Ciro Santilli @cirosantilli 37

Some blogs:

Also resonates with backward design.

One of Ciro Santilli's strongest feeling in education is that material often falls in either of the two categories:

Ciro believes that there is often an important missing link between them, e.g.:

If we as a society are unable to provide this sweet Middle Way sweet-spot, it is unreasonable to expect that learners will ever have the motivation to advance, because it is just too boring! They are just more likely to go play video games instead.

It is Ciro's hope that OurBigBook.com will help to fill exactly that gap.

In Ciro's view, as of the 2020's this critical gap generally lies somewhere between the end of undergraduate studies, and at the start of postgraduate studies.

What we have to do is make this knowledge more accessible all way down to high school and earlier.

Let's take the gloves off more often, and give the full thing to interested students! Let students learn what they want to learn, and do that as soon as possible! Life is too short!

This problem is basically the knowledge version of the last mile problem. When we reach the end of graduate, there are enough directions of knowledge to go off into, that the probability that a great free tutorial exists is relatively low. Of course, as one approaches the realm of novel research, the branching is so wide that having perfect tutorials becomes impossible. Ciro's goal in life go push the last mile marker a bit further out.

Related:

Bibliography:

Lists:

TODO what is the point of them? Why not just sum over every index that appears twice, regardless of where it is, as mentioned at: www.maths.cam.ac.uk/postgrad/part-iii/files/misc/index-notation.pdf.

Vectors with the index on top such as $x^i$ are the "regular vectors", they are called covariant vectors.

Those in indices on bottom are called contravariant vectors.

It is possible to change between them by Raising and lowering indices.

The values are different only when the metric signature matrix is different from the identity matrix.

github.com/cirosantilli/node-express-sequelize-nextjs-realworld-example-app contains the same baseline tech as OurBigBook, and I have been use to quickly test/benchmark new concepts for the website base.

I'm almost proud about that project, as a reasonable template for a Next.js project. It is not perfect, notably see issues on the issue tracker, but it it quite reasonable.

The side effects of ambitious goals are often the most valuable thing achieved once again? I to actually make the project be more important thatn the side effects this time, but we'll see.

Since the last update, I've made some major improvements to the baseline tech of the website, which I'll move little by little into OurBigBook. Some of the improvements actually started in OurBigBook.com. The improvements were:

Mordell's theorem guarantees that the rank (number of elements in the generating set of the group) is always well defined for an elliptic curve over the rational numbers. But as of 2023 there is no known algorithm which calculates the rank of any curve!

It is not even known if there are elliptic curves of every rank or not: Largest known ranks of an elliptic curve over the rational numbers, and it has proven extremely hard to find new ones over time.

TODO list of known values and algorithms? The Birch and Swinnerton-Dyer conjecture would immediately provide a stupid algorithm for it.

Magic software that allows you to write a single program that runs on a wide range of hardware.

TODO, come on, Internet!

Bibliography.

They come up a lot in many contexts, e.g.:

The big breakthrough of the vertebrates appears to be the ability to swim around in a straight line and eat smaller species that are floating about.

Bones appear to help that a lot!

It is likely the most efficient design to travel long distances. Be thin and wiggle your tail around.

Perhaps smaller animals can skip the bone thing. Maybe a notable example are the lancelets, which look a bit like small fish. But they only go up to 8 cm.