Ciro Santilli @cirosantilli 37

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:

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!

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?

The best example to look at first is the penalty kick left right Nash equilibrium.

Then, a much more interesting example is choosing a deck of a TCG competition: Magic: The Gathering meta-based deck choice is a bimatrix game, which is the exact same, but each player has N choices rather than 2.

The next case that should be analyzed is the prisoner's dilemma.

The key idea is that:

An impossible AI-complete dream!

It is impossible to understand speech, and take meaningful actions from it, if you don't understand what is being talked about.

And without doubt, "understanding what is being talked about" comes down to understanding (efficiently representing) the geometry of the 3D world with a time component.

Not from hearing sounds alone.

The Klein-Gordon equation directly uses a more naive relativistic energy guess of $p^2+m^2$ squared.

But since this is quantum mechanics, we feel like making $p$ 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...

So we just cheat and try to use the laplace operator instead because there's some squares on it:

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.

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:

The derivative of a function gives its slope at a point.

More precisely, it give sthe inclination of a tangent line that passes through that point.

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.

Name origin: likely because it "determines" if a matrix is invertible or not, as a matrix is invertible iff determinant is not zero.

How genes form bodies.

法 (fa3) is the Chinese name for Dharma, and sometimes used as a way short way to refer to Buddhism.

NCBI online tool to find and view all open reading frames in a given FASTA: www.ncbi.nlm.nih.gov/orffinder/

Previously known as "Food From Electricity", "NeoCarbonFood" sounds like a more commercializable version of it.

Uses electricity to electrolyse water into hydrogen and oxygen molecules, and then use bacteria that do hydrogen chemosynthesis to convert it into food.

Some coverage:

TODO find a concrete numerical example of doing calculus on a differentiable manifold and visualizing it. Likely start with a boring circle. That would be sweet...