Ciro Santilli @cirosantilli 40

Notation used in quantum mechanics.

Ket is just a vector. Though generally in the context of quantum mechanics, this is an infinite dimensional vector in a Hilbert space like $L^2$.

Bra is just the dual vector corresponding to a ket, or in other words projection linear operator, i.e. a linear function which can act on a given vector and returns a single complex number. Also known as... dot product.

For example:is basically a fancy way of saying:that is: we are taking the projection of $y$ along the $x$ direction. Note that in the ordinary dot product notation however, we don't differentiate as clearly what is a vector and what is an operator, while the bra-ket notation makes it clear.

The projection operator is completely specified by the vector that we are projecting it on. This is why the bracket notation makes sense.

It also has the merit of clearly differentiating vectors from operators. E.g. it is not very clear in $x\cdot y$ that $x$ is an operator and $y$ is a vector, except due to the relative position to the dot. This is especially bad when we start manipulating operators by themselves without vectors.

This notation is widely used in quantum mechanics because calculating the probability of getting a certain outcome for an experiment is calculated by taking the projection of a state on one an eigenvalue basis vector as explained at: Section "Mathematical formulation of quantum mechanics".

Making the projection operator "look like a thing" (the bra) is nice because we can add and multiply them much like we can for vectors (they also form a vector space), e.g.:just means taking the projection along the $x+y$ direction.

Ciro Santilli thinks that this notation is a bit over-engineered. Notably the bra's are just vectors, which we should just write as usual with $\overrightarrow{v}$... the bra thing makes it look scarier than it needs to be. And then we should just find a different notation for the projection part.

Maybe Dirac chose it because of the appeal of the women's piece of clothing: bra, in an irresistible call from British humour.

But in any case, alas, we are now stuck with it.

The Portuguese term for it is "música popular brasileira". The widely recognized Brazilian acronym is "MPB".

"Brazilian pop" and "Br-pop" are inventions by Ciro Santilli, which are how Ciro thinks Brazil should market it to the world.

Unfortunately "B-pop" is too ambiguous with British pop music, and should be avoided.

YouTube playlist by Ciro Santilli containing all the songs in this section: www.youtube.com/playlist?list=PLcZOZrP1P_V4_SBDnegcLTcP-5YhNmWBB

Bibliography:

Self promoted at:Not self-promoted at:

Reactor of the Hanford site of the produced the plutonium used for Trinity and Fat Man.

This was the first full scale nuclear reactor in the world, and was brought up slowly to test it out.

This is how electronic circuits are normally prototyped!

Once you validate them like this, the next step is usually to move on to printed circuit boards for more reliable production setups.

Breadboards are a thing of beauty and wonder.

To break the meta means to find a new strategy that offers a significant advantage over the existing meta.

For the specific of video game glitch breaks see: Section "Meta breaking glitch".

Due to Ciro Santilli's self perceived creative personality, Ciro Santilli is very attracted to meta breaks.

By Zuckerberg. The selection seems decent. And natural sciences only, which is good. A bit more application oriented than the Nobel Prize it seems, e.g. 2022 separates physics and fundamental physics.

Appears to explain award reasoning even worse than the Nobel Foundation.

There are valid reasons to be pro-Brexit, given the uselessness of the European Union.

The problem was how the campaign was conducted, in a purely nationalistic, populist and fake news manner, and largely supported by business leaders who immediately after still wanted to hire cheap foreign labour, use tax havens and move headquarters to other countries, e.g.:

It's just too charming, and has some deep themes.

$BB(n)$ is the largest number of 1's written by a halting $n$-state Turing machine on a tape initially filled with 0's.

A cool thought about cancer expressed at Power, Sex, Suicide by Nick Lane (2006) is that cancer it is the direct product of natural selection gone wrong!

Cancer cells are obviously selected against anti-cancer mechanism, which when they manage to evade, they reproduce uncontrollably, gaining more and more momentum.

The British are very pragmatic. This has good and bad effects.

For example, a good effect is that many things work pretty well, such as the government. This also helped industry develop.

A bad effect is that they sometimes settle on local minima forever. Examples:If it ain't totally broken, just let it continue forever! See also: Section "History of the University of Oxford".