Pair programming Updated 2025-07-16
Polymorphism (computer science) Updated 2025-07-16
Server form factor Updated 2025-07-16
Wealth distribution in the United States Updated 2025-07-16
www.cbpp.org/wealth-concentration-has-been-rising-toward-early-20th-century-levels-2 shows historical for top 1% and 0.5% from 1920 to 2010.
TODO why is it so hard to find a proper cumulative distribution function-like curve? OMG. This appears to be also called a Lorenz curve.
Wealth Inequality in America by politizane
. Source. Amazon product Updated 2025-07-16
Gwern Branwen Updated 2025-07-16
Accounts:He posts insanely much on these websites. It's a bit like Ciro Santilli on Stack Overflow.
- news.ycombinator.com/user?id=gwern
- www.lesswrong.com/users/gwern LessWrong
- twitter.com/gwern locked 2021: www.reddit.com/r/slatestarcodex/comments/kp2fek/does_anybody_know_what_happened_to_gwern/
- www.reddit.com/user/gwern/
- en.wikipedia.org/wiki/User:Gwern on Wikipedia. Self summary: gwern.net/wikipedia-resume. Also he is a critic of deletionism on Wikipedia like Ciro Santilli
Ciro Santilli envies this guy a bit. He dumps his brain more or less full time on his highly customized static website partly due to early Bitcoin investments gwern.net/me says:
Also unsurprisingly he likes Haskell:
Ciro Santilli considers Gwern Ciro Santilli's e-soulmates due to his interest in "dark web things" like Bitcoin and Silk Road, his immense writing output in encyclopedic book-sized articles on a static website, and his desire to live frugally and just research and write all day. Ah, if only Ciro had some old coins!!!
This is likely a pseudonym, his real name not being publicly unknown, e.g. at news.ycombinator.com/item?id=5659278:
Why do you choose relative anonymity?For the reasons I've said in the past. To which I can add personal safety: my Silk Road page is a bit questionable legally, and we all know that there are ways to exploit knowledge of one's True Name and address (even if, as far as I know, I have no enemies willing to resort to, say, 'swatting' me) - one group of stalkers called up a college they thought I worked at to see if they could get me fired or otherwise ruin my day.
Hamiltonian mechanics Updated 2025-07-16
Equivalent to Lagrangian mechanics but formulated in a different way.
Motivation: Lagrangian vs Hamiltonian.
TODO understand original historical motivation, www.youtube.com/watch?v=SZXHoWwBcDc says it is from optics.
Intuitively, the Hamiltonian is the total energy of the system in terms of arbitrary parameters, a bit like Lagrangian mechanics.
Bibliography:
"Hello, World!" program Updated 2025-07-26
The most important program ever written!!!
Reproductive cue Updated 2025-07-16
Fizeau experiment Updated 2025-07-16
Hafele-Keating experiment Updated 2025-07-16
Nabla symbol Updated 2025-07-16
As if Greek letters weren't enough, physicists and mathematicians also like to make up tons of symbols, some of which look like the could actually be Greek letters!
Positive definite symmetric bilinear form Updated 2025-07-16
Sine Updated 2025-07-16
Sulfur hydrade Updated 2025-07-16
Sycee Updated 2025-07-16
Water Margin scene Updated 2025-07-16
American learned society Updated 2025-07-16
American Physical Society Updated 2025-07-16
Bra-ket notation Updated 2025-07-16
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 .
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 along the 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 that is an operator and 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 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 ... 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.
Unlisted articles are being shown, click here to show only listed articles.