The orthogonal group is the group of all matrices with orthonormal rows and orthonormal columns Updated 2025-04-24 +Created 1970-01-01
Or equivalently, the set of rows is orthonormal, and so is the set of columns. TODO proof that it is equivalent to the orthogonal group is the group of all matrices that preserve the dot product.
Ciro Santilli's Stack Overflow suspension for vote fraud script 2019 Updated 2025-04-24 +Created 1970-01-01
After Ciro Santilli got a lot of attention on Hacker News news.ycombinator.com/item?id=19428700 his Stack Overflow account was suspended for 3 days web.archive.org/web/20190320163458/https://stackoverflow.com/users/895245/ciro-santilli-新疆改造中心-六四事件-法轮功 and he received a magic notification that led to a private message:
Hello,I've removed this from your profile github.com/cirosantilli/stack-overflow-vote-fraud-script and do not expect you to post it around the site.Regards,Stack Overflow Moderation TeamTo: Aaron Hall ♦;Andy ♦;Baum mit Augen ♦;Bhargav Rao ♦;Bohemian ♦;BoltClock ♦;Brad Larson ♦;ChrisF ♦;Cody Gray ♦;deceze ♦;Ed Cottrell ♦;Flexo ♦;George Stocker ♦;Jean-François Fabre ♦;Jon Clements ♦;josliber ♦;Madara Uchiha ♦;Martijn Pieters ♦;meagar ♦;Michael Myers ♦;Rob ♦;Robert Harvey ♦;Ry- ♦;Samuel Liew ♦;Undo ♦;Yvette Colomb ♦
Ciro's reply was:
Hi mods,
Reply and unsuspend quickly followed, with link still removed:
I suspended you to get your attention. Your attitude about going to Twitter about it does not bode well with me.Feel free to have whatever you want in your GitHub repo. Just don't advertise tools to make it easier for people to circumvent the rules. As easy or as hard as it may be to circumvent them, you're handing it to people who may not be capable of doing so. It doesn't help.Don't make threats to upload on an anonymous account. Accounts created to circumvent previous warnings are not welcomed on the site.We don't need a meta thread to discuss whether it's ok to post voting fraud links in your profile and we definitely don't need to give it anymore publicity.Regards,Stack Overflow Moderation Team
A meta thread was later created by Yvette, kudos, to which Ciro answered with the correct unpopular answer that will be downvoted to oblivion: meta.stackoverflow.com/questions/381577/is-it-ok-to-have-links-on-how-to-create-sock-puppets-and-gain-rep-fraudulently-i/381635#381635
Yvette had also previously deleted one or two of Ciro's answers for being duplicates, which is a policy Ciro is against: if the questions are not dupes, a single answer might still directly reply to both of them.
Yvette later announced that she was leaving the website: meta.stackoverflow.com/questions/399495/leaving-the-site-and-the-network-mid-election-is-not-the-best-but-theres-no. This is evil, but Ciro was happy. He does not mean harm to Yvette, but in their limited interaction, Ciro disagreed with her choices.
The Great Places Erased by Suburbia by Not Just Bikes (2022)
Source. Stack Overflow, and other online forums, can serve as a sort of a third place for its more active users. Ciro Santilli's hardware 2017-04 Nike Flex Experience RN 6 Grey running shoes Updated 2025-04-24 +Created 1970-01-01
Here is a more understandable description of the semi-satire that follows: math.stackexchange.com/questions/53969/what-does-formal-mean/3297537#3297537
You start with a very small list of:
- certain arbitrarily chosen initial strings, which mathematicians call "axioms"
- rules of how to obtain new strings from old strings, called "rules of inference" Every transformation rule is very simple, and can be verified by a computer.
Using those rules, you choose a target string that you want to reach, and then try to reach it. Before the target string is reached, mathematicians call it a "conjecture".
Since every step of the proof is very simple and can be verified by a computer automatically, the entire proof can also be automatically verified by a computer very easily.
Finding proofs however is undoubtedly an uncomputable problem.
Most mathematicians can't code or deal with the real world in general however, so they haven't created the obviously necessary: website front-end for a mathematical formal proof system.
The fact that Mathematics happens to be the best way to describe physics and that humans can use physical intuition heuristics to reach the NP-hard proofs of mathematics is one of the great miracles of the universe.
Once we have mathematics formally modelled, one of the coolest results is Gödel's incompleteness theorems, which states that for any reasonable proof system, there are necessarily theorems that cannot be proven neither true nor false starting from any given set of axioms: those theorems are independent from those axioms. Therefore, there are three possible outcomes for any hypothesis: true, false or independent!
Some famous theorems have even been proven to be independent of some famous axioms. One of the most notable is that the Continuum Hypothesis is independent from Zermelo-Fraenkel set theory! Such independence proofs rely on modelling the proof system inside another proof system, and forcing is one of the main techniques used for this.
The landscape of modern Mathematics comic by Abstruse Goose
. Source. This comic shows that Mathematics is one of the most diversified areas of useless human knowledge.On one hand, yes, we need knowledge at all levels, and it is fine to start top-to-bottom with an overview.
The problem is, however, that there is a huge knowledge gap between the one liner "this is the truth" and the much more important "this is how we know it, these are the experiments" as mentioned at how to teach and learn physics.
Therefore, if you have that extremely rare knowledge, you should be writing that in addition to the dumbed down version with an open knowledge license. It takes time, but that's what really changes the world.
Ciro Santilli has always felt that there is a huge gap between "the very basic" and "the very advanced", as mentioned at: Section "The missing link between basic and advanced", which existing scientific vulgarization is not doing enough to address. In a sense, filling out this "middle path" is the main goal of OurBigBook.com.
Ciro really enjoyed the description of the "Arindam Kumar Chatterjee" youTube channel:
Theoretical/mathematical physics at the graduate level and above. This is NOT a popular science channel. Here you find real theoretical physicists doing real theoretical physics. We think it is important for people to get a taste of the real deal, and for aspiring theoretical physicists to see what they are working towards, i.e., to provide the public with something beyond the ubiquitous Michio Kaku and Brian Cox.
One thing must be said however: there seems to be an actual bias against researchers tho try to create vulgarization material: How To Get Tenure at a Major Research University by Sean Carroll (2011), and that is terrible.
There is often more value in a tutorial by a beginner who is trying to fully learn and explain a subject, than by an expert who is trying to "dumb it down" too much.
In "practice" it is likely "useless", because the functions that it can integrate that Riemann can't are just too funky to appear in practice :-)
Its value is much more indirect and subtle, as in "it serves as a solid basis of quantum mechanics" due to the definition of Hilbert spaces.
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