Ciro Santilli @cirosantilli 37

Is the set of all n-by-y square matrices.

Because $GL(n)$ is a Lie group we can use Section "Lie algebra of a matrix Lie group".

For every matrix $x$ in the set of all n-by-y square matrices $M_n$, $e^x$ has inverse $e^{-}x$.

Note that this works even if $x$ is not invertible, and therefore not in $GL(n)$!

Therefore, the Lie algebra of $GL(n)$ is the entire $M_n$.

Full set of all possible special relativity symmetries:

In simple and concrete terms. Suppose you observe N particles following different trajectories in Spacetime.

There are two observers traveling at constant speed relative to each other, and so they see different trajectories for those particles:Note that the first two types of transformation are exactly the non-relativistic Galilean transformations.

The Poincare group is the set of all matrices such that such a relationship like this exists between two frames of reference.

17 of them.

"Water" is the name for both:

Subtle is the Lord by Abraham Pais (1982) mentions that this has a good summary of the atomic theory evidence that was present at the time, and which had become basically indisputable at or soon after that date.

On Wikimedia Commons since it is now public domain in most countries: commons.wikimedia.org/w/index.php?title=File:Perrin,_Jean_-_Les_Atomes,_F%C3%A9lix_Alcan,_1913.djvu

An English translation from 1916 by English chemist Dalziel Llewellyn Hammick on the Internet Archive, also on the public domain: archive.org/details/atoms00hammgoog

4 K. Enough for to make "low temperature superconductors" like regular metals superconducting, e.g. the superconducting temperature of aluminum if 1.2 K.

Contrast with liquid nitrogen, which is much cheaper but only goes to 77K.

Very easy to use and pretty powerful MIDI creator!!!

One of the rare audio applications actually works with PulseAudio on Ubuntu 20.04 out-of-the-box, so you don't have to turn off every other audio application!!!

Has lot's of plugins built-in just working out of the box, e.g. ZynAddSubFX out-of-the-box without doing a gazillion complex setup connections.

Most plugins are just simple toys however, ZynAddSubFX is the only super powerful one. The others are more LMMS integrate however, and seem to use a more dedicated LMMS GUI style.

TODO can you do liver performance with a virtual instrument?

If you open vmpk, you can then right click on a piano track, and go MIDI, Input and it just shows up there, and it does produce sound as shown at: www.youtube.com/watch?v=NpeP2th08ak

TODO: what about recording the input MIDI? Yes, there is a record button on the piano roll!

So simple!! You can either:

A handle cancels out a Möbius strip, so adding one of each does not lead to a new object.

You can glue a Mobius strip into a single hole in dimension larger than 3! And it gives you a Klein bottle!

Intuitively speaking, they can be sees as the smooth surfaces in N-dimensional space (called an embedding), such that deforming them is allowed. 4-dimensions is enough to embed cover all the cases: 3 is not enough because of the Klein bottle and family.

The opposite of freedom of speech.

For censorship in China see: cirosantilli.com/china-dictatorship/censorship

Chanbara (チャンバラ).

Those movies are "all the same". A quasi lone superhuman samurai with a good inside but painful problems helping out random people, mostly villagers in trouble and bitches in debt.

His films Blaise Pascal (1972) and Cartesius (1974) have the greatest scenery and wardrobe ever. The eerie horror movie soundtrack is also very interesting. Ciro was weirdly reminded of Cosmos: A Personal Voyage (1980).

A function: