Ciro Santilli @cirosantilli 40

Postulates are what we now call axioms.

There are 5: en.wikipedia.org/w/index.php?title=Euclidean_geometry&oldid=1036511366#Axioms, the parallel postulate being the most controversial/interesting.

Let's start with the one dimensional case. Let the $q:\mathbb{R}\to \mathbb{R}$ and a Functional $I$ defined by a function of three variables $F:{\mathbb{R}}^3\to \mathbb{R}$:

Then, the Euler-Lagrange equation gives the maxima and minima of the that type of functional. Note that this type of functional is just one very specific type of functional amongst all possible functionals that one might come up with. However, it turns out to be enough to do most of physics, so we are happy with with it.

Given $F$, the Euler-Lagrange equations are a system of ordinary differential equations constructed from that $F$ such that the solutions to that system are the maxima/minima.

In the one dimensional case, the system has a single ordinary differential equation:

By $\frac{\partial F}{\partial q}$ and $\frac{\partial F}{\partial \dot{q}}$ we simply mean "the partial derivative of $F$ with respect to its second and third arguments". The notation is a bit confusing at first, but that's all it means.

Therefore, that expression ends up being at most a second order ordinary differential equation where $q$ is the unknown, since:

Now let's think about the multi-dimensional case. Instead of having $q:\mathbb{R}\to \mathbb{R}$, we now have $q:\mathbb{R}\to {\mathbb{R}}^n$. Think about the Lagrangian mechanics motivation of a double pendulum where for a given time we have two angles.

Let's do the 2-dimensional case then. In that case, $F$ is going to be a function of 5 variables $F:{\mathbb{R}}^5\to \mathbb{R}$ rather than 3 as in the one dimensional case, and the functional looks like:

This time, the Euler-Lagrange equations are going to be a system of two ordinary differential equations on two unknown functions $q_1$ and $q_2$ of order up to 2 in both variables:At this point, notation is getting a bit clunky, so people will often condense the $q_i$ vectoror just omit the arguments of $F$ entirely:

For the most part, a great pseudo-country to live in with lots of cultural diversity, art and safety.

However, Europe is in economic decline after all its Jewish and German geniuses fled in/after World War II and due to having more than one natural language is bad for the world.

Ciro Santilli moved to Europe in 2010.

Europe has made good regulations to limit the absolute power of immoral companies. Partly because it does not have any companies anymore, but so be it.

But the law that forces every fucking website to show a message "Do you consent to cookies?" is not one of them.

Ciro cannot stand fucking clicking the "I consent" button anymore.

Please stop, for the love of God.

At most, there must be a standardized API that allows your browser to say "I agree or I disagree" automatically to all of them, e.g. an HTTP header.

2021: United Kingdom is considering it post-Brexit: techcrunch.com/2021/09/06/after-years-of-inaction-against-adtech-uks-ico-calls-for-browser-level-controls-to-fix-cookie-fatigue/. Something good might actually come out of Brexit!

Sample usage by Andy Matuschak (possible coiner): notes.andymatuschak.org/About_these_notes

Appears to be a Wikipedia clone but with much lower/no notability requirements guidelines, which overcomes one of Wikipedia's main issues: deletionism.

They do have the interesting idea of importing deleted Wikipedia pages as a source of content, which leads to some epic "most viewed pages" such as en.everybodywiki.com/List_of_erotic_and_sex_workers_with_unnatural_death which currently reads:

We can for example see Ciro Santilli's deleted entry PsiQuantum at: en.everybodywiki.com/PsiQuantum, Wikipedia deletion page: en.wikipedia.org/wiki/Wikipedia:Articles_for_deletion/PsiQuantum. Their attribution is atrocious however, e.g. it does not seem possible to find any mention of "Ciro Santilli" on the edit history, which just points to the delete article which is not visible anymore. They could really get into trouble for this one day.

Their main use case, as suggested by the website itself, if for people/brands to create pages about themselves.

This combined with the lack of "one version of each page per person" seems like an explosive invitation for unsolvable edit wars.

The website is backed by a French startup: jobs.stationf.co/companies/wiki-valley.

This simply connected is called the universal covering group.

E.g. in the case of $SO(3)$ and $SU(2)$, $SU(2)$ is simply connected, but $SO(3)$ is not.

Got it working as mentioned at: github.com/cirosantilli/feathers-chat/tree/sequelize-pg

One major step was to port to PostgreSQL as shown at feathers-chat PostgreSQL.

Bibliography:

There's also a heroku branch at: github.com/feathersjs/feathers-chat/tree/heroku, but it also seems to use NeDB? So you can have a filesystem in Heroku? Doesn't seem so: stackoverflow.com/questions/42775418/heroku-local-persistent-storage

This is Ciro Santilli's name for the idea that we should not have structured degrees at university that require entry exams, only tests that anybondy could take, likely for free, and then they would just have proof that they know the stuff for e.g. teachers that care about a subject while selecting students to work with them in research.

We just need control rooms where someone can watch students for cheating. Multiple different exams can be taken in the same room of course, students just have to sign up in advance. The exams should happen regularly depending on demand. E.g. extremelly common subjects should happen every month, and highly specialized ones every 6 months or 1 year.

Questions should be always taken from an open question pool which also contains answers, thus allowing anyone to effectively study for it.

How many questions can you actually come up with about a given non research subject, right?

We then make an API available, so that students can grant access to specific results to anyone they choose, or even make the results public for anyone to see. This way the people that care about the exams can just machine learn what exams correlate with their desired performance.

Bibliography:

Oh, and the dude who created the en.wikipedia.org/wiki/Exceptional_object Wikipedia page won an Oscar: www.youtube.com/watch?v=oF_FLN-TmCY, Dan Piponi, aka @sigfpe. Cool dude.

Cool examples:

Some anecdotes.

Ciro Santilli never splits up functions unless there is more than one calling point. If you split early, the chances that the interface will be wrong are huge, and a much larger refactoring follows.

If you just want to separate variables, just use a scope e.g.:

int cross_block_var;

// First step.
{
    int myvar;
}

// Second step.
{
    int myvar;
}

Ciro has seen and had to deal with in his lifetime with two projects that had like 3 to 10 git separate Git repositories, all created and maintained by the same small group of developers of the same organization, even though one could not build without the other. Keeping everything in sync was Hell! Why not just have three directories inside a single repository with a single source of truth?

Another important case: Linux should have at least a C standard library, init system, and shell in-tree, like BSD Operating Systems, as mentioned at: Section "Linux".

If you have a PDE that models physical phenomena, it is fundamental that:

Unlike for ordinary differential equations which have the Picard–Lindelöf theorem, the existence and uniqueness of solution is not well solved for PDEs.

For example, Navier-Stokes existence and smoothness was one of the Millennium Prize Problems.

en.wikipedia.org/wiki/Logarithm_of_a_matrix#Existence mentions it always exists for all invertible complex matrices. But the real condition is more complicated. Notable counter example: -1 cannot be reached by any real $e^{tk}$.

The Lie algebra exponential covering problem can be seen as a generalized version of this problem, because

Experiment and theory are like the yin and yang: opposites, but one cannot exist without the other.