Modulation by Ciro Santilli 40 Updated 2025-07-16
Modulation basically means encoding data on a carrier wave.
Image that we are at a point in history where spark-gap transmitters can send Morse code.
But now people want to send voice. How to do it?
It would not be practical without modulation: Why can't you send voice without modulation?
Whenever Ciro Santilli learns about molecular biology, he can't help but to feel that it feels like programming, and notably systems programming and computer hardware design.
In some sense, the comparison is obvious: DNA is clearly a programmable medium like any assembly language, but still, systems programming did give Ciro some further feelings.
Ciro likes to think that maybe that is why a hardcore systems programmer like Bert Hubert got into molecular biology.
Some other people who mention similar things:
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.
Momentum operator by Ciro Santilli 40 Updated 2025-07-16
One dimension in position representation:
In three dimensions In position representation, we define it by using the gradient, and so we see that
Video 1.
Position and Momentum from Wavefunctions by Faculty of Khan (2018)
Source. Proves in detail why the momentum operator is . The starting point is determining the time derivative of the expectation value of the position operator.
Inanna is an ancient Sumerian goddess, one of the most important deities in the Mesopotamian pantheon. She is associated with various aspects, including love, beauty, fertility, war, and political power. Inanna's dual nature embodies both nurturing and fierce qualities, reflecting the complexities of human experience.
As of my last knowledge update in October 2023, there is no widely recognized entity or concept specifically known as "Femisphere." It's possible that it could refer to a brand, a product, an organization, or a concept that emerged after that date, or it may be a colloquial term or niche concept that wasn't widely documented.
Organicism is a philosophical and theoretical perspective that emphasizes the idea that systems, whether they are biological, social, or artistic, are best understood as wholes rather than simply as the sum of their parts. This approach draws analogies between living organisms and various systems, positing that these systems exhibit structural and functional relationships similar to those found in nature.
Kinetic art is a genre of art that incorporates movement as a fundamental aspect of its expression. This movement can be induced by a variety of mechanisms, such as motors, wind, water, or the action of viewers interacting with the artwork. Kinetic art can take many forms, including sculptures, installations, and works on paper.
Ferdinand Minding does not appear to have significant recognition or established relevance in widely known fields, such as history, literature, science, or popular culture, based on the information available up to October 2023. It's possible that he could be a lesser-known figure, or the name might be relevant in a specific niche context.
Paul Émile Appell was a French mathematician known for his contributions to various areas of mathematics, particularly in geometry and analysis. Born on 8 February 1855 and passing away on 7 January 1931, he is perhaps best known for his work in projective geometry and for his involvement in the development of mathematical education in France. In addition to his research contributions, Appell was also recognized for his role as an educator and in the promotion of mathematics as a discipline.
The Reuleaux tetrahedron is a three-dimensional geometric shape that is a type of convex hull formed around a tetrahedron. A Reuleaux tetrahedron is created by taking the convex hull of four points that are the vertices of a regular tetrahedron and then forming a shape by connecting arcs of circles centered at these vertices.
Gerard of Brussels, also known as Gerardus Brabantius, was a Flemish painter from the late 15th to early 16th century. He is often associated with the Northern Renaissance and is recognized for his contributions to the art of the period in the region of present-day Belgium. Although specific details about his life are scarce, his works typically feature themes common to the time, such as religious subjects, landscapes, and portraits.
The Minkowski–Hlawka theorem is a result in number theory and the geometry of numbers that pertains to the representation of integer points in geometric space. Specifically, it addresses the existence of points with integer coordinates within certain convex bodies in Euclidean space.
An oloid is a three-dimensional geometric shape formed by the combination of two circular disks of equal radius, which are joined at their edges. The shape has a distinctive smooth, continuous surface and unique mathematical properties. When one of the disks rolls on a flat surface, the oloid can create a fascinating motion because of its unique curvature. The oloid was first described by the mathematician Paul Schatz in the 1920s.

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact