Topics Top articles New articles Updated articles Top users New users New discussions Top discussions New comments+ New article
Naming taxonomic ranks like genus, domain, etc. is a fucking waste of time, only useful before we developed molecular biology.
All that matters is the tree of clades with examples of species in each clade, and common characteristics shared by the clade.
And with molecular biology, we can build those trees incredibly well for extant species. When extinct species are involved however, things get more complicated.
The complex number analogue of a symmetric bilinear form.
The prototypical example of it is the complex dot product.
Note that this form is neither strictly symmetric, it satisfies:where the over bar indicates the complex conjugate, nor is it linear for complex scalar multiplication on the second argument.
Bibliography:
Perhaps the appeal of Zen is that it stepped away from Mahayana's "God and entities", and went a bit back towards the Buddhist psychology-like/self improvement grassroots?
Same value if you swap any input arguments.
Proprietary extension to Mozilla rr by rr lead coder Robert O'Callahan et. al, started in 2016 after he quit Mozilla.
TODO what does it add to
rr
?It is good to watch the Out For blood in Silicon Valley (2019) documentary after this to see how the characters look like in real life. Many feel amazingly cast, very close to the original. The only great exception is the Indian dude, who is completely different. Was it that hard to find some indian dude who looked and felt a little more like the real one?
Application of matrix multiplication by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Number of elements of an elliptic curve over a finite field by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
There's nothing like seeing the hypocrisy of the "Liberté, Égalité, Fraternité" people destroyed.
Interesting how Algeria now supports China's Xinjiang policy in 2019. But of course, dictatorships tend to work together
Ciro Santilli's father, an avid history reader, and in particular interested in the military dictatorship in Brazil through which he lived, once told Ciro how the French torture doctrine was directly adopted by Brazillian military, e.g. then even invited general Paul Aussaresses who had served in Algeria, to help them out with intelligence operations and give courses. Bro, fuck that.
But of course, the Americans weren't too far behind in Guantanamo.
KNF Laboport series laboratory vacuum pump by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli intends to move his beauty list here little by little: github.com/cirosantilli/mathematics/blob/master/beauty.md
The most beautiful things in mathematics are results that are:
- simple to state but hard to prove:
- Fermat's Last Theorem
- transcendental number conjectures, e.g. is transcendental?
- basically any conjecture involving prime numbers:
- many combinatorial game questions, e.g.:
- surprising results: we had intuitive reasons to believe something as possible or not, but a theorem shatters that conviction and brings us on our knees, sometimes via pathological counter-examples. General surprise themes include:Lists:
- classification of potentially infinite sets like: compact manifolds, etc.
- problems that are more complicated in low dimensions than high like:
- generalized Poincaré conjectures. It is also fun to see how in many cases complexity peaks out at 4 dimensions.
- classification of regular polytopes
- unpredictable magic constants:
- why is the lowest dimension for an exotic sphere 7?
- why is 4 the largest degree of an equation with explicit solution? Abel-Ruffini theorem
- undecidable problems, especially simple to state ones:
- mortal matrix problem
- sharp frontiers between solvable and unsolvable are also cool:
- attempts at determining specific values of the Busy beaver function for Turing machines with a given number of states and symbols
- related to Diophantine equations:
- applications: make life easier and/or modeling some phenomena well, e.g. in physics. See also: explain how to make money with the lesson
Good lists of such problems Lists of mathematical problems.
Whenever Ciro Santilli learns a bit of mathematics, he always wonders to himself:Unfortunately, due to how man books are written, it is not really possible to reach insight without first doing a bit of memorization. The better the book, the more insight is spread out, and less you have to learn before reaching each insight.
Am I achieving insight, or am I just memorizing definitions?
Pinned article: ourbigbook/introduction-to-the-ourbigbook-project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
- Internal cross file references done right:
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact