Why I Don’t Believe It’s 1/e




The above picture, showing the Leap-the-Dips roller coaster at Lakemont Park before its renovation, kind of answers why despite my neat reasoning and mental calculations I don’t really believe that there’s a chance of something like one in three that any particular board from the roller coaster’s original, 1902, construction is still in place. The picture — from the end of the track, if I’m not mistaken — dates to shortly before the renovation of the roller coaster began in the late 90s. Leap-the-Dips had stood without operating, and almost certainly without maintenance, from 1986 (coincidental to the park’s acquisition by the Boyer Candy company and its temporary renaming as Boyertown USA, in miniature imitation of Hershey Park) to 1998.

The result of this period seems almost to demand replacing every board in the thing. But we don’t know that happened, and after all, surely some boards took it better than others, didn’t they? Not every board was equally exposed to the elements, or to vandalism, or to whatever does smash up wood. And there’s a lot of pieces of wood that go into a wooden roller coaster. Surely some were lucky by virtue of being in the right spot?

And that’s what smashes my simple model of how likely it is any particular board lasts. I made the assumption that the probability any board survives a year to be independent of everything: there’s no privileged positions that make it more likely to survive, there’s no unfavored spots that get worse treatment. There’s no boards that are just made from a stronger batch of wood, there’s none that got an appreciably better layer of paint, there’s none that get weaker as they age.

That’s almost certainly not true: I’d expect older boards to be worse at taking the stress of normal operation, and of surviving the sun and rain and wind and whatever else Altoona, Pennsylvania, does to wooden structures. I’d also expect brand-new boards to suffer more than average, since some pieces are just going to be weak and they have to be shaken out. I’d also expect that some boards are put under much greater stress than others. You can see this at many wooden roller coasters if you watch as a train goes past: they sway, and they are designed to sway, but that swaying is making some of the wood work harder than others is.

So some boards probably need replacement every couple of years, while others might plausibly be able to go decades, or centuries, without needing attention. I don’t know the details of how this particular roller coaster was designed, or how it’s been maintained, but the fact I can’t trust in independence — and that I don’t think it’s approximately true, that the difference between (say) the chance of a board that actually carries the heavier loads surviving a year is only slightly more than the average, and one that’s (say) just part of the overhang and probably less-strained only slightly below the average — means I don’t believe the estimate of \frac{1}{e} for the survival of any particular board.

Mind you, I think it’s almost certain that at least one board from before the renovation has survived, but that’s a matter of psychology. There seems to be an intuitive rejection, by many people, of the idea that you can rapidly replace every component of a thing and still keep it “the same” thing. This is the core of every boring argument in science fiction circles about whether the transporters on Star Trek “really” just kill you and make a duplicate; I’m also reminded that when the tea clipper Cutty Sark caught on fire the people in charge of renovations promised the public, almost before the embers were out, that more than half the planking had survived. (I may be mis-remembering and am open to correction, but I don’t promise to be happy about it.) (Also I’m aware of the difference between “from before the renovation” and “from the original construction”, although there might well be no way to tell what boards date from original construction, and people seem more willing to accept something as “the original” if the replacement has been gradual, and non-publicized.)

I don’t know where such might be; if any original or suspected-original parts of the Leap-the-Dips were displayed or highlighted I didn’t notice them. It doesn’t matter; the ride is a grand one, much more thrilling than its dry facts of height and maximum speed and maximum drop would suggest. If you should have reason to be somewhere near Altoona, say for that railroad thing everybody gets excited about, I recommend taking a side trip to the park.

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Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there.

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