Also way too idealistic :Sliding Scale of Idealism vs. Cynicism.
Also the good/evil is way too black and white.
If only everything was instead funny and charming and intelligent like the very first part in the Shire... that section and others interspersed withing the running are good film level.
Ciro Santilli's favorite religion. He does not believe fully in it, nor has he studied it besides through brief Wikipedia and Googling.
Ciro likes Buddhism because it feels like the least "metaphysical explanations to things you can't see" of the religions he knows.
Rather, it feels more like "a plausible theory of the mind" and highly compatible with physics.
Ciro also believes that there is a positive correlation between being a software engineer and liking Buddhist-like things, see also: the correlation between software engineers and Buddhism.
An Introduction to Tensors and Group Theory for Physicists by Nadir Jeevanjee (2011) by 
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01This does not seem to go deep into the Standard Model as Physics from Symmetry by Jakob Schwichtenberg (2015), appears to focus more on more basic applications.
But because it is more basic, it does explain some things quite well.
Lie group-Lie algebra correspondence by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01The Baker-Campbell-Hausdorff formula basically defines how to map an algebra to the group.
Bibliography:
- Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 7 "EXPonentiation"
Cardinality dimension of the vector space.
An Introduction to Tensors and Group Theory for Physicists by Nadir Jeevanjee (2011) shows that this is a tensor that represents the volume of a parallelepiped.
It takes as input three vectors, and outputs one real number, the volume. And it is linear on each vector. This perfectly satisfied the definition of a tensor of order (3,0).
Given a basis and a function that return the volume of a parallelepiped given by three vectors , .
A measurable function defined on a closed interval is square integrable (and therefore in ) if and only if Fourier series converges in norm the function:
An LC circuit is analogous to a spring-mass system by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01Both are harmonic oscillators.
In the LC circuit:
- the current current may be seen as the velocity and containing the kinetic energy
- the charge stored in the capacitor as the potential energy
You can kickstart motion in either of those systems in two ways:
- charge the capacitor, i.e. pull the string, and then let it go, i.e. close the circuit. This is the simpler one to realise. Shown concretely at: Video "LC circuit dampened oscillations on an oscilloscope by Queuerious Guy (2014)"
- give speed to the mass, i.e. make a current pass through the inductor
The function that fully describes a physical system in Lagrangian mechanics.
A waste of time like the rest of the knowledge olympiads.
You can learn more from older students than from faculty by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01Wikipedia mentions quoting his Nobel Prize biography:
In Monod's studies he discovered that the course work was decades behind the current biological science. He learned from other students a little older than himself, rather than from the faculty.
Like a heat equation but for functions without time dependence, space-only.
TODO confirm: does the solution of the heat equation always converge to the solution of the Laplace equation as time tends to infinity?
In one dimension, the Laplace equation is boring as it is just a straight line since the second derivative must be 0. That also matches our intuition of the limit solution of the heat equation.
Uniqueness: Uniqueness theorem for Poisson's equation.
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