Ciro Santilli @cirosantilli 37

Then, 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

This is basically what Jimmy Wales had originally set out to make Wikipedia, a peer reviewed thing.

But then he noticed the entry barrier was too high while inviding an economist to review an article he wrote, and just made the more open thing instead.

A generalized definition of derivative that works on manifolds.

TODO: how does it maintain a single value even across different coordinate charts?

Oh, and if it weren't enough, mathematicians have a separate name for the damned nabla symbol : "del" instead of "nabla".

TODO why is it called "Del"? Is is because it is an inverted uppercase delta?

Dual vectors are the members of a dual space.

In the context of tensors , we use raised indices to refer to members of the dual basis vs the underlying basis:The dual basis vectors $e^i$ are defined to "pick the corresponding coordinate" out of elements of V. E.g.:By expanding into the basis, we can put this more succinctly with the Kronecker delta as:

Note that in Einstein notation, the components of a dual vector have lower indices. This works well with the upper case indices of the dual vectors, allowing us to write a dual vector $f$ as:

In the context of quantum mechanics, the bra notation is also used for dual vectors.

Bibliography:

ChatGPT produces:Omid Kordestani - Joined in 1999 as Google’s first business hire, focusing on sales and revenue generation.

These are some users Ciro Santilli particularly respects, mostly due to their contributions to systems programming subjects:

Ciro also really likes the following users, a bit less like Gods, and bit more like friends:

Other interesting people:

Was the first model to explain the Balmer series, notably linking atomic spectra to the Planck constant and therefore to other initial quantum mechanical observations.

This was one of the first major models that just said:

It still treats electrons as little points spinning around the nucleus, but it makes the non-classical postulate that only certain angular momentums (and therefore energies) are allowed.

Bibliography:

Large but ephemeral storage for EC2 instances. Predetermined by the EC2 instance type. Stays in the local server disk. Not automatically mounted.