Of course those racist Nazis are a bunch of idiots, but how can you be surprised when freedom-of-speech focused tech gets used by them? www.theverge.com/2019/7/12/20691957/mastodon-decentralized-social-network-gab-migration-fediverse-app-blocking
Obviously, a few large instances dominate the user base for all practical purposes: kevq.uk/centralisation-and-mastodon/. And likely the network splits into hate-speech/non-hate-speech blacklist boundaries. And since the dominating closed networks will never lose user counts (???), the only instance that dominates will be the main hate speech one.
The flagship instance was mastodon.social and then in 2020 they closed signups for it and created a secondary mastodon.online.
The "advanced interface" feature is bad. Really bad. MacOS file browser inspired.
Ciro Santilli enjoyed watching the temple flashback moments on YouTube.
Combat in the USA is of course terribly ridiculous due to guns Are Worthless.
Good modern OpenGL tutorial in retained mode with shaders, see also: stackoverflow.com/questions/6733934/what-does-immediate-mode-mean-in-opengl/36166310#36166310
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.
The Process of Opening a MTG Store by Alpha Investments (2016)
Source. Spending $500,000 per month on Pokemon & Magic by Alpha Investments (2021)
Source. 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”.
Name origin: likely because it "determines" if a matrix is invertible or not, as a matrix is invertible iff determinant is not zero.
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.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
- ctext.org/zhuangzi side by side with Chinese, one chapter per page. Dividies it into three parts:
Ross Ulbricht told her about Silk Road, but then later said he had sold the website to someone else, without really doing that.
- LinkedIn profile: www.linkedin.com/in/julia-vie-35296959/
- Twitter profile: twitter.com/destenyrangel
As of 2023, she's apparently a photographer with a porny focus (boudoir photography).
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.
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:Those last two rules are also known as the Born rule.
- 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)"
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.
This naturally generalizes to Schrödinger equation solution for the hydrogen atom.
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 .
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