Linear map of two variables.

More formally, given 3 vector spaces X, Y, Z over a single field, a bilinear map is a function from:that is linear on the first two arguments from X and Y, i.e.:Note that the definition only makes sense if all three vector spaces are over the same field, because linearity can mix up each of them.

The most important example by far is the dot product from ${\mathbb{R}}^n\times {\mathbb{R}}^n\to \mathbb{R}$, which is more specifically also a symmetric bilinear form.

This notation is so confusing! People often don't manage to explain the intuition behind it, why this is an useful notation. When you see Indian university entry exam level memorization classes about this, it makes you want to cry.

The key reason why term symbols matter are Hund's rules, which allow us to predict with some accuracy which electron configurations of those states has more energy than the other.

web.chem.ucsb.edu/~devries/chem218/Term%20symbols.pdf puts it well: electron configuration notation is not specific enough, as each such notation e.g. 1s2 2s2 2p2 contains several options of spins and z angular momentum. And those affect energy.

This is why those symbols are often used when talking about energy differences: they specify more precisely which levels you are talking about.

Basically, each term symbol appears to represent a group of possible electron configurations with a given quantum angular momentum.

We first fix the energy level by saying at which orbital each electron can be (hyperfine structure is ignored). It doesn't even have to be the ground state: we can make some electrons excited at will.

The best thing to learn this is likely to draw out all the possible configurations explicitly, and then understand what is the term symbol for each possible configuration, see e.g. term symbols for carbon ground state.

It also confusing how uppercase letters S, P and D are used, when they do not refer to orbitals s, p and d, but rather to states which have the same angular momentum as individual electrons in those states.

It is also very confusing how extremelly close it looks to spectroscopic notation!

The form of the term symbol is:

The $2S+1$ can be understood directly as the degeneracy, how many configurations we have in that state.

Bibliography:

Publishes through the Fermilab YouTube channel under the playlist "Fermilab - Videos by Don Lincoln"

Some insights, but too much on the popular science side of things.

Sometimes Ciro Santilli regrets not having done a PhD. But this section makes him feel better about himself. To be fair, part of the merit is on him, part of the reason he didn't move on was the strong odour of bullshit oozing down to Masters level. A good PhH might have opened interesting job opportunities however, given that you don't really learn anything useful before that point in your education.

twitter.com/togelius/status/1584611702691483648:

60,000 32x32 color images in 10 different classes: airplanes, cars, birds, cats, deer, dogs, frogs, horses, ships, and trucks.

TODO release date.

This dataset can be thought of as an intermediate between the simplicity of MNIST, and a more full blown ImageNet.

Ciro Santilli is very fond of this result: the beauty of mathematics.

How can so much complexity come out from so few rules?

How can the proof be so long (thousands of papers)?? Surprise!!

And to top if all off, the awesomely named monster group could have a relationship with string theory via the monstrous moonshine?

all science is either physics or stamp collecting comes to mind.

The classification contains:

"Game" is a bit of a stretch as there are no player choices at all.

A more precise word would be simulation.

More precise, this "game" is exactly an absorbing Markov chain.

Since Snakes and Ladders is nothing but a Absorbing Markov chain, the results are exactly the same as for that general problem.

www.jstor.org/stable/3619261: How Long Is a Game of Snakes and Ladders? by Althoen, King and Schilling (1993), paywalled.

His combination of politically incorrect dirt talk with amazing quirky decks captures Ciro's imagination.

Anonymous no face-reveal.

The videos are heavily edited with all pauses cut out, which makes them very quick to watch and saves viewer time.

Modern focused, with some occasional newer formats mixed in.

When Wizards publishes several useless sets in a row without a single modern playable card, he's just forced into Standard.

When a characteristic is basal, it basically means the opposite of it being polyphyletic.

E.g. monotremes laying eggs did not evolve separately after function loss, it comes directly from reptiles.

Open source MtG engine implementation written in Java.

Seems to have an option to download art from internet as well.

Ciro Santilli wonders how legal it is. They very explicitly do not mention the words Magic: The Gathering anywhere.

Their UI does a good job at being self explanatory. Space is the shortcut to skip phases.

No online play.

TODO it appears to parse card functionality out of the human readable text! That's genius, as it helps automatically get new cards working, and squirt around legal issues.

Other people with similar philosophies: