Ciro Santilli @cirosantilli 35

Ciro Santilli considered this as the basis for Ciro's 2D reinforcement learning games, but ultimately decided it was a bit too messy. Nice overall though.

First proper nearest galaxy to the Milky Way. Everything in the middle in the Local group is either a satellite of the Milky Way or Andromeda.

Many Andromeda satellite galaxies are simply numbered Andromeda II, Andromeda III and so on.

As described on Wikipedia, the observational history of Andromeda is fascinating. Little by little, people noticed that it had a different nature to many other objects observed on the sky, and the hypothesis that there are other galaxies like ours grew in force.

Part of our fascination with Andromeda is due to how similar in size and shape and close it is to the Milky Way.

It is clearly the only thing so large and so close.

Andromeda is, without a doubt, our sister galaxy.

One can't help but wonder if there is some alien looking back at us when we are looking at them through our Telescope.

Andromeda is also the furthest object from Earth that can be seen with the naked eye.^[ref] Not surprising, as it literally shines with the strength of a trillion suns!

Subset of recursively enumerable language as explained at: difference between recursive language and recursively enumerable language.

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.