Jonah Goldberg has been discussing the probability of a catastrophic asteroid impact with the earth, based on this post by Ron Bailey. He has an email from one of his very confused readers:

You probably have a lot of others e-mailing as well to point this out, but while that 0.3% seems like a small probability it is wholly implausible. Just as a point of comparison given what I’ve seen on the departure screens at every airport I’ve been in, there has to be at least 1000 or more domestic airline flights every single day - probably many times that number. If the probability of an accident were 0.3% that would translate into an expected 3 crashes every single day (0.003*1000)! So are we to believe that the probability of an aircraft accident is many orders of magnitude smaller than the probability of an asteroid destroying all life on the planet? Preposterous.

But of course that is exactly what we are to believe, and why not? The probability of an aircraft accident is in fact vanishingly small, which is why we don't have airplane crashes every day. But the reader is confused on two levels. First, I don't think that anyone claims that it would destroy "all life on the planet." The concern is that it would merely wipe out human civilization.

But the probability is what it is, and it's based on the current limits of our understanding of the object's current position and ability to integrate its orbit forward in time with confidence, including all of the secondary and tertiary perturbations (other planets, other objects, etc.). As time gets closer, we will both have a better idea of its actual trajectory, and be better able to model its (and our) destiny as computers get more powerful. At that point we'll have a much better assessment of the probability (in fact, at some point we'll determine it to be either zero, or one, with the former much more likely, given how low it currently is).

But there's certainly nothing preposterous about the number as it stands today. Large objects have hit the planet in the past, much more frequently than we've previously thought (there were two hits in Norway just in the past few months that would have wiped out thousands had they hit a city, as would Tonguska have killed millions were it better targeted, a century ago) and they will do so in the future, unless we go out and herd them.

Frankly, I don't even understand the emailer's argument. Perhaps he's making sort of a category error in comparing aircraft and asteroids. In the case of aircraft, we're talking about the probability of any particular plane going down on any particular flight which, for reasons stated above, is extremely low. But for the asteroid, we're talking about this particular asteroid, hitting us once decades from now, given its trajectory as currently understood, not a generic probability of any asteroid hitting us. Obviously, if there were a 0.3 percent chance of any asteroid hitting us on a given day, we'd be hit many times a day (and in fact we are, but most of them are too small to do any damage), given the large number of objects out there. But he's comparing apples and oranges.

A decent refutation, Rand. However, I understood that the asteroid in question was not a threat to human civilization, but merely to a large, regional area, e.g. the Pacific basin and coastline. Presumably it would have large scale negative climatic effects, but this asteroid isn't likely to destroy all human civilization, as I understand it. Which doesn't mean it won't do trillions of dollars in damage and kill millions if it hits. Or that we shouldn't make some serious efforts to determine if it will get close enough to hit us by going through the keyhole or otherwise.

Forgive my skepticism, but the article doesn't say who calculated the orbit, how much data was used in determining it and if the orbit will continue to be revised as more data comes in.

The last time I remember this type of thing, the calculations were revised based on earlier data moving the distance from 20K miles out to 600K miles. I might also point out that predicting earth ending catastrophes seems to be the most effective and popular method to fill one's scientific rice bowl these days.

I love to use this type of article to put the present rice bowl recipient’s arguments in perspective. There is a possibility that human interaction with the planet is creating some amount of global warming, but there is a certainty that a 25 million ton rock will have an effect on the environment. An effect that will dwarf any amount of good or bad we may be doing now or in the future. It’s also a certainty that eventually one of these mid size rocks will hit the earth. It’s also true that something north of 90 percent of all the species that have lived on the earth have gone the way of the Dodo bird. So that leaves only one logical conclusion long term. Leave or join the others. Saving the planet is an impossible and wasteful enterprise. We haven’t the time or resources to truly save the planet in any meaningful way. We as a species have been given a window if indefinite size to use to flee this planet. The good news is in the long term is that we are just about there.

OK, I confess. I'm Jonah's very confused e-mailer on the topic. I'll admit that the "apples and oranges" criticism is telling, but I think it’s mainly because I didn't go into sufficient detail to explain the purpose of my analogy between airplanes and asteroids. Once I make myself clear, I think you'll see where I was going with it.

My overarching point is simply that 0.3% is an astonishingly large probability to assign to a truly rare event. An event that has a 0.3% probability of occurring is uncommon but by no means rare. Consider U.S. corporations as an alternative example. A company that has a 0.3% probability of going broke over the coming year would typically be rated a BBB by rating agencies. We're not quite dipping down into junk bond territory here, but any debt issued by such a company would be considered quite risky by most financial institutions. Many financial institutions are expressly prohibited by law from holding debt from companies like this because, although bankruptcy is uncommon, it’s frequent enough to endanger the well-being of the debt holder. A 0.3% probability of a bad event is more than large enough to cause significant concern on the part of the person exposed to such a risk.

And if you take the apples and oranges argument to its logical conclusion, it makes the 0.3% probability look even more suspiciously large. I keep hearing that because this number applies to this particular asteroid only and not asteroids in general it’s more acceptable. I think the exact opposite is the truth. After all, bankruptcy is not an uncommon phenomenon in the U.S. I can look back at all companies that have been rated BBB and follow their history forward and observe the frequency at which they've gone bankrupt. This has happened often enough to give me a basis for assigning a small but distinct positive probability to such a thing happening. On the other hand, if this current asteroid is truly unique then we've never seen one on a similar trajectory while the earth, sun, planets, other asteroids, etc. are in their current positions while making all the same measurement errors as to its position, speed, etc. much less observed one striking the earth. Even if I give you the one that wiped out the dinosaurs and allow that its path was similar or even the same, we still only have one observable event in how many umpteen million years? All I can say is that if the guy who performed this calculation can accurately derive a very high tail probability for the occurrence of an event that has either never occurred or occurred one time in 50+ million years, then that man needs to get work at a hedge fund so that he can rake in millions and live well before that darn asteroid wipes us all out.

I still say emphatically – preposterous!

R. Dittmar et al - Here is some more info which may be helpful:

1. Graze on over to the NEO Program page on Apophis for the details. Highest impact probability is 1 in 45,000 (more like 0.002% than 0.3%); orbit is very well-characterized, being based on many hundreds of separate observations; impact energy is around 400 megatons, which while you wouldn't want to be right under it, would not affect a large area relative to the size of the Earth. Not a civilization-wrecker, in other words.


2. Please keep in mind that asteroid sizes follow a power-law distribution. For every asteroid the size of Apophis (800 feet in diameter), for example, there are perhaps 200 asteroids 80 feet in diameter -- which I note is about 2½ times smaller than the Tunguska impactor was.


3. The point, then, is that there are asteroids and there are asteroids. Size relates sharply and inversely with frequency of impact. At the low end, there are events like the meteor that hit Chicago in '03. We don't even see those coming.

Well, first of all, the .3% applies to this asteriod only, but it also pretty much applies to all asteriods, since we're (somewhat) sure that this is the only one likely to hit in the near future.

The rock is question is unpleasantly big, but not the size of a dinosaur killer. We know that something decent-sized (not this big) hit Siberia in 1908, which isn't that long ago, and similar small objects could have hit the sea and been missed.

The NY Times had a nice article recently; middling-sized impacts may be a lot more common than was generally thought.

I'm afraid Mr. Dittmar that you're still off-track. The occurrence or non-occurrence of prior events have nothing to do with the probability of this particular asteroid hitting the earth. In fact, assuming Earth had never been hit by an asteroid in the past (which is categorically false...we get hit all the time), if we had the scientific knowledge and data collection ability, we could say that this asteroid has a 100% chance of hitting the Earth. The predicted orbit will fall within some arc or span which will or will not include the Earth's orbital path. The extent of that span and what proportion intersects the Earth's path determine the probability. With enough data and time, the span will be narrowed and shift, hopefully to exclude Earth. But at this time, the best estimate is the 0.3%.

This is not equivalent to calculating the possibility of a single outcome amongst 2 possible outcomes for numerous repeated events (i.e. plane either crashes or doesn't out of numerous takeoffs and landings involving numerous planes). It's more like a roulet_te wheel on a single turn: the ball has a 1 in 37 chance of falling in a specific slot. Put Earth in the 00 slot and you have a 2.7% chance of it getting smacked by the Roulet_te ball. Now imagine a Roulet_te wheel with 1000 slots, with 00, 0 and Red 1 being Earth...the ball falls in any other slot, which is 99.7% likely, the game goes on. The ball falls on 00, 0, or Red 1, and the Roulet_te wheel explodes, killing X number of players. Would you play with those odds?

I wouldn't count on Goldberg to add, let alone run a
calculation as subtle as this.