Mechanics before quantum mechanics and special relativity.
Written mostly by Eric W. Weisstein.
Ciro once saw a printed version of the CRC "concise" encyclopedia of mathematics. It is about 12 cm thick. Imagine if it wasn't concise!!!
Infinite Napkin is the one-person open source replacemente we needed for it! And OurBigBook.com will be the final multi-person replacement.
If a product of a big company has a catchy name it came from an acquisition by 
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01If a Big Company makes a product that Does Something, they just call it Big Company Does Something.
If a product is called "Big Company Catchy Name Does Something", then it came from an acquisition, and they wanted to keep the name due to its prestige and to not confuse users.
TODO what's the point of it.
Bibliography:
- www.youtube.com/watch?v=j1PAxNKB_Zc Manifolds #6 - Tangent Space (Detail) by WHYB maths (2020). This is worth looking into.
- www.youtube.com/watch?v=oxB4aH8h5j4 actually gives a more concrete example. Basically, the vectors are defined by saying "we are doing the Directional derivative of any function along this direction".One thing to remember is that of course, the most convenient way to define a function and to specify a direction, is by using one of the coordinate charts.We can then just switch between charts by change of basis.
- jakobschwichtenberg.com/lie-algebra-able-describe-group/ by Jakob Schwichtenberg
- math.stackexchange.com/questions/1388144/what-exactly-is-a-tangent-vector/2714944 What exactly is a tangent vector? on Stack Exchange
Everybody Was Kung-Fu Fighting (trope) by Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01By the Open University. "Open" I mean.
Some/all courses expire in 4 weeks: www.futurelearn.com/courses/intro-to-quantum-computing. Ludicrous.
Like everything else in Lie groups, first start with the matrix as discussed at Section "Lie algebra of a matrix Lie group".
Intuitively, a Lie algebra is a simpler object than a Lie group. Without any extra structure, groups can be very complicated non-linear objects. But a Lie algebra is just an algebra over a field, and one with a restricted bilinear map called the Lie bracket, that has to also be alternating and satisfy the Jacobi identity.
Another important way to think about Lie algebras, is as infinitesimal generators.
Because of the Lie group-Lie algebra correspondence, we know that there is almost a bijection between each Lie group and the corresponding Lie algebra. So it makes sense to try and study the algebra instead of the group itself whenever possible, to try and get insight and proofs in that simpler framework. This is the key reason why people study Lie algebras. One is philosophically reminded of how normal subgroups are a simpler representation of group homomorphisms.
To make things even simpler, because all vector spaces of the same dimension on a given field are isomorphic, the only things we need to specify a Lie group through a Lie algebra are:Note that the Lie bracket can look different under different basis of the Lie algebra however. This is shown for example at Physics from Symmetry by Jakob Schwichtenberg (2015) page 71 for the Lorentz group.
- the dimension
- the Lie bracket
As mentioned at Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 4 "Lie Algebras", taking the Lie algebra around the identity is mostly a convention, we could treat any other point, and things are more or less equivalent.
Lebesgue integral of is complete but Riemann isn't by Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01 is:
- complete under the Lebesgue integral, this result is may be called the Riesz-Fischer theorem
- not complete under the Riemann integral: math.stackexchange.com/questions/397369/space-of-riemann-integrable-functions-not-complete
And then this is why quantum mechanics basically lives in : not being complete makes no sense physically, it would mean that you can get closer and closer to states that don't exist!
TODO intuition
For Ciro Santilli's campaign for freedom of speech in China: Section "github.com/cirosantilli/china-dictatorship".
Ciro has the radical opinion that absolute freedom of speech must be guaranteed by law for anyone to talk about absolutely anything, anonymously if they wish, with the exception only of copyright-related infringement.
And Ciro believes that there should be no age restriction of access to any information.
People should be only be punished for actions that they actually do in the real world. Not even purportedly planning those actions must be punished. Access and ability to publish information must be completely and totally free.
If you don't like someone, you should just block them, or start your own campaign to prepare a counter for whatever it is that they are want to do.
This freedom does not need to apply to citizens and organizations of other countries, only to citizens of the country in question, since foreign governments can create influence campaigns to affect the rights of your citizens. More info at: cirosantilli.com/china-dictatorship/mark-government-controlled-social-media
Limiting foreign influence therefore requires some kind of nationality check, which could harm anonymity. But Ciro believes that almost certainly such checks can be carried out in anonymous blockchain consensus based mechanisms. Governments would issues nationality tokens, and tokens are used for anonymous confirmations of rights in a way that only the token owner, not even the government, can determine who used the token. E.g. something a bit like what Monero does. Rights could be checked on a once per account basis, or yearly basis, so transaction costs should not be a big issue. Maybe expensive proof-of-work systems can be completely bypassed to the existence of this central token authority?
Some people believe that freedom of speech means "freedom of speech that I agree with". Those people should move to China or some other dictatorship.
Some key points that are a bit hard to grasp, at least in some versions:
- How did Bill Haydon know Jim Prideaux was going to Prague if it appears to be organized as a closely guarded secret by Control?so which one is it?
- the film suggests Prideaux must have told Haydon himself, his close friend, against Control's orders of secrecy, out of loyalty, and in order to protect his friend.
- The series suggests it was a honeypot
- How does Smiley deduce that the Witchcraft source, Merlin, is Poliakov? A key step is when top people at the Circus question him about Ricki Tarr, and appear to suggest that there is a link between Ricki Tarr and Merlin. And Ricki told Smiley that Poliakov as the link to the Mole. Smiley understands that it was Karla who tipped off London Center about Ricki's coming through Merlin. He also observers that Witchcraft gives ideological infiltration campaign intelligence after Ricki comes back, as a way to discredit Ricki. It is still all a bit indirect.
Previously called "Lending Library" it seems: help.archive.org/hc/en-us/articles/360016554912-Borrowing-From-The-Lending-Library
You can borrow online books from them for a few hours/days: help.archive.org/hc/en-us/articles/360016554912-Borrowing-From-The-Lending-Library This is the most amazing thing ever made!!! You can even link to specific pages, e.g. archive.org/details/supermenstory00murr/page/80/mode/2up
They seem to a have a separate URL with the same content as well for some reason: openlibrary.org/, classic messy Internet Archive style.
Bastards are suing them www.theverge.com/2020/6/1/21277036/internet-archive-publishers-lawsuit-open-library-ebook-lending: Hachette, Penguin Random House, Wiley, and HarperCollins
It is quite hard to decide if an upload is from the official legal lending library, or just some illegal upload, e.g.:so the URLs are basically the same style. Some legality indicators:
- archive.org/details/TheGoogleStory likely illegal
- archive.org/details/isbn_9780385342728 likely legal
Access-restricted-item: true- present in the collection: archive.org/details/internetarchivebooks?tab=about
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