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.
There are unlisted articles, also show them or only show them.