Following a(n old) comment by @JDHamkins on MathOverflow (mathoverflow.net/a/42998/17064), I realized something about the “dangerous bend” sign that's used by Donald Knuth to draw attention to difficult parts in a textbook. 🧵⤵️ •1/6
The Americans will think it's a European sign, and the Europeans will think it's an American sign. Why? Well, It's Complicated™. •2/6
The dangerous bend inside the sign was introduced by Bourbaki (and made its way into Unicode as U+2621 CAUTION SIGN; here's one: ☡). •3/6
But this is NOT what “dangerous bend” signs in contemporary European road signage look like. They look like this (this is the French sign, but most European signs should look pretty similar): •4/6
European countries, following the Vienna Convention on Road Signs and Signals use triangular shapes to denote danger signs. Furthermore, the Bourbaki sign is derived from the old version of this sign, which looked like this [source: commons.wikimedia.org/wiki/File:Born…]: •5/6
But Knuth took this (old French) “dangerous bend” symbol from Bourbaki and added an American-style warning sign around it, namely a yellow diamond. The closest actual American road sign seems to be this: •6/6
Slight correction: tweet 4/6 above, I should maybe have used this sign instead, which means “dangerous bends” rather than just “dangerous bend”. I'm not sure if the older signage had both versions or just one. But in any case, both shape and content differ. •7/(6+1)
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OK, this 🔽 blew up (and I'll need to mute the thread). I can't respond to every reply individually, but there are a few common ones that deserve specific attention. So here are a few followup points. 🧵⤵️ •1/15
First, there are number of things that I forgot to mention. Like how many homeless people were forcibly removed from Paris ahead of the games, or students being told to vacate their residence because they would be used as lodging for the games. •2/15
Or how the price of metro tickets has been suddenly doubled(!) for the games. Admittedly this is more of a tourist tax, because locals typically have monthly cards or could buy their tickets well in advance, but this is still crazy from a supposed public service. •3/15
I think non-French and non-French-speaking readers should be told about how utterly insane things are now in and around Paris because of the Olympics are. The opening ceremony is one week away and they've already barred any access to the Seine! 🧵⤵️ •1/19
The different levels of security perimeters are incomprehensible, but basically all areas within ~100m of the Seine are now completely off-limits. You can only go there, even by foot, if you live there or work there, and you need to get a special permit in advance. •2/19
Getting the permit is no sure thing: apparently some people have had their application denied (no explanations given), so they're not allowed to go where they work, or even where they live. Nobody knows what's supposed to happen to them. •3/19
En tant que Français et Canadien, je pense qu'il est nécessaire que je dise un mot au sujet du fait que les binationaux sont soudainement considérés comme suspects en France, presque des ennemis de l'intérieur. 🧵⤵️ •1/22
Je suis né en France d'une mère française, et j'ai vécu quasi toute ma vie en France, je parle français depuis que je sais parler, j'ai fait mes études en France, mes amis vivent en France, je m'intéresse à l'histoire de France, au droit français, à la langue française… •2/22
Bref, je suis non seulement légalement français, mais, que ça me plaise ou non, je suis aussi culturellement français, et, je n'ai aucune honte à le dire, j'aime profondément ce pays, au moins autant que Monsieur Bardella. Même si en ce moment j'ai du mal à en être fier. •3/22
Une chose fascinante avec le regard que la droite et le centre portent sur la gauche française, c'est que la gauche du passé leur semble toujours plus acceptable que celle du présent: Gambetta, Briand, Blum, Mendès-France, on conteste très rarement leur héritage, … •1/11
… souvent même la droite reconnaît explicitement que c'étaient de grands hommes et affirme que la gauche les aurait ensuite trahis (Sarkozy en 2007 par exemple: «la gauche d'aujourd'hui [n'a] plus grand-chose à voir avec la gauche de Jaurès»). •2/11vie-publique.fr/discours/16640…
La gauche du présent, en revanche, ou du passé proche, paraît toujours détestable: la victoire du Front populaire de 1936, et l'alliance des socialistes et radicaux avec les communistes, n'a pas été accueillie avec enthousiasme par le centre-droit d'alors, … •3/11
J'ai calculé les coefficients de corrélation des résultats entre toutes les listes des dernières européennes, et je trouve ça très intéressant pour se faire une idée de la proximité idéologique entre elles (notamment, de qui se rapprochent les «petites» listes). 🧵⤵️ •1/14
(Désolé pour ce dump sous forme d'images: si vous voulez le résultat sous format texte, il est là: — la même page comporte le script Perl abominable que j'ai utilisé pour le calculer.) •2/14gist.github.com/Gro-Tsen/e54a8…
La source des données est là: (il faut fournir ce fichier csv en entrée à mon script Perl pour produire le résultat). •3/14 data.gouv.fr/fr/datasets/re…
Let me say a few things about “random” versus “generic” sequences (binary sequences, say). A random sequence of 0's and 1's everyone has some idea of what that looks like: take a fair coin and flip it repeatedly. But what in the world is a “generic” sequence? 🤔🧵⤵️ •1/21
There are many flavors of randomness and correspondingly many flavors of genericity, but the overall theme seems to be that a random object is one that doesn't belong to any “easily explicitly described” set of measure zero, … •2/21
… whereas a generic object is one that doesn't belong to any “easily explicitly described” meager set. What does all of this mean? Well, “easily explicitly described” depends on the flavor we're talking about: but clearly we need some kind of restriction, … •3/21