pglpm

I was reading some works – true pearls! – by Synge: his conference contribution Tensorial integral conservation laws in general relativity (1959/1962) and his book Relativity: The General Theory (1960). In these works Synge introduces an extremely interesting definition of four-momentum and of rotational momentum, based on two-point tensors. The definition is interesting because (1) it involves the full Riemann tensor, not just the Einstein tensor, (2) it includes the (or rather, defines a) four-momentum and rotational momentum of the gravitational field, (3) it obeys a conservation law as opposed to a balance law (the equation ∇⋅T=0 expresses in general just balance, not conservation).

The definition for rotational momentum is also interesting because it appears as the natural generalization of the one in Newtonian mechanics, which is based on the affine structure of its 3D space. Roughly speaking, in Newtonian mechanics we have (r-a)∧p, where a is a fixed point, r the point of interest, and p the momentum (density) at the point r. Synge essentially replaces the difference "r-a", which relies on an affine structure, with the geodesic distance between two points R and A in spacetime, through his two-point "world function". In his book he explains that general relativity requires the appearance of a reference point (a or A) also in the definition of four-momentum, whereas such reference point is superfluous in Newtonian mechanics.

OK this was a very poor summary, just to pique your interest. For details see Synge's conference contribution, and chapter VI, especially §4, of his book (refs below).

Bryce DeWitt even commented "Je suis tout à fait de l'avis du professeur Synge qui insiste sur le fait que ces fonctions de deux points se montreront très importantes dans le futur développement de la théorie de la relativité générale" on the conference contribution. Two-point tensors were quite fashionable in the 1960s, they are used in interesting ways also in Truesdell & Toupin's The Classical Field Theories (see Part F and Appendix III there).

Yet, these definition venues seem to have been abandoned today. Here are my questions to you: why? just for unfathomable sociology-of-science reasons, or because of physical-mathematical ones? Are there works today which further explore these venues?

References:

• Synge: Tensorial integral conservation laws in general relativity, in Lichnerowicz,Tonnelat: Les théories relativistes de la gravitation (CNRS 1962), pp. 75–83. https://libgen.is/book/index.php?md5=74345AB69DDF9EE233FA55F55FDCB057

• Synge: Relativity: The General Theory (North-Holland 1960). https://libgen.is/book/index.php?md5=7AE08880CF8086FED4D3BCF732BE8E54

• Truesdell, Toupin: The Classical Field Theories, in Flügge: Handbuch der Physik: III/1 (Springer 1960), pp. I–VII, 226–902. https://doi.org/10.1007/978-3-642-45943-6_2 https://libgen.is/book/index.php?md5=728F54156B632C44EAC2C559F120DDAB

A little advertisement for a new free online course about the foundations of data science, machine learning, and – just a little – artificial intelligence. It's been designed for students in computer science and data science, who could be uncomfortable with a head-on probability-theory or statistics approach, and who might have a lighter background in maths. The main point of view of the course is how to build an artificial-intelligence agent who must draw inferences and make decisions. As a course, it's still a sort of experiment.

https://pglpm.github.io/ADA511/

In more technical terms, the course is actually about so-called "Bayesian nonparametric density inference" and Bayesian decision theory.

What are the comparative and superlative of the adjective "fun"? I'd say "more fun" and "most fun"...

But I'm somehow slightly tempted by "funnier" and "funniest", which should be for "funny" though, not "fun"...

I didn't find anything about this in the main dictionaries.

I wonder how many in this community resonate with this.

For years I've been using DejaVu fonts, but in the last years I had the feeling that this project had been abandoned. And indeed it has.

Does anyone know of good open-source alternatives?

I've heard of GNU Unifont, which seems still alive, but it isn't the kind of font one would use for, say, slides or websites.

Liberation and Kurinto were interesting (though not au par with DejaVu, in my opinion), but seem to have been abandoned as well.

I'm tired of Google and personally am not interested in fonts commissioned by them.

There's an old youtube channel by "Avamogal" (apparently "a mom to 7 boys. 10 grandkids 8 boys, 2 girls") which is full of great collages of Buster clips, with interesting music backgrounds. Recommended.

Sadly it seems the channel hasn't been active for 6 years or so...

Imagine there's a sequence of items, it started somewhere in the past and will keep on going. The kind of items could be anything – say days, or football matches, or lectures, or widgets out of an assembly line.

I'd like to refer to the future item that will be, say, the 100th if I start counting them from now. I hope you understand what I mean: the 1st would be the next, the 2nd would be the one after the next, and so on.

How do I denote that future 100th item with a concise expression? I thought of "the next 100th item", but it doesn't sound right.

The problem is that if I just say "the 100th item", that refers to the number 100 since the sequence started, not the number 100 starting counting from now.

Example:

The last 10 widgets were red and blue; the 20th widget from now will be yellow.

Saying "the 20th widget from now" doesn't sound right – but maybe it is? Nor does "the next 20th widget" sound right.

As usual, if possible please also give some references. Cheers!

There are many videos showing Buster's stunts and athletic prowess. But he could also make great romantic scenes.

I'd be interested in joining a community like this, but one where people explain things themselves, maybe even with experiments they did; or where people comment and compare different explanations found online – also to check their correctness. At the moment I only see links to (mostly) youtube videos. But then I can simply do a search on youtube myself. I wonder if this community would like to do something more.

This is just my opinion and a question, I completely understand if people prefer to do differently!

Moderators: please feel free to delete this comment if unimportant. Sorry for the outlier.

Old post (still true). Almost a meme now :)

Today there's an abundance of textbooks and webbooks on Bayesian probability theory, decision theory, and statistics, at very diverse technical levels. I wanted to point out three books whose main topic is not probability theory, but which give very good introductions (even superior to those of some specialized textbooks, in my opinion) to Bayesian probability theory:

• Artificial Intelligence: A Modern Approach by S. J. Russell, P. Norvig. Part IV is an amazing introduction to Bayesian theory – including decision theory – with many connections with Artificial Intelligence and Logic.

• Medical Decision Making by H. C. Sox, M. C. Higgins, D. K. Owens. This is essentially a very clear and insightful textbook on Bayesian probability theory and decision theory, but targeted to clinical decision-making.

• Sentential Probability Logic: Origins, Development, Current Status, and Technical Applications by T. Hailperin. This is a book on Bayesian probability theory, presented as a generalization of propositional logic. This point of view is the most powerful I know of. The books also has important results on methods to find probability bounds, and on combining evidence.