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We can reach it by taking the rotations in three directions, e.g. a rotation around the z axis:then we derive and evaluate at 0: therefore represents the infinitesimal rotation.
Note that the exponential map reverses this and gives a finite rotation around the Z axis back from the infinitesimal generator :
Repeating the same process for the other directions gives:We have now found 3 linearly independent elements of the Lie algebra, and since has dimension 3, we are done.
Because the Minkowski inner product product is not positive definite, the norm induced by an inner product is a norm, and the space is not a metric space strictly speaking.
Answer: it can give some qualitative intuition on what is larger/smaller happens before/after based only on arguably more intuitive geometric considerations, without requiring you to do any calculations, see e.g. Figure "Spacetime diagram illustrating how faster-than-light travel implies time travel".
In the standard formulation of Maxwell's equations, the electric current is a convient but magic input.
Would it be possible to use Maxwell's equations to solve a system of pointlike particles such as electrons instead?
The following suggest no, or only for certain subcases less general than Maxwell's equations:
This is the type of thing where the probability aspect of quantum mechanics seems it could "help".
The Engineering Puzzle of Storing Trillions of Bits in your Smartphone / SSD using Quantum Mechanics by Branch Education (2020)
Source. Nice animations show how quantum tunnelling is used to set bits in flash memory.This is a good approach. The downside is that while you are developing the implementation and testing interactively you might notice that the requirements are wrong, and then the tests have to change.
One intermediate approach Ciro Santilli likes is to do the implementation and be happy with interactive usage, then create the test, make it pass, then remove the code that would make it pass, and see it fail. This does have a risk that you will forget to test something, but Ciro finds it is a worth it generally. Unless it really is one of those features that you are unable to develop without an automated test, generally more "logical/mathematical" stuff. This is a sort of laziness Driven Development.
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.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact