Galilean invariance by Ciro Santilli 40 Updated 2025-07-16
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 must also predict , even though of course both of those 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.
Integer factorization by Ciro Santilli 40 Updated 2025-10-14
Complexity: NP-intermediate as of 2020:
The basis of RSA: RSA. But not proved NP-complete, which leads to:
Mass cytometry by Ciro Santilli 40 Updated 2025-07-16
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.
As seen from explicit scalar form of the Maxwell's equations, this expands to 8 equations, so the question arises if the system is over-determined because it only has 6 functions to be determined.
As explained on the Wikipedia page however, this is not the case, because if the first two equations hold for the initial condition, then the othe six equations imply that they also hold for all time, so they can be essentially omitted.
It is also worth noting that the first two equations don't involve time derivatives. Therefore, they can be seen as spacial constraints.
TODO: the electric field and magnetic field can be expressed in terms of the electric potential and magnetic vector potential. So then we only need 4 variables?
Free will by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli does not believe in free will of course because he is an agnostic and he believes that brains are controlled by the laws of physics, see also: physics and the illusion of life.
Real projective line by Ciro Santilli 40 Updated 2025-07-16
Just a circle.
Take with a line at . Identify all the points that an observer
Stack Overflow by Ciro Santilli 40 Updated 2025-07-16
The best place to get answers to programming questions as of 2019. Google into Stack Overflow is always the best bet.
An overview of Ciro Santilli's Stack Overflow contribution can be found at: Ciro Santilli's Stack Overflow contributions.
Figure 1.
Stack Overflow in a nutshell
. Source.
As the "WTF look at my points" guy, Ciro Santilli approves of this meme. A few more elements could be added, notably deletion of the last link-only answer, but good enough.
By the profile image, the "Grammar Nazi" editor is actually appropriately the notorious serial editor Peter Mortensen. Ciro Santilli welcomes grammar fixes, but more subjective style fixes can be a bit annoying.

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