A Ring can be seen as a generalization of a field where:
- multiplication is not necessarily commutative. If this is satisfied, we can call it a commutative ring.
- multiplication may not have inverse elements. If this is satisfied, we can call it a division ring.
Addition however has to be commutative and have inverses, i.e. it is an Abelian group.
The simplest example of a ring which is not a full fledged field and with commutative multiplication are the integers. Notably, no inverses exist except for the identity itself and -1. E.g. the inverse of 2 would be 1/2 which is not in the set. More specifically, the integers are a commutative ring.
A polynomial ring is another example with the same properties as the integers.
The simplest non-commutative, non-division is is the set of all 2x2 matrices of real numbers:Note that is not a ring because you can by addition reach the zero matrix.
- we know that 2x2 matrix multiplication is non-commutative in general
- some 2x2 matrices have a multiplicative inverse, but others don't
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!
Nabla is one of those: it was completely made up in modern times, and just happens to look like an inverted upper case delta to make things even more confusing!
Nabla means "harp" in Greek, which looks like the symbol.
- kimchi
- reverse debugging
- E Ink
- web archiving
- Buildroot
- integrated development environments
- degreaser
- UML: while it might seem like a over-thought thing and likely is, the basic idea that understanding "one to one vs one to many vs many to many" relationships between objects and which object can see which object, is a fantastic approach towards understanding complex object oriented code
- open source software, including open source scientific computing consultancies
- computer
- FOSDEM. Ciro Santilli attended in 2016, and felt extremely good together with all those amazingly smart open source hackers: www.quora.com/What-are-the-best-open-source-conferences/answer/Ciro-Santilli
- Sass
- vimium
- bisection
- vector graphics, notably scalable Vector Graphics
- ASCII art
- OAuth
- command-line interface
- virtualization
- Anusol
- autodidacticism and self-directed learning
- end-to-end encryption
- The Criterion Collection
- version control
- SQLite
- Guerrilla Mail
- POSIX
- static website
- Freeman Dyson
- open access academic publishers
- unconditional basic income
- transhumanism
- 2FA, and notably 2FA apps
- human-readable formats
- wealth tax
- Reproducible builds
- F-Droid
- Can't get you out of my head by Adam Curtis (2021)
- drug liberalization
- Wiki-binge
- molecular Sciences Course of the University of São Paulo
- meal deal
- clade, as opposed to taxonomic ranks
- lingua franca, see also: having more than one natural language is bad for the world
- rsync
- zip hoodies
Previously known as "Food From Electricity", "NeoCarbonFood" sounds like a more commercializable version of it.
Uses electricity to electrolyse water into hydrogen and oxygen molecules, and then use bacteria that do hydrogen chemosynthesis to convert it into food.
The "0-width" pulse distribution that integrates to a step.
There's not way to describe it as a classical function, making it the most important example of a distribution.
Applications:
- position operator in quantum mechanics. It's not a coincidence that the function is named after Paul Dirac.
Being a complex holomorphic function is an extremely strong condition.
The existence of the first derivative implies the existence of all derivatives.
Another extremely strong consequence is the identity theorem.
"Holos" means "entire" in Greek, so maybe this is a reference to the fact that due to the identity theorem, knowing the function on a small open ball implies knowing the function everywhere.
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