As if Greek letters weren't enough, physicists and mathematicians also like to make up tons of symbols, some of which look like the could actually be Greek letters!

Nabla is one of those: it was completely made up in modern times, and just happens to look like an inverted upper case delta to make things even more confusing!

Nabla means "harp" in Greek, which looks like the symbol.

Takes a vector field as input and produces a scalar field.

Mnemonic: it gives out the amount of fluid that is going in or out of a given volume per unit of time.

Therefore, if you take a cubic volume:

Generalization of a plane for any number of dimensions.

Kind of the opposite of a line: the line has dimension 1, and the plane has dimension D-1.

In $D=2$, both happen to coincide, a boring example of an exceptional isomorphism.

Lit: fish timber question answer.

On Baidu Baike: baike.baidu.com/item/渔樵问答/336905

The dialog is also known as allegory for an incredibly deep philosophical discussion between an idealized wise woodcutter and a fisherman, e.g. mentioned at: www2.kenyon.edu/Depts/Religion/Fac/Adler/Writings/Fisherman%20and%20Woodcutter.pdf

This song is just too slow for Ciro Santilli to make much out of it.

Bibliography:

Does not require straight line cuts.

Same motivation as Galilean invariance, but relativistic version of that: we want the laws of physics to have the same form on all inertial frames, so we really want to write them in a way that is Lorentz covariant.

This is just the relativistic version of that which takes the Lorentz transformation into account instead of just the old Galilean transformation.

In those cases at least, it is possible to add a metric to the spaces, leading to elliptic geometry.

It good to think about how Euclid's postulates look like in the real projective plane:

Unlike the real projective line which is homotopic to the circle, the real projective plane is not homotopic to the sphere.

The topological difference bewteen the sphere and the real projective space is that for the sphere all those points in the x-y circle are identified to a single point.

One more generalized argument of this is the classification of closed surfaces, in which the real projective plane is a sphere with a hole cut and one Möbius strip glued in.

"Ibis redibis nunquam per bella peribis" is a Latin phrase that translates to "You will go, you will return; you will never die through war." This phrase is part of a longer poem known as "Ibis," attributed to the Roman poet Ovid. The work is characterized by its exploration of themes such as fate, death, and revenge, often invoking mythical references and a sense of foresight.