Ciro Santilli @cirosantilli 37

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:

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!

Now that's some basal shit! It's basically a fucking blob!!! Except that it is flat. No nervous system. Not even tissues. It is basically a multicellular

TODO understand.

Like Google custom silicon, Amazon server operations are so large that with the slowdown of Moore's law, it started being worth it for them to develop custom in-house silicon to serve as a competitive advantage, not to be sold for external companies. Can you imagine the scale required to justify silicon development investment that is not sold externally!

They have been masters of second sourcing things for a long time! One can ony imagine the complexity of the Intel cross licensing deals.

We define a "Procedural AI training game" as an AI training game in which parts of the game are made with procedural generation.

In more advanced cases, the generation itself can be done with AI. This is a possible Path to AGI which reduces the need for human intervention in meticulously crafting the AI game: AI training AI.

Sometimes mathematicians go a little overboard with their naming.

Bibliography:

He's an actor and producer apparently: www.imdb.com/name/nm3438598/