To break the meta means to find a new strategy that offers a significant advantage over the existing meta.
Due to Ciro Santilli's self perceived creative personality, Ciro Santilli is very attracted to meta breaks.
How One Man Changed the High Jump Forever by Olympics (2018)
Source. Dick Fosbury created and implemented the Fosbury Flop jump style in 1968.Akiyo Noguchi asks the rules while climbing! | Beta Break Ep.1 by Albert Ok (2020)
Source. Happened at the 2015 IFSC Climbing World Cup during the Haiyang, China, bouldering event. The author has a playlist of such climbing meta breaks. In climbing, the meta is called "the beta". Climbing competitions are perhaps the sport in which the meta is broken the most often, since each stage is unique.He got so old from 2012 to 2021 :-)
This dude did well. If only he had written a hyperlinked wiki rather than making videos! It would allow people to jump in at any point and just click back. It would be Godlike.
mathdoctorbob.org/About.html says:
Robert Donley received his doctorate in Mathematics from Stony Brook University and has over two decades of teaching experience at the high school, undergraduate, and graduate levels.
Builds on top of propositional logic, adding notably existential quantification.
He's a bit overly obsessed with polynomials for the taste of modern maths, but it's still fun.
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
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