Ciro Santilli @cirosantilli 40

resonance in a mechanical system.

TODO confirm: apparently in the paradigm you can choose to measure only certain output qubits.

This makes things irreversible (TODO what does reversibility mean in this random context?), as opposed to Circuit-based quantum computer where you measure all output qubits at once.

TODO what is the advantage?

In the standard formulation of Maxwell's equations, the electric current is a convient but magic input.

Would it be possible to use Maxwell's equations to solve a system of pointlike particles such as electrons instead?

The following suggest no, or only for certain subcases less general than Maxwell's equations:This is the type of thing where the probability aspect of quantum mechanics seems it could "help".

Subtle is the Lord by Abraham Pais (1982) chapter III "Relativity, the special theory" mentions that this fact and its importance (we want the laws of physics to look the same on all inertial frames, AKA Lorentz covariance) was first fully relized by poincaré in 1905.

And at that same time poincaré also immediately started to think about the other fundamental force then known: gravity, and off the bat realized that gravitational waves must exist. general relativities is probably just "the simplest way to make gravity Lorentz covariant".

Bibliography:

Given a function $f$:we want to find the points $x$ of the domain of $f$ where the value of $f$ is smaller (for minima, or larger for maxima) than all other points in some neighbourhood of $x$.

In the case of Functionals, this problem is treated under the theory of the calculus of variations.

Like the matrix representation of a bilinear form, it is a matrix, but now the matrix has to be a symmetric matrix.

We can then immediately see that the matrix is symmetric, then so is the form. We have:But because $B(x,y)$ is a scalar, we have:and:

Published by Werner Heisenberg in 1925-07-25 as quantum mechanical re-interpretation of kinematic and mechanical relations by Heisenberg (1925), it offered the first general formulation of quantum mechanics.

It is apparently more closely related to the ladder operator method, which is a more algebraic than the more analytical Schrödinger equation.

It appears that this formulation makes the importance of the Poisson bracket clear, and explains why physicists are so obsessed with talking about position and momentum space. This point of view also apparently makes it clearer that quantum mechanics can be seen as a generalization of classical mechanics through the Hamiltonian.

QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga by Silvan Schweber (1994) mentions however that relativistic quantum mechanics broke that analogy, because some 2x2 matrix had a different form, TODO find that again.

Inward Bound by Abraham Pais (1988) chapter 12 "Quantum mechanics, an essay" part (c) "A chronology" has some ultra brief, but worthwhile mentions of matrix mechanics and the commutator.

Is the solution to a system of linear ordinary differential equations, the exponential function is just a 1-dimensional subcase.

Note that more generally, the matrix exponential can be defined on any ring.

The matrix exponential is of particular interest in the study of Lie groups, because in the case of the Lie algebra of a matrix Lie group, it provides the correct exponential map.

From effect of a change of basis on the matrix of a bilinear form, remember that a change of basis $C$ modifies the matrix representation of a bilinear form as:

So, by taking $S=C^T$, we understand that two matrices being congruent means that they can both correspond to the same bilinear form in different bases.

It does a huge percentage of what you want easily, and from the language that you want to use.

Tends to be Ciro's pick if gnuplot can't handle the use case, or if the project is really really serious.

Couldn't handle exploration of large datasets though: Survey of open source interactive plotting software with a 10 million point scatter plot benchmark by Ciro Santilli

Examples:

Tested on Python 3.10.4, Ubuntu 22.04.

In 2019, a paper proved that MTG is Turing complete with a legacy legal deck. Live demo with some hand waving: Video "I Built a COMPUTER in Magic: The Gathering by Because Science (2019)". As Ciro Santilli comments at: github.com/cirosantilli/cirosantilli.github.io/issues/42 this was an interest addition to the previous "indefinite infinite loop" e.g. as found in a Four Horsemen combo deck

It is so close that we can notice its proper motion, and its distance to us will vary significantly across a few tens of thousands of years!

Written mostly by Eric W. Weisstein.

Ciro once saw a printed version of the CRC "concise" encyclopedia of mathematics. It is about 12 cm thick. Imagine if it wasn't concise!!!

Infinite Napkin is the one-person open source replacement we needed for it! And OurBigBook.com will be the final multi-person replacement.

Each elliptic space can be modelled with a real projective space. The best thing is to just start thinking about the real projective plane.

A unique projective space can be defined for any vector space.

The projective space associated with a given vector space $V$ is denoted $\mathbf{P}(V)$.

The definition is to take the vector space, remove the zero element, and identify all elements that lie on the same line, i.e. $\vec{v}=\lambda \vec{w}$

The most important initial example to study is the real projective plane.