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11 Sep, 5 tweets, 3 min read
Saint-Martin-du-Tertre (Yonne), un village qui, par sa position bien en hauteur, offre une vue assez spectaculaire sur les environs: ImageImage
(S'il y en a qui veulent trianguler, la vue est prise depuis là openstreetmap.org/?mlat=48.20775… et sur la photo ci-dessous j'ai entouré la cathédrale de Sens.) Image
L'église éponyme (un peu plus bas que le point de vue des photos précédentes) est d'ailleurs fort bien située pour profiter de la vue magnifique. openstreetmap.org/?mlat=48.21080… Image
⚠️ Attention! Ne pas confondre Saint-Martin-du-Tertre (Yonne), village qui, par sa position bien en hauteur, offre une vue assez spectaculaire sur les environs, …
… avec Saint-Martin-du-Tertre (Val d'Oise), un village qui, par sa position bien en hauteur, offre une vue assez spectaculaire sur les environs. #ClubContexte

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Gro-Tsen Profile picture
13 Sep
Let me use this as a pretext to talk about Conway's field of “nimbers”, which I think is a remarkable construction. It consists of defining two operations, which I'll write ⊕ and ⊗, on ordinals (but if you're afraid of ordinals, they're already interesting on ℕ). ⤵️ •1/30
The operations can be defined by reference to games (below), or given an inductive definition — which is remarkably simple for the complexity it produces:

x⊕y := mex ( {x′⊕y : x′<x} ∪ {x⊕y′ : y′<y})

x⊗y := mex {(x′⊗y)⊕(x′⊗y′)⊕(x⊗y′) : x′<x, y′<y}

That's all! •2/30
Here, “mex S”, means “the smallest [ordinal] which is NOT in the set S”. So x⊕y is the smallest which is NOT of the form x′⊕y for x′<x nor of the form x⊕y′ for y′<y, and x⊗y is the smallest which is NOT of the form (x′⊗y)⊕(x′⊗y′)⊕(x⊗y′) for x′<x and y′<y; … •3/30
Read 30 tweets
Gro-Tsen Profile picture
11 Sep
Le “parc du Moulin à Tan” à Sens (Yonne), classé jardin remarquable, a dans ses serres une très jolie collection de cactées et succulentes: ImageImageImageImage
J'ai essayé de prendre un panorama en faisant un travelling sur une partie de la collection, mais ça donne un résultat un peu bizarre: Image
Très jolis nénuphars géants, aussi: Image
Read 4 tweets
Gro-Tsen Profile picture
27 Aug
I find it very perplexing how some people seem to be either decrying or lamenting this study (showing that covid immunity from infection is more effective than from vaccination) as if it made a case against vaccines. How does that make any kind of sense? •1/8
What this story confirms is that, as should have been clear all along, the doomsayers from early on in the pandemic who suggested (based on a small handful of not-very-concerning reinfection cases) that was no acquired immunity from covid were needlessly catastrophic. •2/8
(Let me recall that, in April 2020, the WHO itself incomprehensibly tweeted a statement that there was “no evidence” that covid recovery confers immunity. This was very stupid even at the time (thread 🔽), and they cancelled their tweet.) •3/8
Read 8 tweets
Gro-Tsen Profile picture
25 Aug
In the tweet below, I mention the variance of the median of three independent standard Gaussian variables to be 0.448…, and I say that it doesn't seem to have a closed form expression. But actually it does! It's 1 − (√3)/π. But now this opens a trove of new questions. •1/17
Thanks to @ArthurB for pointing out this closed form expression to me (below). This reminded me I once knew the max of 4 iid standard Gaussian variables has expected value: (3/√π)·[½+asin(1/3)/π]. Where does this come from? •2/17
More generally, we might ask about the variance of the median of 2s+1 independent standard Gaussian variables (for s∈ℕ). Or we might ask about the expected value of the maximum of r such variables (for r∈ℕ). Can we find closed form formulæ for these? •3/17
Read 17 tweets
Gro-Tsen Profile picture
18 Aug
As I've pointed out a number of times, there is a terribly confusing ambiguity as to what the phrase “herd immunity” (or its synonyms, e.g., “collective immunity”) means. In the SIR model it's the point where R becomes ≤1. But in real life? 🧵⤵️ •1/14 Screenshot of thread ending at https://twitter.com/whophd/st
If we use the same definition (R≤1), then herd immunity is pretty much unavoidable. Barring unrealistic mathematical counterexamples, the only alternative is to have exponential growth forever, which, of course, simply cannot happen. •2/14
(“Unrealistic mathematical counterexamples” here acknowledges the fact that you can have R>1 forever but tending toward 1 so the number of infected remains bounded. Even then, you're still tending toward herd immunity.) •3/14
Read 14 tweets
Gro-Tsen Profile picture
17 Aug
On a enfermé des 67M de personnes pendant des mois pour copier un régime autoritaire (🇨🇳) sans preuve scientifique, et ensuite on s'étonne/énerve que les gens aient perdu confiance en les autorités sanitaires et refusent un vaccin pourtant sûr et efficace. Bizarre, hein?
Comment diable se peut-il que les Français ne fassent plus parfaitement confiance en des autorités qui les ont fait remplir des papiers crétins et humiliants pour faire leurs courses ou se promener après nous avoir promis que nous continuerions à aller au théâtre?
Ont fermé les FORÊTS pour lutter contre une épidémie qui se transmet presque uniquement en espaces clos? Les ont fait tous porter des masques même à l'extérieur après avoir assuré, au moment où ils manquaient, que les masques ne servaient pas à la population générale?
Read 4 tweets

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