Ciro Santilli @cirosantilli 37

Basically it is a larger space such that there exists a surjection from the large space onto the smaller space, while still being compatible with the topology of the small space.

We can characterize the cover by how injective the function is. E.g. if two elements of the large space map to each element of the small space, then we have a double cover and so on.

A metric is a function that give the distance, i.e. a real number, between any two elements of a space.

A metric may be induced from a norm as shown at: Section "Metric induced by a norm".

Because a norm can be induced by an inner product, and the inner product given by the matrix representation of a positive definite symmetric bilinear form, in simple cases metrics can also be represented by a matrix.

This dude is mind blowing. Big respect.

Some of the most impressive videos are the ones in which he goes and extracts metals from minerals himself all the way.

But God, the typography of the channel name is so insane! Why no space???

Shame the academic system wasn't compatible with him: www.reddit.com/r/codyslab/comments/f5531p/codys_qualifications/ Maybe there were safety issues involved though.

This is a good initiative. It doesn't go nearly as deep as it needs to go to fix students must have a flexible choice of what to learn, but it is a start!

I read Human Compatible by Stuart J. Russell (2019). Some AI safety people were actually giving out free copies after a talk, can you believe it! Good book.

One of the causes Ciro Santilli care the most about: motivation.

Ciro Santilli's view of the ideal teaching method: how to teach.

A list of complaints against education: Section "Education is broken".

How to improve education? Simple:

Days of the week where you don't do what you set out to do. And yet, it is in those days that you save your sanity, and possibly the world. Wait, this sounds exactly like a week day?

A unique projective space can be defined for any vector space.

The projective space associated with a given vector space $V$ is denoted $\mathbf{P}(V)$.

The definition is to take the vector space, remove the zero element, and identify all elements that lie on the same line, i.e. $\vec{v}=\lambda \vec{w}$

The most important initial example to study is the real projective plane.