## Riddle of the lanes

Posted in Books, Kids, R with tags , , , , , on July 13, 2020 by xi'an

An express riddle from the Riddler about reopening pools, where lanes are allowed provided there is no swimmer in the lane or in any of the adjacent lanes. If swimmers pick their lane at random (while they can), what is the average number of occupied lanes?

If there are n lanes and E(n) is the expected number of swimmers, E(n) satisfies a recurrence relation determined by the location of the first swimmer:

$E(n)=1+\frac{1}{n}[2E(n-2)+\sum_{i=2}^{n-1}\{E(i-2)+E(n-i-1)\}]$

with E(0)=0, E(1)=E(2)=1. The above can be checked with a quick R experiment:

en=0
for(t in 1:T){
la=rep(u<-0,N)
while(sum(la)<N){
i=sample(rep((1:N)[!la],2),1)
la[max(1,i-1):min(N,i+1)]=1
u=u+1}
en=en+u}

## running in circles

Posted in Mountains, pictures, Running, Travel with tags , , , , , , , , on May 31, 2020 by xi'an

As lockdown rules concerning outdoor activities were rather restrictive (run alone, away from other people, at most one hour and at most 1km away from home), I used the network of streets around my house to design a 13km circuit that was never replicating more than intersecting previously visited roads. And I ran it every one of the 60 days of the lockdown.

This was a purely urban run on pavement only, but offered nice views of the neighbouring suburbs, with three hills to climb.

And hardly anyone in the streets, except for the occasional soul walking her dog. And never a single control of the laisser-passer I had to print every morn.

Going by the park and the local swimming pool every day and unrealistically wishing they would open soon…

## trailers versus mountaineers?

Posted in Kids, Mountains, Running, Travel with tags , , , , , , , , , , , on August 31, 2019 by xi'an

A slight altercation in a swimming corridor during lunch put me back into this Le Monde paper I read yesterday about (real?!) mountaineers being annoyed at trailers, especially those currently running the Ultra-Trail du Mont Blanc (UTMB). A lady stopped me from going further for not crawling as this was a “crawl only” lane and started a lengthy tirade that I cut short by moving to another lane. I find such debates pretty absurd and rather hypocritical. When the fundamental goal is mostly to reduce the number of people on the trails, in the mountains, or in the pool by creating categories with those in and those out. This seems an unavoidable human trend that happened several times in mountaineering, from the early days when going above a certain limited was prohibited to those when climbing solo, rope-free, mixed style, without a registered guide or certificate, &tc. base-jumping, was or became taboo. It is annoying to see crowds in the mountains, whether on the Everest final sketch or on the UTMB track, for sure, but by nature these are singular events and the next peak is almost surely free. It is also annoying to find other climbers on one’s chosen route as they will certainly cause delays, but this is the nature of the game and the next route may well be free. I thus find pretty annoying that some claim their rights to enjoy mountains are higher or purer than others, whom they accuse of elitism and ill-placed competition, when themselves are far from free of the same defect.

## turning forty…

Posted in Kids, pictures with tags , , , , , , , on July 26, 2019 by xi'an

The previous days have been rather tough thanks to another heat wave all over Europe, with the temperatures at home reaching above 40⁰ (outside) yesterday afternoon and more importantly not getting under 30⁰ inside the house at night, as there was no wind at all to cool it down. (Except in the basement  where I ended up sleeping.) After a certain point, as I am pretty susceptible to hot weather, working became impossible and I spent the rest of the day alternating between drinking cold water, taking cold showers, eating radishes, and watching low intensity movies (like The Crimes of Grindelwald!). The day before, my daughter and I tried a late afternoon trip to the nearby outside pool in the parc but this proved quite a disaster as it was so crowded that it was almost impossible to do laps (in a water of questionable composition). Temperatures are now down a wee bit but I wondering at ways to better insulate our house against what is becoming the new “normal”…. Like installing a massive circus tent every summer.

## pool etiquette [and lane rage]

Posted in Statistics with tags , , , , , , , , , on March 15, 2019 by xi'an

A funny entry in The Guardian of today about what turns swimmers mad at the pool. A form (foam?) of road-rage in the water… Since I have started a daily swim since mid-December to compensate for my not-running for an indeterminate length of time, I can primarily if irrationally relate to the reactions reported in the article. About the pain of passing other swimmers and being brushed or kicked by faster runners oops swimmers trying to squeeze in the middle (of nowhere). Irrationally so because at  a rational level there is nowhere to go really, except the end of the lane and back, which means waiting or turning back earlier not much of an imposition. But still feeling a sort of “road rage” when I cannot turn back and start again without delay… I have been thinking for the past weeks (while going back and forth, back and forth, dozens of times) of ways to rationalize the whole operation but cannot see a way to make all swimmers go exactly the same speed in a given lane, if only because most swimmers switch stroke between lengths. Except me as I can only and barely handle the breast stroke, thanks to lessons from Nick!, stroke than many seem to resent. To the point of calling for breast-stroke free lanes… Rationally, I think the problem is the same with every activity involving moving at different relative speeds on a busy lane. Runners get annoyed at breaking their pace, cyclists at braking or worse!, touching ground. It is just more concentrated in a 25m swimming lane on a busy day. (Which is why I really try to optimise my visits to the pool to be in the early morning or in the mid-afternoon. And again and again promise myself to skip the dreadful Sunday morning session!) L’enfer, c’est les autres, especially when they swim at a different pace!