Ciro Santilli @cirosantilli 35

GPIO generally only supports discrete outputs.

But for some types of hardware, like LEDs and some motors, the system has some inertia, and if you switch on and off fast enough, you get a result similar to having an intermediate voltage.

So with pulse width modulation we can fake analog output from digital output in a good enough manner.

Their project lead as of 2018 was pro-CCP: github.com/cirosantilli/china-dictatorship/blob/aa1176c57fc2929465294e520b43b50d44e202ba/communities-that-censor-politics.md

The most powerful GUI file manager ever?? Infinite configurability??

Ciro Santilli wasted some time on it before he gave up on file managers altogether and started using only the CLI with a few aliases.

Like everything else in Lie group theory, you should first look at the matrix version of this operation: the matrix exponential.

The exponential map links small transformations around the origin (infinitely small) back to larger finite transformations, and small transformations around the origin are something we can deal with a Lie algebra, so this map links the two worlds.

The idea is that we can decompose a finite transformation into infinitely arbitrarily small around the origin, and proceed just like the product definition of the exponential function.

The definition of the exponential map is simply the same as that of the regular exponential function as given at Taylor expansion definition of the exponential function, except that the argument $x$ can now be an operator instead of just a number.

Examples: