Analytic continuation Updated 2025-07-16
visualizing the Riemann hypothesis and analytic continuation by 3Blue1Brown (2016) is a good quick visual non-mathematical introduction is to it.
The key question is: how can this continuation be unique since we are defining the function outside of its original domain?
The answer is: due to the identity theorem.
Lysozyme Updated 2025-07-16
Breaks up peptidoglycan present in the bacterial cell wall, which is thicker in Gram-positive bacteria, which is what this enzyme seems to target.
Part of the inate immune system.
It is present on basically everything that mammals and birds excrete, and it kills bacteria, both of which are reasons why it was discovered relatively early on.
R (programming language) Updated 2025-07-16
Ubuntu 23.04 install:
sudo apt install rbase
Hello world:
R -e 'print("hello world")'
Install a package, e.g. Bookdown:
sudo R -e 'install.packages("bookdown")'
RSA (cryptosystem) Updated 2025-07-16
Based on the fact that we don't have a P algorithm for integer factorization as of 2020. But nor proof that one does not exist!
The private key is made of two randomly generated prime numbers: and . How such large primes are found: how large primes are found for RSA.
The public key is made of:
Given a plaintext message m, the encrypted ciphertext version is:
c = m^e mod n
This operation is called modular exponentiation can be calculated efficiently with the Extended Euclidean algorithm.
The inverse operation of finding the private m from the public c, e and is however believed to be a hard problem without knowing the factors of n.
However, if we know the private p and q, we can solve the problem. As follows.
First we calculate the modular multiplicative inverse. TODO continue.
Magazine Updated 2025-07-16
Craig Steven Wright Updated 2025-07-16
This dude actually managed to convince a brain-dead British court that he was Satoshi and force a takedown of the Bitcoin whitepaper from bitcoin.org/bitcoin.pdf where it had been for many years prior: coinmarketcap.com/academy/article/bitcoin-org-ordered-to-take-down-bitcoin-whitepaper-because-of-copyright-infringement The page was updated to simply display the following Satoshi quote:
It takes advantage of the nature of information being easy to spread but hard to stifle. - Satoshi Nakamoto
The mere thought that Satoshi would attempt to copyright takedown the Bitcoin whitepaper, and not be able to back his identidy with any cryptographic keys, makes one shrivel to the bones.
Also, kids, this is why you put a fucking license on everything you release to the public, and especially when doing so anonymously!!! A quick CC BY-SA on that paper would have prevented all this bullshit.
Timeline:
Interesting
Amit Singhal Updated 2025-07-16
Pitched OurBigBook.com to him:
Idea: make all Sitare University materials open, and allow students to write the content
Also, allow anyone to take the exams without enrolling (possibly for a fee if they don't have scholarship).
This is the way to go if you really want to increase your impact/dollar and do something truly innovative that ill make a mark. Why just mirror existing university models that haven't yet caught up to the Internet Age?
Quantum superposition Updated 2025-07-16
Quantum superposition is really weird because it is fundamentally different than "either definite state but I don't know which", because the superposition state leads to different measurements than the non-superposition state.
Examples:

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