Ciro Santilli @cirosantilli 37

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.

Things to do: