Computable number by Ciro Santilli 40 Updated 2025-07-16
There are only boring examples of taking an uncomputable language and converting it into a number?
One of the main reasons why physicists are obsessed by this topic is that position and momentum are mapped to the phase space coordinates of Hamiltonian mechanics, which appear in the matrix mechanics formulation of quantum mechanics, which offers insight into the theory, particularly when generalizing to relativistic quantum mechanics.
One way to think is: what is the definition of space space? It is a way to write the wave function such that:And then, what is the definition of momentum space? It is of course a way to write the wave function such that:
Basically the operators are just analogous to the classical ones e.g. the classical:
becomes:
Besides the angular momentum in each direction, we also have the total angular momentum:
Then you have to understand what each one of those does to the each atomic orbital:
There is an uncertainty principle between the x, y and z angular momentums, we can only measure one of them with certainty at a time. Video 1. "Quantum Mechanics 7a - Angular Momentum I by ViaScience (2013)" justifies this intuitively by mentioning that this is analogous to precession: if you try to measure electrons e.g. with the Zeeman effect the precess on the other directions which you end up modifing.
Spark-gap transmitter by Ciro Santilli 40 Updated 2025-07-16
The first type of device that allowed sending Morse code without wires, as opposed to the wired electrical telegraph that previously existed.
Naval communications was one of the first major applications, as you can't have wires on boats!
Wireless voice transmission came about with modulation.
Video 1.
Spark-gap transmitter at the at the The Museum of Radio and Technology Jeri Ellsworth (2017)
Source.
Translation group by Ciro Santilli 40 Updated 2025-07-16
This is a good and simple first example of Lie algebra to look into.
Operon by Ciro Santilli 40 Updated 2025-07-16
Sequence of genes under a single promoter. For an example, see E. Coli K-12 MG1655 operon thrLABC.
A single operon may produce multiple different transcription units depending on certain conditions, see: operon vs transcription unit.
SendGrid by Ciro Santilli 40 Updated 2025-07-16
The first one Ciro Santilli managed to get working in 2022, and which has a free plan.
You can either verify your sending domain by adding 3 DNS records.
Saw the email on Gmail, but Microsoft Outlook did put it into junk though. Yahoo mail also worked fine.
100 emails a day is not insane, but it is forever and appropriate for a test, I'm happy with that.

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