One lesson of New Guinea life Diamond takes personally concerns small, recurring dangers – “hazards that carry a low risk each time but are encountered frequently”. Once, on a field trip, he proposed setting up camp under a beautiful old tree, but his New Guinean colleagues refused. It was dead, they explained, and might kill them in the night. The chances were tiny – but if you sleep under trees many nights a year, they add up. The biggest dangers in his LA life today, Diamond believes, are slipping in the shower, tripping on uneven paving stones and car accidents. Even if the chance of serious injury or death in the bathroom is one in 1,000, that is far too big for something you do every day.Is that right? Do the chances 'add up'? Not according to probability theory; and yet it seems plausible to say that if you run against 1,000-1 odds a thousand times...
I rode in Tampa's rush-hour traffic, day in and day out, hours a day during the summer a few years ago. In retrospect, that may not have been the best idea I ever had.
The odds drop a lot, though, on these country backroads. They're more fun to ride on anyway.
Let's see...
ReplyDelete1-(1-.001)^1000 = .63
63% chance of at least one accident, assuming the 1/1000 is the same every time. Maybe you get better at driving over time and the single drive accident probability goes down over time, or maybe your hearing deteriorates and it goes up.
Probability math is beautiful, because we end up saying both things. On the one hand, the odds are 63%, and that seems valid. But on the other hand, each ride is 1-in-a-thousand, not 63%. And although that formula accounts for the rides already taken (that's what the '1-.001' is doing), each ride carries its odds independently. Should I get through 999 rides without an accident, the odds of the next ride being a wreck are not 63%, but one in a thousand, even though per our original calculation there ought to be a 63% chance of a wreck since the series had a 63% chance of a wreck and we're almost through it. If I get through that ride safely, the odds drop to zero.
ReplyDeleteOn the other hand, if I had an accident anywhere along the line, the odds of an accident in the series go to one -- not 63%, that is, but 100%.
So do the odds of a series stack, or don't they? Casinos somehow don't go out of business, nor insurance companies; and yet the mechanism for accounting for how multiple events interact is technically an informal fallacy.
the odds of the next ride being a wreck are not 63%, but one in a thousand, even though per our original calculation there ought to be a 63% chance of a wreck
ReplyDeletePick one. Either the rides, in this context, are independent of each other, or they are not.
there ought to be a 63% chance of a wreck since the series had a 63% chance of a wreck and we're almost through it
Not at all. You're not in a series; you're on a statistically independent ride. Or, you're not; see above.
Eric Hines
That's the point, though. It's a fallacy to talk about them as if they were a series, because the odds of one ride don't affect the odds of another. There is no series, not really: there's just a thousand rides.
ReplyDeleteThat's the nominalist, and strictly logical position. Yet, as I said, the casinos don't go out of business. (Although partially that's because of table limits -- a sufficiently rich gambler probably could ride out a losing streak by tripling down forever, such that when you finally win you'd recover all losses and go ahead by the same amount as you'd lost heretofore.)
That's the point, though. It's a fallacy to talk about them as if they were a series....
ReplyDeleteNot at all; it depends on the question being asked. If I want to know the odds of a thing happening on the next try, given the odds that the thing happens on any particular try to be 1:1,000, I've just answered that question.
If, though, I want to know the odds that a thing will happen sometime in 1,000 iterations given odds of 1:1,000 for any particular iteration, that likelihood can be calculated, and it's a different answer.
Casinos, and insurance companies, don't stay in business solely on the basis that the thing won't happen on this iteration. They also set aside funds to cover the event should the thing happen sometime in the next 1,000 iterations.
Eric Hines
Yes, I understand how the math works. The point is that the series doesn't exist: what exists is the man and the motorcycle, and a thousand times he was out on the road.
ReplyDeleteUltimately, the probability of the wreck will turn out to be one or zero -- the two limits of the scale. Just as it should take literally forever to get to the limit by dividing by halves -- 1/2, 1/4, 1/8, etc. never gets to zero -- all of these odds in the middle are finite proportions where the true answer is going to be an absolute limit.
That it works is not in dispute. Why it works is really mysterious.
Years ago, I read a book about the WW2 campaign in New Guinea or the Solomon's or some other South Pacific garden spot-maybe it was "Shots fired in Anger" by John George, I can't remember- what I do remember was the off hand remark that a startling number of troops had been killed by, guess what-falling trees.
ReplyDeleteWe used to have one on the property that my wife called "the Widowmaker." It eventually fell on its own, hurting no one, but she forbade me to cut it down when it was standing.
ReplyDeleteOf course, looking only at the probabilities doesn't take into account the individual factors that any one person brings to the calculation. On average, riding in rush hour traffic may be more risky than riding in the country, but for which style of rider? The one who lane splits at high speed on a really quiet bike, or the one who's riding 'twixt the lanes on a loud Harley at a modest speed? I'm quite sure the odds are significantly different.
ReplyDeleteCar drivers only scare me a little. Contrary to popular biker opinion, the drivers do have a brain-at least some of them-so if you take into account the impaired, the infirm,the hasty, the overly aggressive,light the appropriate candles , and practice quick stops and emergency swerves,there is a chance of evading the predatory Buick.
ReplyDeleteDeer on the other hand- now deer scare me- they are, as John McPhee so eloquently put it , antlered rats. Giant antlered rats, ready to sprint with abandon into your path in a high speed suicide attack. Deer may mentioned in Websters as a synonym for "erratic".
Deer are very dangerous. I had bolt in front of me last year in broad daylight, apparently trying to escape from some hunters.
ReplyDeleteWhen I see them at night, I usually slow down and shout to them that I see them. That seems to cause them to freeze and consider what kind of strange experience they are having, where the growling moving light is suddenly addressing them personally.
It's like John Kerry freezing for 30 minutes on 9/11, while lambasting Bush for functioning properly in a kiddie room for a few minutes.
ReplyDelete