Ciro Santilli @cirosantilli 37

When we particles particles, the action is obtained by integrating the Lagrangian over time:

In the case of field however, we can expand the Lagrangian out further, to also integrate over the space coordinates and their derivatives.

Since we are now working with something that gets integrated over space to obtain the total action, much like density would be integrated over space to obtain a total mass, the name "Lagrangian density" is fitting.

E.g. for a 2-dimensional field $f(x,y,t)$:

Of course, if we were to write it like that all the time we would go mad, so we can just write a much more condensed vectorized version using the gradient with $x\in {\mathbb{R}}^2$:

And in the context of special relativity, people condense that even further by adding $t$ to the spacetime Four-vector as well, so you don't even need to write that separate pesky $t$.

The main point of talking about the Lagrangian density instead of a Lagrangian for fields is likely that it treats space and time in a more uniform way, which is a basic requirement of special relativity: we have to be able to mix them up somehow to do Lorentz transformations. Notably, this is a key ingredient in a/the formulation of quantum field theory.

Hardcoded and unique network addresses for every single device on Earth.

Started with 48 bits (6 bytes), usually given as 01:23:45:67:89:AB but people now encouraged to use 64-bit ones.

How they are assigned: www.quora.com/How-are-MAC-addresses-assigned Basically IEEE gives out the 3 first bytes to device manufacturers that register, this is called the organizationally unique identifier, and then each manufacturer keeps their own devices unique.

This one has students must have a flexible choice of what to learn on the name! Sounds interesting!

XML predecessor.

You need those because it is hard to do the following:

This is hard to do notably because when the update happens, several things might need to change on the webpage at the same time.

Notably, new elements might need to be added to the webpage, which in turn means that new bindings such as button clicks have to be added to those, in a way that keeps the page working.

The only way to do this basically is to have a functional dependency graph that keeps everything in the page in working state as updates come.

In conventional speech of the early 2000's, is basically a synonym for dynamic random-access memory.

One of the things Ciro Santilli really likes, see: Linux Kernel Module Cheat.

If computational physics simulates physics, emulators simulates computers.