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.

Old name for DARPA before 1972, and again for a short time between 1993 and 1996. That's why ARPANET is called "ARPANET" and not "DARPANET".

Ciro Santilli lived in Santos from about the year 1998 to 2007, with a 10 month hiatus in Coventry, UK, until he went to the University of São Paulo.

Santos is the nearest beach city to São Paulo City, and for this reason:

Ciro idolizes Santos as the perfect location to live nature-wise due to its amazing wide sandy beach, in which Ciro spent endless hours walking on the sand and on the largest beachfront garden in the world (archive), meditating, and playing some soccer after school was over. Santos is also the city where Pelé first played professionally.

Ciro has visited Santos several times after leaving Brazil. Doing this gives him a weird feeling of having a separate life, in which time passes 2 weeks every few years. Of course, as your family grows, it gets harder and harder to go back home, and your family members might want to just go travel to more interesting places than just stay at your wonderful beach which you love in part due to nostalgia.

Ciro is also fond of the concept of the small public buildings near the beach garden (postos de praia), which serve different cultural activities: library, comic book store, art cinema, surf school. It is such a shame that the library and comic book ones are in such bad shape as of 2020, old books and poor people who go there to sleep a bit in the barely working air conditioning. Ciro fantasizes how those could instead be cultural hubs for the gathering of the brightest artists, and scientists, of town. Maybe they are just too small. Maybe it is not within the realm of possibility of public service. Maybe, we should focus instead in the poorer regions, far form the beach. But the dream remains.

Santos only has one natural defect: mosquitoes. By the sea it is fine because the wind is strong, and they don't like salt water. But anywhere else, you will be eaten alive, and maybe get dengue, Ciro got it once. Gene drive, please.

This instagram page has several drone videos of the region: www.instagram.com/malta.drone

On Wikipedia we only find the term Scholar-official. But the idea of the ancient Chinese scholar is a bit wider as a concept, and even people who were not trying to be officials could thrive to follow certain aspects of the scholar way of life.