Luxury goods Updated 2025-07-16
One of the things Ciro Santilli most deeply despises.
Real luxury is to understand quantum field theory and number theory.
Clothing/jewelry/car luxury is at worst a way to show off. And at best a replacement for nature/the countryside. People living in big cities have lost nature, and to some, looking at luxury goods (or watching television) serves as a (unsatisfactory) replacement.
Music Updated 2025-07-16
Ciro Santilli took courses once upon a time, maybe that has influenced his passion? Ciro Santilli's musical education.
Pornography Updated 2025-07-16
Distribution (mathematics) Updated 2025-07-16
Generalize function to allow adding some useful things which people wanted to be classical functions but which are not,
It therefore requires you to redefine and reprove all of calculus.
For this reason, most people are tempted to assume that all the hand wavy intuitive arguments undergrad teachers give are true and just move on with life. And they generally are.
One notable example where distributions pop up are the eigenvectors of the position operator in quantum mechanics, which are given by Dirac delta functions, which is most commonly rigorously defined in terms of distribution.
Distributions are also defined in a way that allows you to do calculus on them. Notably, you can define a derivative, and the derivative of the Heaviside step function is the Dirac delta function.
Divergence in Einstein notation Updated 2025-07-16
First we write a vector field as:
Note how we are denoting each component of as with a raised index.
Then, the divergence can be written in Einstein notation as:
It is common to just omit the variables of the function, so we tend to just say:
or equivalently when referring just to the operator:
Double-slit experiment Updated 2025-07-16
Amazingly confirms the wave particle duality of quantum mechanics.
The effect is even more remarkable when done with individual particles such individual photons or electrons.
Richard Feynman liked to stress how this experiment can illustrate the core ideas of quantum mechanics. Notably, he night have created the infinitely many slits thought experiment which illustrates the path integral formulation.
Nested set model Updated 2025-07-16
This is particularly important in SQL: Nested set model in SQL, as it is an efficient way to transverse trees there, since querying parents every time would require multiple disk accesses.
As a tree:
As the sets:
 __________________________________________________________________________
|  Root 1                                                                  |
|   ________________________________    ________________________________   |
|  |  Child 1.1                     |  |  Child 1.2                     |  |
|  |   ___________    ___________   |  |   ___________    ___________   |  |
|  |  |  C 1.1.1  |  |  C 1.1.2  |  |  |  |  C 1.2.1  |  |  C 1.2.2  |  |  |
1  2  3___________4  5___________6  7  8  9___________10 11__________12 13 14
|  |________________________________|  |________________________________|  |
|__________________________________________________________________________|
Consider the following nested set:
0, 8, root
  1, 7, mathematics
    2, 3, geometry
      3, 6, calculus
        4, 5, derivative
        5, 6, integral
      6, 7, algebra
  7, 8, physics
When we want to insert one element, e.g. limit, normally under calculus, we have to specify:
  • parent
  • index within parent
so we have a method:
insert(parent, previousSibling)
Nested set model in SQL Updated 2025-07-16
How to implement Nested set model in SQL:
Neuralink Updated 2025-07-16
Elon Musk's attempt.
Dr. Strangelove Updated 2025-07-16
Video 1.
Inside the Making of 'Dr. Strangelove' part 2
. Source.
Dual space Updated 2025-07-16
The dual space of a vector space , sometimes denoted , is the vector space of all linear forms over with the obvious addition and scalar multiplication operations defined.
Since a linear form is completely determined by how it acts on a basis, and since for each basis element it is specified by a scalar, at least in finite dimension, the dimension of the dual space is the same as the , and so they are isomorphic because all vector spaces of the same dimension on a given field are isomorphic, and so the dual is quite a boring concept in the context of finite dimension.
One place where duals are different from the non-duals however is when dealing with tensors, because they transform differently than vectors from the base space .
Dulong-Petit law Updated 2025-07-16
Observation that all solids appear to have the same constant heat capacity per mole.
It can be seen as the limit case of an Einstein solid at high temperatures. At lower temperatures, the heat capacity depends on temperature.

Unlisted articles are being shown, click here to show only listed articles.