Ciro Santilli @cirosantilli 40

These are "original" thoughts that Ciro had which at some point in the past amused him. Some would call them pieces of wisdom, others self delusion. All have likely been thought by others in the past, and some of them Ciro thinks to himself after a few years: "why did I like this back then??".

After Ciro's colleague was doing that in a project:

On the theory vs practice of computer science:

On how human perception of media is completely unrelated to the computer's transmission mechanism:

On how you make the best friends in life when dealing with hardships together.In Ciro's case, this in particular means going through high school/universities studies and work projects, though of course war would apply particularly well. Perhaps inspired by as iron sharpens iron, so one person sharpens another.

This is of course just another version of one picture is worth a thousand words.

Others:

Wikipedia page: en.wikipedia.org/wiki/List_of_cultural_and_regional_genres_of_music

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

Ciro Santilli's sport of choice circa 2020, see also: Ciro Santilli's cycling.

What do you prefer, 1 \times 10^{10} or 1E10.

When non-specialists say "Ethernet cable", they usually mean twisted pair for Ethernet over twisted pair.

But of course, this term is much more generic to a more specialized person, since notably fiber optics are also extensively used in Ethernet over fiber.

In the past, most computer designers would have their own fabs.

But once designs started getting very complicated, it started to make sense to separate concerns between designers and fabs.

What this means is that design companies would primarily write register transfer level, then use electronic design automation tools to get a final manufacturable chip, and then send that to the fab.

It is in this point of time that TSMC came along, and benefied and helped establish this trend.

The term "Fabless" could in theory refer to other areas of industry besides the semiconductor industry, but it is mostly used in that context.

An efficient algorithm to calculate the discrete Fourier transform.

Most of the videos are crap, but the following ones almost killed Ciro Santilli of laughter:

Monty Python has a few precursors to the "random famous people mixed together compting" format, although not in the rap fight format:

FFmpeg is the assembler of audio and video.

As a result, Ciro Santilli who likes "lower level stuff", has had many many hours if image manipulation fun with this software, see e.g.:

As older Ciro grows, the more he notices that FFmpeg can do basically any lower level audio video task. It is just an amazing piece of software, the immediate go-to for any low level operation.

FFmpeg was created by Fabrice Bellard, which Ciro deeply respects.

Resize a video: superuser.com/questions/624563/how-to-resize-a-video-to-make-it-smaller-with-ffmpeg:Unlike every other convention under the sun, the height in scale is the first number.

A useless piece of paper (or digital version of it) that you can pay taxes with :)

As opposed to:

This is a good first concrete example of a Lie algebra. Shown at Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 4.2 "How to linearize a Lie Group" has an example.

We can use use the following parametrization of the special linear group on variables $x$, $y$ and $z$:

Every element with this parametrization has determinant 1:Furthermore, any element can be reached, because by independently settting $x$, $y$ and $z$, $M_{00}$, $M_{01}$ and $M_{10}$ can have any value, and once those three are set, $M_{11}$ is fixed by the determinant.

To find the elements of the Lie algebra, we evaluate the derivative on each parameter at 0:

Remembering that the Lie bracket of a matrix Lie group is really simple, we can then observe the following Lie bracket relations between them:

One key thing to note is that the specific matrices $M_x$, $M_y$ and $M_z$ are not really fundamental: we could easily have had different matrices if we had chosen any other parametrization of the group.

TODO confirm: however, no matter which parametrization we choose, the Lie bracket relations between the three elements would always be the same, since it is the number of elements, and the definition of the Lie bracket, that is truly fundamental.

Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 4.2 "How to linearize a Lie Group" then calculates the exponential map of the vector $x{M}_x+y{M}_y+z{M}_z$ as:with:

TODO now the natural question is: can we cover the entire Lie group with this exponential? Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 7 "EXPonentiation" explains why not.

We can reach it by taking the rotations in three directions, e.g. a rotation around the z axis:then we derive and evaluate at 0:$L_z$ therefore represents the infinitesimal rotation.

Note that the exponential map reverses this and gives a finite rotation around the Z axis back from the infinitesimal generator $L_z$:

Repeating the same process for the other directions gives:We have now found 3 linearly independent elements of the Lie algebra, and since $SO(3)$ has dimension 3, we are done.

This makes it clear how the Lie bracket can be seen as a "measure of non-commutativity"

Because the Lie bracket has to be a bilinear map, all we need to do to specify it uniquely is to specify how it acts on every pair of some basis of the Lie algebra.

Then, together with the Baker-Campbell-Hausdorff formula and the Lie group-Lie algebra correspondence, this forms an exceptionally compact description of a Lie group.

Recommended from Physics from Symmetry by Jakob Schwichtenberg (2015) page 92: