind, the general form of the Schrödinger equation is:where:

The $\overrightarrow{x}$ argument of $\psi$ could be anything, e.g.:Note however that there is always a single magical $t$ time variable. This is needed in particular because there is a time partial derivative in the equation, so there must be a corresponding time variable in the function. This makes the equation explicitly non-relativistic.

The general Schrödinger equation can be broken up into a trivial time-dependent and a time-independent Schrödinger equation by separation of variables. So in practice, all we need to solve is the slightly simpler time-independent Schrödinger equation, and the full equation comes out as a result.

Existence and uniqueness: mathoverflow.net/questions/212913/existence-and-uniqueness-for-two-dimensional-time-dependent-schr%C3%B6dinger-equation

TODO how close does it get to Shannon's limit?

physics.stackexchange.com/questions/614757/intuitive-explanation-for-why-time-symmetry-implies-conservation-of-energy on Physics Stack Exchange

This is the one that hit Ciro Santilli the hardest, coming in at the point in which he started to discern between games and the real world a little better. His parents bought it for him during a trip to Disney World in Florida in 1996 (?), since electronics were much cheaper in the USA.

So as Ciro became older, and turned into a software engineer, he started to become more and more morbidly curious about "N64 internals": tool-assisted speedrun, how the devkit looks like, how games were developed for it, hardware leaks, etc.

Luckily Ciro's mind is not interested enough by that useless shit for Ciro to seriously study it himself. But that's what YouTube is for, right? Why do useless stuff when other more useless people can do it for you?

The console has only 4 MB of RAM memory. It is quite incredible what can be done with 8 MB, from the point of view of a 2020 worls where 16 GB laptops are the norm.

One of the main children cartoons Ciro Santilli liked to watch. Part of the Pokemon Mania of the 90s of course.

Ciro could not understand why Nintendo won't make a proper 3D MMORPG Pokemon with actually 3D Pokemon roaming the land, which is obviously what everyone wants. There are even fan games getting there!until this explaiend it beautifully Video 1. "The Downfall Of Mainline Pokemon Games by GONZ media (2020)":

A switch is a box with a bunch of Ethernet wires coming into it:Except that it doesn't have to be Ethernet, e.g. it would also be a Wi-Fi.

What the switch does is:After the destination is found, a confirmation is somehow sent back to the switch, which then learns which wire to send each MAC address to.

A switch is a bit like a router but it is a bit dumber/operates at a lower level: it basically operates only on MAC addresses, not on IP addresses.

The Internet service provider boxes most people have at home combines a switch for the local network and a router for the ISP communication.