Kindly comments on Fermi Estimates - Less Wrong
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I'll try. Let's see, grands and baby grands date back to something like the 1700s; I'm sure I've heard of Mozart or Beethoven using pianos, so that gives me a time-window of 300 years for falling pianos to kill people in Europe or America.
What were their total population? Well, Europe+America right now is, I think, something like 700m people; I'd guess back in the 1700s, it was more like... 50m feels like a decent guess. How many people in total? A decent approximation to exponential population growth is to simply use the average of 700m and 50m, which is 325, times 300 years, 112500m person-years, and a lifespan of 70 years, so 1607m persons over those 300 years.
How many people have pianos? Visiting families, I rarely see pianos; maybe 1 in 10 had a piano at any point. If families average a size of 4 and 1 in 10 families has a piano, then we convert our total population number to, (1607m / 4) / 10, 40m pianos over that entire period.
But wait, this is for falling pianos, not all pianos; presumably a falling piano must be at least on a second story. If it simply crushes a mover's foot while on the porch, that's not very comedic at all. We want genuine verticality, real free fall. So our piano must be on a second or higher story. Why would anyone put a piano, baby or grand, that high? Unless they had to, that is - because they live in a city where they can't afford a ground-level apartment or house.
So we'll ask instead for urban families with pianos, on a second or higher story. The current urban percentage of the population is hitting majority (50%) in some countries, but in the 1700s it would've been close to 0%. Average again: 50+0/2=25%, so we cut 40m by 75% to 30m. Every building has a ground floor, but not every building has more than 1 floor, so some urban families will be able to live on the ground floor and put their piano there and not fear a humorously musical death from above. I'd guess (and here I have no good figures to justify it) that the average urban building over time has closer to an average of 2 floors than more or less, since structural steel is so recent, so we'll cut 30m to 15m.
So, there were 15m families in urban areas on non-ground-floors with pianos. And how would pianos get to non-ground-floors...? By lifting, of course, on cranes and things. (Yes, even in the 1700s. One aspect of Amsterdam that struck me when I was visiting in 2005 was that each of the narrow building fronts had big hooks at their peaks; I was told this was for hoisting things up. Like pianos, I shouldn't wonder.) Each piano has to be lifted up, and, sad to say, taken down at some point. Even pianos don't live forever. So that's 30m hoistings and lowerings, each of which could be hilariously fatal, an average of 0.1m a year.
How do we go from 30m crane operations to how many times a piano falls and then also kills someone? A piano is seriously heavy, so one would expect the failure rate to be nontrivial, but at the same time, the crews ought to know this and be experienced at moving heavy stuff; offhand, I've never heard of falling pianos.
At this point I cheated and look at the OSHA workplace fatalities data: 4609 for 2011. At a guess, half the USA population is gainfully employed, so 4700 out of 150m died. Let's assume that 'piano moving' is not nearly as risky as it sounds and merely has the average American risk of dying on the job.
We have 100000 piano hoistings a year, per previous. If a team of 3 can do lifts or hoisting of pianos a day, then we need 136 teams or 410 people. How many of these 410 will die each year, times 300?
(410 * (4700/150000000))*300 = 3.9So irritatingly, I'm not that sure that I can show that anyone has died by falling piano, even though I really expect that people have. Time to check in Google.
Searching for
killed by falling piano, I see:But no actual cases of pianos falling a story onto someone. So, the calculation may be right - 0 is within an order of magnitude of 3.9, after all.
To a very good first approximation, the distribution of falling piano deaths is Poisson. So if the expected number of deaths is in the range [0.39, 39], then the probability that no one has died of a falling piano is in the range [1e-17, 0.677] which would lead us to believe that with a probability of at least 1/3 such a death has occurred. (If 3.9 were the true average, then there's only a 2% chance of no such deaths.)
I disagree that the lower bound is 0; the right range is [-39,39]. Because after all, a falling piano can kill negative people: if a piano had fallen on Adolf Hitler in 1929, then it would have killed -5,999,999 people!
Sorry. The probability is in the range [1e-17, 1e17].
That is a large probability.
It's for when you need to be a thousand million billion percent sure of something.