Natural units Updated 2025-07-16
A series of systems usually derived from the International System of Units that are more convenient for certain applications.
Nabla symbol Updated 2025-07-16
Nabla is one of those: it was completely made up in modern times, and just happens to look like an inverted upper case delta to make things even more confusing!
Nabla means "harp" in Greek, which looks like the symbol.
Lower teens, before discovering more hardcore stuff that is more genial and adult-venerable:So a base mix of what you migth expect from a regular male teenager born in 1989 Brazil.
OK, Ciro still comes back to those from time to time, he confesses. Nostalgia, nostalgia.
The following are also adult venerable though :-)
Video 1.
Killing In the Name by Rage Against The Machine (1992)
Source.
As mentioned on Wikipedia, it has only 8 lines of lyrics.
And the most satisfying "Ugh"s ever recorded on tape. Rap rock perfectly describes the genre.
Musician Updated 2025-07-16
Municipal Market of São Paulo Updated 2025-07-16
Once upon a time, this must have been a nice covered market.
But as of 2020, it is completely surrounded by extremely poor people, to the point that it makes you scared if you stand out in any way by showing any kind of middle/upper class wealth, or being a foreigner.
The market is basically a touristic spot that no person in Sao Paulo will ever go to (unless they are young, single, and can just walk in there by themselves) in the middle of this surreal environment.
In 2020 Ciro was there with his wife on a touristic visit. Living in Europe at the time, he felt even more privileged. So they went to a fruit stand, and the man started giving his wife amazing free samples of very exotic fruit, some of which Ciro had never tasted himself, without saying the price. It did feel like he was giving out too much for free. Then Ciro decided of course to buy some more fruits to pay for the show, which was a nice show. Then while buying, it came out a bit more expensive than would have been reasonable, but Ciro was too dazzled by the speed and noises, and he paid for it. Later on, he told his wife about it, and how he felt that they had added some ultra-expensive bulk fruits that were of a clearly lower level than the gold nuggets of the free samples (especially for Brazil's cost standards). The presenter was an extremely crafty con artist, and Ciro felt like they had specifically preyed on Ciro Santilli's self perceived compassionate personality, because it was apparent that those men were underprivileged and fighting for their living day by day with those over-expensive fruits. This was an extremely valuable lesson, Ciro was glad that it was learnt at a relatively low cost on that occasion.
Nested set model Updated 2025-07-16
This is particularly important in SQL: Nested set model in SQL, as it is an efficient way to transverse trees there, since querying parents every time would require multiple disk accesses.
As a tree:
As the sets:
 __________________________________________________________________________
|  Root 1                                                                  |
|   ________________________________    ________________________________   |
|  |  Child 1.1                     |  |  Child 1.2                     |  |
|  |   ___________    ___________   |  |   ___________    ___________   |  |
|  |  |  C 1.1.1  |  |  C 1.1.2  |  |  |  |  C 1.2.1  |  |  C 1.2.2  |  |  |
1  2  3___________4  5___________6  7  8  9___________10 11__________12 13 14
|  |________________________________|  |________________________________|  |
|__________________________________________________________________________|
Consider the following nested set:
0, 8, root
  1, 7, mathematics
    2, 3, geometry
      3, 6, calculus
        4, 5, derivative
        5, 6, integral
      6, 7, algebra
  7, 8, physics
When we want to insert one element, e.g. limit, normally under calculus, we have to specify:
  • parent
  • index within parent
so we have a method:
insert(parent, previousSibling)
MuJoCo getting started Updated 2025-07-16
Tested on Ubuntu 23.10;
git clone https://github.com/google-deepmind/mujoco
cd mujoco
git checkout 5d46c39529819d1b31249e249ca399f306a108ac
mkdir -p build
cd build
cmake ..
make -j
Now let's play. Minimal interactive UI simulation of a simple MJCF scene with one falling cube:
bin/basic ../doc/_static/hello.xml
Test soure code: github.com/google-deepmind/mujoco/blob/5d46c39529819d1b31249e249ca399f306a108ac/sample/basic.cc. The only thing you can do is rotate the scene with the computer mouse it seems. Mentioned at: mujoco.readthedocs.io/en/2.2.2/programming.html#sabasic
Some more interesting models can be found under the model/ directory: github.com/google-deepmind/mujoco/tree/5d46c39529819d1b31249e249ca399f306a108ac/model E.g. the imaginary humanoid robot DeepMind used in many demos can be seen with:
bin/basic ../model/humanoid/humanoid.xml
A very cool thing about that UI is that you can manually control joints. There are no joints in the hello.xml, but e.g. with the humanoid model:
bin/simulate ../model/humanoid/humanoid.xml
under "Control" you move each joint of the robot separately which is quite cool.
Video 1.
Demo of MuJoCo's built-in simulate viewer by Yuval Tassa (2019)
Source.
There's also a bin/record test executable that presumably renders the simulation directly to a file:
bin/record ../doc/_static/hello.xml 5 60 rgb.out
ffmpeg -f rawvideo -pixel_format rgb24 -video_size 800x800 -framerate 60 -i rgb.out -vf "vflip" video.mp4
Mentioned at: mujoco.readthedocs.io/en/2.2.2/programming.html#sarecord but TODO that produced a broken video, related issues:
Proxima Centauri Updated 2025-07-16
It is so close that we can notice its proper motion, and its distance to us will vary significantly across a few tens of thousands of years!
Projective elliptic geometry Updated 2025-07-16
Each elliptic space can be modelled with a real projective space. The best thing is to just start thinking about the real projective plane.
Projective space Updated 2025-07-16
A unique projective space can be defined for any vector space.
The projective space associated with a given vector space is denoted .
The definition is to take the vector space, remove the zero element, and identify all elements that lie on the same line, i.e.
The most important initial example to study is the real projective plane.

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