Ciro Santilli @cirosantilli 37

Fiscal paradises must be invaded and destroyed.

Vertebrates minus tetrapods.

This paraphyletic subgroup is easy to form the "acquatic only" (fishes) vs "things that come out of water" (tetrapods). Though mudfishes make that distinction harder.

Which kind of makes sense, why would you want for limbs unless you are going to stay out of water!

Gospel of Matthew 4 King James Version:

Once Ciro joked in a twenty questions-like game that humans are animals.

But counting humans a fish would have been a stroke of genius.

Synthesizes MIDI input. vmpk + aconnect + Advanced Linux Sound Architecture hello world: askubuntu.com/questions/34391/virtual-midi-piano-keyboard-setup/1298026#1298026

Supports only very basic effects it seems: chorus effect and reverberation. The main way to add instruments to it is via SoundFont files.

Approximates an original function by sines. If the function is "well behaved enough", the approximation is to arbitrary precision.

Fourier's original motivation, and a key application, is solving partial differential equations with the Fourier series.

Can only be used to approximate for periodic functions (obviously from its definition!). The Fourier transform however overcomes that restriction:

The Fourier series behaves really nicely in $L^2$, where it always exists and converges pointwise to the function: Carleson's theorem.

This is the future of course, fusion power to generate electricity, and then converting electricity into food somehow.

Hopefully without going through photosynthesis, which feels complicated and wasteful.

Others:

The only cases where formal proof of theorems seem to have had actual mathematical value is for theorems that require checking a very large number of case, so much so that no human can be fully certain that no mistakes were made. Some examples: