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NancyLebovitz 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.
Nitpick alert: I believe pianos used to be a lot more common. There was a time when they were a major source of at-home music. On the other hand, the population was much smaller then, so maybe the effects cancel out.
I wonder. Pianos are still really expensive. They're very bulky, need skilled maintenance and tuning, use special high-tension wires, and so on. Even if technological progress, outsourcing manufacture to China etc haven't reduced the real price of pianos, the world is also much wealthier now and more able to afford buying pianos. Another issue is the growth of the piano as the standard Prestigious Instrument for the college arms races (vastly more of the population goes to college now than in 1900) or signaling high culture or modernity (in the case of East Asia); how many pianos do you suppose there are scattered now across the USA compared to 1800? Or in Japan and China and South Korea compared to 1900?
And on the other side, people used to make music at home, yes - but for that there are many cheaper, more portable, more durable alternatives, such as cut-down versions of pianos.
Concert grands, yes, but who has room for one of those? Try selling an old upright piano when clearing a deceased relative's estate. In the UK, you're more likely to have to pay someone to take it away, and it will just go to a scrapheap. Of course, that's present day, and one reason no-one wants an old piano is that you can get a better electronic one new for a few hundred pounds.
But back in Victorian times, as Nancy says elsethread, a piano was a standard feature of a Victorian parlor, and that went further down the social scale that you are imagining, and lasted at least through the first half of the twentieth century. Even better-off working people might have one, though not the factory drudges living in slums. It may have been different in the US though.
Certainly: http://www.nytimes.com/2012/07/30/arts/music/for-more-pianos-last-note-is-thud-in-the-dump.html?_r=2&ref=arts But like diamonds (I have been told that you cannot resell a diamond for anywhere near what you paid for it), and perhaps for similar reasons, I don't think that matters to the production and sale of new ones. That article supports some of my claims about the glut of modern pianos and falls in price, and hence the claim that there may be unusually many pianos around now than in earlier centuries:
At least, if we're comparing against the 1700s/1800s, since the article then goes on to give sales figures:
(Queen Victoria died in 1901, so if this golden age 1900-1930 also populated parlors, it would be more accurate to call it an 'Edwardian parlor'.)
We got ~$75 for one we picked up out of somebody garbage in a garage sale, and given the high interest we had in it, probably could have gotten twice that. (Had an exchange student living with us who loved playing the piano, and when we saw it, we had to get it - it actually played pretty well, too, only three of the chords needed replacement. It was an experience loading that thing into a pickup truck without any equipment. Used a trash length of garden hose as rope and a -lot- of brute strength.)
I was basing my notion on having heard that a piano was a standard feature of a Victorian parlor. The original statement of the problem just specifies a piano, though I grant that the cartoon version requires a grand or baby grand. An upright piano just wouldn't be as funny.
These days, there isn't any musical instrument which is a standard feature in the same way. Instead, being able to play recorded music is the standard.
Thanks for the link about the lack of new musical instruments. I've been thinking for a while that stability of the classical orchestra meant there was something wrong, but it hadn't occurred to me that we've got the same stability in pop music.
Sure, but think how small a fraction of the population that was. Most of Victorian England was, well, poor; coal miners or factory workers working 16 hour days, that sort of thing. Not wealthy bourgeoisie with parlors hosting the sort of high society ladies who were raised learning how to play piano, sketch, and faint in the arms of suitors.
Unless it's set in a saloon! But given the low population density of the Old West, this is a relatively small error.
That article treats all forms of synthesis as one instrument. This is IMO not an accurate model. The explosion of electronic pop in the '80s was because the technology was on the upward slope of the logistic curve, and new stuff was becoming available on a regular basis for artists to gleefully seize upon. But even now, there's stuff you can do in 2013 that was largely out of reach, if not unknown, in 2000.
Have any handy examples? I find that a bit surprising (although it's a dead cert that you know more about pop music than I do, so you're probably right).
I'm talking mostly about new things you can do musically due to technology. The particular example I was thinking of was autotune, but that was actually invented in the late 1990s (whoops).
But digital signal processing in general has benefited hugely in Moore's Law, and the ease afforded by being able to apply tens or hundreds of filters in real time. The phase change moment was when a musician could do this in faster than 1x time on a home PC. The past decade has been mostly on the top of the S-curve, though.
Nevertheless, treating all synthesis as one thing is simply an incorrect model.
Funny coincidence. About a week ago I was telling someone that people sometimes give autotune as an example of a qualitatively new musical/aural device, even though Godley & Creme basically did it 30+ years ago. (Which doesn't contradict what you're saying; just because it was possible to mimic autotune in 1979 doesn't mean it was trivial, accessible, or doable in real time. Although autotune isn't new, being able to autotune on an industrial scale presumably is, 'cause of Moore's law.)
Granular synthesis is pretty fun.
Agreed, although I don't know how impractical or unknown it was in 2000 — I remember playing with GranuLab on my home PC around 2001.