Ciro Santilli @cirosantilli 37

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:

Very good open source book: github.com/csound-flossmanual/csound-floss

Includes introduction to the basic sound synthesis and their implementation in Csound.

Examples run on browser via Emscripten and just worked on Ubuntu 20.04!

Examples can also be downloaded all at once from: www.csound-tutorial.net/floss_manual/ Shame not in Git as standalone files.

flossmanual.csound.com/sound-synthesis/subtractive-synthesis covers Minimoog-like subtractive synthesis.

Best quote at 00:23:01: matters of small concern should be treated seriously.