Ciro Santilli @cirosantilli 35

An algebra over a field where division exists.

Power, Sex, Suicide by Nick Lane (2006) page 53 suggests that one tremendous advantage of eukaryotes over bacteria is their ability to change shape due to the presence of the cytoskeleton, and the lack of a rigid bacterial cell wall.

Imagine in a world where there are only bacteria, and you can eat entire bacteria in one go, what a huge advantage that is!

Shows up when trying to solve 2D wave equation on a circular domain in polar coordinates with separation of variables, where we have to decompose the initial condition in termes of a fourier-Bessel series, exactly like the Fourier series appears when solving the wave equation in linear coordinates.

For the same fundamental reasons, also appears when calculating the Schrödinger equation solution for the hydrogen atom.

Biography of Enrico Fermi by fellow physicist, free rent on the on the Internet Archive: archive.org/details/enricofermiphysi0000segr

Examples:

This section talks about solvers/simulators dedicated solving the wave equation. Of course, any serious solver will likely be able to solve a wider range of PDE, so this section contains mostly fun toys. For more serious stuff see: Section "PDE solver".

JavaScript toy solvers:

Related:

Start with: Section "String polarization".

Then go to: Section "Polarization of light".

Resonance is a really cool thing.

Examples:

Perhaps a key insight of resonance is that the reonant any lossy system tends to look like the resonance frequency quite quickly even if the initial condition is not the resonant condition itself, because everything that is not the resonant frequency interferes destructively and becomes noise. Some examples of that:

Another cool aspect of resonance is that it was kind of the motivation for de Broglie hypothesis, as de Broglie was kind of thinking that electroncs might show discrete jumps on atomic spectra because of constructive interference.

This is a must if the people want to regain control of their society from apathetic politicians.

I would also increase voter percentage due to convenience, and reduce the weight of voting fraud cases, as everyone would be able to check that their own vote was counted correctly.

And then, we would be able to have referendums for basically any important decision being made. No need to go out on the streets and waste your time in a mass protest! Just vote!

It is possible to implement anonymous electronic voting with ring signatures, an algorithm also used by Monero, an anonymity focused cryptocurrency, as mentioned e.g. on this 2004 paper eprint.iacr.org/2004/281.pdf. The system can be set in a way such that you can only deanonymize someone if everyone else, or a very large number of people, conspire against that person.

The same system could also be used to setup forums where only citizens of the country could comment and propose changes and vote on them.

With electronic voting, we could have a system where you can let someone you trust vote for you automatically, or vote automatically for certain subjects alone, a bit like we do by electing senators. But then you would also be able to override specific votes if you wanted to.

In this system therefore, anyone who can proxy vote has to have their vote public, and placed in a decent website that shows clearly who voted for what.

Related: