Journals must require source code and data sets to publish Updated 2025-03-08 +Created 1970-01-01
It is understandable that you might not be able to reproduce a paper that does a natural science experiment, given that physics is brutal.
But for papers that have either source code or data sets, academic journals must require that those be made available, or refuse to publish.
Any document without such obvious reproducibility elements is a white paper, not a proper peer reviewed paper.
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.
This dude mentored Enrico Fermi in high school. Ciro Santilli added some info to Fermi's Wikipedia page at: en.wikipedia.org/w/index.php?title=Enrico_Fermi&type=revision&diff=1050919447&oldid=1049187703 from Enrico Fermi: physicist by Emilio Segrè (1970):
In 1914, Fermi, who used to often meet with his father in front of the office after work, met a colleague of his father called Adolfo Amidei, who would walk part of the way home with Alberto [Enrico's father]. Enrico had learned that Adolfo was interested in mathematics and physics and took the opportunity to ask Adolfo a question about geometry. Adolfo understood that the young Fermi was referring to projective geometry and then proceeded to give him a book on the subject written by Theodor Reye. Two months later, Fermi returned the book, having solved all the problems proposed at the end of the book, some of which Adolfo considered difficult. Upon verifying this, Adolfo felt that Fermi was "a prodigy, at least with respect to geometry", and further mentored the boy, providing him with more books on physics and mathematics. Adolfo noted that Fermi had a very good memory and thus could return the books after having read them because he could remember their content very well.
Ciro Santilli really likes guys like this. Given that he does not have the right genetics, conditions and temperance for scientific greatness in this lifetime, he dreams of one day finding his own Fermi instead.
They do have some really good ones.
It is interesting that in different episodes they often switch the dominant/passive roles, so it's not fixed as in Laurel and Hardy.
Are we the Baddies? by Mitchell and Webb
. Source. See also: cirosantilli.com/china-dictatorship/nazi.Discoverer by Mitchell and Webb
. Source. Makes fun of the many terrible naming choices British navigators have made while discovering/rediscovering new lands.Homeopathic A&E by Mitchell and Webb
. Source. Like everything else in Lie groups, first start with the matrix as discussed at Section "Lie algebra of a matrix Lie group".
Intuitively, a Lie algebra is a simpler object than a Lie group. Without any extra structure, groups can be very complicated non-linear objects. But a Lie algebra is just an algebra over a field, and one with a restricted bilinear map called the Lie bracket, that has to also be alternating and satisfy the Jacobi identity.
Another important way to think about Lie algebras, is as infinitesimal generators.
Because of the Lie group-Lie algebra correspondence, we know that there is almost a bijection between each Lie group and the corresponding Lie algebra. So it makes sense to try and study the algebra instead of the group itself whenever possible, to try and get insight and proofs in that simpler framework. This is the key reason why people study Lie algebras. One is philosophically reminded of how normal subgroups are a simpler representation of group homomorphisms.
To make things even simpler, because all vector spaces of the same dimension on a given field are isomorphic, the only things we need to specify a Lie group through a Lie algebra are:Note that the Lie bracket can look different under different basis of the Lie algebra however. This is shown for example at Physics from Symmetry by Jakob Schwichtenberg (2015) page 71 for the Lorentz group.
- the dimension
- the Lie bracket
As mentioned at Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 4 "Lie Algebras", taking the Lie algebra around the identity is mostly a convention, we could treat any other point, and things are more or less equivalent.
Anti-Piracy Ad by The IT Crowd (2007)
Source. The fundamental concept of calculus!
The reason why the epsilon delta definition is so venerated is that it fits directly into well known methods of the formalization of mathematics, making the notion completely precise.
Generalize function to allow adding some useful things which people wanted to be classical functions but which are not,
It therefore requires you to redefine and reprove all of calculus.
For this reason, most people are tempted to assume that all the hand wavy intuitive arguments undergrad teachers give are true and just move on with life. And they generally are.
One notable example where distributions pop up are the eigenvectors of the position operator in quantum mechanics, which are given by Dirac delta functions, which is most commonly rigorously defined in terms of distribution.
Distributions are also defined in a way that allows you to do calculus on them. Notably, you can define a derivative, and the derivative of the Heaviside step function is the Dirac delta function.
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