Ciro Santilli's sport of choice circa 2020, see also: Ciro Santilli's cycling.
Good film about him: Blaise Pascal (1972).
Good quote from his Les Provinciales (1656-57) Letter XII, p. 227:French version reproduced at: www.dicocitations.com/citation/auteurajout35106.php.
The war in which violence endeavours to crush truth is a strange and a long one.All the efforts of violence cannot weaken truth, but only serve to exalt it the more.The light of truth can do nothing to arrest violence; nay, it serves to provoke it still more.When force opposes force, the more powerful destroys the less; when words are opposed to words, those which are true and convincing destroy and scatter those which are vain and false; but violence and truth can do nothing against each other.Yet, let no one imagine that things are equal between them; for there is this final difference, that the course of violence is limited by the ordinance of God, who directs its workings to the glory of the truth, which it attacks; whereas truth subsists eternally, and triumphs finally over its enemies, because it is eternal, and powerful, like God Himself.
Ciro Santilli's wife, who was frustrated with academia at some point, admires the fact that Simons managed to make infinite money, and then invested back in actual science, e.g. through the Simons Foundation.
The definition of the "dot product" of a general space varies quite a lot with different contexts.
Most definitions tend to be bilinear forms.
We use the unqualified generally refers to the dot product of Real coordinate spaces, which is a positive definite symmetric bilinear form. Other important examples include:The rest of this section is about the case.
- the complex dot product, which is not strictly symmetric nor linear, but it is positive definite
- Minkowski inner product, sometimes called" "Minkowski dot product is not positive definite
The positive definite part of the definition likely comes in because we are so familiar with metric spaces, which requires a positive norm in the norm induced by an inner product.
The default Euclidean space definition, we use the matrix representation of a symmetric bilinear form as the identity matrix, e.g. in :so that:
Chuck Norris counted to infinity. Twice.
There are a few related concepts that are called infinity in mathematics:
- limits that are greater than any number
- the cardinality of a set that does not have a finite number of elements
- in some number systems, there is an explicit "element at infinity" that is not a limit, e.g. projective geometry
Ciro Santilli's account is www.reddit.com/user/cirosantilli/, see also: accounts controlled by Ciro Santillis.
Communicating at a distance, from Greek "tele" for distance!
A very cool thing about telecommunication is, besides how incredibly fast it advanced (in this sense it is no cooler than integrated circuit development), how much physics and information theory is involved in it. Applications of telecommunication implementation spill over to other fields, e.g. some proposed quantum computing approaches are remarkably related to telecommunication technology, e.g. microwaves and silicon photonics.
This understanding made Ciro Santilli wish he had opted for telecommunication engineering when he was back in school in Brazil. For some incomprehensible reason, telecommunications was the least competitive specialization in the electric engineering department at the time, behind even power electronics. This goes to show both how completely unrelated to reality university is, and how completely outdated Brazil is/was. Sad stuff.
Give students answers to all questions.
Explain in extreme detail how each result was reached.
Students have the amazing capacity of not looking at answers if they don't want to.
And when they've had enough, then can read answers and understand while the problem is fresh in their minds.
If you don't give answers, no one will be able to use your online material without you being there to hold their hands.
Forbidding students from publishing their answers also goes against let students learn by teaching.
Publish somewhere people can comment by 
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01Then, if people find errors, or have questions, they will write a comment near the content itself.
Then, next person that comes along and has the same problem, will also find that comment, and your answer will solve their problems too.
The perfect way to do this is to use GitHub issues
Publish your material even if it is not perfect by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01Just make it very clear what you've tried, what you observed, and what you don't understand if anything at all.
This will already open up room for others to come and expand on your attempt, and you are more likely to learn the answers to your questions as they do.
And there's a good chance someone who knows more than you will come along and correct or teach you something new about the subject. For example, this has happened countless times to Ciro Santilli when doing Ciro Santilli's Stack Overflow contributions.
Perfect is the enemy of good.
Examples of famous fails:
- QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga by Silvan Schweber (1994) chapter 7.11 "Epilogue" mentions how Julian Schwinger has lots of unpublished notes, or that his collaborators had to write most of the stuff down themselves in the end because he felt they were not perfect enough
Things that are not nice such as:
- Taboola, Outbrain, and other chumbox
- BLOBs
- Europe cookie law
- adhesive inside mobile phones and more generally, planned obsolescence
- Jupyter Notebook
- typographical characters that look like ASCII ones, but are not the ASCII ones, e.g. typographical quotes, em-dash. The non-breaking hyphen is not even whitespace, and by def Why not stick to ASCII when ASCII is good enough?
- excessive encapsulation
- replacement of master and slave terminology from technology
- mailing lists. And to add insult to injury, HTML on mailing list messages instead of plaintext.
- blank lines in code added by people trying to increase clarity, especially when there is already indentation for that. Every blank line must be preceded by a line comment explaining what the following block is about, or removed.
- messaging software that force you to have a mobile phone
- advertisements by telephone/SMS
- "state" such as global variables and object members, long live functional programming?
- mosquitoes, the only intrinsically bad thing about tropical countries
- projects with slow compilation times
- Microsoft Windows
- the 2019 Chinese government
- e-learning websites that only allows verified teachers to write content. Cowards who can't handle ranking algorithms.
- domain-specific language
- a build system without an out-of-tree option
- non-linear Git history: stackoverflow.com/questions/20348629/what-are-advantages-of-keeping-linear-history-in-git
- visual programming languages like Scratch. Waste of time. Text programming languages are already equally as visual due to indentation:Just make good serious gamedev libraries and integrated development environments for those real languages instead.
if x == 0: x = 1 - software that prevents you from running as root. Let me fucking shoot myself in the foot if I want to. It is better than having to deal with your hand holding bullshit, which is done in a different way for every project. E.g.: stackoverflow.com/questions/17466017/how-to-solve-you-must-not-be-root-to-run-crosstool-ng-when-using-ct-ng/53099177#53099177
- Medium
- luxury goods
- euphemism
- closed access academic journals are evil
- websites without OAuth
- shower room without a window to the exterior (mould!!!)
- single programs with their interface split across multiple windows, e.g. GIMP, ZynAddSubFX
- graphical user interfaces
- logograms
- infinitesimals. Just use limit instead, please
- country
- knowledge olympiads
- programming languages without a decent dominating package system
- closed source offline software used by millions
- exams
- security through obscurities
- dots in Gmail address
- things in websites that look like links, and behave like links, but don't let you middle click to open them on a separate tab
- K-pop
- numerical computing language
- fiscal paradises
- when the front-end of an website changes an important permanent state, but the URL does not change
- splash screens: you should show boot messages so that people will know what to Google for when things fail. Do you think computer newbies will be afraid and have nightmares?
- milk chocolate: why would you eat that instead of dark chocolate if you are older than 10?
- to talk about something without giving the real name to not scare off the audience
- mathematical symbol that looks like a Greek letter but isn't. Or perhaps mathematical notation in general
- when more than two people gather to play a board game or video game, and two or more people start chatting on and on about random subjects rather than concentrating on the game
- watching television while eating. Same for reading, or doing basically anything else but eat. The only acceptable activity is talking relaxedly, not about work.
- noises coming out of your bicycle. It is so hard to find where they come to fix them!!!
- code drop
- private cars as opposed to public transport. As a cyclist, you can just see the effect that large roads have on nearby areas, it just destroys nature.
- closed standards
- double consonants that make no difference to sound. Dilema? Dilemma? Dillema? Dillemma? Please!
- social media websites that show stuff from people you don't follow when you don't explicitly want that, including things which are not ads, just random suggestions. Twitter starting being like that cirac a 2022. Facebook got worse around that time. It is a constant fight against those stupid websites.
- socks with short legs that don't protect your ankle/lower calf from cold/scratches/dirt, e.g. liner socks
- Presta valves. Why would such a flimsy tech have become so popular compared to the infinitely superior Schrader!
This section is about functions that operate on numbers such as the integers or real numbers.
First published by Fourier in 1807 to solve the heat equation.
There are unlisted articles, also show them or only show them.