Ciro Santilli @cirosantilli  40

Ah, the jewel of computational physics.

Also known as an ab initio method: no experimental measurement is taken as input, QED is all you need.

But since QED is thought to fully describe all relevant aspects molecules, it could be called "the" ab initio method.

For one, if we were able to predict protein molecule interactions, our understanding of molecular biology technologies would be solved.

No more ultra expensive and complicated X-ray crystallography or cryogenic electron microscopy.

And the fact that quantum computers are one of the most promising advances to this field, is also very very exciting: Section "Quantum algorithm".

This section is about the definition of the dot product over ${\mathbb{C}}^n$, which extends the definition of the dot product over ${\mathbb{R}}^n$.

Some motivation is discussed at: math.stackexchange.com/questions/2459814/what-is-the-dot-product-of-complex-vectors/4300169#4300169

The complex dot product is defined as:

E.g. in ${\mathbb{C}}^1$:

We can see therefore that this is a form, and a positive definite because:

Just like the usual dot product, this will be a positive definite symmetric bilinear form by definition.

All companies with investors are evil, make no mistake.

They may have nice looking save the world charity campaigns, but once you get even close to affecting their revenue stream, the axe falls. The charity is only a publicity stunt to reduce wages.

Some level of government intervention is needed to control investor's greed.

It is just a question of business model: some business models are eviler than others. Making people pay for operating systems being possible the most evil of all.

One thing must be said however. You can learn a lot by working in a good company, because it ends up putting you in contact with practical real problems that you wouldn't otherwise see by just doing your own random low-tech startup. This is especially valuable if said company is also enlightened enough to use and contribute back to open source software, thus improving the world and paying back the moral debt of using other people's work for free.

Another important point to consider is who in the company is evil. In a sane tech company, the lowly engineers are going to be non-evil. And then the more you go up the management chain, the more aligned you have to be with investors, and thus the more and more evil you get. HR is just evil from the bottom though, it's just the nature of their job.

Once upon a time, when Ciro worked at a company, one day the company decided to give everyone a 20% raise.

The likely reason was that Apple was coming to town, and was sucking the fuck out of the company's talent.

Nothing ever drove it so clearly into Ciro's heart the obvious fact that even for skilled jobs, companies don't pay you what you're worth. They pay you as little as possible so you won't quit to join someone else. It is pure market forces in play.

The annoying thing is that people are highly non-fungible, so much like painting auctions, you can only estimate your price by putting yourself on auction and seeing what people will pay for you, i.e. interviewing for new jobs.

Another point is that people have all sorts of stupid restrictions such as not wanting to work on certain areas for moral reasons, or not wanting to move away from a certain area they like. Companies will of course readily exploit such weakness to be able to pay less. Silly non-rational beings.

A function where the domain is the same as the codomain.

www.cns.gatech.edu/~predrag/courses/PHYS-6124-12/StGoChap6.pdf 6.1 "Classification of PDE's" clarifies which boundary conditions are needed for existence and uniqueness of each type of second order of PDE:

Triangle, tetrahedron.

The name does not imply regular by default. For regular ones, you should say "regular polytope".

Non-regular description: take convex hull take D + 1 vertices that are not on a single D-plan.

square, cube. 4D case known as tesseract.

Convex hull of all $\{-1,1{\}}^D$ (Cartesian product power) D-tuples, e.g. in 3D:

From this we see that there are $2^D$ vertices.

Two vertices are linked iff they differ by a single number. So each vertex has D neighbors.