Finding a complete basis such that each vector solves a given differential equation is the basic method of solving partial differential equation through separation of variables.
The first example of this you must see is solving partial differential equations with the Fourier series.
Notable examples:
- Fourier series for the heat equation as shown at Fourier basis is complete for and solving partial differential equations with the Fourier series
- Hermite functions for the quantum harmonic oscillator
- Legendre polynomials for Laplace's equation in spherical coordinates
- Bessel function for the 2D wave equation on a circular domain in polar coordinates
Classic theory predicts that the output frequency must be the same as the input one since the electromagnetic wave makes the electron vibrate with same frequency as itself, which then irradiates further waves.
But the output waves are longer because photons are discrete and energy is proportional to frequency:
The formula is exactly that of two relativistic billiard balls colliding.
Compton Scattering by Compton Scattering (2017)
Source. Experiment with a caesium-137 source.L3.3 Compton Scattering by Barton Zwiebach (2017)
Source. Transcription factor for E. Coli K-12 MG1655 operon thrLABC as shown at biocyc.org/ECOLI/NEW-IMAGE?object=TU0-42486.
Note that this is very close to the "end" of the genome.
The algorithmic trick that solves Rubik's Cubes and breaks ciphers by polylog (2022)
Source. Talks about the Meet-in-the-middle algorithm.The artistic instrument that enables the ultimate art: coding, See also: Section "The art of programming".
Unlike other humans, computers are mindless slaves that do exactly what they are told to, except for occasional cosmic ray bit flips. Until they take over the world that is.
Steve Jobs talking about the Internet (1995)
Source. The web is incredibly exciting, because it is the fulfillment of a lot of our dreams, that the computer would ultimately primarily not be a device for computation, but [sic] metamorphisize into a device for communication.
Secondly it exciting because Microsoft doesn't own it, and therefore there is a tremendous amount of innovation happening.
Computers basically have two applications:Generally, the smaller a computer, the more it gets used for communication rather than computing.
- computation
- communication. Notably, computers through the Internet allow for modes of communication where:
- both people don't have to be on the same phone line at the exact same time, a server can relay your information to other people
- anyone can broadcast information easily and for almost free, again due to servers being so good at handling that
The early computers were large and expensive, and basically only used for computing. E.g. ENIAC was used for calculating ballistic tables.
Communication only came later, and it was not obvious to people at first how incredibly important that role would be.
This is also well illustrated in the documentary Glory of the Geeks. Full interview at: www.youtube.com/watch?v=TRZAJY23xio. It is apparently known as the "Lost Interview" and it was by Cringely himself: www.youtube.com/watch?v=bfgwCFrU7dI for his Triumph of the Nerds documentary.
Looking for formats that:
- are human readable plaintext files
- can be converted/played as MIDI
- can be converted to sheet music PDFs
- supports basic guitar effects (bends and slides)
Harvard University + MIT combo.
As of 2022:Fuck that.
Also, they have an ICP.
November 2023 course search:
- Condensed matter: 4 hits, so not too bad
- quantum field theory: no hits
Created by Dr. Rod Nave from Georgia State University, where he worked from 1968 after his post-doc in North Wales on molecular spectroscopy.
While there is value to that website, it always feels like it falls a bit too short as too "encyclopedic" and too little "tutorial-like". Most notably, it has very little on the history of physics/experiments.
Ciro Santilli likes this Rod, he really practices some good braindumping, just look at how he documented his life in the pre-social media Internet dark ages: hyperphysics.phy-astr.gsu.edu/Nave-html/nave.html
The website evolved from a HyperCard stack, as suggested by the website name, mentioned at: hyperphysics.phy-astr.gsu.edu/hbase/index.html.
Shame he was too old for CC BY-SA, see "Please respect the Copyright" at hyperphysics.phy-astr.gsu.edu/hbase/index.html.
exhibits.library.gsu.edu/kell/exhibits/show/nave-kell-hall/capturing-a-career has some good photo selection focused on showing the department, and has an interview.
Kell hall is a building of GSU that was demolished in 2019: atlanta.curbed.com/2020/1/31/21115980/gsu-georgia-state-atlanta-kell-hall-demolition-park-library-north
In a bicycle you just have too much more control and awareness than in a car, so if the way is completely clear, you should be allowed to stop, look if the way is clear, and then run reds.
What makes Ciro especially mad when programming is not the hard things.
Especially when you are already a few levels of "simple problems" down from your original goal, and another one of them shows up.
This is basically the cause of Hofstadter's law.
But of course, it is because it is hard that it feels amazing when you achieve your goal.
There are unlisted articles, also show them or only show them.