I find it strange that nobody has ever recreated the classic windows desktop faithfully, except for reactos i suppose. But on Linux i think there are quite a few people around who would happily use it. All sorts of themes for other interfaces aren't quite the same thing
Readit Newsaap_ commented on FVWM-95 (2001) fvwm95.sourceforge.net/... · Posted by u/mghackerlady
aap_ commented on What's the deal with Euler's identity? lcamtuf.substack.com/p/wh... · Posted by u/surprisetalk
Nobody ever considers the spinorial version. e^iπ is a 360° rotation on a spinor, and + is averaging spinors rotationally. so e^iπ + 1 = 0 means there is no way to interpolate between the identity and a twist in the spinor, because the axis of a 360° rotation is undefined.
Things get so much more fun once you embrace spinors.
aap_ commented on A Repository with 44 Years of Unix Evolution spinellis.gr/pubs/conf/20... · Posted by u/lioeters
Hopefully UNIX v4 will soon be in there too :)
I've wanted to try racket a few times but always found the "IDE" to be really unintuitive, clunky and weird. What gives? Is that by design or is it just that nothing better has been created so far?
aap_ commented on Run ancient UNIX on modern hardware github.com/felipenlunkes/... · Posted by u/doener
aap_ commented on Run ancient UNIX on modern hardware github.com/felipenlunkes/... · Posted by u/doener
What about from the 60s? Archaic?
https://www.unisys.com/product-info-sheet/ecs/clearpath-mast...
Is it at all possible to get a peak into that world as a curious person?
aap_ commented on Cloudflare Global Network experiencing issues cloudflarestatus.com/inci... · Posted by u/imdsm
Crazy to think that it's apparently acceptable to centralize the web like that.
aap_ commented on Structure and Interpretation of Classical Mechanics (2014) tgvaughan.github.io/sicm/... · Posted by u/the-mitr
Does anyone know a text which justifies why the Lagrangian approach works? This text and many others I have encountered just start with the Principle of Least Action taken as given and go from there but I'm left wondering why we define the Action as this object and why we should expect it to be minimised for the physical trajectory in the first place.
Failing a full derivation from the ground up, a proof of the equivalence to Newtonian mechanics would be interesting.
Unfortunately I can't help with the classical picture, but in quantum physics it all comes out very nicely:
You can interpret the Lagrangian as giving all possibilities to build a trajectory through spacetime. In the path integral formulation we then follow one such trajectory from one configuration to another configuration and find its amplitude.
And then we integrate over all possible trajectories that we could have picked. For incoherent trajectories there will always be another one that cancels out the amplitude. Where the amplitudes add up constructively you will find stationary action and the classical behavior in the limit.
So this is a depth-first approach: first follow one trajectory completely, then add up all possible trajectories.
The Hamiltonian approach in contrast is breadth-first: you single out a time axis, start with some initial state, and consider all possibilities that a particle (or field in QFT) could evolve forwards in time just a tiny bit (this is what the Hamiltonian operator does). Then you add up all these possibilities to find the next state, and so you move forwards through time by keeping track of all possible evolutions all at once. This massive superposition of everything that is possible (with corresponding amplitudes) is what you call a state (or wavefunction) and the space that it lives in is the Hilbert (or Fock) space.
So Lagrangian/path-integral: follow full trajectories, then add up all possible choices. depth-first
Hamiltonian/time-evolution: add up all choices for a tiny step in time, then simply do more steps: breadth-first
I imagine it a bit like a scanline algorithm calculating an image as it moves down the screen (Hamiltonian) vs something like a stochastic raytracer that can start with an empty image and refine it pixel by pixel by shooting more rays (Lagrangian)
This is my layman explanation anyways...hopefully it helps, even though i can't say much about their relationship in classical physics.