As a Brazilian, Ciro Santilli used to really love playing soccer (but not watching it), until he hurt his knee.
Playing soccer just feels amazing, because you are constantly running around, but with a more specific goal in mind: to get that ball into that goal!
Playing soccer was specially amazing in the flat wet sand beach of Santos. weekend, the sea, feet touching the sand, the sun going down, and your school mates next to you. Nirvana.
It is also true that under those conditions, the skin of your feet will get ripped off due to running on the slightly wet and flat sand no matter how thick it has become. But it is worth it.
Teams would often be slit between "the team with shirts vs the team without shirts", who would just take off their shirts. The two best players would take turns picking players into their teams, the first one to pick would be decided by odds and evens (par ou ímpar).
A pair of Havaianas, or Havaianas rip-offs, stuck into the sand, or even just some school bags, would do as a goal posts. More organized people, especially adults, would have their own water pipe goal with a proper net and all. But doing so would spoil the fun of endless discussions if a non flat ball had gone in or not into an imaginary rectangle.
That's how soccer was meant to be played.
Ciro hates water, so swimming is out of the question. What could be more boring than going back and forth on a fixed location a million times to gain some milliseconds?
Running would have been a consideration, but Ciro Santilli's legs sometimes itch when he runs.
This is until he ended up living in a place with decent roads for cycling in the late 2010's, which led to Ciro Santilli's cycling.
Ciro Santilli's undergrad studies at the University of São Paulo Updated 2025-07-11 +Created 1970-01-01
Ciro's official diploma from the University of São Paulo read "Automation and Control Engineer at the Polytechnic School of the University of São Paulo".
The University of São Paulo had been elected the best South American university in the Times Ranking 2013 (archive) in all subjects.
Ciro finished the course with honors of "The Best Student in Automation and Control of the year 2013".
Ciro didn´t learn basically any control engineering however unfortunately. He did only the 3 base years of the electrical engineering course, and the rest got lost on stupid politics of having to go back to do 6 months from France to validate his Brazilian degree, see also: Section "Don't force international exchange students to come back early".
This is a simple hierarchical plaintext notation Ciro Santilli created to explain programs to himself.
It is usuall created by doing searches in an IDE, and then manually selecting the information of interest.
It attempts to capture intuitive information not only of the call graph itself, including callbacks, but of when things get called or not, by the addition of some context code.
For example, consider the following pseudocode:Supose that we are interested in determining what calls
f1() {
}
f2(i) {
if (i > 5) {
f1()
}
}
f3() {
f1()
f2_2()
}
f2_2() {
for (i = 0; i < 10; i++) {
f2(i)
}
}
main() {
f2_2()
f3()
}f1.Then a reasonable call hierarchy for
f1 would be:f2(i)
if (i > 5) {
f1()
f2_2()
for (i = 0; i < 10; i++) {
f2(i)
main
f3
f3()
main()Some general principles:
The City of London is an obscene thing. Its existence goes against the will of the greater part of society. All it takes is one glance to see how it is but a bunch of corruption. See e.g.: The Spiders' Web: Britain's Second Empire.
The idea tha taking the limit of the non-classical theories for certain parameters (relativity and quantum mechanics) should lead to the classical theory.
It appears that classical limit is only very strict for relativity. For quantum mechanics it is much more hand-wavy thing. See also: Subtle is the Lord by Abraham Pais (1982) page 55.
Examples:
- classification of finite simple groups
- classification of regular polytopes
- classification of closed surfaces, and more generalized generalized Poincaré conjectures
- classification of associative real division algebras
- classification of finite fields
- classification of simple Lie groups
- classification of the wallpaper groups and the space groups
en.wikipedia.org/w/index.php?title=Mathieu_group&oldid=1034060469#Multiply_transitive_groups is a nice characterization of 4 of the Mathieu groups.
Apparently only Mathieu group and Mathieu group .
www.maths.qmul.ac.uk/~pjc/pps/pps9.pdf mentions:Hmm, is that 54, or more likely 5 and 4?
The automorphism group of the extended Golay code is the 54-transitive Mathieu group . This is one of only two finite 5-transitive groups other than symmetric and alternating groups
scite.ai/reports/4-homogeneous-groups-EAKY21 quotes link.springer.com/article/10.1007%2FBF01111290 which suggests that is is also another one of the Mathieu groups, math.stackexchange.com/questions/698327/classification-of-triply-transitive-finite-groups#comment7650505_3721840 and en.wikipedia.org/wiki/Mathieu_group_M12 mentions .
So simple!! You can either:
- cut two holes and glue a handle. This is easy to visualize as it can be embedded in : you just get a Torus, then a double torus, and so on
- cut a single hole and glue a Möbius strip in it. Keep in mind that this is possible because the Möbius strip has a single boundary just like the hole you just cut. This leads to another infinite family that starts with:
You can glue a Mobius strip into a single hole in dimension larger than 3! And it gives you a Klein bottle!
Intuitively speaking, they can be sees as the smooth surfaces in N-dimensional space (called an embedding), such that deforming them is allowed. 4-dimensions is enough to embed cover all the cases: 3 is not enough because of the Klein bottle and family.
There's exactly one field per prime power, so all we need to specify a field is give its order, notated e.g. as .
It is interesting to compare this result philosophically with the classification of finite groups: fields are more constrained as they have to have two operations, and this leads to a much simpler classification!
As shown in Video "Simple Groups - Abstract Algebra by Socratica (2018)", this can be split up into two steps:This split is sometimes called the "Jordan-Hölder program" in reference to the authors of the jordan-Holder Theorem.
Good lists to start playing with:
History: math.stackexchange.com/questions/1587387/historical-notes-on-the-jordan-h%C3%B6lder-program
It is generally believed that no such classification is possible in general beyond the simple groups.
Ciro Santilli is very fond of this result: the beauty of mathematics.
How can so much complexity come out from so few rules?
How can the proof be so long (thousands of papers)?? Surprise!!
And to top if all off, the awesomely named monster group could have a relationship with string theory via the monstrous moonshine?
The classification contains:
- cyclic groups: infinitely many, one for each prime order. Non-prime orders are not simple. These are the only Abelian ones.
- alternating groups of order 4 or greater: infinitely many
- groups of Lie type: a contains several infinite families
- sporadic groups: 26 or 27 of them depending on definitions
Simple Groups - Abstract Algebra by Socratica (2018)
Source. Good quick overview.The 3D regular convex polyhedrons are super famous, have the name: Platonic solid, and have been known since antiquity. In particular, there are only 5 of them.
The counts per dimension are:
The cool thing is that the 3 that exist in 5+ dimensions are all of one of the three families:Then, the 2 3D missing ones have 4D analogues and the sixth one in 4D does not have a 3D analogue: the 24-cell. Yes, this is the kind of irregular stuff Ciro Santilli lives for.
This gate set alone is not a set of universal quantum gates.
Notably, circuits containing those gates alone can be fully simulated by classical computers according to the Gottesman-Knill theorem, so there's no way they could be universal.
This means that if we add any number of Clifford gates to a quantum circuit, we haven't really increased the complexity of the algorithm, which can be useful as a transformational device.
Produced the enriched uranium used for Little Boy, located in the area/predecessor of Oak Ridge National Laboratory.
Movies that are very expensive to make tend to be bad, because they have to make returns and thus appeal to a large amorphous population without any specialization, i.e. the lowest common denominator but in TV Tropes terminology rather than mathematics: tvtropes.org/pmwiki/pmwiki.php/Main/LowestCommonDenominator.
Looking down the largest flops of all time list didn't help much, only Heaven's gate appears reasonable from the top 20.
You are nothing but useless leeches in the Internet age.
You must go bankrupt all of you, ASAP.
Researchers and reviewers all work for peanuts, while academic publishers get money for doing the work that an algorithm could do. OurBigBook.com.
When Ciro learned URLs such as www.nature.com/articles/181662a0 log you in automatically by IP, his mind blew! The level of institutionalization of this theft is off the charts! The institutionalization of theft is also clear from article prices, e.g. 32 dollars for a 5 page article.
Long live the Guerilla Open Access Manifesto by Aaron Swartz (2008).
Key physics papers from the 50's are still copyright encumbered as of 2020, see e.g. Lamb-Retherford experiment. Authors and reviewers got nothing for it. Something is wrong.
Infinite list of other people:
- blog.machinezoo.com/public-domain-theft by Robert Važan:
Scientific journals are perhaps one of the most damaging IP rackets. Scientists are funded by governments to do research and publish papers. Reviews of these papers are done by other publicly funded scientists. Even paper selection and formatting for publication is done by scientists. So what do journals actually do? Nearly nothing.
Academic Publishing by Dr. Glaucomflecken (2022)
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