Magnetism Updated +Created
Point light source Updated +Created
Can be approximated with a diaphragm.
Prime number theorem Updated +Created
Prokaryotic cell organelle Updated +Created
Ross Ulbricht Updated +Created
Voltage Updated +Created
What I cannot create, I do not understand Updated +Created
Eternal September Updated +Created
Euclidean metric signature matrix Updated +Created
Fluid mechanics Updated +Created
Boooooring.
Franck-Hertz experiment Updated +Created
German nuclear weapons program Updated +Created
Memory semantics Updated +Created
These are the rules which specify what different concurrent read/write memory accesses from different threads/processes can or cannot see.
Notable such set of rules include:
Mental state Updated +Created
Quantum key distribution protocol Updated +Created
Transistor Updated +Created
Although transistors were revolutionary, it is fun to note that they were just "way cheaper and more reliable and smaller" versions of exactly the main functions that a vacuum tube could achieve
Vector field Updated +Created
Amazon EC2 hello world Updated +Created
Let's get SSH access, instal a package, and run a server.
As of December 2023 on a t2.micro instance, the only one part of free tier at the time with advertised 1 vCPU, 1 GiB RAM, 8 GiB disk for the first 12 months, on Ubuntu 22.04:
$ free -h
               total        used        free      shared  buff/cache   available
Mem:           949Mi       149Mi       210Mi       0.0Ki       590Mi       641Mi
Swap:             0B          0B          0B
$ nproc
1
$ df -h /
Filesystem      Size  Used Avail Use% Mounted on
/dev/root       7.6G  1.8G  5.8G  24% /
To install software:
sudo apt update
sudo apt install cowsay
cowsay asdf
Once HTTP inbound traffic is enabled on security rules for port 80, you can:
while true; do printf "HTTP/1.1 200 OK\r\n\r\n`date`: hello from AWS" | sudo nc -Nl 80; done
and then you are able to curl from your local computer and get the response.
Golden Crescent Updated +Created
Group homomorphism Updated +Created
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.

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