Ciro Santilli @cirosantilli 40

The name makes absolutely no sense in modern terms, as nor colors nor light are used directly in the measurements. It is purely historical.

Highlighted at the Origins of Precision by Machine Thinking (2017).

The term and idea was first introduced initialized by Hermann Weyl when he was working on combining electromagnetism and general relativity to formulate Maxwell's equations in curved spacetime in 1918 and published as Gravity and electricity by Hermann Weyl (1918). Based on perception that $U(1)$ symmetry implies charge conservation. The same idea was later adapted for quantum electrodynamics, a context in which is has even more impact.

Saves preprocessor output and generated assembly to separate files.

Technique widely used to measure the size of DNA strands, most often PCR output of a region of interest.

A simple sample application is gel electrophoresis alelle determination.

The variables of the Lagrangian, e.g. the angles of a double pendulum. From that example it is clear that these variables don't need to be simple things like cartesian coordinates or polar coordinates (although these tend to be the overwhelming majority of simple case encountered): any way to describe the system is perfectly valid.

In quantum field theory, those variables are actually fields.

There are two cases:

Questions: are all compact manifolds / differential manifolds homotopic / diffeomorphic to the sphere in that dimension?

Unifies both special relativity and gravity.

Not compatible with the Standard Model, and the 2020 unification attempts are called theory of everything.

One of the main motivations for it was likely having forces not be instantaneous, but rather mediated by field to maintain the principle of locality, just like electromagnetism did earlier.

Cardinality $\le$ dimension of the vector space.

High level DNA studies? :-)

This is a good book.

It has some overlap with Surely You're Joking, Mr. Feynman, which it likely takes as primary sources of some stories.

However, while Surely goes into a lot of detail of each event, this book paints a more cohesive and global picture of things.

In terms of hard physics/mathematics, this book takes the approach of spending a few paragraphs in some chapters describing in high level terms some of the key ideas, which is a good compromise. It does sometime fall into the sin of to talk about something without giving the real name to not scare off the audience, but it does give a lot of names, notably it talks a lot about Lagrangian mechanics. And it goes into more details than Surely in any case.

Suppose we specify:The question then is, which transaction is encoded at that position of the file?

This would allow us to index inscriptions in the .dat files directly with fast C tools, and then retrive the transaction ID to get cleaner data and metadata.

It should be possible if we managed to take the information from bitcoindev.network/understanding-the-data/ and dump into an indexed SQLite database.

I tried to start things off with LevelDBDumper:but that consumed all 64 GB of RAM on P51... github.com/mdawsonuk/LevelDBDumper/issues/15

But OK, nevermind that repo, it can be done easily with the LevelDB API of any language: bitcoin.stackexchange.com/questions/121888/what-is-the-data-format-layout-for-txindex-leveldb-values. Just the data seems wrong and we don't know why.

Repeat after me. Inertia is all that matters. Features don't matter. But algorithms matter.

Ciro Santilli tried to add this example to Wikipedia, but it was reverted, so here we are, see also: Section "Deletionism on Wikipedia".

This is a good first example of a field of a finite field of non-prime order, this one is a prime power order instead.

$4=2^2$, so one way to represent the elements of the field will be the to use the 4 polynomials of degree 1 over GF(2):

Note that we refer in this definition to anther field, but that is fine, because we only refer to fields of prime order such as GF(2), because we are dealing with prime powers only. And we have already defined fields of prime order easily previously with modular arithmetic.

Over GF(2), there is only one irreducible polynomial of degree 2:

Addition is defined element-wise with modular arithmetic modulo 2 as defined over GF(2), e.g.:

Multiplication is done modulo $X^2+X+1$, which ensures that the result is also of degree 1.

For example first we do a regular multiplication:

Without modulo, that would not be one of the elements of the field anymore due to the $1X^2$!

So we take the modulo, we note that:and by the definition of modulo:which is the final result of the multiplication.

TODO show how taking a reducible polynomial for modulo fails. Presumably it is for a similar reason to why things fail for the prime case.