*This is part two of a four part essay. In this section I will discuss the question of whether or not we can expect to find intelligence anywhere in the universe.*

Before I begin this section of this essay, I'm going to need to take a bit of a detour in order to introduce the concepts of Vast and Vanishing.

We use these terms to represent sets that are utterly immense and fractions of those sets that are utterly small. A typical example of a Vast set is the set of all possible books that are of a given length. Let us call this set of books the Library of Babel. The number of the books is not infinite but it is intensely huge. If we limit the set to books with five hundred pages (meaning about 1,000,000 characters per book, including spaces), we get a figure of about 10 to the power of 10 million books. For those unfamiliar with scientific notation, that's a one followed by ten million zeros. Given that each zero magnifies the number by a factor of 10, that's a truly Vast quantity. For the sake of comparison, it is estimated that there are approximately 10 to the 80

^{th}particles in the visible universe (give or take a few orders of magnitude). There isn't even enough matter in the universe to merely compile an index of the Library of Babel.

Most of the books in the Library are going to be gibberish: essentially random strings of characters, numerals and spaces. Here and there you will find a word or (much more rarely) even a complete sentence buried within the pages of a selected book. Every book that has ever been written as well as every book that could be written are somewhere in the Library, but unless you had a very, very powerful indexing system (or an omniscient Librarian), it would be unlikely that you could find them.

Let us suppose, however, that we could manage to sneak in and steal copies of all of the books that have ever been written. For the sake of argument, let's be generous and suppose that 10 billion (or 10 thousand million, if you prefer) books have been written over the course of history. That quantity would represent a mere 1 over 10 to the 999,990

^{th}of the books in the library. This would constitute a Vanishing quantity. Assuming that the books were shelved at random, even a googol of years (that's 10 to the 100

^{th}power) would not suffice to find a single gap in the library in spite of our pilfering.

One final thought and then I'll see about getting back on track. Something can simultaneously be Vast and Vanishing. As noted, the Library contains not only every book that has been written, but every book that could ever be written. If we could somehow separate out just the books that had coherent narratives, we would have a Vast quantity of books. However, in spite of the Vastness of this collection, when compared to the Vast set of books that just contain gibberish and random snippets of words and sentences, the set would have to be considered Vanishing. We will use the compound term "Vast but Vanishing" to describe sets that are inconceivably large while, simultaneously, being an inconceivably small fraction of an even Vaster set.

So what does this have to do with cosmology? The answer is that it has to do with Inflationary Theory. Inflationary Theory is actually a collection of theories pertaining to the origin of the universe. Specifically, Inflationary Models are addendums to classic Big Bang models of the universe. The idea that the universe expanded out of a point-like origin (the Bang) has been well supported by empirical data. Unfortunately, there's a number of technical problems with the simplest models (which I won't be going into in this essay – we hardly need even more detours). Inflationary Models address these problems by proposing that the universe went through a brief but important period of inflationary expansion where space-time went through a sequence of exponential doublings (space-time isn't an object and is, therefore, not constrained by speed of light limitations). Inflation has gained wide favor among cosmologists because it not only solves the standard problems that confront classical Big Bang models but because they are extremely good at accounting for all of the observational data that we've accumulated. The COBE microwave background survey is widely viewed as a compelling vindication of Inflationary cosmology.

And what does that have to do with anything? Patience, we are almost there. The visible universe has a radius of about 10 billion light years (give or take a few billion light years). That's a large enough figure but the visible universe is only a portion of the whole universe. We can't see any further because the light from more distant portions of the universe hasn't had time to reach us, yet. In principle, if we could wait another 10 billion years, the radius of the visible universe would be 20 billion years (or not, but more on that next week).

So, how big is the universe? Inflation suggests that it's not only larger but Vastly larger. I've seen estimates that place the size of the universe at 10 to the 2,000,000

^{th}power or even larger (some suggest that it's infinitely large). You might well ask 10 to the 2,000,000

^{th}power of what. Do I mean light years, centimeters, furlongs or smoots? The answer is that at that scale, it doesn't matter. Whether you are talking microns or mega-parsecs, the difference is going to get smeared out by the margin of error. It will suffice to say that the real universe may, in fact, be Vast.

So let us agree that life is rare. Let us, in fact, suppose that it is Vanishingly rare. For the sake of argument, I will propose a value of one planet harboring life for any given radius of a googol light years. I will further postulate that of the worlds that have life, only one in a trillion, trillion (10 to the 24

^{th}power) would harbor intelligence. I think that there is no question that this is a Vanishingly low density of life. It would, never the less, be Vast number (I'll leave it to the mathematically inclined to work out how Vast). Even something that is Vanishingly unlikely can become inevitable against a large enough span.

As an aside, the physicist Max Tegmark actually used a similar idea as basis for arguing that not only ought there be other life in the universe but that, if the universe were infinite (or, at least, sufficiently Vast), there should be a perfect duplicate of

*you*out there. By his estimates, your nearest doppleganger is about 10

^{100,000,000,000,000}light years away from us.

Is this, then, a vindication of the Principle? Only to a degree. When we dream of alien intelligences our dreams aren't limited to the simple hope that they exist. We dream of someday meeting them. In this, the universe may well disappoint us.

*This concludes part two of this essay. Part three will be published next Sunday.*

I would like to acknowledge the philosopher Daniel Dennett for the concepts of Vast and Vanishing.

I would like to acknowledge the philosopher Daniel Dennett for the concepts of Vast and Vanishing.

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