Ciro Santilli @cirosantilli 35

Classic theory predicts that the output frequency must be the same as the input one since the electromagnetic wave makes the electron vibrate with same frequency as itself, which then irradiates further waves.

But the output waves are longer because photons are discrete and energy is proportional to frequency:

The formula is exactly that of two relativistic billiard balls colliding.

Therefore this is evidence that photons exist and have momentum.

Bibliography:

Ultimate explanation: math.stackexchange.com/questions/776039/intuition-behind-normal-subgroups/3732426#3732426

Does not have to be isomorphic to a subgroup:This is one of the reasons why the analogy between simple groups of finite groups and prime numbers is limited.

To some extent, the ultimate achievement of a TAS is to achieve arbitrary code execution (ACE) on a game, although this has been becoming rarer and rarer in newer consoles. The Nintendo 64 is the current interesting ACE discovery frontier as of 2020.

Post ACE, you then get into more subtle categories which tend to be more geometric clipping through wall glitches, but those can still be fun.

The most beautiful TAS content ever made are:

It is also amusing to see console verification of emulations, e.g.: Video 1. "Super Mario 64 '120 Stars' in 1:20:41.52 Console Verified by Soul Umbreon (2012)".

So we can track the music in Git!

A function that maps two sets to a third set.

Related concepts:

The term loosely refers to certain layers of the computer abstraction layers hierarchy, usually high level hardware internals like CPU pipeline, caching and the memory system. Basically exactly what gem5 models.