Ciro Santilli @cirosantilli 37

Appears to be analogous to the dot product, but also defined for infinite dimensions.

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A Hermitian matrix.

Ciro Santilli has some good related articles listed under: the best articles by Ciro Articles.

Good selection: Acústico MTV - Gilberto Gil (1994).

Runner ups:

A law of physics is Galilean invariant if the same formula works both when you are standing still on land, or when you are on a boat moving at constant velocity.

For example, if we were describing the movement of a point particle, the exact same formulas that predict the evolution of $x_{land}(t)$ must also predict $x_{boat}(t)$, even though of course both of those $x(t)$ will have different values.

It would be extremely unsatisfactory if the formulas of the laws of physics did not obey Galilean invariance. Especially if you remember that Earth is travelling extremelly fast relative to the Sun. If there was no such invariance, that would mean for example that the laws of physics would be different in other planets that are moving at different speeds. That would be a strong sign that our laws of physics are not complete.

The consequence/cause of that is that you cannot know if you are moving at a constant speed or not.

Lorentz invariance generalizes Galilean invariance to also account for special relativity, in which a more complicated invariant that also takes into account different times observed in different inertial frames of reference is also taken into account. But the fundamental desire for the Lorentz invariance of the laws of physics remains the same.

Complexity: NP-intermediate as of 2020:

The basis of RSA: RSA. But not proved NP-complete, which leads to:

You label cells with isotopes rather than fluorescent substances. Vendors claim that this allows much wider N-way sorts, e.g. 2022 Fluidigm claims around 40/50, because the fluorecent spectrum is too wide to do much more than 7/8 way splits.

Ciro Santilli was touched by this, and then watched several other documentaries by Curtis.

Part of Ciro asks if it is all a big conspiracy theory. But it feels and sounds so right.

Notably the part of the governments have lost all power to companies, and can't do anything meaningful anymore to actually represent the people, because globalization reduces the power of governments.