Comme mes enseignements sont (pour l'instant) à distance, j'ai décidé de rendre publiquement accessible non seulement les notes des cours dont je suis responsable (c'était déjà le cas), mais aussi les enregistrements. Voici donc:
OK, I may be guilty of a DoS attack attempt on mathematicians' brains here, so lest anyone waste too much precious brain time decoding this deliberately cryptic statement, let me do it for you. •1/15
First, as some asked, it is to be parenthesized as: “∀x.∀y.((∀z.((z∈x) ⇒ (((∀t.((t∈x) ⇒ ((t∈z) ⇒ (t∈y))))) ⇒ (z∈y)))) ⇒ (∀z.((z∈x) ⇒ (z∈y))))” (the convention is that ‘⇒’ is right-associative: “P⇒Q⇒R” means “P⇒(Q⇒R)”), but this doesn't clarify much. •2/15
Maybe we can make it a tad less abstruse by using guarded quantifiers (“∀u∈x.(…)” stands for “∀u.((u∈x)⇒(…))”): it is then “∀x.∀y.((∀z∈x.(((∀t∈x.((t∈z) ⇒ (t∈y)))) ⇒ (z∈y))) ⇒ (∀z∈x.(z∈y)))”. •3/15
Je n'utilise pas moi-même l'écriture «inclusive» (en tout cas pas habituellement) en français, et on ne me l'a jamais reproché, encore moins refusé de lire mes mails ou je ne sais quoi à cause de ça.
Je ne vois pas en quoi cette «écriture inclusive» pourrait être plus gênante que, disons, l'abus d'emojis ou de ponctuations, ou de locutions latines, ou aliud quidlibet.
‣ The ring of Dedekind reals, which is represented by the sheaf of continuous ℝ-valued functions, in the topos of sheaves on many reasonable topological spaces (such as ℝ itself), satisfies ③ ∀x.(x=0⇔¬∃y.(x·y=1)) but fails ② ∀x.(¬(x=0)⇔∃y.(x·y=1)) (so fails ① too).
Indeed, x is invertible iff the continuous ℝ-valued function is everywhere ≠0, but it satisfies ¬(x=0) iff the function does not vanish on any nontrivial open set (so ② fails for a function vanishing somewhere but not on any nontrivial open set); …
I've complained about this a number of times but not, I think, on Twitter: I am very much annoyed by the way many people call “game theory” a field which only includes stuff like normal form games, Nash/correlated equilibria, stochastic games, and the like, … •1/5
… but NOT combinatorial game theory (the Sprague-Grundy theory of games like nim, nor the Conway theory of partizan games), nor Gale-Stewart games and their determinacy, nor Ehrenfeucht-Fraïssé games, nor differential game theory, etc. •2/5
E.g., this online course, game-theory-class.org/game-theory-I.…, which calls itself “Game Theory”, no qualifiers added, doesn't mention any of the things listed in the previous tweet. So I guess the authors think they're not part of “game theory”? But then what are they? •3/5
Let's take a second to ponder how marvelous the human brain is in its versatility and its ability to learn things it never evolved to do. ⤵️ •1/16
You're probably reading my words as squiggles on a computer screen. The absolutely incredible fact, here, is that these squiggles have ❋meaning❋, and your brain is able to decode these squiggles at an incredible speed to extract said meaning. •2/16
So the meaning travels from my brain to yours through an incredible convoluted, almost rube-goldberg-esque path of my moving my fingers to type keys on a keyboard and generate signals which then enter a very sophisticated electronic system which mankind designed, … •3/16