This Saturday, we had two interesting museum experiences, with the kids. Kids are 10, 7 (and a half as she keeps saying) and 2 (and a half, too). In the morning, we went to the MoMaths (which is the pun which stands for Museum of Mathematics, and sounds like MoMA) see e.g. nytimes.com/2012/12/14/arts/…, which opened mid-December.

There were a lot of exhibitions, to illustrate all kinds of mathematical concepts (as described in http://businessinsider.com/…). From a design point of view, what I did prefer was undoubtly the packing problem table. You pick up -say – five disks, and you have to pack them in – say – a triangle (an equilateral one). When you move the disks, the computer locates them and instantaneouldy computed the area of the smallest triangle which contains all of them: you have your own area, as well as the smallest one (known, so far).
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I wanted to see if kids had more intuition than I did, but even if we know the smalled area, unfortunately, we cannot see how to get it, in the museum. Of course, online, one can easily find it, e.g. for circles
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for triangles,
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or for squares
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Nice and fun, isn’t it ? (pictures are from http://mathworld.wolfram.com/…)
About people around, you could hear two kinds of talks in the museum: “look, it’s fun, when you run, the ball is following you” (kids) or “oh, nice, as long as people move, the algorithm removes automatically nodes in the connected graphs” (former kids). Even some people decided to use sheets of paper to prove that they were correct,
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And yes, everyone had fun, even my youngest daugther, who’s only 2 (and a half, I know).
We spent two hours at the MoMaths, and the kids did not want to leave. I have to admit that I was a bit relieved to leave, finally: visiting the museum was like those social events in conferences. Actually, people there were clearly people that I keep seing at work, and in conferences. But there were kids, too, so it was much more convivial. People were also drawing, like in real museums… or like during talks, in conferences. It was work, with fun (and the family). Like my blog, somehow…
Then, we went to the Guggenheim Museum. One has to admit that this is another experience. The building itself is amazing.

But here, it was a more standard museum experience… Except perhaps while we where visiting the Gabriel Orozco exhibition (which was, actually, extremely interesting and reminded me Francis Alÿs ‘s work presented at MoMA last year, http://francisalys.com/…)

There was a guard, in a corner, and when we got too close, he asked us to move back. Trying to understand what was going on, we saw a small stone, behind him (of course “no picture, please“). The guard was waiting for a museum conservator to assess if the stone was from a shoe of a visitor, or a part of the exhibition… The conservator came look clearly at the stone, as well as others, trying to choose (if possible with conviction) whether this was a piece of art (part of the exhibition), or just a vulgar stone. True story…
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We finally left after one hour (my daughter had finished her kids activity, i.e. drawing like Picasso, comparing Picasso and Velasquez’s Meninas, and counting nuances of grays). Now, let us compare those two experiences. For instance, the visitors. At MoMaths, it was half kids, half math professors (from a personal guess), while at Guggenheim, it was more like one third tourists (with their NY Yankees cap, just to pretend they aren’t tourists… which is exactly what I do), and two third retired upper-class New Yorkers (including some much youger models in the arms of golden boys). At MoMaths, most of them were English speakers (and they had to, beacuse it was quite difficult to get information in another language, unfortunately), but at Guggenheim, I heard a lot of French, Italian, even Dutch… The public in those two museums were completely different.
When discussing with kids afterwards, we wanted to know which museum they did prefer. Without any doubts, the answer was MoMaths. And when we asked them in which museum the freakiest people were, they both said the Guggenheim museum. Maybe I am not really a freak, after all, at least in my kids eyes…






































Depuis le début de la semaine, après avoir déposé les enfants au camp de jour du Musée des Beaux Arts, je viens à pieds à l’université. Chaque fois, je me dis que je pourrais prendre le bus, mais comme aucun ne vient, je commence en marchant, en me disant que si un bus passe, je le prendrais. Et tous les matins, j’arrive au bureau sans m’être fait dépassé par le moindre bus. Et bien sur, j’en ai croisé un paquet qui passaient en sens inverse…
à parcourir, on suppose que les bus sont espacés d’une distance
, et qu’ils avancent à une vitesse
. Autrement dit, les bus passent tous les
secondes (si ma vitesse est exprimée en secondes).
avec
(oui, on va supposer que je vais moins vite que le bus… ce qui n’est pas forcément une hypothèse faible aux heures de pointes, mais disons que le problème n’a de sens que si aller en bus me permet d’aller plus vite). Le temps que je vais mettre si je fais tous le trajet à pied est
. Maintenant, comptons les bus qui passent en face. Je vais croiser tous ceux qui sont déjà sur ma portion de trajet, et il y en a
. En plus, je croiserais tous ceux qui vont arriver à l’université, et qui n’y sont pas encore, soit
, i.e. le temps qu’il me reste à marcher divisé par le temps qui s’écoule entre deux bus. On a alors un total de
bus à croiser, en face.



, draw a point
in a neighborhood of
, 
then 
then 
then
then
. To illustrate the idea, consider the following function











chambers, it there are
bullets in
if we don’t. Not spinning is better if and only if

… or
(in that case, it might not be a good idea actually to play the game).
has a priori distribution
, and that
, given
.
? Or is it just trivial ?”. After having those previous philosophical questions, we came to the point that if it was trivial, then we should be able to prove it. A standard way of writing the algorithm is to use the quantile based technique
with
,
with
,
where
and
are two independent random variables with a uniform distribution on the unit interval. Let us try to derive its distribution, i.e.







































so in 5 or 6 steps the algorithm of subdivision should converge. I guess… I mean, I do not know for sure, since 50 is not a power of 2, so it might be difficult, each time, to split in two: we have to deal only with integers here…

Just imagine that your kids need some help, to prepare fishes for April 1st, like

