Bigger Isn't Always Better

"As far as the laws of mathematics refer to reality, they are not certain;
 and as far as they are certain, they do not refer to reality."
                                                                               --Albert Einstein

"Flyin' through hyperspace ain't like dustin' crops, boy."
                                                                               --Han Solo

commentary by killre

[Note: due to length and a self-imposed Sunday deadline, I have split what was to have been one post into two parts. Hopefully, I will have the sequel available in a few days.]

I used to be a long-haul truck driver. Before that and since, I've had a healthy if decidedly amateur interest in astronomy. Late one night, a number of years ago that will too soon qualify for the adjective many, I stopped my rig in an isolated pull-out alongside a lonely stretch of Interstate to "cool a tire," which is trucker-speak for "relieve my bladder." It was an exceptionally clear night, and I was at a relatively high elevation. Having successfully completed my primary task without incident, I spent ten minutes or so taking in the dazzling display of stars. This activity --standing slack-jawed in the dark, head back, eyes bugged-- is one I've engaged in many times, but this particular night stands out in memory. I had never before, nor have I since, seen so many stars at one time. If asked in that moment how many I thought there were, I could have managed only the grossest of guesses.

Since then, I've learned the likely approximate number. A person with average eyesight, in the right location --an open area far from any population center and its accompanying light pollution, and preferably at a fairly high elevation-- on a very clear night, with their unaided eyes, can see perhaps 2,500 stars. (Some estimates are a bit higher.) That, dear reader, is 0.000001% of the stars in the Milky Way galaxy. As an illustration, I submit to you the link below. You'll have to scroll down a few inches after the jump, to the second picture.

The small red circle represents everything you've ever seen without a finely crafted telescope. It denotes a sphere somewhere just shy of 1,000 light-years in radius. One light-year is just under six trillion miles. Expressed more precisely, with good old-fashioned Arabic digits, it looks like this:

5,878,625,373,183.61 miles.

One thousand light-years, then, is this:

5,878,625,373,183,610 miles. That puts the "5" in the quadrillion column, meaning that a person with average eyes, in the right location on a clear night, can see more than five quadrillion miles. Betcha didn't know that, didja? Still, as you have seen and/or read, it is a tiny fraction of what's out there.

The site on which that picture is posted is called Wait But Why. The accompanying article is titled for its topic, "The Fermi Paradox." The article's author is Tim Urban.

Named for Nobel Prize-winning physicist Enrico Fermi, whose bio you can search-engine yourself if you really need more reading material, the Fermi Paradox (henceforth "FP") refers to the apparent contradiction between (a) the high mathematical probability of the existence of intelligent alien civilizations and (b) the lack of contact with same.

Urban's essay is a bit lengthy because it touches upon a small host of related theories, all pertaining in some way to our perceived aloneness as an intelligent species in an inconceivably vast universe. It covers the bases pretty clearly, and nothing screams "badly written" --a ringing endorsement from yours truly-- but there are (of course) aspects of the article that left me a little unsatisfied.

Urban begins with some extremely big numbers, which he then multiplies by some extremely big numbers, making for some mind-blowingly ginormous math. That isn't his fault. He is discussing the FP, and the FP employs such numbers. It isn't the FP's fault either: those are the numbers, as near as anyone can tell.

All the headache-inducing arithmetic is initially intended to simply answer a question, but it quickly does more than that: it makes an argument. In the total absence of concrete proof that there are intelligent species elsewhere in the universe, Fermi and his followers seek to prove such existence through overwhelming abstract evidence-- numbers that are so far beyond homo sapiens' grounded frame of reference that we are almost powerless to argue with them, even if we were so inclined.

Take a moment to think it over, and be honest with yourself. As often as the word million gets tossed around these days, almost no-one has any real, concrete notion of just how many one million somethings are. It is a number we only think we know. In truth, it hovers out there just beyond tangible comprehension. Now, move beyond that and ponder the concept of a billion, then remember you're still not anywhere close to the numbers Urban is throwing around in virtually the first paragraph. You're not in the ballpark; you're not in the city; you're not even in the same state.

The end result of all that exponent-laced, to-the-power-of-holy-[expletive] math is this: the probable Number of Earth-like planets in the entire Known Universe. The problem with such a concept is that the Number is purely theoretical, in more ways than one. First, it is theoretical in its very mechanics: the equation leading to it is full of variables, estimates, assumptions-- each one wilder than the last. The Number itself means nearly nothing, outside of being [fudgin'] H-U-G-E. That, ultimately, is the Number's primary, graspable value: simply being huge. Don't get me wrong: I don't blame anyone for wondering how many Earth-like planets there are in the universe, nor do I blame them for trying to find a Number. It must be recognized, however, that the Number given is little more than a rhetorical prop.

That points to the second way in which the Number is theoretical: its practical application. Having some vague idea of how many alien civilizations there may be in the Known Universe is interesting, passingly, for about eight or ten seconds, but then reality sets in and you remember how utterly useless the information is. Realistically, there isn't a foreseeable future in which our species makes any sort of contact with an intelligent race in, say, the Andromeda galaxy, which is our closest intergalactic neighbor. Ergo, I don't much care. I don't care about a Type 2 civilization dominating one quadrant of a nameless galaxy far, far away --unless, of course, they have a suped-up bucket of bolts named Millennium Falcon-- and I don't care about a 1.5 in Andromeda and I don't care about a full-grown 1 on the far side of the Milky Way. Even my wildest dreams are more pragmatic than that.

What I do care about is this: How many intelligent species, roughly comparable to our own, are there in just this little grove of the interstellar woods? You know-- someone our descendants might actually talk to in the next twenty centuries or so. That's the question I found myself wanting Urban to address. He didn't, but that isn't his fault. He didn't address it is because the FP doesn't address it. So I decided to crunch some of the numbers myself...

Now, the first thing I have to tell you --in the interest of seeming reasonable and conscientious and scientific and journalistic and maybe a few other noble-sounding things I'll not bother to list, all geared toward coming across as sufficiently self-deprecatingly credible while also drawing a bit of breechclout across my backside-- is that my own equations are, in truth, just as full of assumptions, estimates, variables and wild guesses as the FP's. It is the nature of such speculations.

For example... The FP seems to assume that any alien civilization, even one far beyond our ken, must have arisen on a planet much like our own, orbiting a star that is also much like our own. Why it makes this assumption I don't know --it seems surprisingly limited and limiting-- but I make the same assumption because I'm not looking for just any civilization, I'm looking for one similar to ours.

Also... One giant assumption I make --one which departs from the essence of the FP pretty drastically-- is that the monstrously big numbers the FP employs for the Known Universe can be similarly used for a specific area of space-- in this case, within 1,000 or so light-years of Earth. This is a dangerous assumption on my part. Whereas the math of the FP inherently "averages out" regions possessing a high density of such planets with regions where it is low, applying the same formula to one very small, very specific region assumes a fairly even distribution of such worlds throughout the galaxy. Such uniformity seems unlikely on the one hand, but that doubt is mitigated somewhat by the thought that the FP's theories on the matter are at least partially based on "local" observations. Besides, at this point it is a matter of either running the numbers I have or not running any, and I haven't typed this many words to bail now.

So, let's get to it. According to the Yale Bright Star Catalog, a comprehensive list of "naked eye visible stars," there are 9,110 stars in the roughly 1,000 light-year radial sphere surrounding the Solar system. Astronomers, astrophysicists, and others in similar fields of study estimate that 12.5% (one in eight) of all the stars in the Milky Way galaxy are "sun-like," meaning they are reasonably similar in size, mass, and radiation --both in type and in output-- to Sol (the official name of the sun). 12.5 is an admittedly rough estimate. It could be off by 60% either way, possibly more. Blithely assuming the figure is only slightly optimistic, and that what is estimated for the galaxy as a whole holds true in our little pocket of it, the total number of sun-like stars in our 1,000 light-year sphere is... oh, look at that: 1138. (Could it be that a certain Mr. Lucas already trod this path, a long time ago? Your guess.)

The experts further estimate that 36% of all sun-like stars govern systems that include an Earth-like planet. (The over/under on that figure is a mere 39%.) If that's true, then the number of Earth-like planets within 1,000 light-years of our own is 409. (Skeptics who have made it this far will want to know what the number is if the more conservative estimates are applied. It is 100.)

That's as far as I've gotten: 409 Earth-like worlds within 1,000 light-years of Earth. That was the easy part. Estimating how many of them may harbor a race like ours is, frankly, algebra I've only glanced at. As I said at the top, I hope to have an answer in a few days.

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P.S.... Bud "I Have A T-shirt That Shows A Donkey In A Lab Coat
         Pointing At A Blackboard That Reads 'E=MC-squared, I Think';
        The Caption Says 'Smart Ass'; My Mother Gave It To Me" Selig must go.