By 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 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +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
Half-precision floating-point format by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01Keep the example/theory ratio high, very, very high.
For natural sciences, add as many reproducible experiment images/videos/descriptions as you can.
It is OK to treat things as black boxes by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01Nature is a black box, right?
You don't need to understand the from first principles derivation of every single phenomena.
And most important of all: you should not start learning phenomena by reading the from first principles derivation.
Instead, you should see what happens in experiments, and how matches some known formula (which hopefully has been derived from first principles).
Only open the boxes (understand from first principles derivation) if the need is felt!
E.g.:
- you don't need to understand everything about why SQUID devices have their specific I-V curve curve. You have to first of all learn what the I-V curve would be in an experiment!
- you don't need to understand the fine details of how cavity magnetrons work. What you need to understand first is what kind of microwave you get from what kind of input (DC current), and how that compares to other sources of microwaves
- lasers: same
Physics is all about predicting the future. If you can predict the future with an end result, that's already predicting the future, and valid.
See also some remarks of Ciro Santilli's thoughts on the instrument Ciro Santilli's musical education.
Like isomorphism, but does not have to be one-to-one: multiple different inputs can have the same output.
The image is as for any function smaller or equal in size as the domain of course.
This brings us to the key intuition about group homomorphisms: they are a way to split out a larger group into smaller groups that retains a subset of the original structure.
As shown by the fundamental theorem on homomorphisms, each group homomorphism is fully characterized by a normal subgroup of the domain.
Globalization reduces the power of governments by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01While Ciro Santilli is a big fan of having "one global country" (and language), which is somewhat approximated by globalization, he has come to believe that there is one serious downside to globalization as it stands in 2020: it allows companies to pressure governments to reduce taxes, and thus reduces the power of government, which in turn increases social inequality. This idea is very well highlighted in Can't get you out of my head by Adam Curtis (2021).
The only solution seems to be for governments to get together, and make deals to have fair taxation across each other. Which might never happen.
A set of theorems that prove under different conditions that the Fourier transform has an inverse for a given space, examples:
There are unlisted articles, also show them or only show them.