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<blockquote data-quote="tomBitonti" data-source="post: 6652347" data-attributes="member: 13107"><p>Re: What is the chance we are the first intelligent life in the universe.</p><p></p><p>That would seem to depend on parameters which we don't know.</p><p></p><p>If we assume that life could arise anytime after, say, population II stars began forming, with a minimum time life to arise around a star, and that the chances don't change very much for some long period of the universe (starting after a fixed time, and ending at a later time, and roughly constant during that time), and if the process were memory-less, then an exponential distribution could be used as candidate distribution.</p><p></p><p>For an exponential distribution, the rate parameter would make a huge difference as to whether we are first: With a low parameter (say, 1 every billion years, starting at say, 5 billion years), we would very probably not be first.</p><p></p><p>With a rate parameter more like 1 every 10 billion years, starting after 5 billion years, then the probability might be that we are first.</p><p></p><p>For a much longer rate parameter, say, 1 every 50 billion years, then we would almost definitely be first, (and very lucky).</p><p></p><p>If the rate parameter has a value very much smaller than 1 every billion years, we might have to change the question to whether we are first in our galaxy. If the rate is 1 every 10 billion years per milky way sized galaxy, then we should be one of billions of life forms, and very very probably not the first.</p><p></p><p>The problem sounds like a nice probability problem: Assuming an exponential distribution that determines the probability of intelligent life arising starting at 5 billion years, and with a given rate parameter (set in units of 1/billion years), what is the chance that life which arises after a given number of years is first?</p><p></p><p>It might be interesting to do a bayesian analysis to see if the timing of our arrival can tell us anything about the probable rate parameter. Or maybe not, since we have only one data point, and the shift in the post and posterior distributions might not change the expectation of us being first.</p><p></p><p>Thx!</p><p></p><p>TomB</p></blockquote><p></p>
[QUOTE="tomBitonti, post: 6652347, member: 13107"] Re: What is the chance we are the first intelligent life in the universe. That would seem to depend on parameters which we don't know. If we assume that life could arise anytime after, say, population II stars began forming, with a minimum time life to arise around a star, and that the chances don't change very much for some long period of the universe (starting after a fixed time, and ending at a later time, and roughly constant during that time), and if the process were memory-less, then an exponential distribution could be used as candidate distribution. For an exponential distribution, the rate parameter would make a huge difference as to whether we are first: With a low parameter (say, 1 every billion years, starting at say, 5 billion years), we would very probably not be first. With a rate parameter more like 1 every 10 billion years, starting after 5 billion years, then the probability might be that we are first. For a much longer rate parameter, say, 1 every 50 billion years, then we would almost definitely be first, (and very lucky). If the rate parameter has a value very much smaller than 1 every billion years, we might have to change the question to whether we are first in our galaxy. If the rate is 1 every 10 billion years per milky way sized galaxy, then we should be one of billions of life forms, and very very probably not the first. The problem sounds like a nice probability problem: Assuming an exponential distribution that determines the probability of intelligent life arising starting at 5 billion years, and with a given rate parameter (set in units of 1/billion years), what is the chance that life which arises after a given number of years is first? It might be interesting to do a bayesian analysis to see if the timing of our arrival can tell us anything about the probable rate parameter. Or maybe not, since we have only one data point, and the shift in the post and posterior distributions might not change the expectation of us being first. Thx! TomB [/QUOTE]
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