Ciro Santilli @cirosantilli 40

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.

Can you imagine when those guys started to see moons in other planets? They must have shat bricks. What better evidence can you have that the geocentric model could be wrong?

Game AI is an artificial intelligence that plays a certain game.

It can be either developed for serious purposes (e.g. AGI development in AI games), or to make games for interesting for humans.

The Quora question: www.quora.com/Are-there-any-PhD-programs-in-training-an-AI-system-to-play-computer-games-Like-the-work-DeepMind-do-combining-Reinforcement-Learning-with-Deep-Learning-so-the-AI-can-play-Atari-games

A good way to find labs is to go down the issues section of projects such as:and then stalk them to see where they are doing their PhDs.

As mentioned at Human Compatible by Stuart J. Russell (2019), game theory can be seen as the part of artificial intelligence that deas with scenarios where multiple intelligent agents are involved.

Most commonly known as a byproduct radioactive decay.

Their energy is very high compared example to more common radiation such as visible spectrum, and there is a neat reason for that: it's because the strong force that binds nuclei is strong so transitions lead to large energy changes.

A decay scheme such as Figure "caesium-137 decay scheme" illustrates well how gamma radiation happens as a byproduct of radioactive decay due to the existence of nuclear isomer.

Gamma rays are pretty cool as they give us insight into the energy levels/different configurations of the nucleus.

They have also been used as early sources of high energy particles for particle physics experiments before the development of particle accelerators, serving a similar purpose to cosmic rays in those early days.

But gamma rays they were more convenient in some cases because you could more easily manage them inside a laboratory rather than have to go climb some bloody mountain or a balloon.

The positron for example was first observed on cosmic rays, but better confirmed in gamma ray experiments by Carl David Anderson.

This technique is crazy! It allows to both:You actually see discrete peaks at different minute counts on the other end.

It is based on how much the gas interacts with the column.

Detection is usually done burning the sample to ionize it when it comes out, and then you measure the current produced.

The procedure remind you a bit of gel electrophoresis, except that it is in gaseous phase.

The name makes absolutely no sense in modern terms, as nor colors nor light are used directly in the measurements. It is purely historical.

Highlighted at the Origins of Precision by Machine Thinking (2017).

The term and idea was first introduced initialized by Hermann Weyl when he was working on combining electromagnetism and general relativity to formulate Maxwell's equations in curved spacetime in 1918 and published as Gravity and electricity by Hermann Weyl (1918). Based on perception that $U(1)$ symmetry implies charge conservation. The same idea was later adapted for quantum electrodynamics, a context in which is has even more impact.

Saves preprocessor output and generated assembly to separate files.

Technique widely used to measure the size of DNA strands, most often PCR output of a region of interest.

A simple sample application is gel electrophoresis alelle determination.

The variables of the Lagrangian, e.g. the angles of a double pendulum. From that example it is clear that these variables don't need to be simple things like cartesian coordinates or polar coordinates (although these tend to be the overwhelming majority of simple case encountered): any way to describe the system is perfectly valid.

In quantum field theory, those variables are actually fields.

There are two cases:

Questions: are all compact manifolds / differential manifolds homotopic / diffeomorphic to the sphere in that dimension?