Max Tegmark, in his book *Our Mathematical Universe*, gives an interesting argument for no other life besides ours, based on something called a **uniform logarithmic prior**. I don't have the book in front of me, so let's see if I can do justice to the argument.

Since we don't know how near is the nearest other intelligent life, then it could be anywhere from 10^21 meters (in our galaxy) 0r 10^100, or 10^1000, or any other order of magnitude, and they are all, a priori, equally likely. Since our observable universe is 10^26 meters, it's unlikely that the correct number is between the 10^21 meters and 10^26 meters, since such a small range is too small to be statistically likely, as any larger order of magnitude is equally likely.

I hope that's clear, if not I can find the book and give it in Tegmark's words.

I have that book, and I don't care for his reasoning. The implicit assumption here is that intelligent life is exceedingly rare.

Well, it might be. Or, it might

*not* be.

We don't know because we only have one data point to draw on: ourselves. Trying to make assumptions based off of that is mathematically unwise.

What we

*observe* is that at least one intelligent life form can arise in an area containing one hundred to four hundred billion stars because a) we are here and b) that's how many stars are around us, in our galaxy. Call it an average of one in a quarter trillion, or 2.5x10

^{11}.

There are something on the order of 10

^{23} stars in the universe. So if it's an average of one intelligent life form per quarter trillion stars, and there are a hundred billion trillion stars, I come out of that with an average of four trillion intelligent life forms in the universe -- which, because of the vast nature of intergalactic distances, will probably never be in contact with each other.

Tegmark's mistake is assuming we're on the tapering end of the bell curve, when he should be assuming we're in the middle of it.