Ciro Santilli @cirosantilli 35

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.

Conveyor belt 2D top down mining like Factorio, but with more emphasis on tower defense/real-time strategy, PvP looks a lot like StarCraft or Age of Empires.

As of pre alpha 135, the most annoying thing is that you can't easily start a campaign scenario from fresh, if you lose you have to start from wave 1 but with everything already half built as you left it. This gives you a huge advantage...

It is also annoying that you have to manually rebuild everything that was destroyed afer each attack, unless you have some unit that you can only unlock later on...

mindustry-unofficial.fandom.com/wiki/Future_Content#New_Google_Play_Listing suggests freemium features being considered, but they are mostly minor or plaform specific. There seems to be no server list by default however, making the Steam multiplayer freemium valuable.

www.youtube.com/watch?v=o5ThSECaAwA suggests code drop is used.

It is a bit annoying that you have to unlock the tech tree little by little in campaign, but it does serve as a reasonable introduction to the general order of development. Games with progression state are boring, except when there is permadeath. But custom play scenarios have everything unlocked immediately, much better.

It is very cool that you can copy chunks of buildings as macros, and save them for later.

The game runs very well it feels like.

The logic blocks are particularly interesting, and allow you to program a block yourself.