Ciro Santilli once talked to a man who had been working on high-frequency trading for the last six years.
He was quite nice.
Ciro asked him in what way did he feel his job contributed to the benefit of society.
He replied that it didn't contribute at all. It was completely useless. More than that, it so completely useless, that it was even pure. A bit like advanced mathematics, but not even providing beauty for anybody outside of the company, since everything is a closely guarded trade secret, unlike mathematics which is normally published for the vanity recognition.
A great mind can work in the most useless branches of finance, without the desire to improve the world, nor make it worse. Not to compete, nor be afraid, nor anxious. A sand mandala.
Only being. Being, in the exact fraction of a moment where bid meets ask.
That is, two electrons per atomic orbital, each with a different spin.
As shown at Schrödinger equation solution for the helium atom, they do repel each other, and that affects their measurable energy.
However, this energy is still lower than going up to the next orbital. TODO numbers.
This changes however at higher orbitals, notably as approximately described by the aufbau principle.
Aufbau principle by Ciro Santilli 40 Updated 2025-07-16
Boring rule that says that less energetic atomic orbitals are filled first.
Much more interesting is actually determining that order, which the Madelung energy ordering rule is a reasonable approximation to.
Equation "Hydrogen spectral series mnemonic" gives for example from principal quantum number 1 to 2 a difference:
which with Planck-Einstein relation gives about 121.6 nm ( Hz), which is a reasonable match with the value of 121.567... from the NIST Atomic Spectra Database.
Pull request by Ciro Santilli 40 Updated 2025-07-16
The heart/main innovation of GitHub!

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