Ciro Santilli @cirosantilli 35

Equivalent to Lagrangian mechanics but formulated in a different way.

Motivation: Lagrangian vs Hamiltonian.

TODO understand original historical motivation, www.youtube.com/watch?v=SZXHoWwBcDc says it is from optics.

Intuitively, the Hamiltonian is the total energy of the system in terms of arbitrary parameters, a bit like Lagrangian mechanics.

Bibliography:

${\mathbb{R}}^4$ with a weird dot product-like operation called the Minkowski inner product.

Because the Minkowski inner product product is not positive definite, the norm induced by an inner product is a norm, and the space is not a metric space strictly speaking.

The name given to this type of space is a pseudometric space.

Symmetric bilinear form that is also positive definite, i.e.:

TODO freely licensed image of sycees presented on a plate. This is how gifts/prizes would be formally handed in ancient China, possibly wrapped in silk to make it more discrete.

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.

A multilinear form with a domain that looks like:where $V\ast$ is the dual space.

Because a tensor is a multilinear form, it can be fully specified by how it act on all combinations of basis sets, which can be done in terms of components. We refer to each component as:where we remember that the raised indices refer dual vector.

Some examples:

Explain it properly bibliography:

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.

Great overview of the earlier history of unit standardization.

Gives particular emphasis to the invention of gauge blocks.