Every vector space is defined over a field.

E.g. in ${\mathbb{R}}^3$, the underlying field is $\mathbb{R}$, the real numbers. And in ${\mathbb{C}}^2$ the underlying field is $\mathbb{C}$, the complex numbers.

Any field can be used, including finite field. But the underlying thing has to be a field, because the definitions of a vector need all field properties to hold to make sense.

Elements of the underlying field of a vector space are known as scalar.

Magic is the best card game of all time. Ciro Santilli agrees with this fact, and this has nothing to do with the nostalgia factor of having played it while being a teenager.

It is also the one with the most cumbersome name possible, containing even a bloody colon punctuation in it!

However, besides that, Magic has another major flaw: the cards of old formats (Legacy and Modern), which are the only really interesting ones, are fucking expensive: Section "Magic: The Gathering is too expensive".

Like in mathematics, the most beautiful decks are those that do crazy things:All of this comes to a certain extent from the deep asymmetry that permeates the game.

It is also really interesting to watch as new sets as spoiled and try to guess if certain cards will have any impact on the Modern or Legacy metagame.

Here are some cool decks:

If Ciro were to ever overcome his cheapness and play the legacy forma (which will never happen), he would likely play one of the following decks when trying to be able to win at all:Both of this decks focus on cheating a huge creature into play in one go, and both have combo protection methods (discard for turbo depths, and counterspells for sneak and show). Ciro believes that those decks reflect his personality well, notably Ciro Santilli's self perceived creative personality. Related decks that don't appeal as much to Ciro:And above all, Ciro would never play a fair deck. Grinding victories is not for him. He'd rather quickly decide win/lose status and move on.

Competitive commander is also interesting, although matches tend to be much more random so the format is harder to digest, see for example this channel; Playing With Power MTG channel.

In Ciro's mind, Urza's block is the most epic of all, followed by the masques block. Those sets had a ridiculous power level and epic art, and they happened just before Ciro Santilli started playing during Invasion, which had an extremely low power level in comparison. So Ciro saw some cards from those slightly older formats floating around, but not many, and they felt so mystical and awesome.

ChannelFireball is one of the best Legacy resources out there, but they have too much crap filling in between legacy videos unfortunately.

The following creators share many of Ciro's interests and output large quantities of interesting content covering all memes/overpowered combos of new sets:

Ciro was pleased when he learnt that Steve Wozniak plays magic the gathering.

Magic's competitive play became a mess in the late 2010's. They had a clear tournament structure, but they decided to start changing things every 6 months, and give tournaments meaningless names like "Mythic championship", and it just became impossible to follow what is what.

The mtg.fandom.com/wiki/Card_frame#Original_frame is the best, much more epic all others (notably since 2003 update) ware bullshit, good overview medium.com/@raphaelaleixo/the-graphic-design-for-magic-the-gathering-card-frames-b3b6da4cd003

www.youtube.com/watch?v=5hk3IOQiisg Crazy MTG Scandals That Changed The Game by Nikachu (2021). Good list:

An easy to prove theorem that follows from a harder to prove theorem.

This shows that viewing electromagnetism as gauge theory does have experimentally observable consequences. TODO understand what that means.

In more understandable terms, it shows that the magnetic vector potential matters where the magnetic field is 0.

Classic theory predicts that the output frequency must be the same as the input one since the electromagnetic wave makes the electron vibrate with same frequency as itself, which then irradiates further waves.

But the output waves are longer because photons are discrete and energy is proportional to frequency:

The formula is exactly that of two relativistic billiard balls colliding.

Therefore this is evidence that photons exist and have momentum.

No matter how hight the wave intensity, if it the frequency is small, no photons are removed from the material.

This is different from classic waves where energy is proportional to intensity, and coherent with the existence of photons and the Planck-Einstein relation.

cat-v.org/ by Rob Pike, co-creator of Go, looong time Unixer, and some kind of leader of a 9p resurrection cult. That one's spicy. E.g.: harmful.cat-v.org/, Ciro's version: good and evil.

Created by Dr. Rod Nave from Georgia State University, where he worked from 1968 after his post-doc in North Wales on molecular spectroscopy.

While there is value to that website, it always feels like it falls a bit too short as too "encyclopedic" and too little "tutorial-like". Most notably, it has very little on the history of physics/experiments.

Ciro Santilli likes this Rod, he really practices some good braindumping, just look at how he documented his life in the pre-social media Internet dark ages: hyperphysics.phy-astr.gsu.edu/Nave-html/nave.html

The website evolved from a HyperCard stack, as suggested by the website name, mentioned at: hyperphysics.phy-astr.gsu.edu/hbase/index.html.

Shame he was too old for CC BY-SA, see "Please respect the Copyright" at hyperphysics.phy-astr.gsu.edu/hbase/index.html.

exhibits.library.gsu.edu/kell/exhibits/show/nave-kell-hall/capturing-a-career has some good photo selection focused on showing the department, and has an interview.

Kell hall is a building of GSU that was demolished in 2019: atlanta.curbed.com/2020/1/31/21115980/gsu-georgia-state-atlanta-kell-hall-demolition-park-library-north

A linear map $A$ can be seen as a (1,1) tensor because:is a number, $v\ast$. is a dual vector, and W is a vector. Furthermoe, $T$ is linear in both $v\ast$ and $w$. All of this makes $T$ fullfill the definition of a (1,1) tensor.

Bibliography: