[maximin] geometric climbing

A puzzle from The Riddler this week returning to the ranking of climbing competitors in Tokyo. And asking for the maximin score, that is, the worst possible absolute score guaranteeing victory. In the case of eight competitors, a random search for a maximin over 10⁶ draws leads to a value of 48=1x7x8, for a distribution of ranks as follows

[1,]    1    8    8
[2,]    2    6    4
[3,]    3    4    5
[4,]    4    2    6
[5,]    5    5    2
[6,]    6    3    3
[7,]    7    7    1
[8,]    8    1    7

while over seven competitors (the case with men this year, since one of the brothers Mawem got hurt during the qualification), the value is 35=1x5x7, for a distribution of ranks as follows

[1,]    1    7    5
[2,]    2    3    6
[3,]    3    4    3
[4,]    4    5    2
[5,]    5    2    4
[6,]    6    1    7
[7,]    7    6    1

exhibiting a tie in the later case (and no first position for the winners!).

At the hospital

Spending three weeks in an hospital has certainly been a novel experience for me! Except for the boredom (reflected by the many books reviews found in the past posts) and the uncertainty about the success of the graft, not mentioning the occasional pain, I found the experience interesting in several ways. First, I discussed a lot with nurses (and very little with doctors). As I stayed on observation for two weeks, my thumb was checked by a nurse at least every two hours. This (and the heating lamp) did not help with my sleep, but I was amazed by the dedication of those nurses and their constant good cheer, even after my next door neighbour repeatedly crashed out of his bed in an alcohol-detox crisis (no, I was not hospitalised for alcohol related problems!) or when a leech did not want to get to work at three in the morning. They certainly provided a very efficient psychological help during the first days. And then later when I would see them again. On the other hand, my surgeon was extremely busy between emergency surgeries and courses at the university, and he would/could only come to check on the thumb a few minutes every day.  Second, I realised how empirical the whole operating process was. There were certainly protocols and rules, but the surgeries and the treatments I received were empirical attempts to save the thumb based on the actors’ past experience. For instance; my surgeon used antibiotics while others did not. And kept using leeches longer than others. Although this is frustrating to me as a patient (what if they had tried something else? &tc.), I understand it makes sense in a Bayesian sense, i.e. that doctors and nurses have to rely on their past experience and on the specificities of the patient to try to find the most efficient treatment. Or to provide me with honest evaluations of my chances of recovery. Third, having the right arm anaesthetised three times  provided me with interesting sensorial experiments, from the impression of having my arm raised in the air when it was sitting on the operation table, to the complete lack of control of the same arm after the operation and it coming with a vengeance to hit me in the face later that night! Having medical students run the anaesthesia on me was not the most enjoyable moment of the stay, making me feel like a guinea-pig, but hearing the senior anaesthetists provide pieces of advice and warnings was certainly informative. The same impression applies to staying awake during the surgeries. Fourth and last, I noticed the “hospital weekend effect“, in that doctors were much less available over the weekends (there were days I did not see one at all) and nurses had longer shifts and were obviously more tired (to the point of once confusing head and tail of a leech).

leeches [another gory story]

Besides anticoagulant drugs, my postsurgery treatment involves leeches that stay on my thumb a few hours a day, sucking blood away and dispensing anticoagulants of their own. The hospital actually produces its own stock of leeches for this very purpose and most nurses are quite at ease with the procedure, even though a few seem reluctant to touch the animals. This morning I fell asleep during a leech visit and woke up to see it crawling across the corridor outside my bedroom, leaving a rather obvious trace on the ground…

(truly) gory details

As several friends and readers sent me best recovery wishes as well as queries about my health, here are a few details that you do not have to read as they are only details and mostly gory:

• the accident took place in the climbing gym where my daughter and I usually practice, when I fell when holding the rope to set it through a quickdraw (carabiner);
• the rope severed my right thumb when it stretched at the end of the fall, as the rope got into a loop around the thumb;
• I was quickly and efficiently evacuated to the “hand hospital” in Paris, Saint Antoine, by the local firemen, and got my thumb grafted back by two surgeons in the following (4) hours;
• the chances of success for the graft are evaluated at 50-50 by the surgeon, even now, a week after the accident, because the tissues got crushed;
• this is why I am (or rather my thumb is) still and rather closely monitored in a postsurgery department, under heating lamps, and I cannot move around (although I feel fine if restless…);
• I am also unable to draw plans on the near future, as I do not know when I will be realeased from the hospital and how operational my right hand will be (typing on a computer with my left hand is not that hard!);
• I alas had to cancel my talk next week at AISTAT in Phoenix but still hope to be able to take part in the coming i-like workshop in Warwick, next  month…