### Thought Experiment

I'm working on a story, and I need an estimate of what the odds are that two spacefaring cultures would reach the same uninhabited planet within a few years of each other.

So, first off, there are an estimated 100 billion stars in our galaxy, which I think I can take as average for the purposes of this thought experiment. There are, supposedly, about 100 billion galaxies in the universe. That means that the population of stars is about 10,000,000,000,000,000,000,000, or 1 x 1022. Of those, only perhaps 10% have planets, and of those, only about 1% are estimated to be Earth-like, but that still leaves 100,000,000 per galaxy, or 1 x 108. If we say that the average life of a planet is five billion years, and that 'within a few years' is a window of, say, 1000 years, then each Earth-like planet has 5,000,000 windows, or 5 x 106, for a total of 5 x 1014 planetary co-occupation windows per galaxy.

Ok, ignore the universe numbers. Let's just keep it to one galaxy, because now we have to estimate the numbers of planets that develop space-flight and the will to explore extra-solar systems. Let's just say that 1% of all earth-like planets develop life, and 1% of those develop practical space-flight, and 1% of those decide to make the very, very long journey to nearby stars1. Let us ignore the problem of adjacency, in which it becomes clear that civilizations that meet the above requirements are not going to start exploring planets ten thousand light years away, they're going to start close by. Let's assume that they have equal access to any system, because this is just a wild-assed guess.

Ok, so 0.01 x 0.01 x 0.01 = 0.0001, across time. That is too high, because that is the wild-assed guess of the number of systems that will develop spaceflight at any time, including in the future. Let's assume that the average length of time to develop a lifeform to spaceflight-ness is, oh, 100,000,000 years. Let's assume it takes 2 billion of our estimated planetary lifespan of 5 billion years to actually get life going. That leaves 3 billion, divided up into 100 million year 'windows', or only about 30 per planet.

1/30 x 0.0001 x 1/(5 x 1014), or 1 in 5 x 1019, or maybe 20. Damn long odds2.

The (sup) tag has been brutally abused in the making of this poast.

1. These numbers are wild over-estimates, IMO.

2. I realize that this whole thing reveals my mathematical weakness. So be it, it's just to arrive at a somewhat reasonable number for a short story. I didn't want to use 1 in 100, for example, nor 1 in 104392.

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