Tangent space Updated 2025-07-16
Bibliography:
- www.youtube.com/watch?v=j1PAxNKB_Zc Manifolds #6 - Tangent Space (Detail) by WHYB maths (2020). This is worth looking into.
- www.youtube.com/watch?v=oxB4aH8h5j4 actually gives a more concrete example. Basically, the vectors are defined by saying "we are doing the Directional derivative of any function along this direction".One thing to remember is that of course, the most convenient way to define a function and to specify a direction, is by using one of the coordinate charts.
- jakobschwichtenberg.com/lie-algebra-able-describe-group/ by Jakob Schwichtenberg
- math.stackexchange.com/questions/1388144/what-exactly-is-a-tangent-vector/2714944 What exactly is a tangent vector? on Stack Exchange
One-form Updated 2025-07-16
www.youtube.com/watch?v=tq7sb3toTww&list=PLxBAVPVHJPcrNrcEBKbqC_ykiVqfxZgNl&index=19 mentions that it is a bit like a dot product but for a tangent vector to a manifold: it measures how much that vector derives along a given direction.
Chinese character Updated 2025-07-16
Backstory Updated 2025-07-16
Damsel in distress Updated 2025-07-16
Everybody Was Kung-Fu Fighting (trope) Updated 2025-07-16
Guns Are Worthless Updated 2025-07-16
Lotus-Eater Machine Updated 2025-07-16
Fan service Updated 2025-07-16
Justified criminal Updated 2025-07-16
Monster of the week Updated 2025-07-16
Sliding scale of idealism vs. cynicism Updated 2025-07-16
Supernatural martial arts Updated 2025-07-16
Shame that the Chinese in the lat 20th early 21st like that bullshit so much. It just weakens everything. Just imaginge those works with more realistic fighting! Would be amazing.
Super Strength Updated 2025-07-16
Suspension of disbelief Updated 2025-07-16
It's Popular Now It Sucks Updated 2025-07-16
This is true: high budget movies are shit. Just TV Trops can articular it infinitely better than Ciro Santilli can.
Related:
Lean (proof assistant) Updated 2026-01-30
Source code:
- github.com/leanprover/lean4 why a separate repo per version... but it is what it is.
- github.com/leanprover/lean
The way Lean and Coq mix programming and mathematics is a thing of great beauty. This is especially notable in lean as you start to play with with things such as:
partialenv lean functions, and usingterminates_byto prove that certain functions terminate. Lean requires explicitly known if functions terminate or not to be able to use them in proofs.noncomputablefunctions. Lean allows you to define mathematical functions which you can't actually execute, and it tracks that explicitly
They are huge fans of Unicode characters! Check this out from a formal proof of the prime number theorem: github.com/AlexKontorovich/PrimeNumberTheoremAnd/blob/fbdbb5310d036d33b9797b35f3b04b08f2447a6e/PrimeNumberTheoremAnd/ZetaBounds.lean Here's map to Ascii: proofassistants.stackexchange.com/questions/954/does-lean-have-a-standard-ascii-representation/5289#5289
Their dependency graph thingy is just beautiful however: alexkontorovich.github.io/PrimeNumberTheoremAnd/web/dep_graph_document.html
Coursera Updated 2025-07-16
Some courses at least allow you to see material for free, e.g.: www.coursera.org/learn/quantum-optics-single-photon/lecture/UYjLu/1-1-canonical-quantization. Lots of video focus as usual for MOOCs.
Some are paywalled: www.coursera.org/learn/theory-of-angular-momentum?specialization=quantum-mechanics-for-engineers
It is extremely hard to find the course materials without enrolling, even if enrolling for free! By trying to make money, they make their website shit.
The comment section does have a lot of activity: www.coursera.org/learn/statistical-mechanics/discussions/weeks/2! Nice. And works like a proper issue tracker. But it is also very hidden.
November 2023 topics:
- quantum field theory: no
- condensed matter: 1 by Rahul Nandkishore from Colorado Boulder: www.coursera.org/specializations/the-physics-of-emergence-introduction-to-condensed-matter
EdX Updated 2025-07-16
Harvard University + MIT combo.
As of 2022:Fuck that.
Also, they have an ICP.
November 2023 course search:
- Condensed matter: 4 hits, so not too bad
- quantum field theory: no hits
FutureLearn Updated 2025-07-16
Some/all courses expire in 4 weeks: www.futurelearn.com/courses/intro-to-quantum-computing. Ludicrous.
There are unlisted articles, also show them or only show them.