Ciro Santilli @cirosantilli 40

As mentioned on the introduction, the main objective of the course is to try predict qualitative properties of materials, notably the existence of certain phase transitions, starting from first principle toy models.

Key phenomena covered include:

Low budget.

Good theory of Jesus.

List of similar feeling films: www.youtube.com/watch?v=zwYwFoanrNg 11 Underrated Hard Sci-fi Movies by Marvelous Videos (2021)

We are at a point in history where the electrical telegraph is well established.

But people don't want to press letters one by one on a switch. They want to talk!

The first phones appear to have used telegraph lines directly.

Also wired phones don't require modulation, which likely made their development much easier than wireless voice transmission. You just send the signal as a voltage differential directly obtained from the air pressure: how the telephone works.

Let's show that this definition is equivalent to the orthogonal group is the group of all matrices that preserve the dot product.

Note that:and for that to be true for all possible $x$ and $y$ then we must have:i.e. the matrix inverse is equal to the transpose.

Conversely, if:is true, then

These matricese are called the orthogonal matrices.

TODO is there any more intuitive way to think about this?

Some cool ones:

Persistent undo history: