@johncarlosbaez Additionally, players of instruments often have their own vocal language for the sounds/notes their instrument can play. Here is an example of the Tabla (a percussion instrument!!) At various points the player will vocally sing what he plays before or while playing.
@johncarlosbaez The most popular traditional music in Pakistan is the same as in Northern India. For the scale we use the vocal sounds
Sa Re Ga Ma Pa Dha Ni Sa
Here is one done in the Qawalli form https://youtu.be/-MQXfjJGPJQ?si=ZzHY5lz8aR6VJ6M5
Here is one in the Ghazal form
https://youtu.be/AQcxlLyE-A8?si=CB-spxqAUJjryOeu (starts at 3:30).
Read a fascinating idea today, that universities must separate their legislative, executive and judicial functions, same as country governments do. Since, politics has permeated all aspects of universities, this might help to contain the bad effect.
I wonder what other publicly valuable institutions should also follow the same schematic.
The Remaining Carbon Budget for 50% chance of 2C warming is 1200GtCO2. https://www.nature.com/articles/s41558-023-01848-5
Doing a naive calc: 1200e9/8e9 world pop/50 years of your remaining life = 3 tCO2/year.
Driving 20km/day will set you back 1.2tCO2 of that.
1. To opinions! Solar is the cheapest source of bulk electricity in many countries, and the quickest to deploy, and now you couldn't stop it being built if you wanted to.
The limits to PV build in most places are grid access, permitting, and sometimes installation labour.
2. We don’t need a solar technology breakthrough. Today, solar developers just need a grid connection and permission to sell electricity, and then they’ll be off building solar plants whether it’s a good idea or not.
I am seriously tempted to prove this result using the fundamental theorem of algebra and the Gauss-Lucas theorem, which is a ridiculous way to prove a purely real-variable result, but would obviate the need to figure out how to arrange all the roots in order and study their multiplicities. It's interesting how the need to formalize a result significantly changes one's preferences in which approach one would take to create a proof.
@ColinTheMathmo I would say "One repeated solution". Later on they study second order ordinary differential equations with constant coefficients. There the "One repeated solution" case of the characteristic equation does yield two solutions of the ODE. So the repetition here matters.
@TaliaRinger I usually give out prizes for catching my mistakes - some of which are delibrate. Really helps with student engagement sometimes.
@ddrake How were you taught? The article follows the standard way tensor products are introduced to Physicists in Quantum Mechanics 1 course. Sometimes, a bit more abstractly with their properties as axioms, but then immediately jumping to this discussion so it's not confusing.
David Deutsch (paraphrasing): There is a distinction between experiments, demonstration and measurements.
Experiments are done to test rival theories (at least 2). At the end of the experiment, your doubt in each theory must change from before.
Demonstration: just show that the predictions of a theory are indeed born out in practice.
Measurement: determine the value of a parameter in a single theory.
He says that the latter two are often confused for the first.
@gregeganSF What are the ergonomics of reading a math book laid out on a desk in front of you, basically at the same height as a laptop keyboard?
The mathematical "reason" is that at low energies all potentials are linear or quadratic, or the inverse square of planetary motion.
But that doesn't explain why at a very wide variety of length scales, all human-sense-observable phenomena settled down to such energies.
@smari Thank you. I am glad you recommended a recent book, which are usually aware of the impacts of modern high-technology on the feasibility of political and economic theories.
quantum scientist, trying to build a quantum computer, hoping for singularity and space travel in lifetime. want to stop surveillance dystopia, climate change.
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