de Broglie relations Updated 2025-07-16
Deep learning is mostly matrix multiplication Updated 2025-07-16
Defining properties of elementary particles Updated 2025-07-16
A suggested at Physics from Symmetry by Jakob Schwichtenberg (2015) chapter 3.9 "Elementary particles", it appears that in the Standard Model, the behaviour of each particle can be uniquely defined by the following five numbers:
Once you specify these properties, you could in theory just pluck them into the Standard Model Lagrangian and you could simulate what happens.
Setting new random values for those properties would also allow us to create new particles. It appears unknown why we only see the particles that we do, and why they have the values of properties they have.
Definition of the exponential function Updated 2025-07-16
Definition of the indefinite orthogonal group Updated 2025-07-16
Given a matrix with metric signature containing positive and negative entries, the indefinite orthogonal group is the set of all matrices that preserve the associated bilinear form, i.e.:Note that if , we just have the standard dot product, and that subcase corresponds to the following definition of the orthogonal group: Section "The orthogonal group is the group of all matrices that preserve the dot product".
As shown at all indefinite orthogonal groups of matrices of equal metric signature are isomorphic, due to the Sylvester's law of inertia, only the metric signature of matters. E.g., if we take two different matrices with the same metric signature such as:and:both produce isomorphic spaces. So it is customary to just always pick the matrix with only +1 and -1 as entries.
Definition of the orthogonal group Updated 2025-07-16
Mathematical definition that most directly represents this: the orthogonal group is the group of all matrices that preserve the dot product.
Degree (algebra) Updated 2025-07-16
The degree of some algebraic structure is some parameter that describes the structure. There is no universal definition valid for all structures, it is a per structure type thing.
This is particularly useful when talking about structures with an infinite number of elements, but it is sometimes also used for finite structures.
Examples:
- the dihedral group of degree n acts on n elements, and has order 2n
- the parameter that characterizes the size of the general linear group is called the degree of that group, i.e. the dimension of the underlying matrices
DELETE with JOIN (SQL) Updated 2025-07-16
Demo under: nodejs/sequelize/raw/many_to_many.js.
NO way in the SQL standard apparently, but you'd hope that implementation status would be similar to UPDATE with JOIN, but not even!
- PostgreSQL: possible with
DELETE FROM USING
: stackoverflow.com/questions/11753904/postgresql-delete-with-inner-join - SQLite: not possible without subqueries as of 3.35 far: stackoverflow.com/questions/24511153/how-delete-table-inner-join-with-other-table-in-sqlite, Does not appear to have any relevant features at: www.sqlite.org/lang_delete.html
ORM
- Sequelize: no support of course: stackoverflow.com/questions/40890131/sequelize-destroy-record-with-join
Deletionism Updated 2025-07-16
The problem of deletionism is that it removes users' confidence that their precious data will be safe. It's almost like having a database that constantly resets itself. Who will be willing to post on a website that deletes the content they created for free half of the time thus wasting people's precious time?
Democracy Updated 2025-07-16
Derivation of the Klein-Gordon equation Updated 2025-07-16
But since this is quantum mechanics, we feel like making into the "momentum operator", just like in the Schrödinger equation.
But we don't really know how to apply the momentum operator twice, because it is a gradient, so the first application goes from a scalar field to the vector field, and the second one...
But then, we have to avoid taking the square root to reach a first derivative in time, because we don't know how to take the square root of that operator expression.
So the Klein-Gordon equation just takes the approach of using this squared Hamiltonian instead.
Since it is a Hamiltonian, and comparing it to the Schrödinger equation which looks like:taking the Hamiltonian twice leads to:
We can contrast this with the Dirac equation, which instead attempts to explicitly construct an operator which squared coincides with the relativistic formula: derivation of the Dirac equation.
Derivation of the Schrodinger equation Updated 2025-07-16
Where derivation == "intuitive routes", since a "law of physics" cannot be derived, only observed right or wrong.
TODO also comment on why are complex numbers used in the Schrodinger equation?.
Some approaches:
- en.wikipedia.org/w/index.php?title=Schr%C3%B6dinger_equation&oldid=964460597#Derivation: holy crap, this just goes all in into a Lie group approach, nice
- Richard Feynman's derivation of the Schrodinger equation:
- physics.stackexchange.com/questions/263990/feynmans-derivation-of-the-schrödinger-equation
- www.youtube.com/watch?v=xQ1d0M19LsM "Class Y. Feynman's Derivation of the Schrödinger Equation" by doctorphys (2020)
- www.youtube.com/watch?v=zC_gYfAqjZY&list=PL54DF0652B30D99A4&index=53 "I5. Derivation of the Schrödinger Equation" by doctorphys
Derivative Updated 2025-07-16
Deriving magnetism from electricity and relativity Updated 2025-07-16
It appears that Maxwell's equations can be derived directly from Coulomb's law + special relativity:
This idea is suggested by the charged particle moving at the same speed of electrons thought experiment, which indicates that magnetism is just a consenquence of special relativity.
Why moving charges produce magnetic field? by FloatHeadPhysics (2022)
Source. Determinant Updated 2025-07-16
Name origin: likely because it "determines" if a matrix is invertible or not, as a matrix is invertible iff determinant is not zero.
Deterministic perfect information board game Updated 2025-07-16
Developmental biology Updated 2025-07-16
Where is Anatomy Encoded in Living Systems? by Michael Levin (2022)
Source. - we are very far from full understanding. End game is a design system where you draw the body and it compiles the DNA for you.
- some cool mentions of regeneration
Developmental genetics Updated 2025-07-16
How genes form bodies.
Developmental Genetics 1 by Joseph Ross (2020)
Source. Talks about homeobox genes. Dharma name Updated 2025-07-16
Diamond Sutra Updated 2025-07-16
Unlisted articles are being shown, click here to show only listed articles.