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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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
L'édition (Livre de Poche / “Classiques de Poche”) que j'avais achetée de “La Légende des siècles” comportait la note suivante sur cette phrase:
«Reprise telle quelle d'un vers du psaume CXXXIX dans la traduction de Sacy de la Bible, que Hugo avait en sa possession.»
… •2/6
Bon alors le psaume 139, qui est en fait numéroté 138 dans la bible de Sacy (=Port-Royal) est ici: — et on voit que s'il ressemble vaguement dans l'esprit au vers cité de Hugo, ce dernier n'est certainement pas une reprise “telle quelle”! … •3/6fr.wikisource.org/wiki/Bible_Sac…
This made-up map actually seems to have an interesting history: there is indeed a 1973 paper by Stewart W. Hindley & Albert Damon in ‘Am. J. Phys. Anthropol.’ but it's on mid-phalangeal hair of Solomon Island populations. •1/7 onlinelibrary.wiley.com/doi/abs/10.100…
It does give “hairiness” data (again, mid-phalangeal!) on p. 192 for various populations taken from other sources in the scientific literature, but clearly not enough to make a map, let alone of “male androgenic hair” in general. •2/7
The interest in mid-digit hair is explained in the page “Mid-digital hair: The myth” by evolutionary geneticist John H. McDonald of U. Delaware. Basically it is/was hoped it was controlled by a single allele, making it useful to study populations. •3/7udel.edu/~mcdonald/myth…
Je vois souvent passer l'argument «si on taxe X, cela fera fuir X hors de France». Il y a certainement des cas où cet argument est plausible, mais il ne peut pas être universellement valable, sinon tout impôt progressif serait impossible et inexistant.
(Je veux dire, si le but est d'attirer des richesses dans le pays, avec le raisonnement simpliste et inconditionnel ci-dessus, c'est facile: au lieu de taxer les riches, taxons les pauvres, ils partiront ailleurs, et le pays sera plus riche.)
Un argument sérieux consisterait certainement à étudier la mobilité de X, et aussi l'utilité relative de la présence de X dans le pays par rapport à celle de la taxation de X. C'est forcément complexe, et il y a beaucoup d'inconnues. En aucun cas ça ne peut tenir en un tweet.
This 🔽 is perhaps what baffles me most about flat earth conspiracy theories: never mind that they can't explain something as basic as sunrise and sunset, what makes even less sense is whyever anyone would want to keep the shape of the Earth a secret.
Some seem to believe (or claim to believe…) that it's because there's something hidden behind the Great Ice Wall that takes the place of the south pole in their theories. But why not just claim there's nothing behind that wall but the edge of the world, or something?
Still not sure whether most flat earthers really believe in what they claim to believe, or whether they're just trying to get attention: you have to admit that “globe conspiracy” is an attention-grabber (as: “they can't possibly be that stupid can they?”).
Quelques remarques sur la rédaction d'une demande d'accès aux documents administratifs: le problème est que chaque tournure peut être problématique dans certaines conditions.
Si on demande «tous les documents relatifs à X», on risque de faire face à une interprétation minimaliste, donc incomplète, de X. Mais si on précise «notamment X1, X2, X3…», il y a un risque que X1, X2, X3 n'existent pas, …
… mais si on cherche une formulation pour dire «absolument tout ce qui concerne X de près ou de loin», il y a un risque que la demande soit jugée abusive. Bref, il faut jongler avec ces différentes possibilités, faire un pari sur ce qui marchera le mieux.