Ciro Santilli @cirosantilli 35

Ciro's theory for his disappearance is that he became a Majorana fermion and flew off into the infinite.

Ciro Santilli's favorites, including album when they're more of a one hit wonder:

Complexity: NP-intermediate as of 2020:

The basis of RSA: RSA. But not proved NP-complete, which leads to:

What you see along a line or plane in a wave interference.

Notably used for the pattern of the double-slit experiment.

Plutonium-based.

Its plutonium was produced at Hanford site.

Microbit simulator using some Microsoft framework.

TODO the Python code from there does not seem to run on the microbit via uflash, because it is not MicroPython.

support.microbit.org/support/solutions/articles/19000111744-makecode-python-and-micropython explains.

forum.makecode.com/t/help-understanding-local-build-options/6130 asks how to compile locally and suggests it is possible. Seems to require Yotta, so presumably compiles?

Presumably this is because Microsoft ported their MakeCode thing to the MicroBit, and the Micro Bit foundation accepted them.

E.g. there toggling a LED:but the code that works locally is a completely differently named API set_pixel:Microsoft going all in on adopt extend extinguish from an early age!

Mordell's theorem guarantees that the rank (number of elements in the generating set of the group) is always well defined for an elliptic curve over the rational numbers. But as of 2023 there is no known algorithm which calculates the rank of any curve!

It is not even known if there are elliptic curves of every rank or not: Largest known ranks of an elliptic curve over the rational numbers, and it has proven extremely hard to find new ones over time.

TODO list of known values and algorithms? The Birch and Swinnerton-Dyer conjecture would immediately provide a stupid algorithm for it.

Many good albums, Ciro Santilli's favorites:

TODO: it would be cool to have something like bitcoinstrings.com but including the actual transactions:

Local methods:

Further bibliography:

This resonates a lot with Ciro Santilli's ideas!

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:

Allows us to draw with JavaScript pixel by pixel! Great way to create computational physics demos!

Here is an animation demo with some useful controls:

new class extends OurbigbookCanvasDemo {
  init() {
    super.init('hello');
    this.pixel_size_input = this.addInputAfterEnable(
      'Pixel size',
      {
        'min': 1,
        'type': 'number',
        'value': 1,
      }
    );
  }
  draw() {
    var pixel_size = parseInt(this.pixel_size_input.value);
    for (var x = 0; x < this.width; x += pixel_size) {
      for (var y = 0; y < this.height; y += pixel_size) {
        var b = ((1.0 + Math.sin(this.time * Math.PI / 16)) / 2.0);
        this.ctx.fillStyle =
          'rgba(' +
          (x / this.width) * 255 + ',' +
          (y / this.height) * 255 + ',' +
          b * 255 +
          ',255)'
        ;
        this.ctx.fillRect(x, y, pixel_size, pixel_size);
      }
    }
  }
}

Bibliography: developer.mozilla.org/en-US/docs/Web/API/Canvas_API/Tutorial/Basic_animations">https://developer.mozilla.org/en-US/docs/Web/API/Canvas_API/Tutorial/Basic_animations

The first Bitcoin exchange. Coded as a hack, and they didn't manage to fix the hacks as the site evolved in a major way, which led to massive hacks.

Their creation is clearly visible on the archive history of bitcoin.org: web.archive.org/web/20100701000000*/bitcoin.org which started having massively more archives since Mt. Gox opened.

If you are a programmer, grep becomes a verb: "to grep" means "to search text files", much like "to Google" means "to search random stuff online".

Section type: sh_type == SHT_STRTAB.

Common name: "section header string table".

The section name .shstrtab is reserved. The standard says:

This section gets pointed to by the e_shstrnd field of the ELF header itself.

String indexes of this section are are pointed to by the sh_name field of section headers, which denote strings.

This section does not have SHF_ALLOC marked, so it will not appear on the executing program.outputs:

The data in this section has a fixed format: www.sco.com/developers/gabi/2003-12-17/ch4.strtab.html

If we look at the names of other sections, we see that they all contain numbers, e.g. the .text section is number 7.

Then each string ends when the first NUL character is found, e.g. character 12 is \0 just after .text\0.