Ciro Santilli @cirosantilli 35

Some sources say that this is just the part that says that the norm of a $L^2$ function is the same as the norm of its Fourier transform.

Others say that this theorem actually says that the Fourier transform is bijective.

The comment at math.stackexchange.com/questions/446870/bijectiveness-injectiveness-and-surjectiveness-of-fourier-transformation-define/1235725#1235725 may be of interest, it says that the bijection statement is an easy consequence from the norm one, thus the confusion.

TODO does it require it to be in $L^1$ as well? Wikipedia en.wikipedia.org/w/index.php?title=Plancherel_theorem&oldid=987110841 says yes, but courses.maths.ox.ac.uk/node/view_material/53981 does not mention it.

Maximum current that can flow across a Josephson junction, as can be directly seen from the Josephson equations.

Is a fixed characteristic value of the physical construction of the junction.

A pre-Jesus-like figure, likely possibly a mentor or competitor with Jesus.

He would have deserved a scene in Jesus Christ Superstar (1973).

Turkish Islamic sect.

Ciro Santilli once was at student a hackthon, where he proposed working on OurBigBook.com to others.

The only person who showed interest was a follower of the sect.

It seems that they put a lot of emphasis in education.

Also, their self-name is Hizmet, which translates as "service".

That day, Mr. Fethullah Gülen gained some Cirocoins.

Magazine of the Institute of Physics.

Good Portuguese overview: www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172017000300301&lng=pt&tlng=pt

A fantastic sounding full time 4-year course that any student could transfer to called that teaches various natural science topics, notably mathematics, physics, chemistry and molecular biology.

Many past students Ciro talked to however share a common frustration with the course: in the first 2 years at least, the "basic cycle", you have infinitely many courses, and no time to study, and no choice of what to study, it is only in the latter 2 years (the advanced cycle) that you get the choices.

Also, if you get low grades in a single subject, your out. And exams are useless of course.

Here's a Quora question in Portuguese about the course: pt.quora.com/Como-funciona-o-tal-do-curso-secreto-da-USP, the only decent answer so far being: pt.quora.com/Como-funciona-o-tal-do-curso-secreto-da-USP/answer/Victor-Soares-31. Very disappointing to hear.

On the advanced cycle, you have a lot of academic freedom. You are basically supposed to pick a research project with an advisor and go for it, with a small amount of mandatory course hours. Ciro was told in 2022 that you can even have advisors from other universities or industry, and that it is perfectly feasible to take courses in another university and validate the course hours later on. Fantastic!!!

Students from the entire University of São Paulo can apply to transfer to it only after joining the university, with the guarantee that they can go back to their original courses if they don't adapt to the new course, which is great!

Not doing it is one of Ciro Santilli's regrets in life, see also: don't be a pussy.

Around 2007, they were in a really shady building of the University, but when Ciro checked in 2021, they had apparently moved to a shiny new entrepreneurship-focused building. Fantastic news!!!

This place has one of the best changes of spawning the first Brazilian Nobel Prize or unicorn.

One of the Brazilians who came to École Polytechnique together with Ciro was from this course. The fact that he is one of the most intelligent people Ciro knows gave further credit to that course in his eyes.

Inkscape is a a good software for editing/creating SVG files.

Its functionality is fundamental for as a software for drawing geometry diagrams, as it is a good middle ground between algorithmic generation, and raster graphics.

At 1.0.2, its UI is a bit terrible:

And it crashes from time to time on Ubuntu 21.04. And it has some glaring bugs, e.g.:

But still, it is a very good initiative.

What would be really amazing is if they had constraints: gitlab.com/inkscape/inbox/-/issues/1465 like proper CAD software, it would make it possible to not have to redo entire diagrams when you want to change a small part of them.

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

Heinrich Hertz's main initial experiment used a spark-gap transmitter. It is not something that transmits recorded sounds like voice: it only transmits noisy beeps. And as such was used for wireless telegraphy.

Correspond to the angular part of Laplace's equation in spherical coordinates after using separation of variables as shown at: en.wikipedia.org/wiki/Spherical_harmonics#Laplace's_spherical_harmonics