If we treat the flybys as a Poisson process with a mean waiting time between successive flyby events of 40 years and define a simultaneous flyby as successive flybys separated by less than one day, we get a mean waiting time of approximately 585,000 years from simultaneous flyby to the next. This still suggests much higher odds than the original naive calculation odds, doesn't it?
Date: Thu, 28 Feb 2013 12:41:11 -0600 Subject: Re: [Vo]:Russian meteor coincidence odds From: [email protected] To: [email protected] You obviously misunderstand the Poisson process and/or my calculation. There is nothing about any specific date in it. On Thu, Feb 28, 2013 at 12:22 PM, George Paulson <[email protected]> wrote: James, Your calculation was of the odds of a simultaneous flyby occurring on February 15th, 2013, that is, occurring on a specific date. The odds of it occurring on another specific date, say tomorrow, March 1st, 2013, are also as low as you calculated. The odds of it happening in general, that is on any day rather than on a particular date, are much higher. If we're trying to make some reasonable judgments about possible causes, it seems we should test our speculations against these latter odds, rather than the former odds, unless there is something special about that particular date, Feb. 15th, 2013, or some other reason or piece of information that suggests we should pay attention to the odds of the flyby occurring on that day, rather than any day. Date: Thu, 28 Feb 2013 09:30:52 -0600 Subject: Re: [Vo]:Russian meteor coincidence odds From: [email protected] To: [email protected] If my counting units had been years then you'd be right to imply my degree of error was wildly off the mark, but they weren't. If the two events had occurred within the same hour instead of within the same day, my calculation would have been an even greater "far cry" from the time base of years but it is still reasonable to base the calculation on counting units derived from the distance in time between the events. What if they had occurred within the same minute? The same second? In fact, the two events occurred within 16 hours of each other, not 24 hours. Otherwise, thanks for pursuing a less naive calculation but you failed to show your work. "Taylor expansion" doesn't cut it. Please update it for 16 hours rather than 24 hours and show your work. By work I mean something more specific than "taylor expasion" which is about as vague as you can get. On Thu, Feb 28, 2013 at 2:36 AM, George Paulson <[email protected]> wrote: 271.8*16,000 comes out to 4,348,800 days. 4,348,800/365 comes out to 11,915 years. So like I said we can expect an event like this roughly every 10,000 years or so. That's a far cry from the one in one billion odds or the one in one million odds after discounting by a factor of a thousand, isn't it? Date: Thu, 28 Feb 2013 01:04:34 -0600 Subject: Re: [Vo]:Russian meteor coincidence odds From: [email protected] To: [email protected] You quote me incorrectly. My actual words were "less than one in a million". I stated so because mine was a "naive calculation" that came up with 1/1332250000 to which I then applied a "discount by a factor of a thousand" precisely to address such arguments as yours. To normalize your calculation properly you have to multiply 271.8*16,000. Now, can you do that arithmetic for us to complete your "critique"? On Wed, Feb 27, 2013 at 11:13 PM, George Paulson <[email protected]> wrote: In an earlier message, James Bowery claimed that the odds of the Russian meteor and asteroid DA14 passing Earth on the same day were "one in a billion": http://www.mail-archive.com/[email protected]/msg76844.html "The odds of this coincidence are literally far less than one in a million. The naive calculation is based on two like celestial events that independently occur once in a hundred years occurring on the same day:1/(365*100)^2 = 1/1332250000 Note: that is one in a billion. Discount by a factor of a thousand for whatever your argument is and you are still one in a million. This is not a coincidence." This is incorrect. It is more like the birthday problem, where we're looking for the number of "years" that pass until two wandering asteroids have the same "birthday". A birthday here is when they fly by the Earth. We can expect the fly by of a DA14 type object every 40 years. If we also assume that something like the Russian meteor passes by every 40 years, this gives us a 16,000 day "year", and with a Taylor expansion you get a 99% probability of there being a coincident "birthday" after 271.8 "years", or roughly 10,000 of our years. So we can expect an event like this once every 10,000 years.
