Nikolaj-K

Text discussed in the video

https://youtu.be/uso0RZvgiWY

===== su(2) basis vs. Pauli matrices vs. quaternions =====
==== 2x2 Hermitian matrices ====
Looking at complex matrices in ${\mathbb M}({\mathbb C})_{2\times 2}$.
Conjugate transpose function:
$\begin{pmatrix} \alpha & \beta \\ \gamma & \delta \end{pmatrix}^*:=\begin{pmatrix} \bar\alpha & \bar\gamma \\ \bar\beta & \bar\delta \end{pmatrix}$

Nikolaj-K

This is the script used in the video

https://youtu.be/DkgpE2MVDrs

===== SU(2) actions for spherical coordinates =====
==== Convention ====
$\bullet$ Righthanded rotations, a.k.a. counterclockwise in plane (as supposed to lefthanded)
(like standard complex number multiplication in the plane of rotation, with the axis pointing towards you).

$\bullet$ Extrinsic rotation (as opposed to intrinsic):

Nikolaj-K

import matplotlib.pyplot as plt
import numpy as np


def weighted_mean(weights, values):
    assert len(weights) == len(values)

    terms = (w * v for w, v in zip(weights, values))

    return sum(terms) / sum(weights)

Nikolaj-K

"""
Run via
python /Users/amoogle/Documents/Pages/pages_video/spherical_pendulum_sim.py

I have explained the animation tool in
https://youtu.be/rQwnOZFuYsU
"""

import math
import matplotlib

Nikolaj-K

{
  "201201": {
    "1": [
      "Toma Dup",
      "Johni Johni"
    ],
    "2": [
      "Toma Dup"
    ]
  },

Nikolaj-K

So this is 170 years ago when Germany isn’t really Germany, you have Hegel (and e.g. Schopenhauer) lecturing about his dialectical logic and view of history, in Berlin, and there emerges the group of young Hegelians arguing with each other. Completely contrary to Hegels view on the state, but very much in line with his logic and methods, they (Marx, Feuerbach, Stirner, etc.) all start writing books (and being censored). In particular Feuerbach writing the The Essence of Christianity, in which - after Nietzsches death of god at the same time - he makes the ideal human get the centerstage. A proper humanism. Stirner writes his treaty of the self and what it means to own in this context (“The Unique one and his Property”.) The chapter structure parodies Feuerbach and the first dozen of pages of the book parodies Hegels perspective on the world. Stirner criticises that Feuerbach makes “the good human“ a new abstraction that merely replaces the perfect god Feuerbach wants to part with in his ideology. He takes tha

Nikolaj-K

This is the text for the video

https://youtu.be/pYBLStI9VlE

=== SO(2, Q) ===
Given any two ${\mathrm e}^{ia},{\mathrm e}^{ib}\in {\sf{U}}(1)$, their product ${\mathrm e}^{ia}\cdot{\mathrm e}^{ib}$ is again in ${\sf{U}}(1)$.
Various subgroups embed into ${\sf{U}}(1)$.
The upper left point in that Wikipedia picture 
https://en.wikipedia.org/wiki/Template:Group_theory_sidebar#/media/File:Cyclic_group.svg

Nikolaj-K

"""
Code for the video:

https://youtu.be/MUbZ9XqWsuc

https://en.wikipedia.org/wiki/List_of_formulae_involving_%CF%80
"""

import math
import time

Nikolaj-K

"""
Scrpt for the video here:

https://youtu.be/Gzz5_BbvGos

References
See also: https://rosettacode.org/wiki/Formal_power_series#Python
https://en.wikipedia.org/wiki/Formal_power_series
https://en.wikipedia.org/wiki/Lazy_evaluation
https://en.wikipedia.org/wiki/Computable_analysis

Nikolaj-K

"""
This is the script discussed in the video:

https://youtu.be/dmSK0siN7c4
"""

N = 5

"""
Compute the commutative semirings of size N > 1 that are