The wave equation can be seen as infinitely many infinitesimal coupled oscillators Updated 2025-06-17 +Created 1970-01-01
TODO confirm, see also: coupled oscillators. And then this idea can be used to define/motivate quantum field theory in terms of quantum harmonic oscillators with second quantization.
- youtu.be/SMmFgIEGYtw?t=324 Quantum Field Theory 2a - Field Quantization I by ViaScience (2018)
Chapter 2 paragraph 14:
Formerly, I, Zhuang Zhou, dreamt that I was a butterfly, a butterfly flying about, feeling that it was enjoying itself. I did not know that it was Zhou. Suddenly I awoke, and was myself again, the veritable Zhou. I did not know whether it had formerly been Zhou dreaming that he was a butterfly, or it was now a butterfly dreaming that it was Zhou. But between Zhou and a butterfly there must be a difference. This is a case of what is called the Transformation of Things.'
Fundamental question related to Ciro's 2D reinforcement learning games.
Bibliography:
- youtu.be/i0UyKsAEaNI?t=120 How to Build AGI? Ilya Sutskever interview by Lex Fridman (2020)
Started at Google Quantum AI in 2014.
Has his LaTeX notes at: github.com/DanielSank/theory. One day he will convert to OurBigBook.com. Interesting to see that he is able to continue his notes despite being at Google.
Existence and uniqueness results are fundamental in mathematics because we often define objects by their properties, and then start calling them "the object", which is fantastically convenient.
But calling something "the object" only makes sense if there exists exactly one, and only one, object that satisfies the properties.
One particular context where these come up very explicitly is in solutions to differential equations, e.g. existence and uniqueness of solutions of partial differential equations.
How To Get Tenure at a Major Research University by Sean Carroll (2011) Updated 2025-06-17 +Created 1970-01-01
We define this as the functional equation:It is a bit like cauchy's functional equation but with multiplication instead of addition.
This idea comes up particularly in the phase space coordinate of Hamiltonian mechanics.
Initially light was though of as a wave because it experienced interference as shown by experiments such as:
But then, some key experiments also start suggesting that light is made up of discrete packets:and in the understanding of the 2020 Standard Model the photon is one of the elementary particles.
- Compton scattering, also suggests that photons carry momentum
- photoelectric effect
- single photon production and detection experiments
This duality is fully described mathematically by quantum electrodynamics, where the photon is modelled as a quantized excitation of the photon field.
GPIO generally only supports discrete outputs.
But for some types of hardware, like LEDs and some motors, the system has some inertia, and if you switch on and off fast enough, you get a result similar to having an intermediate voltage.
So with pulse width modulation we can fake analog output from digital output in a good enough manner.
You can connect form an Ubuntu 22.04 host as:When in but be aware of: Raspberry Pi Pico W freezes a few seconds after after screen disconnects from UART.
screen /dev/ttyACM0 115200screen, you can Ctrl + C to kill main.py, and then execution stops and you are left in a Python shell. From there:- Ctrl + D: reboots
- Ctrl + A K: kills the GNU screen window. Execution continues normally
Other options:
- ampy
runcommand, which solves How to run a MicroPython script from a file on the Raspberry Pi Pico W from the command line?
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