Ciro Santilli @cirosantilli 37

Ciro Santilli considered it before he stopped using file managers altogether, it is not bad.

The differential equation that is solved by the exponential function:with initial condition:

TODO find better name for it, "linear homogenous differential equation of degree one" almost fully constrainst it except for the exponent constant and initial value.

www.urbandictionary.com/define.php?term=turd%20polishing on Urban Dictionary.

Ciro Santilli learned this expression from Angry Video Game Nerd.

First we write a vector field as:Note how we are denoting each component of $F$ as $F^i$ with a raised index.

Then, the divergence can be written in Einstein notation as:

It is common to just omit the variables of the function, so we tend to just say:or equivalently when referring just to the operator:

Sometimes Ciro Santilli says half jokingly that user interface does not matter.

This software circa 2010-2020 makes that joke not be funny.

How can a UI feel so clunky!

The most aggravating thing is that it is not immediately obvious why it feels so bad.

Dual vectors are the members of a dual space.

In the context of tensors , we use raised indices to refer to members of the dual basis vs the underlying basis:The dual basis vectors $e^i$ are defined to "pick the corresponding coordinate" out of elements of V. E.g.:By expanding into the basis, we can put this more succinctly with the Kronecker delta as:

Note that in Einstein notation, the components of a dual vector have lower indices. This works well with the upper case indices of the dual vectors, allowing us to write a dual vector $f$ as:

In the context of quantum mechanics, the bra notation is also used for dual vectors.

Ways in which it can happen: