It turns out that the coincidence involved in the null hypothesis is somewhat less improbable than I thought.
The situation: we were waiting for “the closest-ever predicted approach to Earth for an object this large” (asteroid 2012 DA 14), and with just hours remaining, “the largest recorded object encountered by Earth since 1908″ suddenly showed up, above a populated area, and blew up spectacularly.
The consideration which reduces the improbability slightly, is that new records and notable events in the former category, now occur almost every year. So rather than a coincidence between a once-in-a-century event and a once-in-a-decade event, it’s more like a once-in-a-century event and a once-a-year event, occurring on the same day.
Assuming the null hypothesis for the moment (pure coincidence), we should still be aware that this is a remarkable coincidence. The Chelyabinsk fireball would have been a notable event of the 21st century anyway, but now it will go into history accompanied by the spooky fact that the world was already watching the skies that day; so it will have a place, not just in the annals of the space age, but in those chronicles of weird coincidences that titillate agnostics and agitate fringe believers.
I see that Phil Plait says he thought it was a hoax at first. That reminds me of my own idea that it was probably an audacious covert operation. We were each applying a familiar template to an unlikely-sounding event, something which at first sight was too unlikely to be regarded as a coincidence, so either it had to be denied or given a causal connection to the other part of the coincidence, after all.
And I’m still wary of letting go of that feeling that here is a glimpse of hidden connections. If Earth is being trolled by the long tail of the FSM, part of the divine entertainment might be to see the efficiency with which certain humans can dismiss even the highly improbable as just a coincidence, if they can’t see a satisfactory explanation.
More mundanely, although the hypothesis that the fireball was something artificial is looking weak—I cannot think of any scenario which makes much physical and political sense—I wonder what the relative likelihood of “natural but related” and “natural but unrelated” really is. If the probability of “natural but related” is as high as 1 in 500, it may after all compare favorably with the alternative.
Not only the space of the solar system, but the space of all possible orbital energies and orientations, is so vast that the probability of two rocks with a common origin going onto completley different orbits and then coming together again is too tiny for me to even figure out how to properly calculate. The profusion of rocks (many many millions the size of the small one, probably a million plus for the big one) from a huge number of sources means the odds of any two objects not on a very similar orbit having a related origin is basically nill.
Coincidence, as unlikely as it is, is orders of magnitude more likely than any other option.
I wonder what the relative likelihood of “natural but related” and “natural but unrelated” really is. If the probability of “natural but related” is as high as 1 in 500, it may after all compare favorably with the alternative.
It seems to me that your incredibly poor probability estimates stem from a complete unfamiliarity with even the basics of orbital mechanics. If I had to come up with a number for “natural but related”, it’d be orders of magnitude less probable than that.
This was my thought process: Let’s suppose that a “closest asteroid observed” record happens once every few years. Now suppose that a once-in-a-century fireball is going to happen. What are the odds that it will happen on the same day as a “closest asteroid observed” event, assuming that the latter are independently distributed with respect to fireball events? About 1 in 1000 (order of magnitude). And then I chose 1 in 500 as a representative probability that is greater than 1 in 1000, that’s all—it didn’t derive from any reasoning about orbital mechanics, it was chosen to illustrate the possibility that “natural but related” might be more probable than “natural but unrelated”.
But how could the “related” probability be that low? Well, the solar system contains all sorts of weird orbital resonances. Maybe there are multiple earth-crossing orbits which for dynamical reasons cross Earth’s orbit at the same point, and on this occasion, there was debris in two of these orbits at the same time.
And that’s just events in inhabited areas witnessed by people with a camera. Most of the Earth is either ocean or uninhabited wilderness, so it stands to reason that most such events will go unrecorded.
As for the second one… “The meteoroid … is estimated to have been about the size of a desk and have had a mass of approximately 10 tonnes.”
Compare to the Chelyabinsk meteor: “With an initial estimated mass of 10,000 tonnes, the Chelyabinsk meteor is the biggest object to have entered the Earth’s atmosphere since the 1908 Tunguska event, and the only meteor known to have resulted in a large number of injuries.”
It turns out that the coincidence involved in the null hypothesis is somewhat less improbable than I thought.
The situation: we were waiting for “the closest-ever predicted approach to Earth for an object this large” (asteroid 2012 DA 14), and with just hours remaining, “the largest recorded object encountered by Earth since 1908″ suddenly showed up, above a populated area, and blew up spectacularly.
The consideration which reduces the improbability slightly, is that new records and notable events in the former category, now occur almost every year. So rather than a coincidence between a once-in-a-century event and a once-in-a-decade event, it’s more like a once-in-a-century event and a once-a-year event, occurring on the same day.
Assuming the null hypothesis for the moment (pure coincidence), we should still be aware that this is a remarkable coincidence. The Chelyabinsk fireball would have been a notable event of the 21st century anyway, but now it will go into history accompanied by the spooky fact that the world was already watching the skies that day; so it will have a place, not just in the annals of the space age, but in those chronicles of weird coincidences that titillate agnostics and agitate fringe believers.
I see that Phil Plait says he thought it was a hoax at first. That reminds me of my own idea that it was probably an audacious covert operation. We were each applying a familiar template to an unlikely-sounding event, something which at first sight was too unlikely to be regarded as a coincidence, so either it had to be denied or given a causal connection to the other part of the coincidence, after all.
And I’m still wary of letting go of that feeling that here is a glimpse of hidden connections. If Earth is being trolled by the long tail of the FSM, part of the divine entertainment might be to see the efficiency with which certain humans can dismiss even the highly improbable as just a coincidence, if they can’t see a satisfactory explanation.
More mundanely, although the hypothesis that the fireball was something artificial is looking weak—I cannot think of any scenario which makes much physical and political sense—I wonder what the relative likelihood of “natural but related” and “natural but unrelated” really is. If the probability of “natural but related” is as high as 1 in 500, it may after all compare favorably with the alternative.
http://www.youtube.com/watch?v=eo0zFQkYsf4
http://blogs.nasa.gov/cm/blog/Watch%20the%20Skies/posts/post_1361037562855.html
Not only the space of the solar system, but the space of all possible orbital energies and orientations, is so vast that the probability of two rocks with a common origin going onto completley different orbits and then coming together again is too tiny for me to even figure out how to properly calculate. The profusion of rocks (many many millions the size of the small one, probably a million plus for the big one) from a huge number of sources means the odds of any two objects not on a very similar orbit having a related origin is basically nill.
Coincidence, as unlikely as it is, is orders of magnitude more likely than any other option.
It seems to me that your incredibly poor probability estimates stem from a complete unfamiliarity with even the basics of orbital mechanics. If I had to come up with a number for “natural but related”, it’d be orders of magnitude less probable than that.
This was my thought process: Let’s suppose that a “closest asteroid observed” record happens once every few years. Now suppose that a once-in-a-century fireball is going to happen. What are the odds that it will happen on the same day as a “closest asteroid observed” event, assuming that the latter are independently distributed with respect to fireball events? About 1 in 1000 (order of magnitude). And then I chose 1 in 500 as a representative probability that is greater than 1 in 1000, that’s all—it didn’t derive from any reasoning about orbital mechanics, it was chosen to illustrate the possibility that “natural but related” might be more probable than “natural but unrelated”.
But how could the “related” probability be that low? Well, the solar system contains all sorts of weird orbital resonances. Maybe there are multiple earth-crossing orbits which for dynamical reasons cross Earth’s orbit at the same point, and on this occasion, there was debris in two of these orbits at the same time.
The Chelyabinsk meteorite wasn’t anything like “once-in-a-century”. Off the top of my head, here’s a couple recorded a few years ago:
http://www.youtube.com/watch?v=pRtucs6D0KA
http://www.youtube.com/watch?v=8q3qWV4Ks3E
And that’s just events in inhabited areas witnessed by people with a camera. Most of the Earth is either ocean or uninhabited wilderness, so it stands to reason that most such events will go unrecorded.
The first video doesn’t show a meteor, it shows trails from a plane, lit by the setting sun.
As for the second one… “The meteoroid … is estimated to have been about the size of a desk and have had a mass of approximately 10 tonnes.”
Compare to the Chelyabinsk meteor: “With an initial estimated mass of 10,000 tonnes, the Chelyabinsk meteor is the biggest object to have entered the Earth’s atmosphere since the 1908 Tunguska event, and the only meteor known to have resulted in a large number of injuries.”