Alpha Investments Updated +Created
Very good channel that gives some idea of the behind the scenes of working with card stores and secondary market trading.
Such lessons can have applicability in business and investment outside of the Magic The Gathering context as well. Yet another example that usefulness can come out of uselessness.
Video 1.
The Process of Opening a MTG Store by Alpha Investments (2016)
Source.
Video 2.
Spending $500,000 per month on Pokemon & Magic by Alpha Investments (2021)
Source.
Observable Updated +Created
PlanetMath Updated +Created
Based on GitHub pull requests: github.com/planetmath
Joe Corneli, of of the contributors, mentions this in a cool-sounding "Peeragogy" context at metameso.org/~joe/:
I earned my doctorate at The Open University in Milton Keynes, with a thesis focused on peer produced support for peer learning in the mathematics domain. The main case study was planetmath.org; the ideas also informed the development of “Peeragogy”.
Determinant Updated +Created
Name origin: likely because it "determines" if a matrix is invertible or not, as a matrix is invertible iff determinant is not zero.
Maxwell-Boltzmann statistics Updated +Created
Solutions of Maxwell's equations Updated +Created
Video 1.
Understanding Electromagnetic Radiation! by Learn Engineering (2019)
Source. Shows animations of a dipole antenna which illustrates well how radiation is emitted from moving charges and travels at the speed of light.
Zhuangzi Updated +Created
33 chapters. The first 7 are likely by Zhuang Zhou himself, and the rest a mishmash.
Translations:
  • James Legge (1891):
    • ctext.org/zhuangzi side by side with Chinese, one chapter per page. Dividies it into three parts:
      • Inner Chapters
      • Outer Chapters
      • Miscellaneous Chapters
Yahoo! Updated +Created
Scientific visualization Updated +Created
Plane wave function Updated +Created
In this solution of the Schrödinger equation, by the uncertainty principle, position is completely unknown (the particle could be anywhere in space), and momentum (and therefore, energy) is perfectly known.
The plane wave function appears for example in the solution of the Schrödinger equation for a free one dimensional particle. This makes sense, because when solving with the time-independent Schrödinger equation, we do separation of variable on fixed energy levels explicitly, and the plane wave solutions are exactly fixed energy level ones.
James Clerk Maxwell Updated +Created
J. J. Thomson Updated +Created
Schrödinger picture Updated +Created
To better understand the discussion below, the best thing to do is to read it in parallel with the simplest possible example: Schrödinger picture example: quantum harmonic oscillator.
The state of a quantum system is a unit vector in a Hilbert space.
"Making a measurement" for an observable means applying a self-adjoint operator to the state, and after a measurement is done:
  • the state collapses to an eigenvector of the self adjoint operator
  • the result of the measurement is the eigenvalue of the self adjoint operator
  • the probability of a given result happening when the spectrum is discrete is proportional to the modulus of the projection on that eigenvector.
    For continuous spectra such as that of the position operator in most systems, e.g. Schrödinger equation for a free one dimensional particle, the projection on each individual eigenvalue is zero, i.e. the probability of one absolutely exact position is zero. To get a non-zero result, measurement has to be done on a continuous range of eigenvectors (e.g. for position: "is the particle present between x=0 and x=1?"), and you have to integrate the probability over the projection on a continuous range of eigenvalues.
    In such continuous cases, the probability collapses to an uniform distribution on the range after measurement.
    The continuous position operator case is well illustrated at: Video "Visualization of Quantum Physics (Quantum Mechanics) by udiprod (2017)"
Those last two rules are also known as the Born rule.
Self adjoint operators are chosen because they have the following key properties:
  • their eigenvalues form an orthonormal basis
  • they are diagonalizable
Perhaps the easiest case to understand this for is that of spin, which has only a finite number of eigenvalues. Although it is a shame that fully understanding that requires a relativistic quantum theory such as the Dirac equation.
The next steps are to look at simple 1D bound states such as particle in a box and quantum harmonic oscillator.
The solution to the Schrödinger equation for a free one dimensional particle is a bit harder since the possible energies do not make up a countable set.
This formulation was apparently called more precisely Dirac-von Neumann axioms, but it because so dominant we just call it "the" formulation.
Quantum Field Theory lecture notes by David Tong (2007) mentions that:
if you were to write the wavefunction in quantum field theory, it would be a functional, that is a function of every possible configuration of the field .
Mahatma Gandhi Updated +Created
Variety Jones Updated +Created
2023 Silk Road's Second-in-Command Gets 20 Years in Prison www.wired.com/story/silk-road-variety-jones-sentencing/
2015 The Variety Show On the trail of the man believed to be Variety Jones, one of the architects of the defunct drug marketplace Silk Road. www.vice.com/en/article/wnx5qn/the-variety-show
www.justice.gov/usao-sdny/file/797251/download some kind of case file of his trial.
The curious thing about VJ is that he actually has some culture and says cool things, e.g.:
IRL - is there anyone with a clue at all? Girlfriend, boyfriend, bunny you talk to, online buddy's who you've know for years? Gramma, priest, rabbi, stripper?
Two photon interference experiment Updated +Created
The basic experiment for a photonic quantum computer.
Can be achieved in two ways it seems:
Animation of Hong-Ou-Mandel Effect on a silicon like structure by Quantum Light University of Sheffield (2014): www.youtube.com/watch?v=ld2r2IMt4vg No maths, but gives the result clear: the photons are always on the same side.
Video 1.
Quantum Computing with Light by Quantum Light University of Sheffield (2015)
Source. Animation of in-silicon single photon device with brief description of emitting and receiving elements. Mentions:
Video 2.
Quantum Optics - Beam splitter in quantum optics by Alain Aspect (2017)
Source. More theoretical approach.
Video 3.
Building a Quantum Computer Out of Light by whentheappledrops (2014)
Source. Yada yada yada, then at youtu.be/ofg335d3BJ8?t=341 shows optical table and it starts being worth it. Jacques Carolan from the University of Bristol goes through their setup which injects 5 photons into a 21-way experiment.
Reputation system Updated +Created
Symmetry Updated +Created
Directly modelled by group.
John C. Baez Updated +Created

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