Ciro Santilli @cirosantilli 37

Adds up chemical energy and kinetic energy.

Wikipedia mentions however that the kinetic energy is often negligible, even for gases.

The sum is of interest when thinking about reactions because chemical reactions can change the number of molecules involved, and therefore the pressure.

To predict if a reaction is spontaneous or not, negative enthalpy is not enough, we must also consider entropy via Gibbs free energy.

Bibliography:

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:

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.

A good project to see UARTs at work in all their beauty is to connect two Raspberry Pis via UART, and then:

Part of the beauty of this is that you can just connect both boards directly manually with a few wire-to-wire connections with simple jump wire. Its simplicity is just quite refreshing. Sure, you could do something like that for any physical layer link presumably...

Remember that you can only have one GNU screen connected at a time or else they will mess each other up: unix.stackexchange.com/questions/93892/why-is-screen-is-terminating-without-root/367549#367549

On Ubuntu 22.04 you can screen without sudo by adding yourself to the dialout group with:

en.wikipedia.org/wiki/Logarithm_of_a_matrix#Existence mentions it always exists for all invertible complex matrices. But the real condition is more complicated. Notable counter example: -1 cannot be reached by any real $e^{tk}$.

The Lie algebra exponential covering problem can be seen as a generalized version of this problem, because

As of 2020, university has the following very important applications:Notably, Education is an IQ test, not a way to learn useful and beautiful things.

One major issue is that teachers don't have the right incentive to, nor are selected to, teach well. Thus the existence of Rate My Professors! But we can do better...

Which is why Ciro Santilli wants to destroy its current format with OurBigBook.com. He believes that we can find a more efficient organization to achieve both the social and research functions of university, by first doing as much as possible online

Ciro's university experiences are mentioned at: Ciro Santilli's formal education.

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.

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:

The author seems to have uploaded the entire book by chapters at: www.physics.drexel.edu/~bob/LieGroups.html

And the author is the cutest: www.physics.drexel.edu/~bob/Personal.html.

Overview:

Lance instructor of the 800,000 Imperial Guards (八十万禁军枪棒教头). TODO understand the "枪棒" part: zhidao.baidu.com/question/206659649.html.

The adopted son of Gao Qiu wanted to fuck his wife, and because of this they frame him of planning to take revenge by killing Go Qiu, even though Lin Chong had decided not to take revenge to avoid harming his wife further.

They just keep trying to kill him, until at one point he just gives up and becomes a fugitive.

His story is well told in The Water Margin.

Usually called by others as 林教头 (lin jiaotou, literally Head Instructor Lin, but usually translated as just Instructor Lin).