Inferior compared to self-directed learning, but better than the traditional "everyone gets the same" approach.
Ciro Santilli feels a bit like this guy:
- he's also an idealist, even more than Ciro. So cute. Notably, he he also dumps his brain online into pages that no-one will ever read
- he also thinks that the 2010's education system is bullshit, e.g. settheory.net/learnphysics
- trust-forum.net/ some kind of change the world website. But:is a sin to Ciro. Planning a change the world thing behind closed doors? Really? Decentralized, meh.
- antispirituality.net/ his atheism website
singlesunion.org/ so cute, he's looking for true love!!! This is something Ciro often thinks about: why it is so difficult to find love without looking people in the eye. The same applies to jobs to some extent. He has an Incel wiki page: incels.wiki/w/Sylvain_Poirier :-)
The strongest are:
- early 20th century: Annalen der Physik: God OG physics journal of the early 20th century, before the Nazis fucked German science back to the Middle Ages
- 20s/30s: Nature started picking up strong
- 40s/50s: American journals started to come in strong after all the genius Jews escaped from Germany, notably Physical Review Letters
The main interest of this theorem is in classifying the indefinite orthogonal groups, which in turn is fundamental because the Lorentz group is an indefinite orthogonal groups, see: all indefinite orthogonal groups of matrices of equal metric signature are isomorphic.
It also tells us that a change of basis does not the alter the metric signature of a bilinear form, see matrix congruence can be seen as the change of basis of a bilinear form.
The theorem states that the number of 0, 1 and -1 in the metric signature is the same for two symmetric matrices that are congruent matrices.
For example, consider:
The eigenvalues of are and , and the associated eigenvectors are:symPy code:and from the eigendecomposition of a real symmetric matrix we know that:
A = Matrix([[2, sqrt(2)], [sqrt(2), 3]])
A.eigenvects()
Now, instead of , we could use , where is an arbitrary diagonal matrix of type:With this, would reach a new matrix :Therefore, with this congruence, we are able to multiply the eigenvalues of by any positive number and . Since we are multiplying by two arbitrary positive numbers, we cannot change the signs of the original eigenvalues, and so the metric signature is maintained, but respecting that any value can be reached.
Note that the matrix congruence relation looks a bit like the eigendecomposition of a matrix:but note that does not have to contain eigenvalues, unlike the eigendecomposition of a matrix. This is because here is not fixed to having eigenvectors in its columns.
But because the matrix is symmetric however, we could always choose to actually diagonalize as mentioned at eigendecomposition of a real symmetric matrix. Therefore, the metric signature can be seen directly from eigenvalues.
What this does represent, is a general change of basis that maintains the matrix a symmetric matrix.
Good:
- WYSIWYG
- Extended-Markdown-based
- help.obsidian.md/Getting+started/Sync+your+notes+across+devices they do have a device sync mechanism
- it watches the filesystem and if you change anything it gets automatically updated on UI
- help.obsidian.md/links#Link+to+a+block+in+a+note you can set (forcibly scoped) IDs to blocks. But it's not exposed on WYSIWYG?
Bad:
- forced ID scoping on the tree as usual
- no browser-only editor, it's just a local app apparently:
- obsidian.md/publish they have a publish function, but you can't see the generated websites with JavaScript turned off. And they charge you 8 dollars / month for that shit. Lol.
- block elements like images and tables cannot have captions?
- they kind of have synonyms: help.obsidian.md/aliases but does it work on source code?
It good to think about how Euclid's postulates look like in the real projective plane:
- Since there is one point of infinity for each direction, there is one such point for every direction the two parallel lines might be at. The parallel postulate does not hold, and is replaced with a simpler more elegant version: every two lines meet at exactly one point.One thing to note however is that ther real projective plane does not have angles defined on it by definition. Those can be defined, forming elliptic geometry through the projective model of elliptic geometry, but we can interpret the "parallel lines" as "two lines that meet at a point at infinity"
- points in the real projective plane are lines in
- lines in the real projective plane are planes in .For every two projective points there is a single projective line that passes through them.Note however that not all lines in the real plane correspond to a projective line: only lines tangent to a circle at zero do.
Unlike the real projective line which is homotopic to the circle, the real projective plane is not homotopic to the sphere.
The topological difference bewteen the sphere and the real projective space is that for the sphere all those points in the x-y circle are identified to a single point.
One more generalized argument of this is the classification of closed surfaces, in which the real projective plane is a sphere with a hole cut and one Möbius strip glued in.
There are unlisted articles, also show them or only show them.