[Cube Inmate]

Good grief...a debate on math when we're talking about asteroids.

Might as well add another voice to the insanity...

1) ericshand: Yes, the cumulative probability function of a regular stochastic process approaches 1 as more time passes (more accurately, as more "tests" occur in this binary problem..."Hit" or "No Hit" in any given year). That doesn't say anything about the probability of an event occurring in any given year, though. The "Big One" is not a valid example here because it will be caused, presumably, by the ever-increasing stresses at the plate boundaries.

Even if a set of lottery numbers has never been called in 50 million draws, the chances of those numbers winning the next draw are no better than any other. On average, with an ever-increasing number of draws, the probability of those numbers eventually winning approaches 1, but there's no impact on a draw-to-draw basis. On the other hand, consider two people: the probability of dying approaches 1 for any two humans, but an 85-year-old has a 50% chance of dying in the next 2 years, whereas a 30-year-old has a 1% chance (I made those numbers up). Some systems have probabilities that change due to past events (e.g. the passage of time); these systems have memory. Others have unchanging probabilities...these are so-called memoryless systems.

2) This raises the question as to whether or not the concept of a devastating asteroid impact qualifies as a memoryless system. As Mr. Pi mentioned, the number of possible impactors decreases over time, thereby reducing the odds of collision (odds/probability...interchangeable in my lexicon). Are there other factors which would cause us to expect asteroid impacts to be fairly evenly spaced? I can't think of any. I'll agree, then, that the odds of getting hit next year are no worse than those of getting hit this year.

So why the confusion?

This is another example of the fallacious "law of averages" being applied. Flip 10 heads in a row, and the human tendency is to feel that we're "due" for a tail. If the coin is actually fair, though, you'll have a 50/50 shot on your next flip. We can also consider the possibility that the 10 heads in a row might actually indicate that we're not using a truly "fair" coin. So, really, the only thing that could happen when we go longer and longer without an impact is that our estimation of the probability of impact might have to go down, but certainly not up.

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